Hydrol Earth Syst Sci 23 2813ndash2822 2019httpsdoiorg105194hess-23-2813-2019copy Author(s) 2019 This work is distributed underthe Creative Commons Attribution 40 License

Lidar-based approaches for estimating solarinsolation in heavily forested streamsJeffrey J Richardson1 Christian E Torgersen2 and L Monika Moskal31Sterling College Craftsbury Common VT USA2US Geological Survey Forest and Rangeland Ecosystem Science Center Cascadia Field StationUniversity of Washington Seattle WA USA3Precision Forestry Cooperative School of Environmental and Forest Science University of Washington Seattle WA USA

Correspondence Jeffrey J Richardson (jrichardsonsterlingcollegeedu)

Received 12 September 2018 ndash Discussion started 18 February 2019Revised 19 May 2019 ndash Accepted 21 June 2019 ndash Published 5 July 2019

Abstract Methods to quantify solar insolation in riparianlandscapes are needed due to the importance of stream tem-perature to aquatic biota We have tested three lidar predic-tors using two approaches developed for other applicationsof estimating solar insolation from airborne lidar using fielddata collected in a heavily forested narrow stream in westernOregon USA We show that a raster methodology based onthe light penetration index (LPI) and a synthetic hemispher-ical photograph approach both accurately predict solar inso-lation explaining more than 73 of the variability observedin pyranometers placed in the stream channel We apply theLPI-based model to predict solar insolation for an entire ri-parian system and demonstrate that no field-based calibrationis necessary to produce an unbiased prediction of solar inso-lation using airborne lidar alone

1 Introduction

Accurately quantifying solar insolation defined as theamount of solar radiation incident on a specific point onthe Earthrsquos surface for a given period of time is importantto many fields of study such as solar energy glacier dy-namics and climate modeling In this study we focus onthe importance of solar insolation for ecological applica-tions In forested ecosystems trees interact with solar radi-ation through shading and thus solar insolation at fine spa-tial scales in these systems can vary widely Understandingthe heterogeneous patterns of insolation below tree canopieshas been important for numerous applications such as under-

standing the importance of sun flecks for understory photo-synthesis gaining insight into the patterns of seedling regen-eration in dense forests (Nicotra et al 1999) and explainingpatterns of snowmelt (Hock 2003) and soil moisture (Bres-hears et al 1997)

The relationship between stream temperature and solar in-solation is of particular interest in this study as high amountsof solar energy irradiating a stream can cause adverse ecolog-ical effects due to directly increasing the temperature of thestreams In northwestern North America a large amount ofresearch has focused on the relationship between forest prac-tices stream temperature and the corresponding effect onriver salmonid fishes (Holtby 1988 Leinenbach et al 2013Moore et al 2005a b) Direct measurement of stream tem-perature with in-stream thermographs can be used to quantifythermal diversity (Torgersen et al 2007 2012) but ground-based measurements are time consuming expensive andimpractical for large areas In addition stream temperaturemeasurements can only show the effect of forest manage-ment practices if taken before and after trees are removedIn order to predict the potential effect of forest managementpractices on stream temperature models are often employedto estimate the amount of solar insolation irradiating streamsusing remotely sensed data (Forney et al 2013)

Several different methods have been utilized for measuringor predicting solar insolation on the ground Pyranometersare the most direct method for measuring insolation captur-ing the solar radiation flux density above a hemisphere as anelectrical signal and cataloguing those signals in a datalogger(Kerr et al 1967) Once calibrated these signals give a mea-

Published by Copernicus Publications on behalf of the European Geosciences Union

2814 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

sure of the total direct and diffuse solar radiation irradiatinga point for a given period of time (Bode et al 2014 For-ney et al 2013 Musselman et al 2015) While pyranome-ters give direct measurement of solar insolation for a definedperiod of time hemispherical photographs allow indirect es-timation of solar insolation for any point in time (Bode etal 2014 Breshears et al 1997 Rich et al 1994) Plot-ting the path of the sun in the area of sky captured by thehemispherical photograph allows for calculation of direct so-lar radiation through identified canopy gaps while gap frac-tion across the entire hemisphere allows for calculation ofdiffuse radiation Analysis of hemispherical photographs re-quires assumptions of extra-terrestrial solar radiation and skyconditions in order to produce solar insolation estimates Un-derstory light conditions can also be modeled by creating athree-dimensional reconstruction of a forest from field-basedbiophysical measurements (Ameztegui et al 2012) or terres-trial laser scanning (Ni-Meister et al 2008) Ground-basedmeasurements are limited by the time and cost required tocollect data and thus solar insolation can only be calculatedfor relatively small spatial extents

Airborne and satellite remote sensing methods provide ameans for estimating solar insolation over large spatial ex-tents Satellite-based methods utilizing passive remote sens-ing data can provide coarse-scale estimates of solar radiationabsorbed by tree canopies through radiative transfer mod-els based on spectral indices (Field et al 1995 Asrar et al1992) but these methods are not suitable for fine-scale appli-cation such as modeling stream temperature Airborne lidaris the preferred method for characterizing three-dimensionalstructure of forest canopies and thus is also used to assessthe shading effect of those canopies Below we discuss threedifferent approaches that have been used in previous studiesto quantify solar insolation at ground level using aerial lidar

11 Raster approaches

Lidar data can be used to create raster datasets by select-ing various attributes of lidar points within a defined spatialneighborhood around a raster cell One of the most commonraster products for assessing canopy structure is the light pen-etration index (LPI) the ratio of ground first return points(typically less than 2 m in elevation above ground) to the to-tal number of lidar first return points within a given rastercell This ratio has been shown to be useful for characterizinglight extinction in canopies according to the BeerndashLambertlaw (Richardson et al 2009) and thus has been exploredas a predictor of understory light conditions (Musselman etal 2013 Alexander et al 2013 Bode et al 2014) Solarradiation calculators in GIS software can also be used tocompute solar insolation on a lidar-derived digital elevationmodel (DEM) Bode et al (2014) combined an rsun solar in-solation model for the GRASS GIS software based on a DEMwith LPI to produce estimates of ground-level solar insola-tion that showed high accuracy compared to pyranometer-

collected field data in a mixed forest in northern CaliforniaUSA

12 Lidar point reprojection

Lidar point returns can be reprojected from the x y z Carte-sian coordinate system in which they are most often deliv-ered by a vendor into a spherical coordinate system whichcenters the point cloud around a specific location on theground This reprojection allows for a circular graph of thelidar point returns to be created around a point at groundlevel Alexander et al (2013) created a canopy closure met-ric from these projected point graphs based on gap fractionand found that this metric was correlated to Ellenburg in-dicator values (which relate plants to their ecological nichealong an environmental gradient) of understory light avail-ability Moeser et al (2014) created synthetic hemisphericalphotographs from reprojected lidar returns and solar irradi-ance at ground level was calculated using traditional hemi-spherical photograph analysis software The processed syn-thetic hemispherical photographs showed good correlation topyranometer measured solar irradiance at three field sites ineastern Switzerland

13 Point cloud approaches

Because lidar point clouds are typically represented in athree-dimensional Cartesian coordinate system it is possi-ble to model the sunrsquos position in relation to that three-dimensional space The number of lidar returns that are re-flected from a defined volume between the direction of thesun and the ground can then be calculated These methods arecomputationally intensive but have shown promise for pro-viding the most direct measure of understory light availabil-ity Lee et al (2008) calculated the number of points withina conical field of view directed at the sunrsquos location and cre-ated a model to relate this to ceptometer measurements ofphotosynthetically active understory solar radiation at spe-cific times and locations in a pine forest in northern FloridaUSA This method is limited by its reliance on raw lidarpoint counts specific to the actual and relative point densi-ties within their lidar acquisition Raw point counts are af-fected by both changes in flight characteristics between mis-sions and the patterns of flight line overlap within a mis-sion A different point cloud approach involves a linear trac-ing of the sunrsquos rays along their path to the ground andMartens et al (2000) demonstrated how a ray-tracing algo-rithm could be used to characterize understory light condi-tions in a computer-simulated forest Peng et al (2014) com-bined a lidar-based ray tracing algorithm with field-collectedcanopy base heights to produce an estimate of understorysolar insolation based on the BeerndashLambert law that com-pared well to field-collected pyranometer data but is lim-ited in practical application because of its reliance on field-measured data in its model Musselman et al (2013) used a

