Remote Sens. 2013, 5, 5926-5943; doi:10.3390/rs5115926
A Production Efficiency Model-Based Method for Satellite
Estimates of Corn and Soybean Yields in the Midwestern US
Qinchuan Xin 1,*, Peng Gong 1,2,*, Chaoqing Yu 1, Le Yu 1, Mark Broich 3, Andrew E. Suyker 4
and Ranga B. Myneni 5
1 Ministry of Education Key Laboratory for Earth System Modeling, and Center for Earth System
Science, Tsinghua University, Beijing 100084, China; E-Mails: firstname.lastname@example.org (C.Y.);
2 Department of Environmental Science, Policy and Management, University of California, Berkeley,
Berkeley, CA 94720, USA
3 Plant Functional Biology and Climate Change Cluster Department, University of Technology
Sydney, Broadway, NSW 2007, Australia; E-Mail: email@example.com
4 School of Natural Resources, University of Nebraska-Lincoln, Lincoln, NE 68583, USA;
5 Department of Earth and Environment, Boston University, Boston, MA 02215, USA;
* Authors to whom correspondence should be addressed; E-Mails: firstname.lastname@example.org (Q.X.);
email@example.com (P.G.); Tel.: +86-188-1025-3088; Fax: +86-10-6279-7284.
Received: 26 September 2013; in revised form: 6 November 2013 / Accepted: 7 November 2013 /
Published: 14 November 2013
Abstract: Remote sensing techniques that provide synoptic and repetitive observations over
large geographic areas have become increasingly important in studying the role of
agriculture in global carbon cycles. However, it is still challenging to model crop yields
based on remotely sensed data due to the variation in radiation use efficiency (RUE) across
crop types and the effects of spatial heterogeneity. In this paper, we propose a production
efficiency model-based method to estimate corn and soybean yields with MODerate
Resolution Imaging Spectroradiometer (MODIS) data by explicitly handling the following
two issues: (1) field-measured RUE values for corn and soybean are applied to relatively
pure pixels instead of the biome-wide RUE value prescribed in the MODIS vegetation
productivity product (MOD17); and (2) contributions to productivity from vegetation other
than crops in mixed pixels are deducted at the level of MODIS resolution. Our estimated
yields statistically correlate with the national survey data for rainfed counties in the
Remote Sens. 2013, 5 5927
Midwestern US with low errors for both corn (R2 = 0.77; RMSE = 0.89 MT/ha) and
soybeans (R2 = 0.66; RMSE = 0.38 MT/ha). Because the proposed algorithm does not
require any retrospective analysis that constructs empirical relationships between the
reported yields and remotely sensed data, it could monitor crop yields over large areas.
Keywords: remote sensing; crop yield; MODIS GPP; radiation use efficiency;
Because agricultural productivity directly influences food prices, trade and greenhouse-gas emission
policies, and human livelihood [1,2], accurate and timely yield estimation is of primary interest to the
scientific community and governments . Compared with traditional ground-based methods, such as
visual examination and survey sampling, remote sensing that provides synoptic and repetitive
observations of the land surface is well suited for agricultural mapping [4–6] and monitoring [7,8] large
geographic areas. In particular, satellite-derived vegetation indices, as measures of plant chlorophyll
abundance and vegetation radiation absorption , have proven to be closely related to crop growth in
field studies and theoretical models [10–12].
Despite tremendous efforts, obtaining accurate yield estimations based on remotely sensed data
remains difficult [13,14]. One approach develops regression models that relate satellite-derived
vegetation indices directly to historical yield data [15–17]. These models are essentially retrospective
and are based empirically on indirect inferences, whereby changes in vegetation indices can determine
variations in plant productions [14,18]. Because the regression relationship varies largely on a
year-to-year basis due to inter-annual variations in climate, water availability, and management
practices, the application of these models is limited to the studied regions and periods and is difficult
under extreme conditions (e.g., flooding and drought) beyond historical records. Another approach
applies satellite data to calibrate physiology-based crop models [19–21] that simulate the physical
process of crop growth, where energy, water, carbon dioxide, and nutrients are converted into biomass [22,23].
These models have proven useful at the field scale but possess one limitation for large-scale application:
they often require numerous inputs related to soil characteristics, management practices, and local
weather conditions [24–26].
