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Remote Sensing of Environment

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Optimizing a remote sensing production efficiency model for macro-scaleGPP and yield estimation in agroecosystems

Michael Marshalla,⁎, Kevin Tub, Jesslyn Brownc

a Climate Research Unit, World Agroforestry Centre, United Nations Ave, Gigiri, P.O. Box 30677-00100, Nairobi, KenyabDuPont Pioneer, 7000 NW 62nd Ave, PO Box 1000, Johnston, IA 50131, USAcU.S. Geological Survey, Earth Resources Observation and Science Center, 47914 252nd Street, Sioux Falls, SD, USA

A R T I C L E I N F O

Keywords:NPPBiomassEvapotranspirationWUEEarth observation

A B S T R A C T

Earth observation data are increasingly used to provide consistent eco-physiological information over large areasthrough time. Production efficiency models (PEMs) estimate Gross Primary Production (GPP) as a function of thefraction of photosynthetically active radiation absorbed by the canopy, which is derived from Earth observation.GPP can be summed over the growing season and adjusted by a crop-specific harvest index to estimate yield.Although PEMs have many advantages over other crop yield models, they are not widely used, because per-formance is relatively poor. Here, a new PEM is presented that addresses deficiencies for macro-scale applica-tion: Production Efficiency Model Optimized for Crops (PEMOC). It was developed by optimizing functions fromthe literature with GPP estimated by eddy covariance flux towers in the United States. The model was evaluatedusing newly developed Earth observation products and county-level yield statistics for major crops. PEMOCgenerally performed better at the field and county level than another commonly used PEM, the ModerateResolution Imaging Spectroradiometer GPP (MOD17). PEMOC and MOD17 estimates of GPP had an R2 and rootmean squared error (RMSE) over the growing season of 0.71–0.89 (9.87–17.47 g CO2 d−1) and 0.59–0.83(6.86–22.20 g CO2 d−1) with flux tower GPP. PEMOC produced R2s and RMSE of 0.70 (0.52), 0.60 (0.61), and0.62 (0.59), while MOD17 produced R2s and RMSE of 0.65 (0.57), 0.53 (0.66), and 0.65 (0.57) with corn,soybean, and winter wheat crop yield anomalies. The sample size of rice was small, so yields were compareddirectly. PEMOC and MOD17 produced R2s and RMSE of 0.53 (3.42 t ha−1) and 0.40 (4.89 t ha−1). The mostsizeable model improvements were seen for C3 and C4 crops during emergence/senescence and peak season,respectively. These improvements were attributed to C3 and C4 partitioning, optimized temperature andmoisture constraints, and an evapotranspiration-based soil moisture index.

1. Introduction

Global warming is projected to drive crop yield losses over much ofthe globe in the second half of the 21st century (Challinor et al., 2014).These losses are expected to increase world food prices, affect the tradebalance in favor of net exporters of agricultural products, and reducethe real income of those lacking sufficient coping mechanisms (Hertelet al., 2010). From a supply-side perspective, management practicescould be implemented to reduce the impact of climate-driven yield loss.These include: changing or engineering new crop varieties; adjustingplanting dates; expanding irrigation or transferring cultivation to coolerclimates; and improving crop residue management (Lobell et al., 2011).Crop yield models quantify plant-climate-soil interactions in order toidentify management practices that improve crop yield. Large-area cropyield models (LACMs) are crop models that are intended to inform

decision-making at the macro-scale under various climate change tra-jectories (Challinor et al., 2004). Earth observation is increasingly usedfor the macro-scale approach, because it provides spatially consistenteco-physiological information over large areas and a long time frame(Doraiswamy et al., 2003). Although Earth observation has advantagesover other techniques, bias and uncertainties must be reduced, beforemacro-scale research questions are addressed.

Moulin et al. (1997) and Lobell (2013) review crop yield modelsutilizing Earth observation. The models typically estimate total cropbiomass or the amount of aboveground dry matter generated over thegrowing season, which is then converted to seed or crop yield using theharvest index (Hay, 1995).

Models for estimating biomass from remote sensing can be em-pirical, semi-empirical, or mechanistic. Empirical models consist ofstatistical relationships between biomass and the Normalized

https://doi.org/10.1016/j.rse.2018.08.001Received 30 December 2016; Received in revised form 30 July 2018; Accepted 2 August 2018

⁎ Corresponding author at: Natural Resources Department, University of Twente/ITC, P.O. Box 217, 7500 AE Enschede, The Netherlands.E-mail address: m.t.marshall@utwente.nl (M. Marshall).

Remote Sensing of Environment 217 (2018) 258–271

Available online 24 August 20180034-4257/ © 2018 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

T

Difference Vegetation Index (NDVI) (Tucker, 1979) or other vegetationindex derived from red and near infrared (NIR) reflectance. Photo-synthetically active canopies preferentially absorb in the red and scatterin the NIR due to the composition and size of leaves and stems(Ollinger, 2011). Although NDVI has been widely used to estimatebiomass, it tends to saturate for dense canopies and is sensitive to soilwetness (Huete et al., 2002). As remote sensing platforms improved andincluded more spectral information, new broadband indices (e.g. En-hanced Vegetation Index: EVI) were developed to overcome theselimitations. Data mining techniques, such as singular value decom-position and stepwise regression, were later used to develop indicesmore sensitive to biomass when hyperspectral data became available(Mariotto et al., 2013; Marshall and Thenkabail, 2015). Empiricalmodels are typically developed and tuned to biomass estimates in aparticular area. These models are prone to over-fitting and often mustbe recalibrated or may not produce reliable results at all when appliedin other areas.

Semi-empirical models, also known as light-use efficiency orProduction Efficiency Models (PEMs), rely on the conservative andpositive response of carbon assimilation to increased solar radiation(Monteith, 1972; Monteith and Moss, 1977). This makes transferabilityto other regions less of an issue. In addition, the models are relativelyeasy to parameterize and can be run efficiently over large areas. Theyestimate Gross Primary Production (GPP) from Photosynthetically Ac-tive Radiation (PAR) weighted by the fraction of photosyntheticallyactive radiation absorbed by the canopy (FPAR) and energy to drymatter or quantum conversion efficiency (ε). FPAR is derived from re-mote sensing. Climate constraints are typically used to further down-regulate GPP. GPP is integrated over the growing season to estimate NetPrimary Production (NPP). Growth and maintenance respiration costs

for NPP are either accounted for indirectly, e.g. Carnegie-Ames-Stan-ford Approach (CASA: Potter et al., 1993) and the Moderate ResolutionImaging Spectroradiometer GPP/NPP product (MOD17A2 hereafterMOD17: Running et al., 2004; Zhao et al., 2005) or directly, e.g.GLOPEM2 (Goetz et al., 1999). PEMs do not directly account for non-climatic constraints, such as management practices or nutrient avail-ability (Grassini et al., 2015), but assume these effects are captured byFPAR (Garcia et al., 1988; Squire et al., 1986; Field, 1991). Further, theytend to underperform in agroecosytems and other non-forested eco-systems, because eco-physiological constraints on GPP are more com-plex and phenological changes are subtler (Yuan et al., 2014; Schaeferet al., 2012).

