creating a topoclimatic daily air temperature dataset for the conterminous united ... ·...

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. (2014)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/joc.4127

Creating a topoclimatic daily air temperature datasetfor the conterminous United States using homogenized station

data and remotely sensed land skin temperature

Jared W. Oyler,a,b* Ashley Ballantyne,b Kelsey Jencso,b Michael Sweetb and Steven W. Runninga

a Numerical Terradynamic Simulation Group, Department of Ecosystem and Conservation Sciences, University of Montana, Missoula, MT, USAb Montana Climate Office, Montana Forest and Conservation Experiment Station, University of Montana, Missoula, MT, USA

ABSTRACT: Gridded topoclimatic datasets are increasingly used to drive many ecological and hydrological models andassess climate change impacts. The use of such datasets is ubiquitous, but their inherent limitations are largely unknownor overlooked particularly in regard to spatial uncertainty and climate trends. To address these limitations, we presenta statistical framework for producing a 30-arcsec (∼800-m) resolution gridded dataset of daily minimum and maximumtemperature and related uncertainty from 1948 to 2012 for the conterminous United States. Like other datasets, we use weatherstation data and elevation-based predictors of temperature, but also implement a unique spatio-temporal interpolation thatincorporates remotely sensed 1-km land skin temperature. The framework is able to capture several complex topoclimaticvariations, including minimum temperature inversions, and represent spatial uncertainty in interpolated normal temperatures.Overall mean absolute errors for annual normal minimum and maximum temperature are 0.78 and 0.56 ∘C, respectively.Homogenization of input station data also allows interpolated temperature trends to be more consistent with US HistoricalClimate Network trends compared to those of existing interpolated topoclimatic datasets. The framework and resultingtemperature data can be an invaluable tool for spatially explicit ecological and hydrological modelling and for facilitatingbetter end-user understanding and community-driven improvement of these widely used datasets.

KEY WORDS kriging; air temperature; land skin temperature; homogenization; MODIS

Received 28 January 2014; Revised 31 May 2014; Accepted 14 July 2014

1. Introduction

Given that climate is a key driver of many ecological andhydrological processes (Running et al., 1987), the effectsof climate change have increasingly become a centralfocus within different areas of environmental research,conservation, and natural resource management (Wiensand Bachelet, 2010; Glick et al., 2011; Millard et al.,2012; Morisette, 2012). As a result, the demand for accu-rate and spatially continuous climate data that match thescales of local environmental processes and land manage-ment decision-making has continued to rise (Daly, 2006;Wiens and Bachelet, 2010; Beier et al., 2011). Assess-ments of climate change impacts across smaller regionspresent a challenge, however, owing to the mismatch inscale between local topoclimatic factors and synoptic out-puts from global climate models (GCMs) and atmosphericreanalyses (Beniston, 2006; Daly, 2006). This mismatchis especially apparent in mountainous landscapes wheretopography frequently drives rapid changes in temperature

* Correspondence to: J. W. Oyler, Numerical Terradynamic SimulationGroup, Department of Ecosystem and Conservation Sciences, Universityof Montana, 32 Campus Drive, Missoula, MT 59812, USA. E-mail:[email protected]

and precipitation over relatively small spatial scales(Beniston, 2006; Barry, 2008).

Accordingly, gridded topoclimatic datasets (TCDs) thataccount for local topoclimatic factors are often necessaryto assess local environmental impacts. TCDs generallyexist at spatial resolutions ≤10 km, the scale at which theinfluence of topoclimatic factors such as elevation, coldair drainage potential, and coastal zones becomes great-est (Daly, 2006). Within the conterminous United States(CONUS), the most frequently used TCDs are the inter-polated PRISM (Daly et al., 2002; Daly et al., 2008) andDaymet (Thornton et al., 1997) datasets. Both datasets usepoint-source weather station data and a digital elevationmodel (DEM) to incorporate the effects of topoclimaticfactors and statistically interpolate climate variables to aregular grid. The use of PRISM and Daymet is ubiquitousand recent environmental modelling applications includevarious GCM statistical downscaling efforts (e.g. Maurerand Hidalgo, 2008; Abatzoglou and Brown, 2012), climateimpact assessments (e.g. Elsner et al., 2010; Littell et al.,2010), wildfire hazard and risk assessments (e.g. Keaneet al., 2010), and analyses of trends in ecosystem produc-tivity (e.g. Turner et al., 2011) and plant species distribu-tions (e.g. Crimmins et al., 2011).

While TCDs like PRISM and Daymet are clearly valu-able and have been diligently maintained over many

© 2014 Royal Meteorological Society

J. W. OYLER et al.

Figure 1. Process flow diagram of the TopoWx (‘Topography Weather’) statistical framework. Numbers above components represent sections wherecomponents are described. GWR is geographically weighted regression.

years, their inherent limitations are often overlooked byend-users, particularly in regard to spatial interpolationuncertainty and their appropriateness in assessing inter-decadal and long-term climate trends (Beier et al., 2011;Bishop and Beier, 2013). Although model validation andperformance evaluations have been conducted by TCDdevelopers (Thornton et al., 1997; Daly et al., 2008), thereare currently no grid-cell-specific metrics of uncertainty.It is consequently difficult for end-users to determine thequality of a TCD for a specific region of interest or toincorporate uncertainty into subsequent analyses.

Additionally, while TCDs usually have basic qualityassurance (QA) checks on input station data, they donot account for changes in station siting, instrumenta-tion, exposure or observation and data processing practicesthrough time – types of changes, termed inhomogeneities,that can result in significant artificial jumps and trends inclimate (Menne et al., 2009; Trewin, 2010). The climatecommunity has conducted substantial research in this area(e.g. Alexandersson, 1986; Peterson et al., 1998; Reeveset al., 2007; Menne et al., 2009) and four global griddedtemperature datasets that account for inhomogeneities arenow available (Smith et al., 2008; Hansen et al., 2010;Jones et al., 2012; Rohde et al., 2013), but inhomogeneitydetection and correction algorithms (i.e. homogenizationalgorithms) have not yet been integrated into TCDs. Lastly,most TCD models require expert knowledge to run andare closed-source systems that cannot be easily extendedor improved by the general climate impacts researchcommunity.

Addressing these limitations, we present an open sourcestatistical framework for modelling topoclimatic air tem-perature (Figure 1). Targeted to create a 30-arcsec (∼800m) resolution CONUS dataset of 1948–2012 daily min-imum and maximum temperatures (Tmin, Tmax), theobjectives of the framework, termed TopoWx (‘Topogra-phy Weather’), are to provide (1) improved temporal andspatial representations of topoclimatic air temperature; (2)grid-cell level uncertainty estimations; and (3) an impetus

to increase both end-user understanding of TCD limita-tions and end-user involvement in TCD development.

2. Materials and methods

2.1. Overview

Similar to existing TCDs (Thornton et al., 1997; Dalyet al., 2008), we use weather station data and spatialgrids of auxiliary predicators to model the influence oftopoclimatic factors and spatially interpolate daily Tminand Tmax. However, to address the limitations of exist-ing TCDs and meet the framework objectives, we differ-entiate the TopoWx framework through several carefullyconstructed components (Figure 1). A first componentconsists of comprehensive QA procedures (Durre et al.,2010) that better ensure the overall quality of the input sta-tion observation records (Section 2.2.2.). The second com-ponent consists of homogenization procedures (Menneand Williams, 2009) that we apply to the quality assuredstation data (Section 2.2.3.). Without homogenization,inhomogeneities in the station records have the potentialto significantly bias temperature trends in the final griddedoutput (Menne et al., 2009). The third component con-sists of missing value infilling procedures (Schafer, 1997;Stacklies et al., 2007) that generate a serially completerecord at each station location (Section 2.2.4.). Missingvalue infilling ensures a spatially consistent set of inputstations throughout the entire 1948–2012 time period,yet still allows for the incorporation of important datafrom short-term or incomplete station records. Lastly, aset of several interpolation components consists of themain spatio-temporal interpolation procedures that takethe homogenized, serially complete station data as inputand produce the final gridded topoclimatic temperature anduncertainty estimates (Section 2.3.). The spatio-temporalinterpolation procedures include both geostatistical krig-ing (Isaaks and Srivastava, 1989; Hengl, 2009), geograph-ically weighted regression (GWR) (Fotheringham et al.,

© 2014 Royal Meteorological Society Int. J. Climatol. (2014)

TOPOCLIMATIC DAILY AIR TEMPERATURE

(a)

(b)

Figure 2. Maps of (a) the final set of 14 087 stations used as input to TopoWx and (b) underlying topography of the conterminous US. Stationnetworks include the daily Global Historical Climatology Network (GHCN-D), Remote Automatic Weather Stations (RAWS) network, and the

Snowpack Telemetry (SNOTEL) network. Each station has ≥5 years of raw data for each month. Boundaries represent US climate divisions.