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2815

Figure 1 Study area in northwestern Oregon (USA) The grey polygon is the extent of the 2015 lidar acquisition The black circles surroundedby white circles represent the 19 point locations The letters AndashD denote the four transects The inset shows transect D and the backgroundraster in the inset is the lidar-derived canopy height model with green representing tall trees and purple representing the lowest heights Thedirection of flow is from west to east

ray-tracing algorithm to produce highly detailed estimates ofdirect beam solar transmittance in 5-minute increments byvoxelizing the lidar data and summing the number of vox-els that a ray intercepted between the point of origin and thesun The algorithm relied on site-specific pyranometer mea-surements to calibrate and adjust the beam transmittance andtherefore we were restricted from testing this method in thisstudy

Our objectives were to test the accuracy and precisionof established methods of quantifying solar insolation fromaerial lidar within areas of narrow heavily forested streamsWe utilized two raster approaches and one lidar point repro-jection approach three methodologies that had not been pre-viously applied and tested using high-quality field data col-lected in heavily forested streams We evaluated the threemethodologies using simple linear regressions that com-pared lidar-derived metrics to field-based pyranometer mea-surements of solar insolation and hemispherical photograph-based measures of shade in western Oregon USA Furtherwe sought to apply this method to quantify solar insolationthroughout a small headwater stream network

2 Methods

21 Study site

All field locations were located within the wetted channel ofPanther Creek and a tributary (Fig 1) in narrow streams (1ndash6 m in width) located in the east side of the Coast Range ofOregon USA within a larger research area in which lidar hasbeen used to quantify forest canopy structure (Flewelling andMcFadden 2011) All field sites were within a mature Dou-glas fir (Pseudotsuga menziesii) forest with other dominanttrees including red alder (Alnus rubra) western red-cedar(Thuja plicata) and western hemlock (Tsuga heterophylla)The elevation profile and description of the stream can befound in Richardson and Moskal (2014) The center of thechannel was manually digitized as a polyline in ArcGIS us-ing a combination of aerial imagery and the vendor-providedlidar DEM

Four transects were installed in late June 2015 using a Le-ica Builder Total Station and georeferenced using a JavadMaxor GPS unit The locations of the transects can be seenin Fig 1 with the 19 point locations used for capturingfield data denoted by black dots surrounded by white circles(A contains 3 points B and C contain 4 points and D con-tains 8 points) Transect locations were chosen manually inorder to maximize variability in forest shade while allowingfor safe access by the field crew Each point location was lo-

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2816 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 2 Example of hemispherical photograph acquisition at aplot location in transect D

cated within the stream channel and marked by driving rebarinto the substrate until only 1 m was exposed above the wa-ter surface Point locations were approximately 15 m apartwithin a transect in order to allow data from multiple pointlocations to be collected by a single datalogger

Two datasets were collected at each point location duringthe last 2 weeks of June in 2015 A hemispherical photographwas collected using a Nikon CoolPix 4500 digital cameraleveled on a tripod 1 m above the ground under uniform skyconditions (Fig 2) utilizing a method to find the optimumlight exposure (Zhang et al 2005) Each hemispherical pho-tograph was analyzed using the Gap Light Analyzer (GLA)program (Frazer et al 1999) in order to produce estimatesof percent transmittance for diffuse and direct sunlight AnApogee Instruments SP-110 self-powered silicon-cell pyra-nometer leveled and mounted to the rebar pole at 1 m height(Fig 3) was used to collect a full dayrsquos solar output at eachpoint location using the datalogger The raw voltage valuescollected by the datalogger were calibrated to solar irradianceusing the closest publicly available meteorological data Allpyranometer datasets were collected on cloudless days ex-cept for transect A and pyranometer data from transect Awere not used in this study The calibrated pyranometer datafrom a point location from transect D are shown in Fig 4Note that the silicon-cell photodiodes such as the SP-110can produce erroneous readings under conifer canopies Ablack body thermopile pyranometer would have been moreappropriate for this study but was not available to the authors

22 Lidar data and analysis

Airborne discrete-return lidar was acquired in June of 2015according to the specifications described in Table 1 The ven-dor provided processed discrete lidar point returns as well asa lidar DEM and highest hit model at a pixel resolution of1 m The highest hit model was subtracted from the DEM tocreate a canopy height model (CHM) describing the vege-

Figure 3 Example of pyranometer installation at transect D (notethat pyranometer is mounted on south side of pole at a height of1 m)

Figure 4 Daily pyranometer output from sunset to sundown for aplot in Transect D

tation height normalized to the ground surface In additionFUSION (McGaughey 2009) was used to subtract the eleva-tions of the raw lidar points from the ground elevation in theDEM to produce a normalized point cloud dataset (NPCD)Note that the perspective of the lidar analyses is in referenceto ground height while the field data were collected at 1 mabove the ground While this is a small difference it could

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2817

Table 1 Lidar data specifications

Acquisition date 18 June 2015Sensor Leica ALS80Survey altitude 1400 mPulse rate 3948 kHzField of view 30

Mean pulse density 2535 pulses per square meterOverlap 100 with 65 side lapRelative accuracy 4 cmVertical accuracy 5 cm

be a source of error in comparisons especially at low solarangles

LPI was computed as follows

LPI=(RgRt

) (1)

LPI was computed in ArcGIS using a circular buffer withradius 10 m around each field point location mirroring theradius used in Richardson et al (2009) LPI was also com-puted using a shifted square buffer modified from the methodof Bode et al (2014) where the buffer side length (s) was cal-culated based on the following

s =h

tanθ (2)

where h is equal to the modal tree height across all our plots(34 m) and θ is equal to the maximum lidar scan angle sub-tracted from 90 (75) resulting in a buffer side length of912 m The square buffer was shifted south to account forthe seasonal solar angle in the Northern Hemisphere accord-ing to the following

shift=(

s

1+ cosσ

)minus s (3)

where σ is equivalent to the solar angle at noon on the date ofinterest A solar angle of 68 was used in this study resultingin a southern shift of 342 m The buffer tool zonal statisticstool and move command were used to achieve the shift inArcGIS We also computed topographically influenced solarradiation using the lidar DEM and the solar radiation func-tion in ArcGIS but found that there was no significant dif-ference across the plot locations and thus did not use theseresults in subsequent analysis

Synthetic hemiphotos were created in MATLAB using themethod of Moeser et al (2014) and analyzed for diffuse anddirect light transmittance in GLA All statistical analyseswere performed in R (version 34)

Longitudinal profiles of stream shading were created inArcGIS in 1 m increments based on the intersections of thestream polyline center line with the raster output of modeledsolar insolation

Figure 5 Comparison between pyranometer-measured solar inso-lation and daily diffuse and direct radiation canopy transmittancecalculated from hemispherical photographs

3 Results and discussion

31 Comparison between pyranometers andhemispherical photographs

Figure 5 shows the correlation between field-collected pyra-nometer data and processed hemispherical photographs withdata from transect A removed These data are highly cor-related (r2

= 087) but these data are also not equally dis-tributed across a range of solar insolation Many more plotlocations were at low levels of solar insolation than in areasof relatively low shade This is very typical of the heavilyforested streams in northwestern North America Note thatnone of our plot locations contained transmittance greaterthan 40