Mechanistic models can be driven by light adaptive crop growth,but also include several interactive modules that deal with crop typeand variety, soil moisture, soil carbon and nitrogen, and managementpractices such as inter-cropping. Remote sensing is primarily used forre-initialization or re-calibration, i.e. crop model initial conditions orparameters are adjusted until they match a remote sensing biophysicalparameter, such as the leaf area index (de Wit et al., 2012; Dente et al.,2008; Li et al., 2015; Wang et al., 2013). Fully mechanistic approachescan be very accurate, provided they are properly calibrated, but are themost computationally demanding, making their use for macro-scaleapplications difficult unless several simplifying assumptions are made(Grassini et al., 2015).

LACMs have been used to inform a wide range of climate-relateddecisions in the 20th century, but improved accessibility and reliabilityis needed to address the challenges of the 21st century (Rotter et al.,2011). Challinor et al. (2009) recommends that model improvementshould involve three synergistic activities given the large number ofmodels and range of strengths and weaknesses of each. These include:

Fig. 1. Workflow illustrating major inputs ( ), intermediary processes ( ), and final outputs ( ) with site-level and macro-scale data.

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1) quantification of impacts uncertainty via sensitivity analysis or en-semble modeling; 2) coupling eco-physiological constraints or modelingapproaches to account for non-linear interactions; and 3) rigorousmodel calibration/optimization and validation to achieve parsimonyand prevent over-fitting.

This paper presents a new PEM (Production Efficiency ModelOptimized for Crops –PEMOC) to improve crop yield estimation at themacro-scale using Earth observation data. The PEM approach was se-lected over empirical or fully mechanistic approaches, given its sim-plicity, direct use of Earth observation, and compatibility with remotesensing models that compute the moisture counterpart to GPP, evapo-transpiration (ET) (see Cleugh et al., 2007; Fisher et al., 2008; Mu et al.,2007a, 2007b, 2011 for examples). PEMOC was developed from theground up using the activities suggested by Challinor et al. (2009). Adiagram of the complete workflow is shown in Fig. 1. First, eco-phy-siological functions taken from the remote sensing-based crop biomass/yield and ET model literature were integrated. Second, the functionconstraints were optimized with site-level eddy-covariance flux towerGPP and micrometeorological data. Third, a sensitivity analysis wasperformed on the optimized model. Finally, the model was driven byrecently developed Earth observation products and geospatial climatedata across the Contiguous United States (CONUS) to evaluate modelperformance with coarser spatial resolution and county-level crop yielddata. PEMOC was evaluated alongside the MOD17 formulation, whichwas used to estimate yield for important field crops across CONUS (Xinet al., 2013; Johnson, 2016).

2. Data and processing

2.1. Site-level data

Micrometeorological data were acquired for model developmentand site-level evaluation. The dataset consisted of eight eddy-covar-iance flux towers in croplands of CONUS that are part of the Amerifluxnetwork (http://ameriflux.ornl.gov/) (Table 1). Sites were selected ifGPP was available or could be derived over a period of three or moreyears during the MODIS era. The stations yielded 66 years of dailystation data. The sites consisted of rainfed and irrigated fields that wereoften rotated between C3 (canola, cowpeas, rice, soybean, and winterwheat) and C4 (corn) crops. With the exception of US-TWT, the stationswere in the interior of the country and had a continental climate. US-TWT was near the Pacific coast and experienced a Mediterranean cli-mate. The interior sites had higher annual rainfall and lower but morevariable average daily temperatures than US-TWT. Rainfall at the in-terior sites occurred during May–October when most crops are grown inthe U.S. Conditions at US-Twt were generally dry during the primarygrowing season. The stations either recorded data at hourly or half-hourly intervals, which were aggregated to a daily time step. GPP inμmol CO2m−2 s−1 was derived using the Marginal Distribution Sam-pling method (Reichstein et al., 2005). It was provided by the principle

investigators for US-Ne1, US-Ne2, US-NEe3, and US-Twt. For the re-maining stations, GPP was estimated using the Marginal DistributionSampling method. Shortwave incoming radiation (Wm−2), tempera-ture (°C), and the vapor pressure deficit (VPD: kPa) were also collectedfor model-building. Shortwave incoming radiation was masked fordaytime values outside the range of instrument error (> 5Wm−2) andconverted to PAR (μmol m−2 d−1) using the sw.to.par function in R(Britton and Dodd, 1976). Maximum daytime VPD and temperaturewere used for model-building instead of daily averages, because plant-atmosphere coupling is strongest at midday when eddy formation ishighest (Fisher et al., 2008). Other PEMs typically assume the plantresponse to eco-physiological factors is instantaneous, but in reality,plants take several days to acclimate to new conditions (Field, 1991;Pearcy and Sims, 1994; Thornley, 1998). The climate data weretherefore smoothed using a 5-day exponential moving average filter toaccount for the time lag. Surface reflectance was not available for allthe sites, so Moderate Resolution Imaging Spectroradiometer (MODIS)Terra 16-day 250m NDVI (MOD13Q1) was used instead. NDVI wasestimated by averaging 3×3 MOD13Q1 grid cells selected with theMODIS subset tool (http://daac.ornl.gov/) over the fetch of each tower.The fetch is defined here as the upwind area that contributes to eddyformation during daylight hours in the growing season. Poor qualityMODIS data were masked and filled using an adaptive Savitsky-Golayfilter (Chen et al., 2004). In some cases, the boundary of the 3×3window included areas outside the fetch. These pixels were omittedfrom the average to avoid mixed pixel effects. Finally, the data weremasked for the primary growing season. Start and end of season dateswere provided by growers or farm managers.

2.2. Macro-scale data

County-level crop yield and pixel-based crop area for corn, rice,soybean, and winter wheat were used to evaluate the model at themacro-scale. County-level crop yield was collected on an annual basisand downloaded from the U.S. Department of Agriculture NationalAgriculture (USDA) Statistics Service (NASS https://www.nass.usda.gov/). Following Lobell et al. (2002), counties where cropped area of agiven crop were< 25% of the total county area were omitted from theanalysis to avoid over-fitting sparsely cropped counties. Only NASSdata from 2010 to 2015 were analyzed, because high quality pixel-based crop-specific area mosaics for CONUS were available over theperiod through the USDA Cropland Data Layer (CDL: http://nassgeodata.gmu.edu/). CDL is created on an annual basis using deci-sion-tree classification and surface reflectance retrieved from severalsources (Landsat, MODIS, IRS RESOURCESAT-1 Advanced Wide FieldSensor) (Boryan et al., 2011). Post 2011, CDL was generated exclusivelywith Landsat and the new Disaster Monitoring Constellation (Deimos-1and UK2). The maps are trained and validated with extensive groundsurveys collected by the Farm Service Agency. On a pixel-by-pixel basis,CDL is 80% accurate, but is generally more accurate (mid-90%) for

Table 1Site descriptions for eight micrometeorological stations used to develop PEMOC. All data were retrieved from the AmeriFlux network (http://ameriflux.ornl.gov/).Long-term average annual cumulative precipitation (PPT) and average daily temperature (T) were estimated from a 1961–1990 climatology.