2002), and a novel application of remotely sensed land skintemperature (LST) as a spatial predictor of topoclimatic airtemperature (Wan and Li, 2011).

2.2. Weather station data

2.2.1. Data sources

As our primary weather station data source, we use thedaily Global Historical Climatology Network (GHCN-D;Menne et al., 2012), a global weather station dataset con-sisting of observations from a multitude of different net-works and sources. We spatially limit GHCN-D stationsto North America between 53 and 22∘N latitude and 126and 64∘W longitude resulting in a total of 14 729 poten-tial stations with temperature observations (Figure 2(a)).To gain better spatial cover in the topographically com-plex areas of the western CONUS (Figure 2(b)), wealso obtain 764 potential station records from the moreremote Natural Resources Conservation Service (NRCS)

Snowpack Telemetry (SNOTEL) network and 1308 poten-tial station records from the US Forest Service and Bureauof Land Management Remote Automatic Weather Stations(RAWS) network.

For inclusion in the TopoWx framework, we require astation to have at least 5 years of observations in eachmonth, a threshold much shorter than the 20-year thresh-old imposed by other longer-term TCDs (e.g. Livneh et al.,2013). Our 5-year threshold was chosen based on the find-ing that at least 5–7 years of observations are requiredbefore pairwise relationships between stations begin to sta-bilize (Hubbard, 1994; Camargo and Hubbard, 1999). Theability to reliably model relationships between a stationand its neighbours is critical for infilling and extendingshorter station records back to 1948 (see Section 2.2.4.).

2.2.2. Quality assurance

To check for possible duplicate observations, outliers andnumerous internal, temporal, and spatial inconsistencies


J. W. OYLER et al.

in the GHCN-D, RAWS, and SNOTEL station data, weuse the QA procedures of Durre et al. (2010). After wemark any QA-flagged observation as missing, if a sta-tion falls below the 5-year threshold in any 1 month,we drop it from the framework. Similar to PRISM (Dalyet al., 2008), we additionally check all station elevationsfor consistency with corresponding location elevationsfrom a DEM. We manually investigate any station ele-vation having a discrepancy greater than 200 m (Dalyet al., 2008) and modify either the station elevation orlocation.

2.2.3. Homogenization

Although the QA procedures remove bad observations,they address neither potential inhomogeneities nor theoccurrence of time of observation departures (TODs)where a station’s reported daily Tmin or Tmax is off by acalendar day (Janis, 2002). TOD can be a significant prob-lem for daily spatial interpolations given that the variousinput station time series are assumed to be aligned at a dailytime step. To reduce TOD and inhomogeneities in the inputstation data, we apply two adjustment procedures: a simpledaily time-step correction of Tmax observations having amorning observation time and a homogenization algorithmdeveloped by Menne and Williams (2009).

Many US stations within GHCN-D are part of theNational Oceanic and Atmospheric Administration(NOAA) Cooperative Observer Program (COOP) Net-work and staffed by volunteers. For convenience, Tminand Tmax observations at COOP stations are often man-ually taken once daily over a 24-h period that does notdirectly correspond to the typical midnight-to-midnightcalendar day (Karl et al., 1986). For these non-midnightobservation times, the most common and consistentinstance of TOD is for morning observations of Tmaxas the recorded Tmax is likely for the previous calendarday (Janis, 2002; Holder et al., 2006). Therefore, we shiftall morning Tmax observations back a day. For morningTmax observations at COOP stations in North Carolina,Holder et al. (2006) found that this simple shift signifi-cantly improved correlations with midnight-to-midnightobservations at automated collocated stations. While lessfrequent, depending on the time of year and the passageof fronts, TOD issues can also occur for other observationtimes of Tmin and Tmax, but their detection and correc-tion are more complex and would likely require the use ofhourly data (Janis, 2002). Consequently, we limit explicitdaily TOD corrections to the more consistent and frequentTOD occurrence within morning observations of Tmax.We also do not apply the Tmax TOD correction to the7.9% of input GHCN-D COOP Tmax observations thatare missing a documented observation time (n= 8 706 353of 110 051 460).

In addition to TOD, non-midnight observations can alsoresult in a time-of-observation bias (TOB) where a singleTmin during a very cold morning or a single Tmax during avery warm late afternoon is recorded over two successivedays (DeGaetano, 1999; Janis, 2002). Even slight 1-day

shifts can result in seasonal biases for monthly temperature(Karl et al., 1986). The TOB issue is particularly evidentwhen trying to assess temperature trends at stations whosetime-of-observation has changed through time and is oneof the main network-wide inhomogeneities in the US tem-perature record (Menne et al., 2009). Adjustment methodshave been developed to correct for TOB at a monthly timestep (e.g. Karl et al., 1986), but there has been less focuson corrections for daily data.

For simplicity, we consolidate corrections for TOBchanges and all other network-wide and local inhomo-geneities within the monthly time-step pairwise homoge-nization algorithm (PHA) of Menne and Williams (2009).PHA uses a recursive implementation of the standard nor-mal homogeneity test (SNHT; Alexandersson, 1986) andnumerous pairwise comparisons of temperature time seriesto identify inhomogeneities in a station’s observations rel-ative to surrounding stations (Menne and Williams, 2009).Once specific artificial changepoints in a station’s temper-ature series are identified, PHA estimates their magnitudeand adjusts the segments between changepoints relativeto the most current identifiable homogenous segment.Although these adjustments effectively remove the trendbias at a station, it is important to note that PHA doesnot adjust for a station’s mean temperature bias (Menneet al., 2009). For instance, if a station switches to a morn-ing time-of-observation that causes an artificial drop inmonthly temperature, PHA will adjust all previous obser-vations downward to remove the trend bias caused by thechange. Nonetheless, the station will still have a cool biasin its mean monthly temperatures relative to stations thatare at midnight-to-midnight observation time. In the end,the purpose of PHA is not to adjust all station records to atheoretical set of standard observation practices, siting, andinstrumentation. Instead, the purpose of PHA is to removetrend biases caused by individual station changes in suchitems.

Within the TopoWx framework, we use the default con-figuration of the PHA v52i software (Menne and Williams,2009; Williams et al., 2012), which is currently applied tohomogenize monthly station data for the US Historical Cli-matology Network (USHCN) v2.5 dataset (Menne et al.,2009) and the GHCN-Monthly v3.2 dataset (Lawrimoreet al., 2011). As PHA runs on a monthly time step, wefirst aggregate the daily station data to monthly means,apply PHA, and then scale the daily values to match thePHA-adjusted monthly means. This is similar to the pro-cedure of Vincent et al. (2002) who homogenized dailydata at stations in Canada by adjusting daily observa-tions to match homogenized monthly and annual data.Although scaling daily observations to match the homog-enized monthly data only corrects the mean and not thevariance or skewness of a station’s temperature distri-bution (Della-Marta and Wanner, 2006; Kuglitsch et al.,2009), the approach is relatively straightforward and pro-vides daily temperature series that match the trends andvariations in the homogenized monthly data without theadded complexities and uncertainties in detecting and



correcting inhomogeneities at a daily time step (Vincentet al., 2002).

2.2.4. Missing value infilling

The frequent incompleteness of weather station observa-tions creates an additional challenge for climate researchand spatio-temporal interpolations (Huth and Nemesova,1995). Simply interpolating raw incomplete data couldproduce inhomogeneities in the gridded output as the num-ber of stations and station spatial coverage vary duringthe 1948–2012 time period (Guentchev et al., 2010). Theissue is particularly acute in the mountainous areas of thewestern CONUS where many remote and higher elevationSNOTEL and RAWS stations have only come online in thepast 30 years.

The use of non-missing neighbouring observations toinfill missing data at a target station has been regularly usedto create serially complete station data (DeGaetano et al.,1995; Huth and Nemesova, 1995; Eischeid et al., 2000).The most generally accurate infilling method, termed spa-tial regression (Durre et al., 2010), uses overlapping obser-vation periods to develop regression models between atarget station and neighbouring stations and then usesthe models to infill the target’s missing values (Kempet al., 1983; Huth and Nemesova, 1995; Hubbard and You,2005). Quantified with a correlation metric, more weightis often given to those neighbours having a stronger rela-tionship with the target (Kemp et al., 1983; Hubbard andYou, 2005; Durre et al., 2010).

Building upon the spatial regression assumption thatthere is a useful correlation structure between a targetstation and its neighbours, we adopt a two-step statisticalprocedure (Appendix S1) to infill missing temperaturevalues in the homogenized station records using notonly neighbouring longer-term stations, but also synop-tic atmospheric conditions as provided by the NationalCenters for Environmental Prediction/National Centerfor Atmospheric Research reanalysis dataset (Kalnayet al., 1996). The procedure is identical for Tmin andTmax and we complete it separately for each variable.Using both an expectation maximization-based infill-ing (Schafer, 1997) and a principal component analysismethod robust to missing values (Stacklies et al., 2007),we estimate the 1948–2012 daily temperature mean andvariance for an incomplete station time series and theninfill the daily anomalies around the mean (AppendixS1). We found that this approach reduces mean abso-lute error (MAE) and maintains observed temperaturevariance better than the pure spatial regression methods.To ensure that station time series are consistent throughtime, for any station that has more than 5 continuousyears of missing data from 1948–2012, we replace allthe station’s temperature observations with values fromthe station’s infill model. While this will likely havesome effect on daily interpolation accuracy, the accuracytrade-off allows us to still incorporate valuable data fromshort-term stations while avoiding the introduction of evenslight artificial changepoints in temperature means andvariances.