32 Linear regressions

Pyranometer-based solar insolation and hemispherical pho-tograph percent diffuse and direct radiation transmittancecalculated at all point locations except transect A were com-pared to three lidar predictors using simple linear regressionThese results are shown in Fig 6 The LPI calculated usinga 10 m circle centered on the point location explained about55 of the variability in both response variables but the pre-diction accuracy improved when LPI was calculated usingthe shifted square buffer Shifted LPI explained 74 of thevariability in solar insolation and 64 of the variability inpercent transmittance Synthetic hemispherical photographsexplained 77 of the variability in solar insolation and 60 of the variability in percent transmittance Figure 6 showscomparisons between transects B and D to make interpreta-tion easier but Table 2 shows the results of linear regressionsbetween predicted variables and hemispherical photographtransmittance for all plot locations resulting in small reduc-tions in the amount of variability explained Table 3 givesparameters of slope and intercept resulting from the simplelinear regression

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2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

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2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2814 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

sure of the total direct and diffuse solar radiation irradiatinga point for a given period of time (Bode et al 2014 For-ney et al 2013 Musselman et al 2015) While pyranome-ters give direct measurement of solar insolation for a definedperiod of time hemispherical photographs allow indirect es-timation of solar insolation for any point in time (Bode etal 2014 Breshears et al 1997 Rich et al 1994) Plot-ting the path of the sun in the area of sky captured by thehemispherical photograph allows for calculation of direct so-lar radiation through identified canopy gaps while gap frac-tion across the entire hemisphere allows for calculation ofdiffuse radiation Analysis of hemispherical photographs re-quires assumptions of extra-terrestrial solar radiation and skyconditions in order to produce solar insolation estimates Un-derstory light conditions can also be modeled by creating athree-dimensional reconstruction of a forest from field-basedbiophysical measurements (Ameztegui et al 2012) or terres-trial laser scanning (Ni-Meister et al 2008) Ground-basedmeasurements are limited by the time and cost required tocollect data and thus solar insolation can only be calculatedfor relatively small spatial extents

Airborne and satellite remote sensing methods provide ameans for estimating solar insolation over large spatial ex-tents Satellite-based methods utilizing passive remote sens-ing data can provide coarse-scale estimates of solar radiationabsorbed by tree canopies through radiative transfer mod-els based on spectral indices (Field et al 1995 Asrar et al1992) but these methods are not suitable for fine-scale appli-cation such as modeling stream temperature Airborne lidaris the preferred method for characterizing three-dimensionalstructure of forest canopies and thus is also used to assessthe shading effect of those canopies Below we discuss threedifferent approaches that have been used in previous studiesto quantify solar insolation at ground level using aerial lidar

11 Raster approaches

Lidar data can be used to create raster datasets by select-ing various attributes of lidar points within a defined spatialneighborhood around a raster cell One of the most commonraster products for assessing canopy structure is the light pen-etration index (LPI) the ratio of ground first return points(typically less than 2 m in elevation above ground) to the to-tal number of lidar first return points within a given rastercell This ratio has been shown to be useful for characterizinglight extinction in canopies according to the BeerndashLambertlaw (Richardson et al 2009) and thus has been exploredas a predictor of understory light conditions (Musselman etal 2013 Alexander et al 2013 Bode et al 2014) Solarradiation calculators in GIS software can also be used tocompute solar insolation on a lidar-derived digital elevationmodel (DEM) Bode et al (2014) combined an rsun solar in-solation model for the GRASS GIS software based on a DEMwith LPI to produce estimates of ground-level solar insola-tion that showed high accuracy compared to pyranometer-

collected field data in a mixed forest in northern CaliforniaUSA

12 Lidar point reprojection

Lidar point returns can be reprojected from the x y z Carte-sian coordinate system in which they are most often deliv-ered by a vendor into a spherical coordinate system whichcenters the point cloud around a specific location on theground This reprojection allows for a circular graph of thelidar point returns to be created around a point at groundlevel Alexander et al (2013) created a canopy closure met-ric from these projected point graphs based on gap fractionand found that this metric was correlated to Ellenburg in-dicator values (which relate plants to their ecological nichealong an environmental gradient) of understory light avail-ability Moeser et al (2014) created synthetic hemisphericalphotographs from reprojected lidar returns and solar irradi-ance at ground level was calculated using traditional hemi-spherical photograph analysis software The processed syn-thetic hemispherical photographs showed good correlation topyranometer measured solar irradiance at three field sites ineastern Switzerland

13 Point cloud approaches

Because lidar point clouds are typically represented in athree-dimensional Cartesian coordinate system it is possi-ble to model the sunrsquos position in relation to that three-dimensional space The number of lidar returns that are re-flected from a defined volume between the direction of thesun and the ground can then be calculated These methods arecomputationally intensive but have shown promise for pro-viding the most direct measure of understory light availabil-ity Lee et al (2008) calculated the number of points withina conical field of view directed at the sunrsquos location and cre-ated a model to relate this to ceptometer measurements ofphotosynthetically active understory solar radiation at spe-cific times and locations in a pine forest in northern FloridaUSA This method is limited by its reliance on raw lidarpoint counts specific to the actual and relative point densi-ties within their lidar acquisition Raw point counts are af-fected by both changes in flight characteristics between mis-sions and the patterns of flight line overlap within a mis-sion A different point cloud approach involves a linear trac-ing of the sunrsquos rays along their path to the ground andMartens et al (2000) demonstrated how a ray-tracing algo-rithm could be used to characterize understory light condi-tions in a computer-simulated forest Peng et al (2014) com-bined a lidar-based ray tracing algorithm with field-collectedcanopy base heights to produce an estimate of understorysolar insolation based on the BeerndashLambert law that com-pared well to field-collected pyranometer data but is lim-ited in practical application because of its reliance on field-measured data in its model Musselman et al (2013) used a

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2815

Figure 1 Study area in northwestern Oregon (USA) The grey polygon is the extent of the 2015 lidar acquisition The black circles surroundedby white circles represent the 19 point locations The letters AndashD denote the four transects The inset shows transect D and the backgroundraster in the inset is the lidar-derived canopy height model with green representing tall trees and purple representing the lowest heights Thedirection of flow is from west to east

ray-tracing algorithm to produce highly detailed estimates ofdirect beam solar transmittance in 5-minute increments byvoxelizing the lidar data and summing the number of vox-els that a ray intercepted between the point of origin and thesun The algorithm relied on site-specific pyranometer mea-surements to calibrate and adjust the beam transmittance andtherefore we were restricted from testing this method in thisstudy

Our objectives were to test the accuracy and precisionof established methods of quantifying solar insolation fromaerial lidar within areas of narrow heavily forested streamsWe utilized two raster approaches and one lidar point repro-jection approach three methodologies that had not been pre-viously applied and tested using high-quality field data col-lected in heavily forested streams We evaluated the threemethodologies using simple linear regressions that com-pared lidar-derived metrics to field-based pyranometer mea-surements of solar insolation and hemispherical photograph-based measures of shade in western Oregon USA Furtherwe sought to apply this method to quantify solar insolationthroughout a small headwater stream network

2 Methods

21 Study site

All field locations were located within the wetted channel ofPanther Creek and a tributary (Fig 1) in narrow streams (1ndash6 m in width) located in the east side of the Coast Range ofOregon USA within a larger research area in which lidar hasbeen used to quantify forest canopy structure (Flewelling andMcFadden 2011) All field sites were within a mature Dou-glas fir (Pseudotsuga menziesii) forest with other dominanttrees including red alder (Alnus rubra) western red-cedar(Thuja plicata) and western hemlock (Tsuga heterophylla)The elevation profile and description of the stream can befound in Richardson and Moskal (2014) The center of thechannel was manually digitized as a polyline in ArcGIS us-ing a combination of aerial imagery and the vendor-providedlidar DEM