ID Site name Lat Long Period Crop type Watering Elevation PPT T

Regime (m) (mm) (°C)

US-ARM ARM Southern Great Plains 36.61 −97.49 2003–12 Canola, corn, cowpea Rainfed 314 843 14.8Soybean, winter wheat

US-Bo1 Bondville 40.01 −88.29 2003–7 Corn, soybean Rainfed 219 991 11.0US-Crt Curtice Walter-Berger 41.63 −83.35 2011–13 Soybean, winter wheat Rainfed 180 849 10.1US-Ib1 Batavia 41.86 −88.22 2006–11 Corn, soybean Rainfed 227 929 9.2US-Ne1 Mead Irrigated 41.17 −96.48 2001–12 Corn, soybean Irrigated 361 887 9.7US-Ne2 Mead Irrigated Rotation 41.16 −96.47 2001–12 Corn, soybean Irrigated 362 887 9.7US-Ne3 Mead Rainfed 41.18 −96.44 2001–12 Corn, soybean Rainfed 363 887 9.7US-Twt Twitchell Island 38.11 −121.65 2009–14 Rice Irrigated −5 346 15.9

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crops that have high national coverage such as corn, rice, soybean, andwinter wheat. CDL is projected in Albers Conical Equal Area projection(North American Datum of 1983) at 30m resolution. The mosaics wereresampled to 250m resolution where each new grid cell represented theproportion of 30-meter pixels classified as a particular crop type.PEMOC and MOD17 crop yield estimates were weighted by the mosaicsand then averaged over each county to compare with NASS crop yield.The final dataset consisted of NASS-predicted pairs for 316, 5, 306, and18 corn, rice, soybean, and winter wheat counties, respectively.

MOD17 is typically driven by MODIS 8-day 1 km FPAR (MOD15A2)and surface reanalysis data from the NASA Global Modeling andAssimilation Office (GMAO). In this study, the MOD17 formulation wasdriven instead with the same FPAR and climate data as PEMOC forconsistency. This means that our use of the MOD17 term refers solely tothe formulation and not the product. FPAR and climate inputs werederived from the U.S. Geological Survey (USGS) Earth ResourcesObservation and Science Center (EROS) expedited MODIS-based NDVIproduct (eMODIS) (Brown, 2018; Brown et al., 2015; Jenkerson et al.,2010); and Daymet daily gridded surface climate data Version 2(Thornton et al., 2014). eMODIS is a MODIS product for near real-timeapplications and mosaicked for CONUS. MODIS Terra and Aqua dailysurface reflectance (level 2-MOD09.L2) data are converted to NDVI andprovided in a user-friendly format. The data include a daily cloud mask(MOD35.L2) and are produced as a rolling daily seven-day composite inthe USGS EROS eMODIS system. For this study, we used the archivedCONUS mosaics of MODIS Terra NDVI projected in Lambert AzimuthalEqual Area at 250m horizontal resolution. eMODIS includes a dataquality band, which was used together with a weighted least squaresregression temporal time-series smoother to filter and correct poorquality NDVI. The USGS also produces estimates of the start and lengthof the primary growing season derived from eMODIS NDVI and a curve-derivative approach (Brown, 2016). These data were used to sumMOD17 and PEMOC GPP over the growing season.

Daymet consists of continuous layers of weather data required forplant growth modeling (day length, shortwave incoming radiation,maximum daily temperature, minimum daily temperature, and averagedaily water vapor pressure). The layers are interpolated from weatherstation data distributed by the National Climate Data Center andNatural Resources Conservation Service. Temperature and precipitationestimates are interpolated using an inverse-distance algorithm, as-suming a truncated Gaussian distribution and weighted by a digitalelevation model (Thornton et al., 1997). Shortwave incoming radiationand vapor pressure are derived from the diurnal temperature range anddew-point temperature, respectively. The algorithms for shortwave in-coming radiation and vapor pressure have since been improved fromversion one to account for variable solar geometry and lapse rates incomplex terrain (Thornton et al., 2000). Daymet is available on a dailybasis as CONUS mosaics projected in Lambert Conformal Conic(Datum=WGS-84) at 1 km horizontal resolution. Daymet was re-sampled to 250m resolution using nearest neighbor. 250m resolutionwas selected, because we assumed that the resolution of NDVI was

driving spatial heterogeneity in GPP and crop yield. The assumption isreasonable, because row crops in CONUS are grown primarily on flatterrain and therefore tend to have gentle climate gradients. Dailyaverage VPD was used instead VPDX for the macro-scale assessment.

3. Methods

3.1. Model descriptions

3.1.1. Production Efficiency Model Optimized for Crops (PEMOC)PEMOC assumes maximum GPP (g CO2m−2) from the utilizable

absorbed PAR under “ideal” conditions. Sims et al. (2005) and Owenet al. (2007) showed strong linearity between gross and maximum dailyGPP across multiple ecosystems. Based on their results, the model es-timates gross daily GPP as a conservative fraction (63%) of maximumdaily GPP. The utilizable absorbed PAR is defined by two components:FPAR and εMAX (Table 2).

εMAX(mol mol−1) is the ratio of carbon assimilated to the amount oflight absorbed by the canopy. It is defined in this case separately for thetwo pathways of carbon metabolization: C3 and C4. C3 metabolism ismore common than C4 metabolism, because the latter is better adaptedto hot moist or dry climates (Chapin et al., 2011). C3 metabolism iscatalyzed by the Rubisco enzyme, which is temperature dependent,while C4 metabolism is catalyzed first by PEP carboxylase to con-centrate CO2 for Rubisco catalyzation. The concentration has the effectof minimizing the temperature dependency of Rubisco partitioning(Collatz et al., 1992). Based on Collatz et al. (1991), the temperaturedependency for C3 metabolism was defined in terms of available CO2

(340 μmolmol−1) and the ratio of oxygenase to carboxylase reactionsfor Rubisco. The ratio is partitioned according to temperature.Quantum conversion efficiency is “realized” after accounting for long-term or seasonal temperature (FT), short-term moisture (FM), and long-term or seasonal moisture (FA) functions ranging from zero to one.