2.3. Temperature interpolation

2.3.1. Auxiliary spatial predictors

At smaller spatial scales, synoptic-scale atmospheric con-ditions are mediated in the boundary layer by several maintopoclimatic factors, namely elevation, topographic con-vergence and cold air drainage potential, slope and aspect,water bodies, and land cover (Daly, 2006; Dobrowskiet al., 2009). To define the interpolation grid and repre-sent the main topoclimatic factor of elevation, we use the30-arcsec PRISM DEM derived from the National Eleva-tion Dataset (Gesch et al., 2002) by Daly et al. (2008).We chose the DEM used by PRISM because it facili-tates straightforward comparisons between TopoWx andPRISM and allows for easier development of models thatcan combine the two datasets.

To account for other topoclimatic factors not completelyrepresented by the DEM, we use spatially continuousremotely sensed observations of LST. Compared to thethermodynamic temperature that is typically measured 1.5to 2-m above the ground, LST is the radiometric temper-ature of the ground surface (Jin and Dickinson, 2010).Properties of the land surface, such as land cover, topogra-phy, albedo, and soil characteristics, and their interactionwith atmospheric conditions, control spatial patterns ofLST (Mostovoy et al., 2006; Jin and Dickinson, 2010).While LST and air temperature have different physicalmeanings, LST spatial and temporal variability have beenfound to be highly correlated with air temperature andLST has been used to inform air temperature interpola-tions where weather station observations are sparse (e.g.Mostovoy et al., 2006; Vancutsem et al., 2010; Henglet al., 2011; Benali et al., 2012).

For observations of LST, we use the Moderate Reso-lution Imaging Spectroradiometer (MODIS), 8-day, 1-kmLST product (MYD11A2; Dozier, 1996; Wan, 2008).MYD11A2 estimates LST using the thermal infrared sig-nal received by the MODIS sensor and a split-windowalgorithm that uses differential absorption in adjacentinfrared bands to correct for atmospheric attenuation andland cover classification-based emissivities to account forvariability in surface emissivity (Dozier, 1996; Snyderet al., 1998). The 8-day product is an average of dailyclear-sky LST during a respective 8-day period. We useMYD11A2 from the Aqua satellite since its day and nightoverpass times more closely correspond to the diurnal tim-ing of Tmax and Tmin in the CONUS (Crosson et al.,2012).

As Aqua MYD11A2 is only available from mid-2002and we are interpolating temperature back to 1948, wecalculate 10-year (2003–2012) monthly LST means forboth day and night observations and use them as staticauxilary predictors analgous to the elevation predictor,but monthly-varying. In other words, we use a differentmean LST predictor for each month and temperature vari-able (Tmin or Tmax) for a total of 24 auxilary meanLST predictors. We quantify mean LST using the eightMYD11A2 8-day periods centred around each respectivemonth.


J. W. OYLER et al.

Similar to the station data, MYD11A2 also suffers froma significant amount of missing data largely due to cloudcontamination (Crosson et al., 2012). For a single 8-daypixel value, if the MODIS QA flags indicate cloud con-tamination or other possible issues resulting in an averageemissivity error >0.02 or average LST error >2 ∘C, wedo not consider the value in the 10-year mean. We alsocompletely remove any grid cell missing more than twothirds of its 2003–2012 8-day values. When only usingnon-missing data to calculate mean LST, we found thatmissing data, especially during regional cloudy periodsin winter, resulted in discontinuities and spatial artefacts.Using the three nearest stations to each MYD11A2 gridcell, we consequently apply the same mean estimation pro-cedure used for the station data (Appendix S1) to betterestimate 2003–2012 mean LST values.

To further characterize the influence of topography ondaily cold air drainage, we derive a multi-scale topographicdissection index (TDI; Holden et al., 2011a) from thePRISM DEM:

TDI(s0

)=

n∑i=1

z(s0

)− zmin (i)

zmax (i) − zmin (i)(1)

where TDI(s0) is the final multi-scale TDI value forgrid-cell location s0, z(s0) is the elevation of grid-cell loca-tion s0, zmin(i) is the overall minimum grid-cell elevation inspatial window i, zmax(i) is the overall maximum grid-cellelevation in spatial window i and n is the number of spa-tial windows (Holden et al., 2011a). The TDI for a specificwindow size reflects the height of a grid cell relative tothe surrounding terrain and ranges from 0 (lower than thesurrounding terrain) to 1 (higher than the surrounding ter-rain). Across a network of temperature sensors in complexterrain, Holden et al. (2011a) found a multi-scale TDI tobe well correlated with daily patterns of Tmin anomaliesinfluenced by cold air drainage. Ranging in value from 0to 5, we calculate our multi-scale TDI across a total of fivespatial window sizes (3, 6, 9, 12, and 15 km). Althoughour selection of these five window sizes is subjective, thewindow sizes account for spatial variations in an optimalTDI scale across the CONUS domain, yet still maintain aspatially static definition of the TDI predictor.

2.3.2. Monthly normal temperature interpolation

Similar to the two-step infilling algorithm, we use atwo-step interpolation procedure that first interpolates themonthly temperature normals at a grid cell and then the1948–2012 daily variation around the normals. The proce-dure is again identical for both Tmin and Tmax. We definea month’s normal Tmin or Tmax as the month’s mean valuefrom 1981–2010, the latest 30-year normal period definedby NOAA’s National Climatic Data Center. We adopt aregression-kriging (RK) framework (Hengl et al., 2004)that assumes monthly normal temperature represents a spa-tial process that can be expressed by the sum of determin-istic and spatially autocorrelated stochastic components:

T(s0,m0

)= T𝜇

(s0,m0

)+ Te

(s0,m0

)(2)

where T(s0,m0

)is the final interpolated normal tempera-

ture at grid-cell location s0 and month m0, T𝜇

(s0,m0

)is

the deterministic spatial trend or drift in normal tempera-ture modelled by station horizontal locations and auxiliarypredictors, and Te

(s0,m0

)is a stochastic spatially auto-

correlated residual with mean zero (Hengl et al., 2004;Webster and Oliver, 2007).

Following the RK framework of Hengl et al. (2004) andthe multiple linear regression model of Florio et al. (2004),we use linear regression to fit T𝜇

(s0,m0

)and ordinary

kriging (OK) to interpolate Te

(s0,m0

):

T(s0,m0

)= 𝛽0 + 𝛽1x + 𝛽2y + 𝛽3z + 𝛽4lst

(m0

)+

n∑i=1

wi

(s0,m0

)· Te

(si, m0

)(3)

where 𝛽0, 𝛽1, 𝛽2, 𝛽3, and 𝛽4, are the estimated regressiontrend model coefficients for the intercept, longitude, lat-itude, elevation, and monthly average LST, respectively;x, y, z, and lst(m0) are the longitude, latitude, elevation,and average LST for m0 at grid-cell location s0, wi(s0, m0)are weights defined by residual spatial covariance, andTe

(si, m0

)are the regression residuals for n stations.

In addition to the interpolation of T , RK provides animportant estimate of kriging prediction standard error(𝜎k) at every grid cell and month, which is a straight-forward method to represent general spatial uncertaintyin interpolated monthly normals. RK 𝜎k is a compositeuncertainty measure that reflects not only the interpolationerror associated with the regression trend model, but alsothe geographical arrangement of stations (Hengl et al.,2004). For instance, RK 𝜎k will be higher for grid cellsthat are located further away from station locations andfrom the centre of the station predicator space (Henglet al., 2004). We estimate RK 𝜎k through the calculationof the universal kriging 𝜎k (Cressie, 1993; Hengl et al.,2004).

Like most traditional kriging analyses, we use a var-iogram model to define the spatial covariance structureof Te (Isaaks and Srivastava, 1989). However, given thelarge and diverse landscape of the CONUS, it is likely notvalid to use a single global variogram that assumes thecovariance structure is the same within the entire domainand across months (Lloyd, 2009). Additionally, perform-ing RK at each grid cell using a global regression modeland the entire population of stations would be computa-tionally inefficient (Hengl, 2009) and prone to over smooththe interpolations or result in less accurate predictions anduncertainty estimates compared to more locally definedmodels (Lloyd, 2009). To account for non-stationarity inregression parameters and Te covariance, we use a localmoving window kriging (MWK; Haas, 1990) implemen-tation of RK (MW-RK), a kriging approach that fits aseparate local regression and variogram around each andevery interpolation point using only n surrounding stations(Appendix S2).