Four transects were installed in late June 2015 using a Le-ica Builder Total Station and georeferenced using a JavadMaxor GPS unit The locations of the transects can be seenin Fig 1 with the 19 point locations used for capturingfield data denoted by black dots surrounded by white circles(A contains 3 points B and C contain 4 points and D con-tains 8 points) Transect locations were chosen manually inorder to maximize variability in forest shade while allowingfor safe access by the field crew Each point location was lo-

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2816 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 2 Example of hemispherical photograph acquisition at aplot location in transect D

cated within the stream channel and marked by driving rebarinto the substrate until only 1 m was exposed above the wa-ter surface Point locations were approximately 15 m apartwithin a transect in order to allow data from multiple pointlocations to be collected by a single datalogger

Two datasets were collected at each point location duringthe last 2 weeks of June in 2015 A hemispherical photographwas collected using a Nikon CoolPix 4500 digital cameraleveled on a tripod 1 m above the ground under uniform skyconditions (Fig 2) utilizing a method to find the optimumlight exposure (Zhang et al 2005) Each hemispherical pho-tograph was analyzed using the Gap Light Analyzer (GLA)program (Frazer et al 1999) in order to produce estimatesof percent transmittance for diffuse and direct sunlight AnApogee Instruments SP-110 self-powered silicon-cell pyra-nometer leveled and mounted to the rebar pole at 1 m height(Fig 3) was used to collect a full dayrsquos solar output at eachpoint location using the datalogger The raw voltage valuescollected by the datalogger were calibrated to solar irradianceusing the closest publicly available meteorological data Allpyranometer datasets were collected on cloudless days ex-cept for transect A and pyranometer data from transect Awere not used in this study The calibrated pyranometer datafrom a point location from transect D are shown in Fig 4Note that the silicon-cell photodiodes such as the SP-110can produce erroneous readings under conifer canopies Ablack body thermopile pyranometer would have been moreappropriate for this study but was not available to the authors

22 Lidar data and analysis

Airborne discrete-return lidar was acquired in June of 2015according to the specifications described in Table 1 The ven-dor provided processed discrete lidar point returns as well asa lidar DEM and highest hit model at a pixel resolution of1 m The highest hit model was subtracted from the DEM tocreate a canopy height model (CHM) describing the vege-

Figure 3 Example of pyranometer installation at transect D (notethat pyranometer is mounted on south side of pole at a height of1 m)

Figure 4 Daily pyranometer output from sunset to sundown for aplot in Transect D

tation height normalized to the ground surface In additionFUSION (McGaughey 2009) was used to subtract the eleva-tions of the raw lidar points from the ground elevation in theDEM to produce a normalized point cloud dataset (NPCD)Note that the perspective of the lidar analyses is in referenceto ground height while the field data were collected at 1 mabove the ground While this is a small difference it could

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2817

Table 1 Lidar data specifications

Acquisition date 18 June 2015Sensor Leica ALS80Survey altitude 1400 mPulse rate 3948 kHzField of view 30

Mean pulse density 2535 pulses per square meterOverlap 100 with 65 side lapRelative accuracy 4 cmVertical accuracy 5 cm

be a source of error in comparisons especially at low solarangles

LPI was computed as follows

LPI=(RgRt

) (1)

LPI was computed in ArcGIS using a circular buffer withradius 10 m around each field point location mirroring theradius used in Richardson et al (2009) LPI was also com-puted using a shifted square buffer modified from the methodof Bode et al (2014) where the buffer side length (s) was cal-culated based on the following

s =h

tanθ (2)

where h is equal to the modal tree height across all our plots(34 m) and θ is equal to the maximum lidar scan angle sub-tracted from 90 (75) resulting in a buffer side length of912 m The square buffer was shifted south to account forthe seasonal solar angle in the Northern Hemisphere accord-ing to the following

shift=(

s

1+ cosσ

)minus s (3)

where σ is equivalent to the solar angle at noon on the date ofinterest A solar angle of 68 was used in this study resultingin a southern shift of 342 m The buffer tool zonal statisticstool and move command were used to achieve the shift inArcGIS We also computed topographically influenced solarradiation using the lidar DEM and the solar radiation func-tion in ArcGIS but found that there was no significant dif-ference across the plot locations and thus did not use theseresults in subsequent analysis

Synthetic hemiphotos were created in MATLAB using themethod of Moeser et al (2014) and analyzed for diffuse anddirect light transmittance in GLA All statistical analyseswere performed in R (version 34)

Longitudinal profiles of stream shading were created inArcGIS in 1 m increments based on the intersections of thestream polyline center line with the raster output of modeledsolar insolation

Figure 5 Comparison between pyranometer-measured solar inso-lation and daily diffuse and direct radiation canopy transmittancecalculated from hemispherical photographs

3 Results and discussion

31 Comparison between pyranometers andhemispherical photographs

Figure 5 shows the correlation between field-collected pyra-nometer data and processed hemispherical photographs withdata from transect A removed These data are highly cor-related (r2

= 087) but these data are also not equally dis-tributed across a range of solar insolation Many more plotlocations were at low levels of solar insolation than in areasof relatively low shade This is very typical of the heavilyforested streams in northwestern North America Note thatnone of our plot locations contained transmittance greaterthan 40

32 Linear regressions

Pyranometer-based solar insolation and hemispherical pho-tograph percent diffuse and direct radiation transmittancecalculated at all point locations except transect A were com-pared to three lidar predictors using simple linear regressionThese results are shown in Fig 6 The LPI calculated usinga 10 m circle centered on the point location explained about55 of the variability in both response variables but the pre-diction accuracy improved when LPI was calculated usingthe shifted square buffer Shifted LPI explained 74 of thevariability in solar insolation and 64 of the variability inpercent transmittance Synthetic hemispherical photographsexplained 77 of the variability in solar insolation and 60 of the variability in percent transmittance Figure 6 showscomparisons between transects B and D to make interpreta-tion easier but Table 2 shows the results of linear regressionsbetween predicted variables and hemispherical photographtransmittance for all plot locations resulting in small reduc-tions in the amount of variability explained Table 3 givesparameters of slope and intercept resulting from the simplelinear regression

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2815

Figure 1 Study area in northwestern Oregon (USA) The grey polygon is the extent of the 2015 lidar acquisition The black circles surroundedby white circles represent the 19 point locations The letters AndashD denote the four transects The inset shows transect D and the backgroundraster in the inset is the lidar-derived canopy height model with green representing tall trees and purple representing the lowest heights Thedirection of flow is from west to east

ray-tracing algorithm to produce highly detailed estimates ofdirect beam solar transmittance in 5-minute increments byvoxelizing the lidar data and summing the number of vox-els that a ray intercepted between the point of origin and thesun The algorithm relied on site-specific pyranometer mea-surements to calibrate and adjust the beam transmittance andtherefore we were restricted from testing this method in thisstudy

Our objectives were to test the accuracy and precisionof established methods of quantifying solar insolation fromaerial lidar within areas of narrow heavily forested streamsWe utilized two raster approaches and one lidar point repro-jection approach three methodologies that had not been pre-viously applied and tested using high-quality field data col-lected in heavily forested streams We evaluated the threemethodologies using simple linear regressions that com-pared lidar-derived metrics to field-based pyranometer mea-surements of solar insolation and hemispherical photograph-based measures of shade in western Oregon USA Furtherwe sought to apply this method to quantify solar insolationthroughout a small headwater stream network