Some of the PEMOC functions have been used to estimate cropbiomass/yield in previous studies, while others (FA and FM) were basedon more recent and parallel studies. FPAR is typically computed as alinear function of NDVI or EVI (Mu et al., 2007a, 2007b). Canopies thatare more photosynthetically active have a higher NDVI or EVI (FPAR→1) than less photosynthetically active canopies or bare soils (FPAR→ 0).FM is typically defined as a function of VPD, which is the differencebetween leaf and atmospheric moisture. As VPD increases, crops as-similate less CO2 to prevent stress (FM→ 0). This decay can be definedusing ramp (MOD17) or other concave functions (Fig. 2a). Alter-natively, exponential (Potter et al., 1993) or other convex functions areused. Medlyn et al. (2011) provides the first theoretical basis for FM andconfirms several empirical studies that use the convex approach. FM inPEMOC in line with Medlyn et al. (2011) assumes a logarithmic decay,which occurs when VPD exceeds 1 kPA when crops are more sensitiveto changes in moisture. In reality, this threshold may vary under dif-ferent moisture conditions and for different crop species (Zhou et al.,2013). Using the optimized constraints for C3 and C4 crops derived in

Table 2PEMOC components and descriptions. Daily gross primary production (g CO2m−2 d−1) is assumed to be 63% of maximum daily gross primary production. Datainputs include: photosynthetically active radiation (PAR), the Normalized Difference Vegetation Index (NDVI), maximum daily vapor pressure deficit (VPDX),maximum daily temperature (TX), and the optimal maximum daily temperature (TOPT) defined as TX at maximum seasonal FPAR. FPAR, MAX is the maximum seasonalFPAR. a0, a1, a2, and a4 are optimized constraints.

Parameter Description Equation Reference

GPPMAX Maximum daily gross primary production εMAX FPAR FT FM FA PAR This studyFPAR Fraction of photosynthetically active radiation a0 NDVI+ a1 Potter et al., 1993FT Temperature stress 1.1814 / ((1+ ea2∗(Topt−10−Tx)) (1+ ea3∗(Tx−10−opt))) Potter et al., 1993FM Short-term moisture stress 1− a4 ln (VPDX) Medlyn et al., 2011FA Seasonal moisture stress FPAR / FPAR, MAX Fisher et al., 2008εMAX Maximum quantum conversion efficiency C3 crops: 0.08 ∗ (CA− Γ) / (CA+ 2Γ) Collatz et al., 1991

C4 crops: 0.06 Collatz et al., 1992

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this study, the rate of decline in FM with VPD is much less than thePotter et al. (1993) formulation. FT is defined either as a ramp function(MOD17) or asymmetric curve (Potter et al., 1993) (Fig. 2b). In the caseof the ramp function, as temperature increases, assimilation increasesand saturates at 12 °C. FT in this case is used to capture the cold(nighttime) crop response. With the asymmetric formula, the responseis more gradual and reverses after an optimal temperature (Topt). Unlikethe ramp function, the inflection accounts for heat stress. The re-lationship is asymmetric, because the change is more rapid after Topt

has been exceeded. The optimized FT derived in this study is much moreasymmetric than the Potter et al. (1993) formulation. As one mightexpect, FT for C4 crops is virtually unaffected by temperatures ex-ceeding Topt. Moisture stress can also occur when plants cannot adapt tochanges in soil moisture over the growing season (FA). Although somePEMs include a seasonal soil moisture term, it was not used explicitlyhere, given the difficulty of acquiring calibration data and the goal ofmodel parsimony. Instead, a simplification proposed in Fisher et al.(2008) was used that assumes the relative change in FPAR over theseason responds primarily to changes in plant water status and istherefore indicative of soil moisture stress. With this approach, anymoisture stress before peak light absorption is assumed negligible,meaning it responds primarily to extended dry spells.

The constraints (a0–a4) have been defined empirically in previousstudies, but were estimated in this study via optimization with site-leveldata. The optimization was performed for each micrometeorologicalstation using the Levenberg-Marquardt non-linear fitting algorithmavailable in the minipack.lm package in R (Elzhov et al., 2016). It re-turns the constraints after the sum of squared residuals between thesimulated and observed GPP data is minimized. Seed and boundaryconditions for each constraint were defined posteriori and a maximumof 1000 iterations was set to avoid fitting local optima (Table 3).

3.1.2. MOD17Like PEMOC, MOD17 estimates daily GPP independently from re-

spiration (Table 4). It has been used in a variety of macro-scale studies.MOD17 has two key differences with PEMOC: εMAX is constant for allcrop types and FA is not used. A full description of model inputs can befound in the Biome Parameter Look-Up Table in the MOD17A2/A3user's guide (Running and Zhao, 2015).

3.1.3. Crop yieldGross primary production was converted to crop yield (t ha−1) using

the harvest index (Prince et al., 2001):

∑= ×+

×−

=

Y Pn HI1 RS

11 MCi SOS

n

i(1)

The harvest index (HI) is the ratio of seed yield to the biologicalyield (Y) or total amount of dry matter the crop generates abovegroundover the growing season (Hay, 1995). It is usually determined de-structively, so estimates are generally assumed constant for a given cropor variety and area. The biological yield is the sum of net photo-synthesis (Pn) over each day (i). Pn is summed from the start of season(SOS) and harvest (n). Net photosynthesis equals GPP after above-ground and belowground maintenance respiration costs (R) have been

Fig. 2. Functional relationships used to modify utilizable absorbed short-term soil moisture stress-FM and seasonal temperature stress-FT versus parameter inputs: A)daily vapor pressure deficit (VPD) and B) daily temperature (T). For FT, TOPT was set to 29.3 °C. Functions taken from the literature are illustrated alongside theoptimized functions derived in this study for comparative purposes.

Table 3Seed and boundary conditions used for model optimization.

Parameter Seed Range

a0 1.2 [0, 2]a1 0.11 [0, 0.2]a2 0.2 [0, 1]a3 0.3 [0, 1]a4 0.6 [0, 1]

Table 4Model constraints and equations for MOD17. Daily gross primary production(g CO2m−2 d−1) is assumed here to be 63% of maximum daily gross primaryproduction. Data inputs include: photosynthetically active radiation (PAR),average daytime vapor pressure deficit (VPD), and minimum daily tempera-ture (TN). VPDMIN and TN,MIN, and VPDMAX and TN,MAX are constants re-presenting the lower and upper limits for VPD and TN.