2.3.3. Daily temperature anomaly interpolation

Similar to the MW-RK monthly normal temperature inter-polations, we assume that 1948–2012 daily temperatureanomalies from the 1981–2010 normals can be expressedas the sum of a regression-modelled spatial trend and aninterpolated residual. However, because there are 23 742days from 1948–2012, a daily varying MW-RK approachis not computationally practical. We subsequently apply asimpler daily-varying interpolation model where we usea moving window GWR for the spatial trend and inversedistance weighting (IDW) for the residual interpolation.GWR is similar to regular linear regression except obser-vation points are weighted according to their distancefrom a prediction location (Fotheringham et al., 2002).The GWR model is identical to the regression compo-nent in Equation (3) except we add TDI as an additionalauxiliary predictor. For each month, we use the optimiza-tion procedures discussed in Appendix S2 to obtain locallyoptimal n values for the number of surrounding stations touse in the GWR and IDW. We calculate station weights forthe GWR via a bisquare weighting function:

wi

(s0

)=⎡⎢⎢⎣1 −

(h(s0

)i

r

)2⎤⎥⎥⎦2

(4)

where wi(s0) is the distance-based weight of station i atinterpolation location s0, r is the interpolation windowradius defined as the distance of the n + 1 closest station,and h(s0)i is the distance between station i and interpola-tion location s0. We use a power parameter of 2 for theIDW. While the GWR model and IDW interpolations varydaily, both the locally optimal n and the GWR and IDWweights remain constant for each month. We obtain a finalestimate of actual daily temperature by combining T andthe interpolated anomaly:

T(s0, d0

)= T

(s0,m0

)+ 𝛿T

(s0, d0

)(5)

where T(s0, d0) is the temperature at interpolation point s0for day d0 within m0 and 𝛿T(s0, d0) is the daily temperatureanomaly at interpolation point s0 for day d0.

Our combined use of a more complex procedure to inter-polate T and a simpler, faster method to interpolate 𝛿T canbe considered a form of climatologically aided interpola-tion (CAI; Willmott and Robeson, 1995). However, unliketraditional implementations of CAI that model 𝛿T withunivariate methods like pure IDW (Willmott and Robeson,1995), we incorporate auxiliary predictors that can be crit-ical for properly representing topoclimatic spatial patternsof 𝛿T . Holden et al. (2011b) showed topoclimatic factorsin a mountainous region to be directly related to spatialpatterns of 𝛿T , especially during stable atmospheric con-ditions favourable for cold air inversions.

2.4. Validation

2.4.1. Basic error statistics

For a basic validation of the infilled daily station tem-peratures, interpolated monthly normal temperatures, and

interpolated daily temperatures, we use three main modelperformance metrics: MAE (Willmott and Matsuura,2005), bias, and the refined index of agreement (dr), adimensionless measure of average error (Willmott et al.,2012; Appendix S3). The dr metric (Equation S5) rangesfrom −1.0 to 1.0 with a value >0.5 indicating a pred-icative ability greater than the observed mean (Willmottet al., 2012; Legates and McCabe, 2013). Unlike basiccorrelation measures, dr is sensitive to differences inmagnitude and variance between observed and modelledvalues (Legates and McCabe, 1999). Since the largestmode of variability in a station’s time series is normallythe seasonal cycle, we also apply a baseline adjustmentto dr (Legates and McCabe, 1999; Willmott et al., 2012;Appendix S3). This effectively avoids inflated dr valuesthat are simply the result of the model capturing the mainseasonality, but not necessarily day-to-day variability(Legates and McCabe, 1999; Willmott et al., 2012).

We use three separate sets of stations to validate the dailytemperature infill models: long-term GHCN-D stationsthat are part of USHCN and at least 95% complete for the1948–2012 time period and SNOTEL and RAWS stationsthat have at least 20 years of data. Assuming a worst-casemissing data scenario, for each station, we set all but its last5 years of observations to missing, build the 1948–2012temperature infill models and then compare the infilledvalues with the observed values that were artificially setto missing. We calculate an overall daily MAE, bias, andmean dr (dr) for the three networks. We also calculate theMAE of average station temperatures (AVG-MAE), whichis essentially the mean of the absolute station biases.

To evaluate model performance in the interpolationof 1981–2010 temperature normals and 1948–2012daily Tmin and Tmax, we perform a leave-one-outcross-validation (LOOCV; Willmott and Robeson, 1995)with every station in the interpolation domain. We summa-rize MAE, bias, and dr by US climate division (Guttmanand Quayle, 1996) and, following Abatzoglou (2013),October–April (‘cold’ season) and May–September(‘warm’ season) time periods. For daily temperature,we limit the LOOCV to only non-missing, non-infilledobservations to provide a better indication of the errorassociated with actual observed temperature and not theinfilled values.

2.4.2. Homogenization

Since TopoWx is the first CONUS-scale TCD to usehomogenized station data, it is important to specificallyvalidate the homogenization process. As a validationdataset, we use homogenized monthly observationsfrom the official USHCN v2.5 product (Menne et al.,2009; version 2.5.0 20130622). For each USHCN sta-tion (n= 1218), we extract the TopoWx interpolated1948–2012 daily temperatures from the nearest 30-arcsecgrid cell. Following Menne et al. (2009), we then calculateannual temperature anomalies (1981–2010 base period)for each USHCN station location for both the USHCNv2.5 and TopoWx data and interpolate the anomalies to a


J. W. OYLER et al.

0.25∘ grid using the IDW method of Willmott et al. (1985).From the 0.25∘ anomaly grids, we calculate and com-pare the area-weighted CONUS mean annual anomalies ofTopoWx and USHCN v2.5. If TopoWx effectively homog-enizes the input station data, 1948–2012 CONUS annualanomaly differences between TopoWx and USHCN v2.5should be small. Although USHCN v2.5 is the officialhomogenized station dataset for the CONUS, it also usesPHA and is not completely independent from TopoWx.Therefore, we also compare TopoWx CONUS annualanomalies to those of Berkeley Earth, a global temper-ature dataset that uses an entirely different procedure toaccount for station record inhomogeneities (Rohde et al.,2013).

To examine whether the homogenized TopoWx TCDdoes in fact improve upon non-homogenized TCDs,we additionally apply the same USHCN v2.5 andBerkeley Earth annual anomaly comparison to threenon-homogenized datasets: TopoWx interpolations basedon non-homogenized station data (TopoWx Raw), theDaymet 1-km product (Thornton et al., 2012), and thePRISM 2.5-min monthly product (PRISM Climate Group,2013a). In conducting these comparisons, we acknowl-edge that most non-homogenized TCDs were neverintended to be used to analyse temperature trends (PRISMClimate Group, 2013b). Nonetheless, the use of TCDs insuch a context continues to occur (e.g. Diaz and Eischeid,2007; van Mantgem et al., 2009; Crimmins et al., 2011).

2.4.3. Land skin temperature

Within the TopoWx framework, the application ofremotely sensed LST as an auxiliary predictor likelyhas the greatest potential to improve spatial represen-tations of temperature normals (Hengl et al., 2011). Toquantify the influence of the LST predictors and whetherthe influence differs between Tmin and Tmax, we firstcompare temperature normal biases between TopoWxand three TCDs that do not use LST: TopoWx withoutan LST predictor (TopoWx-No-LST), the Daymet 1-kmproduct (Thornton et al., 2012), and the PRISM 30-arcsec1981–2010 monthly normals product (PRISM ClimateGroup, 2012). Both Daymet and PRISM use a GWRapproach to interpolation, but Daymet only accounts forelevation (Thornton et al., 1997), while PRISM has asophisticated station weighting scheme to account fornumerous other topoclimatic factors (Daly et al., 2002;Daly et al., 2008). We focus the bias analysis on stationsin the more topographically complex western CONUS(n= 4923; Figure 2(a)). For all four datasets, we calculatebias in relation to an index of station LST spatial setting(LST-I). We generate LST-I values for each station byapplying the TDI calculation in Equation (1) to the LSTgrids. An LST-I value of 0 represents an area with an LSTvalue relatively colder than surrounding terrain while avalue of 5 represents an area with an LST value relativelywarmer than surrounding terrain.

In addition to the bias analysis, we also analyse the abso-lute and relative influence of LST and the other MW-RK

predictors (longitude, latitude, and elevation) on interpola-tions of western CONUS monthly normals. At each stationlocation, we perform basic monthly multiple linear regres-sions of the predictors and monthly normals. We quantifyrelative predicator influence by partitioning the propor-tion of model variance explained (R2) accounted for byeach predictor using the ‘lmg’ method (Lindeman et al.,1980) of the relaimp package (Grömping, 2006) withinthe R environment for statistical computing (R Core Team,2012). The lmg method averages the sequential sum ofsquares over different predictor orderings to better accountfor multicollinearity.