2 Methods

21 Study site

All field locations were located within the wetted channel ofPanther Creek and a tributary (Fig 1) in narrow streams (1ndash6 m in width) located in the east side of the Coast Range ofOregon USA within a larger research area in which lidar hasbeen used to quantify forest canopy structure (Flewelling andMcFadden 2011) All field sites were within a mature Dou-glas fir (Pseudotsuga menziesii) forest with other dominanttrees including red alder (Alnus rubra) western red-cedar(Thuja plicata) and western hemlock (Tsuga heterophylla)The elevation profile and description of the stream can befound in Richardson and Moskal (2014) The center of thechannel was manually digitized as a polyline in ArcGIS us-ing a combination of aerial imagery and the vendor-providedlidar DEM

Four transects were installed in late June 2015 using a Le-ica Builder Total Station and georeferenced using a JavadMaxor GPS unit The locations of the transects can be seenin Fig 1 with the 19 point locations used for capturingfield data denoted by black dots surrounded by white circles(A contains 3 points B and C contain 4 points and D con-tains 8 points) Transect locations were chosen manually inorder to maximize variability in forest shade while allowingfor safe access by the field crew Each point location was lo-

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2816 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 2 Example of hemispherical photograph acquisition at aplot location in transect D

cated within the stream channel and marked by driving rebarinto the substrate until only 1 m was exposed above the wa-ter surface Point locations were approximately 15 m apartwithin a transect in order to allow data from multiple pointlocations to be collected by a single datalogger

Two datasets were collected at each point location duringthe last 2 weeks of June in 2015 A hemispherical photographwas collected using a Nikon CoolPix 4500 digital cameraleveled on a tripod 1 m above the ground under uniform skyconditions (Fig 2) utilizing a method to find the optimumlight exposure (Zhang et al 2005) Each hemispherical pho-tograph was analyzed using the Gap Light Analyzer (GLA)program (Frazer et al 1999) in order to produce estimatesof percent transmittance for diffuse and direct sunlight AnApogee Instruments SP-110 self-powered silicon-cell pyra-nometer leveled and mounted to the rebar pole at 1 m height(Fig 3) was used to collect a full dayrsquos solar output at eachpoint location using the datalogger The raw voltage valuescollected by the datalogger were calibrated to solar irradianceusing the closest publicly available meteorological data Allpyranometer datasets were collected on cloudless days ex-cept for transect A and pyranometer data from transect Awere not used in this study The calibrated pyranometer datafrom a point location from transect D are shown in Fig 4Note that the silicon-cell photodiodes such as the SP-110can produce erroneous readings under conifer canopies Ablack body thermopile pyranometer would have been moreappropriate for this study but was not available to the authors

22 Lidar data and analysis

Airborne discrete-return lidar was acquired in June of 2015according to the specifications described in Table 1 The ven-dor provided processed discrete lidar point returns as well asa lidar DEM and highest hit model at a pixel resolution of1 m The highest hit model was subtracted from the DEM tocreate a canopy height model (CHM) describing the vege-

Figure 3 Example of pyranometer installation at transect D (notethat pyranometer is mounted on south side of pole at a height of1 m)

Figure 4 Daily pyranometer output from sunset to sundown for aplot in Transect D

tation height normalized to the ground surface In additionFUSION (McGaughey 2009) was used to subtract the eleva-tions of the raw lidar points from the ground elevation in theDEM to produce a normalized point cloud dataset (NPCD)Note that the perspective of the lidar analyses is in referenceto ground height while the field data were collected at 1 mabove the ground While this is a small difference it could

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2817

Table 1 Lidar data specifications

Acquisition date 18 June 2015Sensor Leica ALS80Survey altitude 1400 mPulse rate 3948 kHzField of view 30

Mean pulse density 2535 pulses per square meterOverlap 100 with 65 side lapRelative accuracy 4 cmVertical accuracy 5 cm

be a source of error in comparisons especially at low solarangles

LPI was computed as follows

LPI=(RgRt

) (1)

LPI was computed in ArcGIS using a circular buffer withradius 10 m around each field point location mirroring theradius used in Richardson et al (2009) LPI was also com-puted using a shifted square buffer modified from the methodof Bode et al (2014) where the buffer side length (s) was cal-culated based on the following

s =h

tanθ (2)

where h is equal to the modal tree height across all our plots(34 m) and θ is equal to the maximum lidar scan angle sub-tracted from 90 (75) resulting in a buffer side length of912 m The square buffer was shifted south to account forthe seasonal solar angle in the Northern Hemisphere accord-ing to the following

shift=(

s

1+ cosσ

)minus s (3)

where σ is equivalent to the solar angle at noon on the date ofinterest A solar angle of 68 was used in this study resultingin a southern shift of 342 m The buffer tool zonal statisticstool and move command were used to achieve the shift inArcGIS We also computed topographically influenced solarradiation using the lidar DEM and the solar radiation func-tion in ArcGIS but found that there was no significant dif-ference across the plot locations and thus did not use theseresults in subsequent analysis

Synthetic hemiphotos were created in MATLAB using themethod of Moeser et al (2014) and analyzed for diffuse anddirect light transmittance in GLA All statistical analyseswere performed in R (version 34)

Longitudinal profiles of stream shading were created inArcGIS in 1 m increments based on the intersections of thestream polyline center line with the raster output of modeledsolar insolation

Figure 5 Comparison between pyranometer-measured solar inso-lation and daily diffuse and direct radiation canopy transmittancecalculated from hemispherical photographs

3 Results and discussion

31 Comparison between pyranometers andhemispherical photographs

Figure 5 shows the correlation between field-collected pyra-nometer data and processed hemispherical photographs withdata from transect A removed These data are highly cor-related (r2

= 087) but these data are also not equally dis-tributed across a range of solar insolation Many more plotlocations were at low levels of solar insolation than in areasof relatively low shade This is very typical of the heavilyforested streams in northwestern North America Note thatnone of our plot locations contained transmittance greaterthan 40

32 Linear regressions

Pyranometer-based solar insolation and hemispherical pho-tograph percent diffuse and direct radiation transmittancecalculated at all point locations except transect A were com-pared to three lidar predictors using simple linear regressionThese results are shown in Fig 6 The LPI calculated usinga 10 m circle centered on the point location explained about55 of the variability in both response variables but the pre-diction accuracy improved when LPI was calculated usingthe shifted square buffer Shifted LPI explained 74 of thevariability in solar insolation and 64 of the variability inpercent transmittance Synthetic hemispherical photographsexplained 77 of the variability in solar insolation and 60 of the variability in percent transmittance Figure 6 showscomparisons between transects B and D to make interpreta-tion easier but Table 2 shows the results of linear regressionsbetween predicted variables and hemispherical photographtransmittance for all plot locations resulting in small reduc-tions in the amount of variability explained Table 3 givesparameters of slope and intercept resulting from the simplelinear regression

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2816 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 2 Example of hemispherical photograph acquisition at aplot location in transect D

cated within the stream channel and marked by driving rebarinto the substrate until only 1 m was exposed above the wa-ter surface Point locations were approximately 15 m apartwithin a transect in order to allow data from multiple pointlocations to be collected by a single datalogger

Two datasets were collected at each point location duringthe last 2 weeks of June in 2015 A hemispherical photographwas collected using a Nikon CoolPix 4500 digital cameraleveled on a tripod 1 m above the ground under uniform skyconditions (Fig 2) utilizing a method to find the optimumlight exposure (Zhang et al 2005) Each hemispherical pho-tograph was analyzed using the Gap Light Analyzer (GLA)program (Frazer et al 1999) in order to produce estimatesof percent transmittance for diffuse and direct sunlight AnApogee Instruments SP-110 self-powered silicon-cell pyra-nometer leveled and mounted to the rebar pole at 1 m height(Fig 3) was used to collect a full dayrsquos solar output at eachpoint location using the datalogger The raw voltage valuescollected by the datalogger were calibrated to solar irradianceusing the closest publicly available meteorological data Allpyranometer datasets were collected on cloudless days ex-cept for transect A and pyranometer data from transect Awere not used in this study The calibrated pyranometer datafrom a point location from transect D are shown in Fig 4Note that the silicon-cell photodiodes such as the SP-110can produce erroneous readings under conifer canopies Ablack body thermopile pyranometer would have been moreappropriate for this study but was not available to the authors