Parameter Equation

GPPMAX εMAX FPAR FT FM PARFPAR MODIS FPARFT 1− (TN− TN,MIN) / (TN,MAX− TN,MIN)FM 1− (VPD−VPDMIN) / (VPDMAX− VPDMIN)εMAX Constant

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removed (Pn=GPP – R). It was assumed that R is a conservativefraction (50%) of GPP (Ryan, 1991; Gifford, 1994; Waring et al., 1998).The harvest index may vary between crop species and under differentmoisture regimes (Unkovich et al., 2010) however previous macro-scalestudies (e.g. Lobell et al., 2002 and Xin et al., 2013) assumed it wasconstant, because it is difficult to obtain crop or location specific values.Further, the variation in HI is smaller than the variation in NPP, so it'simpact on crop yield is comparatively small. Two other crop-specificconstraints shown in Eq. (1) were also assumed constant for each crop:the root to shoot ratio (RS) and harvest moisture content (MC). Thevalues are shown in Table 5. The RS and HI values were taken fromPrince et al. (2001). The MS values were taken from Lobell et al.(2002).

3.2. Analytical approach

3.2.1. Model optimizationThree levels of optimization (C3, C4, and both C3 and C4 crops) were

performed for each station and compared using the coefficient of de-termination (R2) and cross-validated root mean square error (RMSE).The mean of the optimized coefficients for each level was used to es-timate PEMOC GPP and compare to MOD17 GPP. Two additional per-formance metrics were also computed: systematic root mean squareerror (RMSES) and unsystematic root mean square error (RMSEU). Theformer measures the correctable predicted error (bias), while the lattermeasures the random predicted error. The performance metrics werecalculated only for the growing season.

3.2.2. Sensitivity analysisA sensitivity analysis was performed after model optimization to

identify the most important constraints and guide future model im-provements. The sensitivity analysis was performed on the four primaryinputs (NDVI, PAR, TX, and VPDX) using the one-parameter-at-a-timeapproach (Haan, 2002). The inputs at each station were varied ran-domly 10,000 times between±2σ of each station's mean, while theother inputs were kept at their mean. The impact of each input was thentested by relating it to PEMOC GPP. Since most of the functions are non-linear, the non-linear fitting algorithm was used to define each re-lationship. The comparison was made in standard space to determinerelative sensitivity. With this approach, inputs with a larger absoluteslope were more sensitive than inputs with a lower absolute slope.

3.2.3. Macro-scale evaluationPEMOC was compared to MOD17 across CONUS. The two models

were compared against county-level crop yield using R2 and RMSE.Yield data were converted to standardized anomalies to prevent serialautocorrelation and the effects of other inherent non-linearities.Additional statistics (long-term μ and σ) were computed to characterizegeneral patterns across CONUS. To improve PEMOC efficiency, GPPwas computed as a weighted average of C3 and C4 fixation pathways ateach grid cell. The weights were derived from resampled 1° (~111 kmat the equator) resolution proportion of C3 and C4 vegetation maps(Datum=WGS-84) developed by the International Satellite LandSurface Climatology Project Initiative II (Still et al., 2003).

4. Results

4.1. Model optimization and sensitivity analysis

The optimization produced high correlations and low-moderateerror with site-level GPP (Table 6). The low-moderate errors were dueto the underestimation of peak GPP. The highest correlations were forthe corn-soybean sites and the lowest correlation was for the rice site.The optimizations were robust, since the maximum number of itera-tions in each case was≤30, which is well below the maximum set limit.The mean constraints when C3 and C4 crops were optimized togetherwere a0= 1.14, a1= 0.12, a2= 0.17, a3= 0.66, and a4= 0.09. Thesewere used for the sensitivity analysis and model evaluation. The coef-ficient of variation was 0.10, 0.51, 0.28, 0.58, and 0.91, respectively.The coefficient of variation (σ/μ) expresses the variation of a coefficientrelative to other coefficients. The high value for a4 indicates muchvariation among stations, while the small value for a1 indicates rela-tively little variation across stations. Compared to other linear FPARfunctions (Myneni and Williams, 1994; Xiao et al., 2004; Potter et al.,1993), PEMOC FPAR changed at a similar rate, but was higher (e.g.FPAR= 0.12 when NDVI=0). a2, which controls the ascending (“cold”)arm of FT was close to the seed value (0.2) taken from Potter et al.(1993) for both C3 and C4 crops, meaning crops had a fairly consistentresponse to temperatures below TOPT. a3, which controls the descending(“warm”) arm of FT was much higher than the seed value (0.3) takenfrom Potter et al. (1993). For many of the C3 crops, a3 was closer to theseed value, which may reflect that C3 crops are more sensitive totemperatures exceeding TOPT. For other C4 and C3 crops, a3 was muchhigher or one. These crops could be less sensitive to temperatures ex-ceeding TOPT. a4 was generally low, so GPP was only mildly affected bychanges in VPDX. We tested the importance of FM by omitting it fromthe model, since the coefficient of variation was high and the value ofthe optimized constraint for FM was low. But this led to lower modelperformance. The performance of PEMOC when C3 and C4 crops wereconsidered separately was more mixed. The optimized C3 and C4

models produced similar or sometimes lower correlations with ob-served GPP than the optimized model using both C3 and C4 crops.

The relative sensitivity of PEMOC to model inputs for each fluxtower is shown in Table 7. The slope indicates the predicted positive ornegative change in PEMOC GPP due to a standard deviation increase ina given model input (NDVI, PAR, TX, and VPDX). The model was mostsensitive to PAR, because the absolute slope was the largest. The slope

Table 5The dimensionless parameters (HI= harvest index, MC=grain moisture con-tent, and RS= root to shoot ratio) to convert seasonal total net photosynthesis(gross primary production minus respiration costs) to crop yield.

Crop type RS MC HI

Corn 0.18 0.11 0.50Rice 0.10 0.09 0.40Soybean 0.15 0.1 0.41Winter wheat 0.20 0.11 0.37

Table 6Summary statistics (coefficient of determination - R2 and cross validated rootmean squared error-RMSE) for constraints (a0–a4) optimized to predict GPP(g CO2m−2 d−1) at each micrometeorological station. The optimization wasperformed for C3, C4, and both C3 and C4 portion of the time series.