2.4.4. Uncertainty

In addition to improved temporal and spatial represen-tations of topoclimatic air temperature, one of the mainobjectives of TopoWx is to provide accurate grid-celllevel estimations of uncertainty. To assess the accuracyof MW-RK prediction standard error (𝜎k), we evaluatethe relationship between station LOOCV monthly normalMAE and 𝜎k. If 𝜎k properly accounts for local variabil-ity in station monthly normals, 𝜎k should have a strongpositive correlation with MAE (Harris et al., 2010). Wealso examine the relationship between 𝜎k and MAE at aregional scale by quantifying the correlation between cli-mate division average MAE and 𝜎k.

Besides correlating 𝜎k to MAE, by assuming normality,we can use 𝜎k to estimate symmetric prediction confidenceintervals (PCIs). If the PCIs are accurate, a given n% ofLOOCV predictions should fall with their n% PCI (Har-ris et al., 2010). For instance, 95% of LOOCV predictionsshould fall within their respective 95% PCI. We quantifyPCI accuracy across the full range of interval probabil-ities with the G-statistic (Goovaerts, 2001; Harris et al.,2010). The G-statistic ranges from 0.0 to 1.0 with valuescloser to 1.0, indicating higher PCI accuracy. As previ-ously described, 𝜎k is a composite measure that incorpo-rates uncertainty from both the deterministic and spatiallyautocorrelated stochastic components of the MW-RK pro-cedure (Hengl et al., 2004). Because most other TCDsuse forms of GWR that only model a deterministic spa-tial trend (Thornton et al., 1997; Daly et al., 2008), wealso compare 𝜎k to uncertainty estimates from a GWRversion of the MW-RK trend model (Equation (3)). Weuse Equation (4) to define local GWR weights and calcu-late GWR prediction standard errors (𝜎GWR) according toLeung et al. (2000). We compare the 𝜎GWR MAE correla-tions, G-statistics, and average PCI widths to those of 𝜎kand also examine differences in spatial patterns betweenthe two uncertainty measures.

3. Results and discussion

3.1. Basic error statistics

3.1.1. Infilled missing values

After the removal of QA-flagged observations (Table S1),14 087 stations met the minimum criteria of 5 years of



Table 1. Infill error statistics. (a) Cross-validation error statistics for daily 1948–2012 temperature infilling based on using only 5years of data to build the infill models. (b) Error statistics for daily 1948–2012 temperature infilling on days with both infilled and

observed values for stations within the CONUS.

Network(number of stations)

Tmin Tmax

Bias (∘C) AVG-MAE (∘C) DailyMAE (∘C)

dr Bias (∘C) AVG-MAE (∘C) DailyMAE (∘C)

dr

(a)GHCN-D (626) +0.00 0.22 1.36 0.82 +0.01 0.23 1.48 0.82RAWS (376) −0.12 0.19 1.58 0.76 +0.04 0.18 1.40 0.83SNOTEL (541) −0.07 0.15 1.67 0.75 +0.09 0.23 1.77 0.78(b)GHCN-D (9480) +0.00 0.03 1.06 0.85 +0.00 0.03 1.03 0.87RAWS (1244) −0.02 0.06 1.10 0.83 −0.00 0.06 1.01 0.88SNOTEL (691) −0.01 0.04 1.10 0.83 +0.00 0.05 1.14 0.86

Error metrics are defined in Section 2.4.1.

observations for Tmin and/or Tmax (Figure 2(a)). Ofthese, a total of 626 USHCN stations, 376 RAWS sta-tions, and 541 SNOTEL stations were used for infillmodel cross-validation based on their longer periods ofrecord. Overall, cross-validation errors for the infill mod-els appeared to be reasonable, especially considering thatthe cross-validation procedure limited model building toonly 5 years of data (Table 1(a)). Except for a RAWSTmin bias of −0.12 ∘C, temperature bias for each networkwas within ±0.10 ∘C. For all three networks, AVG-MAEwas <0.25 ∘C, daily MAE was <2.0 ∘C, and dr was ≥0.75(Table 1(a)).

As described in Section 2.2.4., to minimize even slightartificial mean and variance changepoints, for any stationwith more than 5 continuous years of missing data fromthe period 1948–2012, we replace all the station’s tem-perature observations with values from the station’s infillmodel. For both Tmin and Tmax, around 80% of stationsfell into this category and had their observations replacedwith infilled values (Tmin n= 11 289; Tmax n= 11 315).This still resulted in around 3000 long-term stations retain-ing non-infilled observations. To make sure that the infilledvalues adequately represented the original observations atthe shorter-term stations, we calculated error summariesfor all stations in the CONUS (Table 1(b)). These errorstatistics are different than those from the cross-validationprocedure as they represent residuals between infilled val-ues and the observations from which the infill modelswere actually built. For all three networks and both Tminand Tmax, bias was within ±0.02 ∘C, AVG-MAE was<0.10 ∘C, daily temperature MAE was <1.15 ∘C, and drwas ≥0.83.

3.1.2. Interpolated monthly normal temperatures

Across the CONUS, overall LOOCV monthly normalTmin MAE (0.80–0.84∘C) was higher than overallmonthly normal Tmax MAE (0.60–0.62 ∘C; Figure 3).Likely a reflection of the multifaceted relationship betweenTmin and elevation (e.g. Bolstad et al., 1998; Lundquistet al., 2008; Daly et al., 2010; Holden et al., 2011a),higher monthly normal Tmin MAE was most apparent in

the topographically complex areas of the western CONUS(Figure 3). Monthly normal Tmin MAE was less elevatedin climate divisions with relatively flat and homogenouslandscapes, especially in the interior plains of the cen-tral CONUS (Figure 3). The highest monthly normalTmax MAE was during the May–September time periodwithin climate divisions along the California Pacific coast(Figure 3). During the summer, owing to the relativelycool California current and the position of the NorthPacific High, coastal marine inversion layers and stratusclouds produce a strong Tmax gradient from the coast tomore inland areas and a greatly complicated relationshipbetween elevation and Tmax (Daly et al., 2008; Iacobellisand Cayan, 2013).

Overall monthly normal Tmin was slightly positivelybiased (+0.01 ∘C) for the CONUS while monthly nor-mal Tmax was slightly negatively biased (−0.03 to−0.01 ∘C; Figure 3). At the scale of individual climatedivisions, Tmin generally had marginally larger biasesthan Tmax. For instance, 33% of climate divisions hada monthly normal Tmin absolute bias >0.1 ∘C for boththe October–April and May–September time periodscompared to 23% of climate divisions for Tmax.

3.1.3. Interpolated daily temperatures

Compared to the monthly normals, daily temperatureLOOCV MAE was greater with overall daily Tmin(Tmax) MAE ranging from 1.43 ∘C (1.34 ∘C) in theMay–September time period to 1.75 ∘C (1.61 ∘C) inthe October–April time period (Figure 4). Similar to themonthly normals, higher daily Tmin MAE was notice-able in the topographically complex areas of the westernCONUS and daily Tmax MAE had higher values alongthe Pacific coast during the May–September time period(Figure 4). From October–April, a north-south swath ofhigher daily Tmax MAE was also evident through portionsof the Rocky Mountains and Great Plains (Figure 4). Thisregion of higher daily Tmax MAE could be a result ofboth the occurrence of wintertime Tmax inversions (Dalyet al., 2010) and the higher frequency and magnitude ofwintertime cold and warm fronts (Camargo and Hubbard,


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Figure 3. Leave-one-out cross-validation error statistics for interpolated 1981–2010 monthly temperature normals summarized by US climatedivision. Statistics are based on all input GHCN-D, SNOTEL, and RAWS stations within the conterminous United States (n= 11 589 for minimumtemperature; n= 11 619 for maximum temperature). MAE is mean absolute error. Point maps of individual station MAE and bias can be found in

Figures S1–S4.

1999). Given the relatively flat, open prairie and agricul-tural landscapes of the Great Plains, it is also likely thatwinter spatial patterns of daily Tmax in the region areless a function of the underlying terrain than they are afunction of air mass and front positions.

Overall LOOCV Tmin dr ranged from 0.73 to 0.78while Tmax dr ranged from 0.79 to 0.82 (Figure 4).Spatial patterns of dr were generally similar to those ofdaily MAE with weaker dr values in the western CONUS(Figure 4). In contrast to daily MAE patterns, weaker drvalues were also found in the Florida peninsula duringthe May–September time period where climate divisionTmin dr ranged from 0.59 to 0.66 and Tmax dr rangedfrom 0.60 to 0.72 (Figure 4). We found summer stationobservations in Florida to have the lowest temporal stan-dard deviations out of any stations in the CONUS. Thus,even though daily MAE is relatively low in Florida duringthe summer (Figure 4), small differences between interpo-lated and observed values have greater potential to reducedr than in regions or time periods with greater observa-tion seasonality and daily variability (Hubbard, 1994). Seabreezes along the Florida coast and associated convectiveactivity are also strongest in summer (e.g. Pielke, 1974),likely making spatial patterns in daily Tmax harder toresolve.