Given the difficulties of the two above-mentioned approaches, improving yield estimation with
satellite data based on the Production Efficiency Models (PEMs) is a highly desirable goal. The theory
proposed by Monteith [27,28] proposes a basis for estimating the primary productivity of vegetation
from remotely sensed data. It suggests that crop yields under non-stressed conditions linearly correlate
with the amount of absorbed photosynthetically active radiation. Satellite data at different resolutions
have been synthesized in production efficiency models to monitor vegetation productivities [29–32] and
estimate crop yields [33–35] on regional or global scales. Based on production efficiency models, a
routine product (MOD17) has been derived from high temporal and moderate spatial resolution MODIS
data, which has proven useful to studies on global carbon cycles [36,37].
Remote Sens. 2013, 5 5928
However, validations against flux tower data indicate that MOD17 estimates exhibit large
uncertainties in croplands . Crop yield estimates based on the MOD17 products were found to have
weak correlation with national agricultural data at the county level for the states of Montana and North
Dakota in the US . The MOD17 algorithm prescribes constant values of model parameters such as
radiation use efficiency (RUE) for the agricultural biome regardless of crop types [36,37]. However,
crops are known to possess distinctive carbon sequestration abilities and thereby different radiation use
efficiencies across species, notably the C3 and C4 pathways. Moreover, yield estimation based on
remotely sensed data requires acknowledging spatial heterogeneity effects because the pixels are
typically mixtures of diverse land-cover types at the MODIS spatial resolution [39,40]. Remote sensing
models that consider the conceptual partition of mixed pixels are likely to improve the yield estimates of
specific crop types.
This study aims to improve yield estimation with MODIS data based on production efficiency
models. Our approach is to apply crop-type specific values of radiation use efficiency (RUE) to MODIS
pixels based on spatially disaggregated fine-resolution land use maps and to deduct the subpixel
productivity contribution from vegetation other than crops. We demonstrate our production efficiency
model-based method by quantifying the corn and soybean yields in the Midwestern US. We validate our
estimates against national survey data at both the county and state levels.
2. Study Area and Materials
The Midwestern US study area (Figure 1), one of the major agricultural regions in the world, includes
12 US states: North Dakota, South Dakota, Nebraska, Kansas, Minnesota, Iowa, Missouri, Michigan,
Wisconsin, Illinois, Indiana, and Ohio. In this region, diversified crops are cultivated but corn
(Zea mays) and soybeans (Glycine max) are the two dominant crops. In general, crop planting is
completed by mid-May, when the daily soil temperatures are warm enough (above 13 °C) to initiate
germination. Corn is often planted approximately one to two weeks earlier than soybeans . The crops
usually mature in late September and are harvested from early October until late October.
The datasets used in this study (Table 1) were collected over a three-year span between 2009 and
2011. The satellite data include two standard Terra/MODIS products: the eight-day 1000 m Leaf Area
Index (LAI) & Fraction of Photosynthetically Active Radiation (FPAR) product (MOD15A2)  and
the eight-day 1,000 m vegetation productivity product (MOD17A2) . The MODIS tiling scheme
separates the earth into 10° by 10° sections referenced with horizontal (H) and vertical (V) notations. Six
MODIS tiles (H09V05, H10V04, H10V05, H11V04, H11V05, and H12V04) that cover the Midwestern
US were downloaded from the U.S. Geological Survey (USGS) EROS data center . All products
were composited every eight days, starting from Day-of-Year (DOY) 1 in each calendar year. The
product details are available on the MODIS data website .
The Quick Stats database from the National Agricultural Statistics Service (NASS) of the US
Department of Agriculture (USDA) provides reliable crop survey data at the county, state, and national
levels . We obtained statistical data describing the yields and harvested areas of corn and soybean in
each county. Based on the Crop Production 2011 Summary released by the USDA, the Midwestern US
produced 277.1 Tg of corn and 70.2 Tg of soybeans in 2011, which were approximately 88.3% and
84.4%, respectively, of the total US corn and soybean productions. Planted areas for corn and soybean in
Remote Sens. 2013, 5 5929
Midwestern US were 5.6 × 107 ha in 2011, which were approximately 70.9% of the total planted areas
(7.9 × 107 ha) for all principle crops such as corn, sorghum, oats, barley, rye, wheat, rice, soybeans,
peanuts, sunflower, cotton, and potatoes.
Figure 1. The study area of the Midwestern US comprises 12 states.
Table 1. The datasets used in this study.