22 Lidar data and analysis

Airborne discrete-return lidar was acquired in June of 2015according to the specifications described in Table 1 The ven-dor provided processed discrete lidar point returns as well asa lidar DEM and highest hit model at a pixel resolution of1 m The highest hit model was subtracted from the DEM tocreate a canopy height model (CHM) describing the vege-

Figure 3 Example of pyranometer installation at transect D (notethat pyranometer is mounted on south side of pole at a height of1 m)

Figure 4 Daily pyranometer output from sunset to sundown for aplot in Transect D

tation height normalized to the ground surface In additionFUSION (McGaughey 2009) was used to subtract the eleva-tions of the raw lidar points from the ground elevation in theDEM to produce a normalized point cloud dataset (NPCD)Note that the perspective of the lidar analyses is in referenceto ground height while the field data were collected at 1 mabove the ground While this is a small difference it could

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2817

Table 1 Lidar data specifications

Acquisition date 18 June 2015Sensor Leica ALS80Survey altitude 1400 mPulse rate 3948 kHzField of view 30

Mean pulse density 2535 pulses per square meterOverlap 100 with 65 side lapRelative accuracy 4 cmVertical accuracy 5 cm

be a source of error in comparisons especially at low solarangles

LPI was computed as follows

LPI=(RgRt

) (1)

LPI was computed in ArcGIS using a circular buffer withradius 10 m around each field point location mirroring theradius used in Richardson et al (2009) LPI was also com-puted using a shifted square buffer modified from the methodof Bode et al (2014) where the buffer side length (s) was cal-culated based on the following

s =h

tanθ (2)

where h is equal to the modal tree height across all our plots(34 m) and θ is equal to the maximum lidar scan angle sub-tracted from 90 (75) resulting in a buffer side length of912 m The square buffer was shifted south to account forthe seasonal solar angle in the Northern Hemisphere accord-ing to the following

shift=(

s

1+ cosσ

)minus s (3)

where σ is equivalent to the solar angle at noon on the date ofinterest A solar angle of 68 was used in this study resultingin a southern shift of 342 m The buffer tool zonal statisticstool and move command were used to achieve the shift inArcGIS We also computed topographically influenced solarradiation using the lidar DEM and the solar radiation func-tion in ArcGIS but found that there was no significant dif-ference across the plot locations and thus did not use theseresults in subsequent analysis

Synthetic hemiphotos were created in MATLAB using themethod of Moeser et al (2014) and analyzed for diffuse anddirect light transmittance in GLA All statistical analyseswere performed in R (version 34)

Longitudinal profiles of stream shading were created inArcGIS in 1 m increments based on the intersections of thestream polyline center line with the raster output of modeledsolar insolation

Figure 5 Comparison between pyranometer-measured solar inso-lation and daily diffuse and direct radiation canopy transmittancecalculated from hemispherical photographs

3 Results and discussion

31 Comparison between pyranometers andhemispherical photographs

Figure 5 shows the correlation between field-collected pyra-nometer data and processed hemispherical photographs withdata from transect A removed These data are highly cor-related (r2

= 087) but these data are also not equally dis-tributed across a range of solar insolation Many more plotlocations were at low levels of solar insolation than in areasof relatively low shade This is very typical of the heavilyforested streams in northwestern North America Note thatnone of our plot locations contained transmittance greaterthan 40

32 Linear regressions

Pyranometer-based solar insolation and hemispherical pho-tograph percent diffuse and direct radiation transmittancecalculated at all point locations except transect A were com-pared to three lidar predictors using simple linear regressionThese results are shown in Fig 6 The LPI calculated usinga 10 m circle centered on the point location explained about55 of the variability in both response variables but the pre-diction accuracy improved when LPI was calculated usingthe shifted square buffer Shifted LPI explained 74 of thevariability in solar insolation and 64 of the variability inpercent transmittance Synthetic hemispherical photographsexplained 77 of the variability in solar insolation and 60 of the variability in percent transmittance Figure 6 showscomparisons between transects B and D to make interpreta-tion easier but Table 2 shows the results of linear regressionsbetween predicted variables and hemispherical photographtransmittance for all plot locations resulting in small reduc-tions in the amount of variability explained Table 3 givesparameters of slope and intercept resulting from the simplelinear regression

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2817

Table 1 Lidar data specifications

Acquisition date 18 June 2015Sensor Leica ALS80Survey altitude 1400 mPulse rate 3948 kHzField of view 30

Mean pulse density 2535 pulses per square meterOverlap 100 with 65 side lapRelative accuracy 4 cmVertical accuracy 5 cm

be a source of error in comparisons especially at low solarangles

LPI was computed as follows

LPI=(RgRt

) (1)

LPI was computed in ArcGIS using a circular buffer withradius 10 m around each field point location mirroring theradius used in Richardson et al (2009) LPI was also com-puted using a shifted square buffer modified from the methodof Bode et al (2014) where the buffer side length (s) was cal-culated based on the following

s =h

tanθ (2)

where h is equal to the modal tree height across all our plots(34 m) and θ is equal to the maximum lidar scan angle sub-tracted from 90 (75) resulting in a buffer side length of912 m The square buffer was shifted south to account forthe seasonal solar angle in the Northern Hemisphere accord-ing to the following

shift=(

s

1+ cosσ

)minus s (3)

where σ is equivalent to the solar angle at noon on the date ofinterest A solar angle of 68 was used in this study resultingin a southern shift of 342 m The buffer tool zonal statisticstool and move command were used to achieve the shift inArcGIS We also computed topographically influenced solarradiation using the lidar DEM and the solar radiation func-tion in ArcGIS but found that there was no significant dif-ference across the plot locations and thus did not use theseresults in subsequent analysis

Synthetic hemiphotos were created in MATLAB using themethod of Moeser et al (2014) and analyzed for diffuse anddirect light transmittance in GLA All statistical analyseswere performed in R (version 34)

Longitudinal profiles of stream shading were created inArcGIS in 1 m increments based on the intersections of thestream polyline center line with the raster output of modeledsolar insolation

Figure 5 Comparison between pyranometer-measured solar inso-lation and daily diffuse and direct radiation canopy transmittancecalculated from hemispherical photographs

3 Results and discussion

31 Comparison between pyranometers andhemispherical photographs

Figure 5 shows the correlation between field-collected pyra-nometer data and processed hemispherical photographs withdata from transect A removed These data are highly cor-related (r2

= 087) but these data are also not equally dis-tributed across a range of solar insolation Many more plotlocations were at low levels of solar insolation than in areasof relatively low shade This is very typical of the heavilyforested streams in northwestern North America Note thatnone of our plot locations contained transmittance greaterthan 40

32 Linear regressions

Pyranometer-based solar insolation and hemispherical pho-tograph percent diffuse and direct radiation transmittancecalculated at all point locations except transect A were com-pared to three lidar predictors using simple linear regressionThese results are shown in Fig 6 The LPI calculated usinga 10 m circle centered on the point location explained about55 of the variability in both response variables but the pre-diction accuracy improved when LPI was calculated usingthe shifted square buffer Shifted LPI explained 74 of thevariability in solar insolation and 64 of the variability inpercent transmittance Synthetic hemispherical photographsexplained 77 of the variability in solar insolation and 60 of the variability in percent transmittance Figure 6 showscomparisons between transects B and D to make interpreta-tion easier but Table 2 shows the results of linear regressionsbetween predicted variables and hemispherical photographtransmittance for all plot locations resulting in small reduc-tions in the amount of variability explained Table 3 givesparameters of slope and intercept resulting from the simplelinear regression