3.2. Homogenization

Compared to the non-homogenizied TCDs, TopoWxCONUS annual temperature anomalies appeared to bemore temporally consistent with USHCN v2.5 data andBerkeley Earth, especially for Tmax (Figure 5). TheTopoWx 1948–2012 CONUS Tmax trend of 0.123 ∘Cdecade−1 was nearly identical to the USHCN v2.5 Tmaxtrend of 0.125 ∘C decade−1 and only slightly warmer thanthe 0.118 ∘C decade−1 Berkeley Earth trend (Table 2).In contrast, TopoWx Raw and PRISM 1948-2012 Tmaxtrends were non-significant and much less positive(Table 2). The cold bias in the TopoWx Raw, PRISM,and Daymet Tmax trends is a well-known attribute of thenon-homogenized US Tmax record and is attributed to thegeneral conversion from evening to morning observationtimes and the switch from liquid-in-glass thermometersto the maximum–minimum temperature system (Menneet al., 2009).

Homogenization also appeared to improve the corre-spondence in CONUS Tmin anomalies between TopoWxand both USHCN v2.5 and Berkeley Earth, but not tothe extent of Tmax (Figure 5). The TopoWx 1948-2012Tmin trend of 0.160 ∘C decade−1, while greater than the0.134 ∘C decade−1 TopoWx Raw and 0.142 ∘C decade−1

PRISM trends, was still biased cold in relation to the



Figure 4. Leave-one-out cross-validation error statistics for interpolated 1948–2012 daily temperatures summarized by US climate division. Statisticsare based on observed, non-missing observations at all input GHCN-D, SNOTEL, and RAWS stations within the conterminous United States(n= 11 589 for minimum temperature; n= 11 619 for maximum temperature). MAE is mean absolute error. Mean dr is the mean refined index

of agreement. Note inverted color bar for dr. Point maps of individual station MAE and dr can be found in Figures S5–S8.

Table 2. Annual temperature trends for the CONUS based onUSHCN v2.5 data, Berkeley Earth, TopoWx, TopoWx Raw,

PRISM, and Daymet.

Dataset 1948–2012Trend(∘C decade−1)

1981–2010Trend(∘C decade−1)

Tmin Tmax Tmin Tmax

USHCN v2.5 +0.185* +0.125* +0.199* +0.266*Berk Earth +0.181* +0.118* +0.182* +0.252*TopoWx +0.160* +0.123* +0.177* +0.272*TopoWx Raw +0.134* +0.025 +0.169* +0.117PRISM +0.142* +0.000 +0.193* +0.080Daymet NA NA +0.191* +0.077

*p-value≤ 0.10.

USHCN v2.5 0.185 ∘C decade−1 and Berkeley Earth0.181 ∘C decade−1 trends (Table 2). Additionally, over the1981–2010 time period, both Daymet and PRISM had1981–2010 Tmin trends more similar to USHCN v2.5while TopoWx was closer to Berkeley Earth (Table 2).The remaining cold bias in the TopoWx Tmin trend inrelation to USHCN v2.5 and Berkeley Earth could be theresult of PHA not entirely adjusting for TOB inhomo-geneities in the Tmin record. For the USHCN v2.5 data,a specific monthly TOB correction (Karl et al., 1986)

is applied before PHA. Additionally, in contrast to the1895-present USHCN v2.5 period-of-record, we onlyrun PHA over the 1948–2012 time period. Nevertheless,given the closer match in annual anomalies betweenTopoWx and both USHCN v2.5 and Berkeley Earth,the 1948–2012 PHA-only homogenization still appearsto largely account for the main network-wide inhomo-geneities in the raw station data and is a clear improvementover the non-homogenized TCDs (Figure 5).

3.3. Land skin temperature

Unlike TCDs without an LST predictor, TopoWx hadconsistently low monthly normal Tmin bias acrossseasons and different LST spatial settings (Figure 6).TopoWx-No-LST, PRISM, and Daymet tended to over-estimate Tmin in areas with colder LST values andunderestimate Tmin in areas with warmer LST values(Figure 6). Averaged across all western CONUS stations,LST was also the most important predictor of monthly nor-mal Tmin accounting for >50% of the variance explainedacross all months (Figure 7(b)). In contrast, the relativeimportance of the elevation predictor remained near orbelow 20% for most months and only rose to near 30%during the spring (Figure 7(b)).

Throughout the mountainous western CONUS, micro-climate influences on Tmin can be strong and Tmin cold


J. W. OYLER et al.

(a) (b)

(c) (d)

Figure 5. Differences in average mean annual temperature anomalies for the conterminous United States. (a) Difference from USHCN v2.5 minimumtemperature anomalies, (b) difference from USHCN v2.5 maximum temperature anomalies, (c) difference from Berkley Earth minimum temperatureanomalies, and (d) difference from Berkeley Earth maximum temperature anomalies. Differences are the respective dataset values minus USHCN

v2.5 or Berkeley Earth values. TopoWx Raw is TopoWx driven by non-homogenized station data. Daymet is only available from 1980 onwards.

(a) (b)

(c) (d)

Figure 6. Dataset bias for stations in the western United States (n= 4923) grouped by an index of land skin temperature (LST). (a) Cold seasonminimum temperature, (b) cold season maximum temperature, (c) warm season minimum temperature, and (d) warm season maximum temperature.An LST index value of 0 represents an area with an LST value relatively colder than surrounding terrain while a value of 5 represents an area with

an LST value relatively warmer than surrounding terrain. TopoWx-No-LST is TopoWx without an LST predictor.



(a)

(b) (c)

Figure 7. Diagnostic statistics of moving window monthly multiple linear regressions relating the moving window regression kriging auxiliarypredictors (elevation, land skin temperature, latitude, and longitude) and 1981–2010 monthly temperature normals within the western United States.(a) Overall variance explained (R2); and proportion of R2 attributed to each predictor for (b) minimum temperature and (c) maximum temperature.

Statistics are averaged across 4923 western US station locations.

air pools and inversions are a common phenomenon, espe-cially during periods of atmospheric stability and signif-icant radiative cooling (e.g. Lundquist et al., 2008; Dalyet al., 2010; Holden et al., 2011b). As a result, Tmin oftendoes not have a simple linear relationship with elevation,which limits the ability of an individual elevation predic-tor to properly represent Tmin spatial patterns (Daly et al.,2008; Dobrowski et al., 2009). On the basis of the high rel-ative importance of the LST predictor and the decreasedbias of TopoWx over TopoWx-No-LST, the addition ofLST appears to help overcome the limitations of the eleva-tion predictor and provides significant added value to themonthly normal Tmin interpolations (Figure 7(b)).

Although the LST predictor appeared to decrease Tmaxbias at the lowest LST-I values, differences betweenTopoWx and TCDs without LST were not as signifi-cant as those seen for Tmin (Figure 6). Except for thelowest LST-I values, Tmax bias for all the datasets was<±0.25 ∘C (Figure 6). Furthermore, in contrast to Tmin,the relative importance of the LST predictor in predict-ing western CONUS Tmax normals was less than thatof elevation in all months except for December and Jan-uary (Figure 7(c)). There are likely two main reasons forthis result. First, since Tmax generally displays a sim-pler linear decrease with elevation, elevation is alreadya strong predictor of Tmax without the addition of LST(Daly, 2006; Daly et al., 2008; Dobrowski et al., 2009).

This was not the case for Tmin where elevation was a rela-tively weak predictor (Figure 7(b)). Second, owing to solarradiation effects on the thermal infrared signal (Vancut-sem et al., 2010; Benali et al., 2012), different mediatingeffects of land cover and moisture regimes on the surfaceenergy balance (e.g. Mildrexler et al., 2011), and increaseddaytime convective turbulence and advection comparedto nighttime conditions (Pielke et al., 2007; Kloog et al.,2012), the relationship between Tmax and LST is oftenmore complex than that of Tmin and LST (Vancutsemet al., 2010; Benali et al., 2012; Kloog et al., 2012). Giventhat MODIS LST can only be retrieved under a relativelycloudless atmosphere, the maximum LST predictor is alsolikely biased to clear-sky conditions when the differencebetween maximum LST and Tmax is normally greatestbecause of increased insolation (Jin et al., 1997). For thewinter months that did display slightly higher relativeinfluence values for LST (Figure 7(c)), lower wintertimeinsolation is likely resulting in a more linear correspon-dence between LST and Tmax across different surfaceconditions. In the winter, climatological Tmax inversionsand snow cover in many mountainous regions of the west-ern CONUS (Whiteman et al., 1999; Pepin et al., 2011)could also be lessoning the predictive power of elevationand increasing that of LST. Ultimately, even though theMW-RK linear model had overall greater predictive powerfor Tmax than Tmin (Figure 7(a)), the added value of LSTon interpolations of monthly normal Tmax in the western


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Table 3. Performance metrics of monthly normal prediction standard error (𝜎) for moving window regression kriging (MW-RK) andgeographically weighted regression (GWR).