Data Type Data Source Description
satellite data USGS EROS center MODIS LAI/FPAR data (MOD15A2)
USGS EROS center MODIS vegetation productivity data (MOD17A2)
classification maps NASS Cropland Data Layer crop-type specific classification maps at 30 or 56 m
USGS early warning program a classification map of irrigated areas at 250 m
national survey NASS Quick Stats statistics of crop yields and harvested areas
The NASS Cropland Data Layer (CDL) program produces crop-type specific classification maps
based on multi-sensor satellite imagery using training data from extensive ground surveys . The
classification map is available for each state at a resolution of 30 m. In the present study, the CDL maps
were reprojected to a sinusoidal projection, mosaicked, and scaled up to 500 m as percent maps (Figure 2)
to match the spatial resolution of MODIS. To avoid errors in regions with sparse agriculture, our analysis
was confined to counties that were planted with corn or soybean on at least 5% of their total areas.
Although irrigation helps boost crop yields, most PEMs to date have not compensated for the impacts
of irrigation. To investigate the yield estimation in irrigated areas, we sourced the irrigation map (Figure 3)
from the USGS early warning program . The irrigated areas in the Midwestern US were mapped for
2007 and were primarily located in Nebraska and Kansas. Because irrigation is unlikely to vary on a
year-to-year basis, no change in irrigated area was assumed during the three years (from 2009 to 2011).
The spatial pattern of irrigated areas was consistent with that of the agriculture areas (Figure 2),
especially for corn (Figure 2A), which consumes large volumes of water before, during and for several
weeks after pollination. To study the effects of irrigation, counties were considered as irrigated if more
than 1% of the crop areas were under some form of irrigation.
Remote Sens. 2013, 5 5930
Figure 2. The percentage maps of corn and soybean in 2011 from the NASS CDL program.
(A) 2011 Corn map from NASS CDL; (B) 2011 Soybean map from NASS CDL.
Figure 3. The map of irrigated areas from the early warning program of USGS in 2007.
Remote Sens. 2013, 5 5931
3. Theoretical Background and Improvements
3.1. A Brief Description of the MOD17 Algorithm
Although the MOD17 algorithm has been described in detail in the MOD17 User’s Guide , we
briefly describe it here because the algorithm is fundamental to understanding our proposed method. The
MOD17 product [37,48] estimates the gross primary production (GPP) and net photosynthesis (PSN) of
each pixel every 8 days and estimates the GPP and NPP for each pixel annually. These estimates are
produced based on three upstream datasets: the MODIS land-cover classification product (MOD12Q1) ,
MODIS LAI/FPAR product (MOD15) , and large-scale meteorological data from the NASA Data
Assimilation Office (DAO). The coefficients for each biome type (decided based on MOD12Q1) are
defined in a Biome Parameter Look-Up Table (BPLUT) from a general ecosystem model .
The daily MODIS GPP is estimated as:
where PAR (MJ·day−1) is the daily incident photosynthetically active radiation, as estimated using the
DAO data; FPAR (dimensionless) is the fraction of absorbed photosynthetically active radiation, as
obtained from the upstream MOD15 product; ɛɡ (g·C·MJ−1 PAR) is the radiation use efficiency (RUE)
for GPP calculations when the environment is not limiting plant carbon uptake, as defined in the BPLUT
for the agricultural biome; and f(ɛ) accounts for the influences of environmental stress, such as
temperature and vapor pressure deficit, as calculated based on the DAO data and BPLUT.
The concept of daily PSN considers the maintenance respiration of leaves and fine roots:
where the daily maintenance respiration is estimated for the leaves (Leaf_MR) and fine roots
where LAI (m2·leaf·m−2 ground area) is the leaf area index and SLA (projected leaf area m2·kg−1·leaf C)
is the specific leaf area for a given pixel; leaf_mr_base and froot_mr_base (kg·C·kg·C−1·day−1·20 C) are
the maintenance respiration of leaves and fine roots per unit mass at 20 C, respectively; froot_leaf_ratio
(unitless) is the ratio of the fine root to leaf mass; Q10_mr (unitless) is an exponent shape parameter that
controls respiration as a function of temperature; and Tavg (°C) is the average daily temperature. LAI is
obtained from MOD15, Tavg is estimated from the DAO meteorological data, and other biome-specific
coefficients are obtained from BPLUT.