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2818 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 6 Simple linear regressions between lidar predictor variables and field-measured pyranometer solar insolation (a c e) and hemi-spherical photograph percentage transmittance (b d f) omitting data from transect A

Table 2 Coefficients of determination for the simple linear re-gression between predictor variables and hemispherical photographtransmittance using three additional point locations from transect A

Predictor variable Coefficient ofdetermination

(r2)

Light penetration index 054Shifted light penetration index 054Synthetic hemispherical photograph transmittance 045

While both the raster-based shifted LPI approach and thelidar point reprojection synthetic hemispherical photographapproach explained more than 60 of the variability in thefield data the limited range of solar insolation conditionsat the point locations in our study may limit some of theconclusions that can be drawn Excluding transect A 14 of

the 16 point locations received less than 08 kWh mminus2 dminus1leading the other two point locations to exert a large degreeof leverage on the results Note that these two point loca-tions received less than 35 of the maximum solar inso-lation The three points in transect A all received less than08 kWh mminus2 dminus1 and their inclusion in Table 2 did not im-prove coefficients of determination suggesting that all meth-ods are not as effective at predicting field-measured valuesin areas of high canopy cover The constraints of the studydesign requiring point locations to be located in the streammade it impossible to achieve a greater range in solar insola-tion It is reasonable to expect that including more point loca-tions receiving larger amounts of insolation would have ledto improved accuracy and greater coefficients of determina-tion as previous studies have shown that accuracy increasesas canopy cover decreases (Moeser et al 2014 Musselmanet al 2013 Richardson and Moskal 2014)

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2819

Figure 7 Sun path superimposed on a synthetic hemispherical photograph (a) and a field-acquired hemispherical photograph (b) at a pointlocation in Transect D The letters represent the four cardinal directions

Table 3 Parameters from simple linear regressions Note that allregressions are significant (p lt 005) Data from transect A are ex-cluded

Response variable Predictor variable Slope Intercept

Hemispherical Light penetration index 12409 minus329

photograph Shifted light1422 minus449

transmittance penetration index

Synthetic hemispherical101 minus032photograph

transmittance

Pyranometer Light penetration index 673 minus019

insolation Shifted light823 minus030

penetration index

Synthetic hemispherical007 minus008photograph

transmittance

One explanation of the decrease in variability at highcanopy cover in regressions E and F shown in figure isdemonstrated in Fig 7 Here a synthetic hemispherical pho-tograph from transect D is compared to a field-capturedhemispherical photograph with the GLA modeled sun pathsuperimposed This sun path is critical for determining thequantity of direct light but very small differences in the cen-ter location of the two images can produce large differencesin the modeled direct light The sun path passes through amodeled canopy gap near solar noon on the synthetic hemi-spherical photograph while it intersects only canopy andmisses the gap on the field-collected hemispherical photo-graph Very small registration errors can cause differences intransmittance at low light levels and we suggest that these er-rors are likely to cause the errors observed in the regressionsThe daily pyranometer output for the same point location is

Figure 8 Daily pyranometer output from sunset to sundown for thesame plot as Fig 7

Figure 9 Model used for generation of landscape-scale solar inso-lation estimates

shown in Fig 8 to further aid comparison The pyranome-ter is only briefly exposed to full sunlight highlighting thecontribution of small gaps in the canopy

Understory vegetation is another likely cause of observederrors as airborne lidar is inherently limited in its abil-ity to fully sample multi-layered canopies (Richardson and

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2820 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

Figure 10 Map of model-derived solar insolation for Panther Creek (top) and graph of model-derived solar insolation for reach AndashC (middle)and reach BndashD (bottom) Point E is a dammed reservoir Note the direction of flow is toward point C

Moskal 2011) We noticed several points with differencesbetween lidar predictors and field data that contained under-story vegetation in close proximity to the field instrumentsThe ideal scenario would be for the lidar scan angles to pre-cisely match the range of potential solar angles at each plotlocation but this is currently impractical leading to an in-complete sample of the canopy light environment which con-tributes to the observed errors

33 Modeled solar insolation

The correlations between lidar predictors and field data werestrongest in Fig 6c and e and these lidar predictors are bothappropriate to use as the basis for estimating solar insolationacross the study area Implementation of shifted LPI was thesimplest and least time-intensive method and we chose tomodel solar radiation by multiplying shifted LPI by the max-imum above-canopy solar insolation for 20 June 2015 andthen computing a non-intercept linear regression (Fig 9)Removing the intercept from the model lowered the coeffi-cient of determination but provided a model that did not es-timate negative values of solar insolation Figure 10 showsthe model applied across the study area The graphs showthe pattern of solar insolation across the two reaches in thestudy highlighting the utility of these methods for predicting

Figure 11 Histogram of solar insolation pixel values alongreach AndashC from Fig 9

solar insolation in heavily forested streams across wide spa-tial extents Figure 11 shows the relative frequency of binnedsolar insolation values highlighting the dominance of heav-ily shaded areas (note that a dammed reservoir point D onthe map contributes the majority of the points in full sun)

The relatively unbiased results shown in Fig 9 show thatfield calibration is not required to produce accurate estimatesof solar insolation However information is still needed onlocal above-canopy meteorological conditions which caneither be modeled from known solar outputs or collectedfrom a nearby meteorological station Little bias was ob-served in comparisons between synthetic hemispherical pho-tograph transmittance and field-based hemispherical photo-

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams 2821

graph transmittance (Table 3) Therefore both approachestested in this study should not require field calibration

4 Conclusions

We tested two approaches for estimating solar insolationfrom airborne lidar using field data collected in a heavilyforested narrow stream showing that an LPI-based raster ap-proach and a synthetic hemispherical photograph approachcan predict solar insolation and light transmittance These re-sults should be interpreted with the caveat that our point lo-cations contained few areas with high insolation We showedthat the LPI-based model can be applied across the land-scape and we demonstrated that no field-based calibrationwas necessary to produce unbiased prediction of solar inso-lation

This study lays the groundwork for additional research onremote sensing methods for quantifying light conditions inriparian areas over heavily forested streams One methodthat we were unable to test is ray-tracing and future re-search should continue to develop this approach Secondresearch should focus on exploring the limit of matchingground-based measurements to lidar-predicted solar insola-tion Lastly the limitation of aerial lidar to quantify under-story light conditions in multi-layered canopies should beexplored in more detail to better understand when and if air-borne sensors are inappropriate for these particular applica-tions In these circumstances other sensors such as terrestriallidar or ground-based digital photographs utilizing structurefrom motion may provide additional useful information

Data availability The GPS data pyranometer data processedhemispherical photograph data spreadsheets used for data analy-sis and access to the lidar data can be found at httpsdoiorg1017632vwmxw4hcj71 (Richardson 2018)

Author contributions JJR LLM and CET designed the study de-sign LLM and CET secured funding JJR performed the data anal-ysis and prepared a draft of the manuscript CET provided reviewand editing of the manuscript

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We are grateful to Dave Moeser for sharing hisMATLAB code for creating synthetic hemispherical photographsand to Keith Musselman for advising on the applicability of ray-tracing methods Guang Zheng also assisted with research into ray-tracing methods Caileigh Shoot and Natalie Gray coordinated fielddata collection This work was supported by the Precision ForestryCooperative the Bureau of Land Management and the US Geologi-cal Survey Any use of trade product or firm names is for descriptive

purposes only and does not imply endorsement by the US govern-ment

Review statement This paper was edited by Martijn Westhoff andreviewed by Collin Bode Caleb Buahin and one anonymous ref-eree

References

Alexander C Moeslund J E Bocher P K Arge L and Sven-ning J C Airborne laser scanner (LiDAR) proxies for under-story light conditions Remote Sens Environ 134 152ndash161httpsdoiorg101016jrse201302028 2013