G-statistic MAE and𝜎 correlation

Average climate divisionMAE and 𝜎 correlation

Average PCIwidth (∘C)

TminMW-RK 0.995 0.41 0.89 1.636GWR 0.984 0.36 0.90 1.735

TmaxMW-RK 0.992 0.35 0.81 1.218GWR 0.981 0.33 0.82 1.274

Metrics are defined in Section 2.4.4.

CONUS appears to be mainly confined to specific months(Figure 7(c)) or environmental settings (Figure 6) and isless significant than the added value seen for Tmin.

3.4. Uncertainty

The 1981–2010 monthly normal temperature PCIs derivedfrom 𝜎k displayed high accuracy with G-statistics of 0.995and 0.992 for Tmin and Tmax, respectively (Table 3). Forinstance, the actual percentage of LOOCV monthly nor-mal predictions within the 95% PCI was 94.6% for Tminand 94.5% for Tmax. Compared to the high PCI accu-racy, the correlation between individual station LOOCVMAE and 𝜎k was positive, but not overwhelmingly strong(Table 3). The MAE and 𝜎k correlation was 0.41 for Tminand 0.35 for Tmax. Nonetheless, the correlations are sim-ilar to those from the best performing kriging modelsreviewed by Harris et al. (2010). At the scale of US cli-mate divisions, the correlations between MAE and 𝜎k werealso much stronger with Tmin and Tmax at 0.89 and 0.81,respectively (Table 3). These results are similar to thoseof Daly et al. (2008) who found PCIs derived from thePRISM interpolation model to be more highly correlatedwith MAE at larger regional aggregations.

Although accuracy metrics for 𝜎k were favourable, theywere not significantly better than those of the deterministicGWR model (Table 3). The GWR G-statistics and individ-ual station MAE and 𝜎GWR correlations were lower thanthose of 𝜎k, but nearly indistinguishable. For similarly per-forming uncertainty models, the one with the smaller aver-age PCI widths is normally preferred (Harris et al., 2010).While 𝜎k again performed better than 𝜎GWR in this regard,differences were not substantial (Table 3). The average 𝜎kPCI widths were 4.4–5.7% smaller than the average 𝜎GWRPCI widths.

In contrast to the accuracy metrics, differences in localspatial patterns between 𝜎k and 𝜎GWR were much more dis-tinguishable. As a local example, in the western climatedivision of Montana, USA, August monthly normal Tmin𝜎k displayed bullseyes of decreased uncertainty aroundstation locations while 𝜎GWR did not (Figure 8). Unlike𝜎GWR, which only represents model goodness of fit (Dalyet al., 2008), 𝜎k accounts for the geographical arrange-ment of stations (Hengl et al., 2004). The 𝜎k field wasalso smooth while 𝜎GWR had circular arcs of discontinu-ities likely resulting from specific stations moving in or outof the local GWR radius. In contrast to these differences,

both 𝜎k and 𝜎GWR had spatial patterns that followed theunderlying elevation and/or LST values of the grid cells.In the end, the uncertainty spatial patterns are reflective ofthe advantages of MW-RK 𝜎k over not only GWR 𝜎GWR,but also OK 𝜎k. The GWR 𝜎GWR measure only representsmodel goodness of fit while OK 𝜎k only accounts for thegeographical arrangement of stations. As evident in thelocal example, MW-RK 𝜎k is able to combine both com-ponents of uncertainty into a single composite measure(Hengl et al., 2004).

3.5. Example output and comparison with other datasets

As an example of the final TopoWx output for theCONUS, we concentrate on the summer month of August.In August, nighttime microclimate influences and Tmininversions are more consistent in many mountainousregions of the western CONUS due to increased nighttimeatmospheric stability (e.g. Finklin, 1986; Holden et al.,2011b). Coastal marine inversions layers also increaseTmax spatial complexity along the Pacific coast (Dalyet al., 2008; Iacobellis and Cayan, 2013). We examinespatial patterns in both August Tmin and Tmax normalsand corresponding uncertainty. We also compare TopoWxAugust Tmin and Tmax normals within the westernCONUS to those of the Daymet 1-km product (Thorntonet al., 2012), and PRISM 30-arcsec 1981–2010 monthlynormals product (PRISM Climate Group, 2012).

In August, TopoWx Tmax displayed a strong correspon-dence to elevation gradients, especially in the westernCONUS (Figure 9). Cooler Tmax temperatures were alsonoticeable along the Pacific coast. In contrast, TopoWxAugust Tmin displayed more complexity with relation-ships to not only elevation, but also convergent valleys,large inland lakes and rivers, and urban areas (Figure 9).Uncertainty patterns for both August Tmin and Tmax(Figure 9) directly corresponded to warm season MAE(Figure 3). Higher August Tmin 𝜎k values were seenthroughout the topographically complex western CONUS,while higher Tmax 𝜎k values were mainly confined to thePacific coast (Figure 9). Although regional differences in𝜎k dominated the spatial patterns at the scale of CONUS,uncertainty patterns related to station locations and topo-graphical patterns were still discernable (Figure 9).

Differences in western CONUS August Tmin normalsbetween TopoWx and the existing PRISM and Daymet



(a) (b) (c)

Figure 8. Maps of prediction standard error for 1981–2010 August minimum temperature normals for the western climate division of Montana,USA. (a) Climate division topography and geographical context; (b) TopoWx moving window regression kriging prediction standard error; and (c)

geographically weighted regression prediction standard error. Dots in (a) are weather station locations.

Figure 9. Conterminous US maps of TopoWx 1981–2010 August temperature normals and corresponding uncertainty. Note different scales for Tminnormals and Tmax normals.


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Figure 10. Western US maps of differences in 1981–2010 August temperature normals between PRISM and TopoWx and between Daymet andTopoWx.

TCDs were substantial (Figure 10). Only 47% of west-ern CONUS grid cells for Daymet were within 1.0 ∘C ofTopoWx Tmin and Daymet had an overall −0.83 ∘C coldbias in relation to TopoWx western CONUS Tmin. Dif-ferences between PRISM and TopoWx western CONUSTmin were smaller, but still significant (Figure 10). PRISMTmin displayed an overall −0.30 ∘C cold bias in relation toTopoWx Tmin and 57% of PRISM grid cells were within1.0 ∘C of TopoWx Tmin.

In mountainous terrain, both Daymet and PRISM gen-erally displayed warmer valley and cooler mountain Tminthan TopoWx, but PRISM tended to better match TopoWxspatial patterns. For instance, within the undulating basinand range topography of the northeastern climate divisionof Nevada, USA, Daymet Tmin significantly smoothed outterrain influences while PRISM displayed Tmin inversionpatterns more similar to TopoWx (Figure 11). Elevation,the only topoclimatic factor accounted for by Daymet, isa poor predictor of August Tmin in this Nevada climatedivision. For the TopoWx MW-RK Tmin model, the aver-age relative importance of elevation within the region wasonly 6% of variance explained. Conversely, LST was thedominant predictor at over 77% of variance explained.Daymet differences from TopoWx were subsequently

negatively correlated with LST (r = −0.82). While thePRISM model does not use LST as a predictor, its sophis-ticated station weighting scheme better accounts for Tmininversions and other topoclimatic factors (Daly et al.,2008). Nevertheless, with a negative correlation betweenPRISM differences from TopoWx and the LST predictor(r = −0.61), PRISM Tmin still tended to be warmer in thevalleys and cooler in the mountains than TopoWx Tmin(Figure 11).

In addition to these differences in mountainous terrain,Daymet and PRISM August Tmin were also cooler thanTopoWx over large inland water bodies like the Great SaltLake (Figure 10). While TCDs are usually only used overland and not expected to be valid over water, an ability tobetter represent temperature patterns directly over waterbodies would be a beneficial advancement. However, giventhe significant differences in LST values over water bodiescompared to their surrounding terrestrial landscapes, a lackof station observations over many lakes, and generallyhigher water body 𝜎k uncertainty values (e.g. Figure 8),further validation is likely required to confirm the accuracyof Tmin spatial patterns over water.

Compared to water bodies, differences related to urbanareas in the western CONUS were less visually discernable



Figure 11. Comparison of TopoWx, PRISM, and Daymet 1981–2010 August minimum temperature normals within the northeastern climate divisionof Nevada, USA.

except in the Central Valley of California. Within the Cen-tral Valley, Daymet and PRISM were generally warmerthan TopoWx except for islands of warmer TopoWx Tminover urban areas like Fresno (Figure 10). Differences likelyunrelated to underlying terrain or land cover were alsonoticeable, especially in northwestern California whereDaymet August Tmin was more than 10 ∘C degrees colderthan both TopoWx and PRISM throughout much of theregion (Figure 10).