3.2. Improvements to Estimate Crop Productivity
Based on the MOD17 algorithm, we attempted to improve the crop yield estimation in the
Midwestern US using the following techniques: (1) crop-type specific masks were derived from
fine-resolution NASS CDL maps to identify relatively pure MODIS pixels; (2) a specific RUE was
GPP = PAR FPAR ( )
PSN = GPP Leaf_MR Froot_MR−−
[(Tavg 20.0) / 10.0]
Leaf_MR = LAI / SLA leaf_mr_base Q10_mr −
[(Tavg 20.0) / 10.0]
Froot_MR = LAI / SLA froot_leaf_ratio froot_mr_base Q10_mr −
Remote Sens. 2013, 5 5932
applied for each crop type; and (3) contributions to primary production from other vegetation types
were deducted when possible.
First, the MOD17 algorithm relies on the MODIS land cover product (MOD12), a classification
scheme that does not differentiate crop types. Several studies have indicated that the use of the MODIS
land cover product is likely to overestimate the agriculture areas relative to those reported by the NASS .
For this reason, we analyzed relatively pure corn or soybean pixels based on spatially disaggregated
CDL maps (Figure 2) rather than applying a general cropland mask based on the MODIS land cover
product. By counting corn pixels in the CDL maps, we observed that the estimated corn areas agreed
well with the harvested corn areas reported by the NASS in 2011 (Figure 4A). The soybean areas were
slightly overestimated, especially for the top soybean-producing counties (Figure 4B). It is appropriate
to assume that pixels with more than 75% corn or soybean cover are relatively pure endmembers [41,50].
The satellite data (resampled to 500 m) were spatially averaged based on those representative pixels to
derive the mean values for each county every 8 days.
Figure 4. Comparisons between crop areas calculated from CDL maps and reported by
NASS in 2011 for counties in the Midwestern US. (A) Corn area estimates; (B) Soybean
Second, we applied crop-type specific RUE values for corn and soybeans (Table 2) instead of a
biome-wide value in the MOD17 algorithm to estimate the yields. The MOD17 algorithm prescribes a
universal RUE value for all crops, regardless of their types [36,49]. However, the field measurements
that quantify RUE values based on the relationship between biomass accumulation and cumulative
radiation interception suggest that the carbon sequestration abilities vary widely across crop types [34,51].
Sinclair and Muchow  reviewed several studies and reported that the seasonal corn RUE ranges from
2.6 to 3.4 g·MJ−1 and soybean RUE ranges from 1.32 to 2.52 g·MJ−1. To account for the RUE
differences, we applied 3.35 g·MJ−1 for corn and 1.44 g·MJ−1 for soybeans as obtained from recent field
Remote Sens. 2013, 5 5933
measurements in Iowa . Although some studies observed that the RUE values varied across
time [38,52], the RUE values applied here were derived as seasonal mean values in the experiments.
Because the respiration costs of annual crop plants were deducted from the field measurements of
accumulated biomass, the use of these RUE values would result in crop productivities that can be linked
to crop yields directly.
Table 2. The parameters used in our study for estimating crop yields.
Parameter Description Corn Soybean Units
the radiation use efficiency 3.35 1.44 g·MJ−1 PAR
RS the root: shoot ratio 0.18 0.15 dimensionless
HI the harvest index 0.53 0.42 dimensionless
MC the moisture content of the grain 0.11 0.10 dimensionless
Finally, our analysis attempted to address the productivity contributed by vegetation other than crops
because pixels are commonly mixed at the subpixel level of MODIS. The conceptual partition of mixed
pixels could avoid the biased estimation of crop yields. In other words, the GPP for each pixel was
partitioned into two components in our algorithm:
where GPPtotal, DOY n is the GPP value for a specific Day Of Year (DOY) n; GPPcrop, DOY n is the
contribution from crops (i.e., corn or soybeans) for the same time period; and GPPother, DOY n is the
contribution from other vegetation types.
Separating each component in mixed pixels is challenging in remote sensing models because
dynamic information of subpixel land-cover composition is often unavailable. Here, we propose an
algorithm to approximate the GPPother, DOY n component based on plant LAI. Given that corn and
soybeans in the Midwestern US have not emerged or in very early growth stages by mid-May, when the
natural vegetation has already accumulated significant leaf area , it is appropriate to approximate the
LAI of vegetation other than crops during the growing season by the maximum LAI before mid-May:
where LAIother is the estimated LAI of vegetation other than crops; and max(LAI, :) is the
maximum LAI value between April (DOY 89) and before mid-May (DOY N0), as obtained from
MOD15. The DOY N0 value was assumed to be 129 for corn and 137 for soybeans because corn is
typically planted approximately one to two weeks earlier than soybeans.