Ameztegui A Coll L Benavides R Valladares F and Paque-tte A Understory light predictions in mixed conifer moun-tain forests Role of aspect-induced variation in crown ge-ometry and openness Forest Ecol Manage 276 52ndash61httpsdoiorg101016jforeco201203021 2012

Asrar G Myneni R B and Choudhury B J Spatial hetero-geneity in vegetation canopies and remote sensing of absorbedphotosynthetically active radiation A modeling study Re-mote Sens Environ 41 85ndash103 httpsdoiorg1010160034-4257(92)90070-Z 1992

Bode C A Limm M P Power M E and Finlay J CSubcanopy Solar Radiation model Predicting solar radiationacross a heavily vegetated landscape using LiDAR and GISsolar radiation models Remote Sens Environ 154 387ndash397httpsdoiorg101016jrse201401028 2014

Breshears D D Rich P M Barnes F J and Campbell KOverstory-imposed heterogeneity in solar radiation and soilmoisture in a semiarid woodland Ecol Appl 7 1201ndash1215httpsdoiorg1023072641208 1997

Field C B Randerson J T and Malmstroumlm C M Global netprimary production Combining ecology and remote sensing Re-mote Sens Environ 51 74ndash88 httpsdoiorg1010160034-4257(94)00066-V 1995

Flewelling J W and McFadden G LiDAR data and cooperativeresearch at Panther Creek Oregon in SilviLaser 16ndash20 Octo-ber 2011 Hobart Australia 2011

Forney W M Soulard C E and Chickadel C C Salmonidsstream temperatures and solar loadingndashmodeling the shade pro-vided to the Klamath River by vegetation and geomorphologyUS Geological Survey Scientific Investigations Report 2013-5022 p 25 available at httppubsusgsgovsir20135022(last access July 2019) 2013

Frazer G W Canham C D and Lertzman K P Gap Light An-alyzer (GLA) Version 20 Simon Fraser University BurnabyBritish Columbia 1999

Hock R Temperature index melt modelling in mountain ar-eas J Hydrol 282 104ndash115 httpsdoiorg101016S0022-1694(03)00257-9 2003

Holtby L B Effects of logging on stream temperatures in Carna-tion Creek British Columbia and associated impacts on the cohosalmon (Oncorhynchus kisutch) Can J Fish Aquat Sci 45502ndash515 httpsdoiorg101139f88-060 1988

Kerr J P Thurtell G W and Tanner C B An in-tegrating pyranometer for climatological observer

wwwhydrol-earth-syst-scinet2328132019 Hydrol Earth Syst Sci 23 2813ndash2822 2019

2822 J J Richardson et al Lidar-based approaches for estimating solar insolation in heavily forested streams

stations and mesoscale networks J Appl Me-teorol 6 688ndash694 httpsdoiorg1011751520-0450(1967)006lt0688AIPFCOgt20CO2 1967

Lee H Slatton K C Roth B E and Cropper W P Predic-tion of forest canopy light interception using three-dimensionalairborne LiDAR data Int J Remote Sens 30 189ndash207httpsdoiorg10108001431160802261171 2008

Leinenbach P McFadden G and Torgersen C E Effects ofriparian management strategies on stream temperature Intera-gency Coordinating Subgroup Seattle WA 22 pp 2013

Martens S N Breshears D D and Meyer C W Spatial distri-butions of understory light along the grasslandforest continuumeffects of cover height and spatial pattern of tree canopiesEcol Model 126 79ndash93 httpsdoiorg101016S0304-3800(99)00188-X 2000

McGaughey R J FUSIONLDV software for LIDAR data anal-ysis and visualization 251 Edn United States Department ofAgriculture Forest Service Pacific Northwest Research StationSeattle WA 2009

Moeser D Roubinek J Schleppi P Morsdorf F and JonasT Canopy closure LAI and radiation transfer from airborneLiDAR synthetic images Agr Forest Meteorol 197 158ndash168httpsdoiorg101016jagrformet201406008 2014

Moore R D Spittlehouse D L and Story A Riparian microcli-mate and stream temperature response to forest harvesting a re-view JAWRA J Am Water Resour Assoc 41 813ndash834 2005a

Moore R D Sutherland P Gomi T and Dhakal A Ther-mal regime of a headwater stream within a clear-cut coastalBritish Columbia Canada Hydrol Process 19 2591ndash2608httpsdoiorg101002hyp5733 2005b

Musselman K N Margulis S A and Molotch N P Esti-mation of solar direct beam transmittance of conifer canopiesfrom airborne LiDAR Remote Sens Environ 136 402ndash415httpsdoiorg101016jrse201305021 2013

Musselman K N Pomeroy J W and Link T EVariability in shortwave irradiance caused by forestgaps measurements modelling and implications forsnow energetics Agr Forest Meteorol 207 69ndash82httpsdoiorg101016jagrformet201503014 2015

Nicotra A B Chazdon R L and Iriarte S V B Spatial hetero-geneity of light and woody seedling regneration in tropical wetforests Ecology 80 1908ndash1926 httpsdoiorg1018900012-9658(1999)080[1908SHOLAW]20CO2 1999

Ni-Meister W Strahler A H Woodcock C E Schaaf CB Jupp D L B Yao T Zhao F and Yang X Model-ing the hemispherical scanning below-canopy lidar and veg-etation structure characteristics with a geometric-optical andradiative-transfer model Can J Remote Sens 34 S385ndashS397httpsdoiorg105589m08-047 2008

Peng S Z Zhao C Y and Xu Z L Modeling spatiotemporalpatterns of understory light intensity using airborne laser scan-ner (LiDAR) ISPRS J Photogramm Remote Sens 97 195ndash203 httpsdoiorg101016jisprsjprs201409003 2014

Rich P Dubayah R Hetrick W and Saving S Using view-shed models to calculate intercepted solar radiation applicationsin ecology American Society for Photogrammetry and RemoteSensing Technical Papers American Society of Photogrammetryand Remote Sensing Reno NV 524ndash529 1994

Richardson J J Lidar-based modelling approaches for estimat-ing solar insolation in heavily forested streams Mendeley Datahttpsdoiorg1017632vwmxw4hcj71 2018

Richardson J J and Moskal L M Strengths and limita-tions of assessing forest density and spatial configurationwith aerial LiDAR Remote Sens Environ 115 2640ndash2651httpsdoiorg101016jrse201105020 2011

Richardson J J and Moskal L M Assessing the utilityof green LiDAR for characterizing bathymetry of heavilyforested narrow streams Remote Sens Lett 5 352ndash357httpsdoiorg1010802150704X2014902545 2014

Richardson J J Moskal L M and Kim S-H Modelingapproaches to estimate effective leaf area index from aerialdiscrete-return LIDAR Agr Forest Meteorol 149 1152ndash1160httpsdoiorg101016jagrformet200902007 2009

Torgersen C E Hockman-Wert D P Bateman D S Leer D Wand Gresswell R E Longitudinal patterns of fish assemblagesaquatic habitat and water temperature in the Lower CrookedRiver Oregon United States Geological Survey Reston VA37 pp httpsdoiorg103133ofr20071125 2007

Torgersen C E Ebersole J L and Keenan D M Primer foridentifying cold-water refuges to protect and restore thermal di-versity in riverine landscapes Seattle WA Document numberEPA 910-C-12-001 US Environmental Protection Agency Seat-tle WA 91 pp 2012

Zhang Y Q Chen J M and Miller J R Determining digitalhemispherical photograph exposure for leaf area index estima-tion Agr Forest Meteorol 133 166ndash181 2005

Hydrol Earth Syst Sci 23 2813ndash2822 2019 wwwhydrol-earth-syst-scinet2328132019