ID a0 a1 a2 a3 a4 N Iteration R2 RMSE

US-Arm 1.36 0.20 0.11 0.05 0.18 2410 9 0.79 4.60C3 1.34 0.20 0.11 0.05 0.13 2050 8C4 0.90 0.20 0.09 1.00 0.00 360 28US-Bo1 1.18 0.10 0.11 1.00 0.02 590 11 0.87 9.72C3 1.06 0.06 0.20 1.00 0.27 174 10C4 1.16 0.10 0.11 0.77 0.00 416 23US-Crt 1.08 0.08 0.16 0.54 0.00 448 26 0.82 9.67US-Ib1 1.18 0.15 0.19 0.28 0.00 795 26 0.89 9.96C3 1.11 0.10 0.06 0.85 0.00 347 30C4 1.20 0.18 0.32 0.31 0.00 448 27US-Ne1 1.21 0.07 0.22 1.00 0.19 1264 7 0.89 9.35US-Ne2 1.02 0.08 0.25 1.00 0.04 978 10 0.86 10.98C3 2.00 0.20 0.04 0.06 0.14 332 18C4 1.25 0.06 0.15 1.00 0.11 646 14US-Ne3 1.12 0.05 0.18 0.44 0.14 1027 12 0.85 10.02C3 1.62 0.13 0.01 1.00 0.23 424 10C4 1.22 0.04 0.16 1.00 0.16 603 15US-Twt 1.00 0.20 0.17 1.00 0.16 815 11 0.77 7.38

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was positive, meaning that as the amount of solar energy available tothe canopy increased, GPP increased. The model was most sensitive toPAR at US-Crt whose signal was dominated by winter wheat. Winterwheat is planted well before the onset of the primary growing seasonwhen light is most abundant. After PAR, the model was most sensitiveto NDVI, which is used to parameterize FPAR and FA. The slopes, withthe exception of US-Arm were similar across sites. The low response atUS-Arm could be due to the presence of canola and cowpeas, which areplanted well before the onset of the primary growing season and haverelatively low FPAR. The model was least sensitive to VPDX and TX,which are used to parametrize FM and FT. NDVI (VPDX) is directly(inversely) proportional to GPP, meaning as photosynthetic activity inthe canopy increases and atmospheric moisture demand decreases, GPPincreases. FT had an inflection point at TOPT. When TX was less thanTOPT, GPP increased with temperature and when TX was higher thanTOPT, GPP decreased with temperature. The asymmetry around TOPT ledto a slightly negative slope for tempeatures exceeded TOPT.

4.2. Model evaluation (site-level)

In general, PEMOC produced higher correlations and lower errorwith the micrometeorological data than MOD17 (Figs. 3 and 4). MOD17tended to under-predict peak GPP. From the time series of observed andpredicted GPP (not shown), it was also apparent that MOD17 over-predicted periods of emergence and senescence. MOD17 was particu-larly poor at predicting peak GPP for corn, the only C4 crop (US-Ne1,US-Ne2, and US-Ne3). Errors from MOD17 estimates were both un-systematic and systematic. PEMOC under-predicted peak GPP for corn,but not as severely as MOD17. It tended to over-predict peak GPP for C3

crops. Predictions during emergence and senescence were more rea-listic. The error of PEMOC for most of the stations was largely sys-tematic and therefore correctable. Two exceptions were at US-Crt andUS-Twt where PEMOC had higher R2, but higher RMSE as well. Thehigher error from PEMOC was due to larger spread and over-predictionof peak GPP, respectively.

4.3. Model evaluation (macro-scale)

There were regional differences between PEMOC and MOD17 GPP/NPP. Fig. 5 shows the μ and σ of NPP for CONUS at 250m resolutionmasked for cropped areas from 2001 to 2015. MOD17 tended to predicthigher and more variable NPP than PEMOC using the eMODIS andDaymet data. Some notable exceptions include the most agriculturallyintensive regions of the country: the corn-soybean dominant upperMidwest and rice dominant lower Mississippi River and upper CentralValley of California; winter-wheat dominant Colombia and SnakeRivers; and mixed crops in the lower Central Valley of California. Inthese regions, PEMOC tended to produce higher and more variableestimates of NPP.

The results of the macro-scale evaluation were fairly consistent withthe site-level evaluation. PEMOC produced higher correlations andlower error with NASS county-level yield anomalies for corn and soy-bean, particularly for low to moderate producing counties (Fig. 6).MOD17 performed slightly better for winter wheat, particularly formoderate to high producing counties. PEMOC and MOD17 significantlyunder-predicted rice yield, which led to the poorest performanceoverall. Fig. 7 shows simulated versus NASS rice yield. The scatter plotsdo not show anomalies, because the sample size was small (N=11).PEMOC showed an upward trend, while MOD17 showed a downwardtrend with rice yield, meaning PEMOC may be able to better captureanomalies if more data were available.

5. Discussion

PEMs represent an important class of remote-sensing based ap-proaches for estimating biomass/yield. Unlike empirical approaches,which represent the other main remote-sensing approach, they can beused for macro-scale applications with sufficient calibration and vali-dation. They were originally designed for forest ecosystems and tend toperform poorly for agroecosystems and grasslands. This study specifi-cally addresses deficiencies in PEMs for estimating crop biomass/yield,but could easily be adapted to improve performance in other ecosys-tems. The results make three important contributions to remote-sensingbased estimation of crop biomass/yield at the macro-scale. First, thelargest improvements in crop yield estimation, particularly for corn andsoybean, were made by simulating C3 and C4 pathways separately.Second, PEMOC was most sensitive to PAR and NDVI, followed bymoisture and temperature. Options exist to reparametrize PAR and FPARthat could lead to further model improvements. Finally, the model wasoptimized with available eddy covariance flux tower data, but couldeasily be re-optimized when more data from agroecosystems becomeavailable. The means of optimized constraints were used in this studyfor comparison purposes, but resulted in a clear systematic bias.Performance was better when the model was optimized by crop type.Quality control issues, particularly with the macro-scale assessmentneed to be addressed, but in the meantime, the model could be used atthe macro-scale with the mean constraints or more effectively with theconstraints optimized to specific crops.

Maximum quantum efficiency is highly variable in space and time.It is considered the major source of MOD17 and other PEM uncertaintyand bias (Zhang et al., 2008). It can be greatly reduced through C3 andC4 partitioning (Schaefer et al., 2012; Zhang et al., 2017). UnlikeMOD17, which assumes that εMAX is constant for all crops, PEMOCassumes that C3 εMAX is temperature-dependent and C4 εMAX is constant.The C3 and C4 partitioning in PEMOC led to higher correlations and

Table 7The slope (B1) of a non-linear fit of PEMOC predicted gross primary production(g CO2m−2 d−1) versus perturbed model inputs (maximum daily temperature –TX, maximum daily vapor pressure deficit–VPDX, photosynthetically activeradiation–PAR, and the Normalized Difference Vegetation Index-NDVI). Targetinputs were perturbed 10,000 times between±2 σ, while other inputs werefixed at their mean. The slope is expressed in standard space.