Similar to Equations (3) and (4), the maintenance respiration of other vegetation is estimated to be:
where MRother is the maintenance respiration of other vegetation; Leaf_MRother and Froot_MRother are the
maintenance respiration of the leaves and fine roots of other vegetation, respectively; Tavg (°C) is the
total, DOY n crop, DOY n other, DOY n
GPP = GPP + GPP
other total, DOY n = 89:N
LAI max(LAI )≈
[(Tavg 20.0) / 10.0]
Leaf_MR = LAI / SLA leaf_mr_base Q10_mr −
[(Tavg 20.0) / 10.0]
Froot_MR = LAI / SLA froot_leaf_ratio froot_mr_base Q10_mr −
other other other
MR Leaf_MR Froot_MR=+
Remote Sens. 2013, 5 5934
average daily temperature, as estimated from the DAO datasets; and the values for the other parameters
are the same as the agricultural biome in the MOD17 algorithm.
Because the ratio of NPP to GPP, termed as the carbon use efficiency (CUE), is modeled as a
constant in many ecosystem models [29,31], the GPP contribution from other vegetation can then be
estimated to be:
where GPPother, DOY n is the GPP of other vegetation types for a specific DOY n, MRother, DOY n is the
maintenance respiration, and CUE is the carbon use efficiency. Published studies indicate a CUE value
from 0.3 to 0.5 for natural vegetation such as forests . We approximated a carbon use efficiency of
0.4 in this study.
Our estimation of each GPP and MR component throughout the growing season is further illustrated
in Figure 5, which presents the example of Olmsted County, Minnesota. The model was applied at the
pixel level, and estimates were aggregated to the county level. The proposed algorithm captured the
subtle variation of the GPP and MR caused by climatic factors in the time series. The sudden drop of
MODIS GPP in the middle of the growing season (DOY 169) was most likely due to cloud
contamination rather than harvest or other cultural practices. Clouds and aerosols can largely influence
crop GPP in a short period of time by reducing the incident PAR .
Figure 5. A simple representation of MODIS GPP (Gross Primary Production) and MR
(Maintenance Respiration) components of corn pixels in Olmsted County, Minnesota.
3.3. Converting MODIS GPP Estimates to Crop Yields
To compare with the NASS Quick Stats dataset, the GPP estimated by our method and the GPP
derived from the MOD17 product (hereafter referred as to the MODIS-GPP algorithm) were converted
to crop yields based on a common method used in agricultural studies [18,56]:
other, DOY n other, DOY n
GPP = MR / (1 CUE)−
n = N
crop, DOY n
n > N
Yield = GPP (1+RS) 1 MC
Remote Sens. 2013, 5 5935
where GPPcrop, DOYn is the estimated GPP of crops (i.e., corn or soybeans) for a specific DOY n. The
yield was integrated for an apparent growing season, which began in mid-May (DOY N0) and ended in
late-October (DOY N1). The value for N1, the growing season endpoint, was set as 297 in our study,
and N0 was defined as 129 for corn and 137 for soybeans, as in Equation (6). RS is the root to shoot ratio,
HI is the harvest index, and MC is the grain moisture content. We chose MODIS GPP instead of NPP in
this formulation because our preliminary tests as similar to other studies  revealed that yield
estimates derived from MODIS NPP were relatively low.
The crop-type specific parameters involved in our calculations are defined in Table 2. The root: shoot
ratio, which depends on the growing stages and fertilization of crops, is considered to be constant for a
specific crop type when harvested. Prince  reviewed past studies and chose the root: shoot ratio of
0.18 for corn and 0.15 for soybeans. The harvest index (HI) varies little for each crop species, except
under extreme stress conditions . The HI of corn is 0.53, as measured by experiments in nine US
locations . The soybean HI is 0.42 based on reported regression equations [56,58]. The moisture
content is estimated as 11% for corn grain and 10% for soybeans . The values of these parameters
vary in different studies. Lobell et al.  observed that regional yield predictions were insensitive to the
variability in the radiation use efficiency and harvest index. Prince et al.  attributed most of the
uncertainty to the variability in the harvest index and root:shoot ratio, which resulted in an overall
variability of ~10%. The uncertainty associated with variation in these defined parameters was
considered to be of secondary importance in the context of other modeling uncertainties such as the RUE
variations and the MODIS data.