In contrast to Tmin, differences between TopoWxAugust Tmax and the other TCDs were not as significant(Figure 10). The percentage of western CONUS grid cellswithin 1.0 ∘C of TopoWx Tmax was 91% for Daymet and90% for PRISM. In relation to TopoWx Tmax, Daymetwas biased +0.06 ∘C and PRISM was biased +0.27 ∘Cwithin the western CONUS. Corresponding to TopoWxTmax uncertainty (Figure 9), the most substantial Tmax

differences were mainly confined to areas near and alongthe Pacific coast (Figures 10 and 12).

Owing to the frequent onshore presence of a marine layerin the summer (Johnstone and Dawson, 2010; Iacobellisand Cayan, 2013), the California Pacific coast representsone of the few areas where Tmax and elevation do nothave a simple linear relationship (Daly et al., 2008). Forexample, within the north coast drainage climate divisionof California (Figure 12), elevation only had an averagerelative importance of 14% within the TopoWx MW-RKTmax model while LST relative importance was 47%.Correspondingly, in viewing TCD outputs for the climatedivision, Daymet Tmax normals were over smoothedin certain areas while both PRISM and TopoWx dis-played more realistic coastal and topographic influences(Figure 12). Similar to the Nevada example for Tmin,TopoWx relies on LST to overcome limitations of the


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Figure 12. Comparison of TopoWx, PRISM, and Daymet 1981–2010 August maximum temperature normals within the north coast drainage climatedivision of California, USA.

elevation predictor while PRISM uses a station weightingscheme based on coastal proximity and terrain blockage ofthe marine layer (Daly et al., 2008). Within this context,TopoWx Tmax tended to display a deeper inland pene-tration of the cooling maritime influence on the Pacificcoast than PRISM Tmax (Figure 12). One reason forthis difference could be related to the fog and low stratusclouds that frequently accompany the marine layer (John-stone and Dawson, 2010; Iacobellis and Cayan, 2013). AsLST observations can only be retrieved under relativelycloudless conditions, the TopoWx Tmax spatial patternscould be biased to what is more frequently seen under aclear-sky atmosphere. While a more detailed validationwould be required to determine the exact advantages anddisadvantages of PRISM and TopoWx along the Pacific

coast, this represents a good example of one potentiallimitation of the LST predictor and the spatial patterns itproduces.

Overall, the differences in western CONUS AugustTmin and Tmax normals between TopoWx and the otherTCDs are consistent with the results of the LST predic-tor analysis (Figures 6 and 7). As a strong predictor ofTmin, LST is likely driving many of the spatial differencesbetween TopoWx and the other TCDs. The influence of theLST predictor was clearly evident in the Nevada example(Figure 11) where it had high relative importance and wasnegatively correlated with Daymet and PRISM differencesfrom TopoWx. In contrast, with the overall lower relativeimportance of LST in Tmax interpolations, there were sub-sequently less differences between the datasets except in



regions where the linear relationship between Tmax andelevation was not as strong (Figure 12).

4. Conclusion

As evident in our validation, TopoWx contributes threemain advancements to topoclimatic temperature interpo-lation: (1) an improved representation of interdecadal andlong-term temperature trends; (2) an improved representa-tion of complex temperature spatial patterns, particularlyfor Tmin; and (3) a spatial representation of uncertaintythat accounts for both model goodness of fit and thegeographical arrangement of stations. These advance-ments were made through the use of previously developedhomogenization procedures (Menne and Williams, 2009),remotely sensed LST as an auxiliary predictor of topocli-matic air temperature, and a unique implementation ofMW-RK.

In the context of these advancements, several caveatsshould still be noted. Homogenization procedures largelyremove artificial jumps and trends, but they can alsosmooth out finer-scale trend variations by imposing theregional climate signal on each station (Pielke et al., 2007).Additionally, as illustrated by differences in USHCNtrends and those of relatively finer resolution reanaly-sis datasets (Vose et al., 2012), there are still uncertain-ties in regional climate signals even within homogenizeddatasets. TopoWx is also a daily product, but homoge-nized on a monthly time step. Future work should look toimprove corrections for daily time-of-observation depar-tures and biases and to incorporate daily homogenizationschemes (e.g. Della-Marta and Wanner, 2006; Kuglitschet al., 2009) that additionally correct for artificial changesin temperature distributions, not just the mean. More rig-orous inter-comparisons with other TCDs that use trulyindependent station data are also warranted to fully under-stand the advantages and disadvantages of TopoWx inspecific regions of interest, particularly in regions ofhigh uncertainty like the California Pacific coast. Sincethe RK approach already lends itself to using any arbi-trary model for the deterministic trend component (Henglet al., 2007), more sophisticated modelling methods thatmove beyond linear regression should also be investigated.Regression trees or generalized additive models could beused to account for complex, nonlinear predictor relation-ships and possibly improve LST predictive power. Lastly,while the 𝜎k metric provides a good indication of spa-tial uncertainty in temperature normals, it does not prop-agate uncertainty from the station data infilling step nordoes it reflect changes in daily temperature uncertaintythrough time. TopoWx will remain a work-in-progressand we encourage community-driven enhancements, feed-back, and derivative datasets. All associated TopoWxinput/output data, software code, validation metrics, andstation QA, homogenization and infill statistics will beavailable at http://www.ntsg.umt.edu/project/TopoWx.

Even with the model’s remaining caveats, TopoWx takesan important next step in addressing the main limitations

of current TCDs particularly in regard to representingtopoclimatic variations in Tmin, improving upon issuesstemming from non-homogenized station data and quan-tifying spatial uncertainty. The TopoWx methods devel-oped for temperature should also be applicable to otherclimate variables. For instance, the station data recordextension methods that combine atmospheric reanalysisand local long-term station data could be key for better rep-resenting interdecadal temporal variability in precipitationat higher elevation station locations (Luce et al., 2013).Ultimately, TopoWx should help advance climate-drivenecological and hydrological modelling and facilitate moreopenness in TCDs and a better end-user understanding oftheir uncertainties and limitations.

Acknowledgements

We thank Dr. Anna Klene and 3 anonymous reviewersfor invaluable feedback on previous drafts. This studyis based on work supported by the National ScienceFoundation under EPSCoR Grant EPS-1101342, the USGeological Survey North Central Climate Science Cen-ter Grant G-0734-2 and the US Geological Survey EnergyResources Group Grant G11AC20487. Any opinions, find-ings, and conclusions or recommendations expressed inthis article are those of the authors and do not necessarilyreflect the views of the National Science Foundation.

Supporting Information

The following supporting information is available as partof the online article:Appendix S1. Methods for missing value infilling.Appendix S2. Methods for moving window regressionkriging.Appendix S3. Model performance metrics.Table S1. Number of daily temperature observations from1948 to 2012 flagged by Durre et al. (2010) quality assur-ance procedures for GHCN-D, SNOTEL and RAWS sta-tion networks.Figure S1. Leave-one-out cross-validation mean absoluteerror (MAE) for interpolated 1981–2010 monthly mini-mum temperature normals. Points are all input GHCN-D,SNOTEL, and RAWS stations within the contiguousUnited States (n= 11 589).Figure S2. Leave-one-out cross-validation mean absoluteerror (MAE) for interpolated 1981–2010 monthly maxi-mum temperature normals. Points are all input GHCN-D,SNOTEL, and RAWS stations within the contiguousUnited States (n = 11 619).Figure S3. Leave-one-out cross-validation bias for inter-polated 1981–2010 monthly minimum temperature nor-mals. Points are all input GHCN-D, SNOTEL, and RAWSstations within the contiguous United States (n= 11 589).Figure S4. Leave-one-out cross-validation bias for inter-polated 1981–2010 monthly maximum temperature nor-mals. Points are all input GHCN-D, SNOTEL, and RAWSstations within the contiguous United States (n = 11 619).


J. W. OYLER et al.

Figure S5. Leave-one-out cross-validation mean absoluteerror (MAE) for interpolated 1948–2012 daily minimumtemperatures. MAE is based on observed, non-missingobservations at all input GHCN-D, SNOTEL, and RAWSstations within the contiguous United States (n= 11 589).Figure S6. Leave-one-out cross-validation mean absoluteerror (MAE) for interpolated 1948–2012 daily maximumtemperatures. MAE is based on observed, non-missingobservations at all input GHCN-D, SNOTEL, and RAWSstations within the contiguous United States (n = 11 619).Figure S7. Leave-one-out cross-validation refined indexof agreement (dr) for interpolated 1948–2012 daily mini-mum temperatures. The dr is based on a monthly-varyingbaseline and observed, non-missing observations at allinput GHCN-D, SNOTEL, and RAWS stations within thecontiguous United States (n= 11 589).Figure S8. Leave-one-out cross-validation refined indexof agreement (dr) for interpolated 1948–2012 daily maxi-mum temperatures. The dr is based on a monthly-varyingbaseline and observed, non-missing observations at allinput GHCN-D, SNOTEL, and RAWS stations within thecontiguous United States (n= 11 619).

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