Station Parameter B1

US-ARM TX −0.52VPDX −2.06PAR 40.90NDVI 13.46

US-Bo1 TX −1.75VPDX −2.34PAR 30.29NDVI 25.25

US-Crt TX −0.87VPDX −2.31PAR 61.31NDVI 19.50

US-Ib1 TX −1.50VPDX −2.31PAR 48.07NDVI 25.78

US-Ne1 TX −1.21VPDX −3.06PAR 36.56NDVI 29.61

US-Ne2 TX −2.20VPDX −2.74PAR 34.48NDVI 28.84

US-Ne3 TX −2.09VPDX −2.94PAR 29.48NDVI 28.91

US-Twt TX −4.10VPDX −3.33PAR 45.78NDVI 26.48

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lower error with micrometeorological GPP and county-level yield data.These improvements can be attributed mainly to lower bias in peakseason GPP and secondly to more realistic estimates of GPP duringemergence/senescence. MOD17 tended to under-estimate peak seasonGPP, particularly for C4 crops. Over-estimation of MOD17 duringemergence/senescence can be impacted by partitioning as well, butothers have observed that poor parameterization of FM with VPD is themain culprit (Schaefer et al., 2012).

Further PEM improvements for agroecosystems could be achievedby improving PAR estimates and the functional relationships for FPAR,FM, and FT. The sensitivity analysis revealed that PEMOC was mostsensitive to PAR and NDVI, meaning they govern most of the variabilityin GPP and should be the first terms addressed to improve model ac-curacy. PEMOC assumes that light use efficiency improves with PAR

under clear sky conditions. Some studies have shown that light useefficiency is higher under diffuse sky (cloudy) conditions (Suyker andVerma, 2012). A cloud-adjusted PAR was recently implemented in aPEM with high success, R2= 0.926 and 0.909 for the calibration andvalidation datasets using US-Ne1, US-Ne-2, and US-Ne-3 simulatedversus observed daily GPP (Nguy-Robertson and Xiao, 2015). NDVI isused to estimate FPAR and FA. The relationship between FPAR and NDVIwas assumed linear. This assumption typically leads to overestimationof FPAR outside the primary growing season when canopy cover is low.Within the growing season, NDVI can saturate when crops reach peakproductivity, which can lead to underestimation of FPAR. The MODISFPAR product or another approach that applies a radiative transfer al-gorithm or a ratio-based EVI FPAR could be used to address non-line-arity. The model showed the least variation among sites for the primary

Fig. 3. Scatterplots of daily PEMOC predicted gross primary production (GPP) versus observed GPP and 1:1 line (canola=+, corn=■, cowpea= x, rice=▲,soybean=●, and winter wheat=♦). Summary statistics include the coefficient of determination-R2, root mean squared error-RMSE, unsystematic root meansquared error-RMSEU, and systematic root mean squared error-RMSES.

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control on FPAR, a0, so we expect re-optimization of FPAR will have littleeffect on improving model accuracy. FA is used in ET models, but hasnot been adopted in PEMs. FA tracks seasonal changes in temperature/light and may not relate to drought. High inter-correlation among PEMparameters has been observed in previous studies (Anav et al., 2015)and parameterizing FA with NDVI gives added weight to this input thatcould amplify errors in the presence of uncertain data. Two other in-dices have been proposed that could be used to constrain soil moistureinstead of FA: thermal inertia (ATI) index (Garcia et al., 2013) and LandSurface Water Index (LSWI) (Xiao et al., 2004). ATI and LSWI utilizeland surface temperature and shortwave infrared, respectively. Both arereadily available in the MODIS-era, but for more historical analyses,NDVI-based FA remains a good alternative.

The model was less sensitive to temperature and moisture

constraints, but showed considerably more variation among sites. Thegreatest variation was with a4, which controlled FM. Average a4 was low(0.09) and zero for many of the sites. For PEMOC, an FM was selectedbased on a consensus reached on moisture limitations to stomatalconductance and GPP. FM is considered a poor indicator of soil moisturestatus, especially for irrigated crops (see Biggs et al., 2016 for an eva-luation of VPD-based techniques), so authors have suggested introdu-cing a suitable short-term soil moisture parameter to reduce over-estimation of GPP (Mu et al., 2007b). There are several alternatives thatcould be evaluated within the optimization work flow, since we ruledout omitting FM entirely. This could include an additional optimizationconstraint that replaces the 1 kPA threshold over which increases inVPD downregulate GPP selected for this study. The temperature func-tion in PEMOC is widely used, but a few alternatives, such as the

Fig. 4. Scatterplots of daily MOD17 predicted gross primary production (GPP) versus observed GPP and 1:1 line (canola=+, corn=■, cowpea= x, rice=▲,soybean=●, and winter wheat=♦). Summary statistics include the coefficient of determination-R2, root mean squared error-RMSE, unsystematic root meansquared error-RMSEU, and systematic root mean squared error-RMSES.

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MOD17 ramp function do exist that could also be evaluated. Perhapsthe most interesting result of the FT optimization was with a3, whichcontrols the descending node when temperatures exceed TOPT. Formany of the sites, a3 approached one, meaning GPP was independent oftemperature fluctuations that do not co-vary with more importantterms, such as FPAR. Aside from a0, a3 was the highest on average (0.66)and well above the seed value taken from the literature (0.3). The re-sults agree with other studies, such as Woodward and Smith (1994)who suggest a more asymptotic FT than Potter et al. (1993). PEMsshould consider a much higher coefficient on the ascending arm of FT.

FA is widely used by the ET modeling community to indicate sea-sonal soil moisture status and therefore should be considered alongwith the C3 and C4 partitioning to reduce PEM bias and uncertainty.

The PEM presented did not consider other factors that could berelatively easy to implement in the optimization work flow. Leaf agecan also impact GPP, as emerging and senescing crops have lower lightuse efficiency than fully productive crops (Kalfas et al., 2011). Onecould argue that FA presented in this study captures leaf age, but it wasnot considered explicitly.

It is difficult to compare the results of this study to others, givendiffering objectives and methods. The primary purpose of this study was

to present a new work flow for developing remote sensing-based macro-scale estimation of crop yield. Instead of simply plugging in and eval-uating new functions, we integrated and optimized functions gleanedfrom an exhaustive literature review. The final model using meanconstraints generally performed better than the MOD17 formulation.On an individual crop basis, performance was higher. Both models werehighly correlated with eddy covariance flux tower data, but RMSE washigher than previous studies conducted in agroecosytems, e.g. 2.81 gCO2m−2 d−1 was reported for corn in Zhang et al. (2008). The higherPEMOC and MOD17 GPP error can be attributed to the period overwhich it was computed for this study. In other studies, RMSE wascomputed over the entire year and included several low GPP estimatesoutside the growing season. Including them would tend to lower RMSE.In this study, RMSE was only computed over the growing season whenGPP is high. This was done because at some sites, data were notavailable outside the primary growing season. In addition, crop yield iscomputed over the primary growing season, so estimates outside theprimary growing season are redundant, because they do not contributeto model performance. PEMOC performance was comparable to the“improved” MOD17 model proposed in Xin et al. (2013) for corn(R2= 0.55–0.77) and soybean (R2= 0.50–0.73. In Xin et al. (2013),

Fig. 5. Long-term mean and standard deviation of PEMOC (A–B) and MOD17 (C–D) NPP estimates for CONUS. The difference (PEMOC – MOD17) between meansand standard deviations are shown in E and F. The figures have been masked with the USDA Cropland Data Layer.

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Fig. 6. Scatterplots of standardized crop yield anomalies from 2010 to 2015 as simulated by PEMOC and MOD17, respectively: A–B) corn and C–D) soybean, andwinter wheat (E–F). The dashed line is a 1:1 relationship.

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only county-level rainfed corn and soybean were evaluated and over amuch smaller spatial domain (12 states in the Midwestern UnitedStates) than this study. They used a more liberal threshold of inclusion(5% versus 25% harvested area). This criterion introduced very lowproducing counties that acted as leverage points and introduced non-linearity that could have inflated the performance of the model. Fur-ther, Xin et al. (2013) was driven by different climate forcing than thisstudy, which may prevent realistic comparison. Johnson (2016) com-pared the relationship between NDVI, GPP, and other MODIS-basedvegetation products with NASS yield statistics for several crops acrossCONUS. Unlike previous studies, they considered timing as a factor forpredictability. For corn and soybean, the highest correlations wereduring the middle of the growing season. NDVI showed the highestcorrelation with corn (R2= 0.64) and soybean (R2= 0.49) yield, whichwere lower than the PEMOC correlations with corn and soybean yield.Similarly, NDVI showed the highest correlation with wheat yields earlyin the primary growing season, but the results were still lower(R2=0.49) than what was reported for PEMOC. For rice there was norelationship (R2= 0.00), because the sample size was small.

Other factors make the comparison of model performance withcounty-level yield difficult. Inherent in the PEM approach, the influenceof non-biophysical influences on yield are subsumed in FPAR, but maybe better simulated separately. The CDL harvested area that was used toweight PEMOC yield for corn includes silage and grain yield. PEMOChowever only predicted grain yield. The conversion between bushels toMT for corn and soybean was assumed constant because more detailedinformation was unavailable, but in reality these terms vary. The eva-luation focused on winter wheat instead of all wheat varieties, becauseit is the dominant variety. This may have proved problematic howeveras winter wheat is grown outside the primary growing season whenother crops with a stronger signal may be grown and could be influ-encing the phenology algorithm. PEMOC is spatially more variable thanMOD17, meaning geo-location errors due to resampling could enhanceerrors in estimates over spatially smoother MODIS estimates, andPEMOC required an additional input (proportion of C3 and C4 photo-synthesis) that was only available at coarse (1°) resolution. Finally, theconversion between GPP and NPP, harvest index, root to shoot ratio,and harvest moisture content, which were assumed constant, can allvary among crop varieties and under different climatic conditions(Sinclair and Muchow, 1999; Turner et al., 2003). Some of these

uncertainties can easily be addressed in the near future. For example,the 1° C3–C4 proportion map could be replaced with the forthcoming10 km resolution map for North America using the methodology pro-posed for South America in Powell et al. (2012). Other issues, parti-cularly concerning yield uncertainties are more difficult and may bebest addressed by comparing the approach to other spatially explicitapproaches derived from observed data, such as machine learning (Youet al., 2017) or solar-induced fluorescence (Guan et al., 2015).

This study did not directly address the impact of different forcingdata on model results. The inputs were selected due in part becausethey are available near real-time and we wanted to demonstrate howcrop yield could be monitored across CONUS with Earth observation forthe first time. Daymet shows a high level of fidelity with other tem-perature and precipitation geospatial datasets (Huang et al., 2016), butlike other geospatial datasets, shortwave radiation remains a leadingsource of bias and uncertainty due to the poor quantification of cloud,aerosol, and water vapor content (Zhao et al., 2013). Since PEMOC wasmost sensitive to PAR, reducing bias and uncertainty in shortwave ra-diation could lead to improvements in GPP and crop yield estimated byPEMOC.

6. Conclusions

Macro-scale crop yield models are an important tool used by prac-titioners and decision-makers to compare options and investments tosupport “best” policies and practices related to sustainable food se-curity. Production efficiency models (PEMs) are an important class ofremote sensing-based models that can be used to address questions inmacro-scale climate change and food security analysis. PEMs still havelarge bias and uncertainties in agroecosystems that need to be ad-dressed in order for best policies and practices to be properly identifiedand implemented. Here we developed a PEM that integrated eco-phy-siological functions taken from the Earth observation light-use effi-ciency and evapotranspiration model literature. The function con-straints were optimized and a sensitivity analysis was performed usingeddy covariance flux and other micrometerological data from agroe-cosystems. The model was evaluated with county-level crop yield sta-tistics and compared against another commonly used PEM formulationused to develop the MOD17 product. Compared to the MOD17 for-mulation, improvements were seen via the integration of C3 and C4

Fig. 7. Scatterplots of A) PEMOC and B) MOD17 versus NASS rice yield. The dashed line is a 1:1 relationship.

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photosynthesis partitioning, optimized moisture and temperature con-straints, and a seasonal soil moisture index taken from the evapo-transpiration model literature. These improvements significantly re-duced Gross Primary Production (GPP) bias and uncertainty duringpeak season for C4 crops and periods of emergence and senescence forC3 crops.

The model was purposely driven by new near real-time Earth ob-servation products to illustrate how it could be used as a crop mon-itoring tool for CONUS in the future. It was calibrated with rainfed andirrigated crops widely grown in CONUS, but should be evaluated forother crops and optimized on a per crop basis, before the workflow isoperationalized.

The model could also be used to conduct historical or projected (i.e.scenario-building) crop yield assessments in CONUS or other regions ofthe world. For example, the model will be optimized with historical riceyield estimates across Asia in the near future to evaluate the transitionof C3 to C4 rice yields under climate change.

Acknowledgements

The work was sponsored by the Consortium of InternationalAgricultural Research (CGIAR) Centers Research Program (CRP) onPolicies, Institutions and Markets (PIM) to improve the crop yieldsubroutines of the International Model for Policy Analysis ofAgricultural Commodities and Trade (IMPACT), which is used toevaluate the projected regional-global impact of agricultural invest-ments on the future. The micrometeorological stations are maintainedthrough support from the U.S. Department of Energy's Office of ScienceAmeriflux program, while crop yield statistics and geospatial data arecollected and processed with support from the U.S. Department ofAgriculture. Special thanks to Dennis Baldocchi and Shashi Verma foradditional input on the micrometerological data, to Muhammad Ahmadwho assisted in collecting and processing the geospatial data used forthe analysis, and to Danny Howard who performed time-seriessmoothing of the eMODIS history. We also thank D. Dye and anon-ymous reviewers for their helpful suggestions. Any use of trade, firm, orproduct names is for descriptive purposes only and does not implyendorsement by the U.S. Government.

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