4.1. Analysis at the County Level
Our estimated corn and soybean yields for 2011 agree well with the NASS reported survey data for
counties dominated by rainfed cultivation (Figure 6). The coefficients of determination (R2), as
measures of the correlations between estimated values and reference data, are 0.77 for corn and 0.66 for
soybeans. The corn yields were slightly underestimated, as indicated by the mean error (ME) of
−0.18 MT·ha−1, which was possibly due to the variation of parameters defined in Table 2. The variation
in the parameters, as the linear coefficients in the GPP-Yield relationship (Equation (11)), has little
influence on the R2 values. The high R2 values obtained for both the corn and soybeans demonstrate
that the crop yields estimated from MODIS data strongly correlate with the NASS survey data at the
Table 3 compares our algorithm with the MODIS-GPP algorithm (in parentheses) in the period 2009
to 2011. Our algorithm demonstrates improved crop yield estimation over the MODIS-GPP algorithm,
as indicated by higher R2 values and lower root mean square errors (RMSE). Similar to the findings in
other studies , the R2 values based on the MODIS-GPP algorithm between estimated crop yields and
NASS survey data were only 0.15~0.46 for corn and 0.35~0.53 for soybeans in rainfed counties. In
addition, the yields were considerably underestimated for corn (negative mean error) but overestimated
for soybeans (positive mean error). Our estimated biases were considerably smaller, as indicated by the
mean errors. Because the soybean RUE (1.44 g·MJ−1 PAR) is close to the biome-wide value in MOD17
Remote Sens. 2013, 5 5936
(1.36 g·MJ−1 PAR), the GPP contributed by other vegetation was the major factor that resulted in
overestimation in MOD17. In contrast, corn as a C4 plant has a much higher RUE value
(3.35 g·MJ−1 PAR) based on a photosynthetic pathway different from soybean, a C3 plant. The low RUE
value prescribed in MOD17 is the main contributor to the large underestimation of corn yields.
Therefore, we need to consider the effects of mixed pixels and the RUE variation across crop types when
estimating yields based on remotely sensed data.
Figure 6. Comparisons between crop yields estimated from MODIS data and reported by the
NASS for rainfed counties in the Midwestern US. The black line is the 1:1 line. (A) Rainfed
corn; (B) Rainfed soybean.
Table 3. Statistics between crop yields estimated from our approach using MODIS data and
reported by the NASS for rainfed counties for each year from 2009 to 2011. For comparison,
values in parentheses are statistics using the standard MOD17 products.
Ye a r Corn Soybean
R2 RMSE (MT/ha) ME (MT/ha) R2 RMSE (MT/ha) ME (MT/ha)
2009 0.55 (0.15) 1.21 (5.52) −0.60 (−5.39) 0.50 (0.35) 0.38 (0.86) −0.07 (0.77)
2010 0.54 (0.22) 1.17 (4.65) −0.14 (−4.38) 0.73 (0.53) 0.30 (0.97) −0.09 (0.89)
2011 0.77 (0.46) 0.89 (4.56) −0.18 (−4.28) 0.66 (0.53) 0.38 (1.06) −0.02 (0.95)
4.2. Analysis at the State Level
The analysis at the state level was performed in the same manner as at the county level, except that we
did not try to separate irrigated counties. The lower R2 values of the yields in 2011 (Figure 7) for corn (0.51)
and for soybeans (0.58) were partly caused by a large underestimation in Kansas and Nebraska due to the
irrigation effects. Because plants in irrigated areas often have higher transpiration rates that help cool
their leaves, the MODIS-GPP algorithm, which is sensitive to the environmental factors such as daily
temperature or vapor pressure deficit, would tend to underestimate GPP in irrigated areas. Interestingly,
the yields were overestimated for the northern states, such as North Dakota and Wisconsin, which may
Remote Sens. 2013, 5 5937
have been because crop planting typically starts later in those states than in other regions. It would be
more appropriate to use the LAI values from late May rather than mid-May to approximate the LAI of
other vegetation during the growing season. Future analysis should incorporate the timing of crop
phenology derived from MODIS to improve the yield estimation .
Figure 7. Comparisons between crop yields estimated from MODIS data and reported by the
NASS for states in the Midwestern US. The black line is the 1:1 line. (A) Corn;
We also estimated the final crop production based on satellite data using the following techniques:
(i) the crop yields were estimated from MODIS data; (ii) the harvested areas were derived from the CDL
maps by counting pixels within each state, and (iii) the crop production was calculated as the product of
crop yields and harvested areas. Compared with the NASS reported data in the Midwestern US, the total
crop productions were underestimated (Table 4) due to the underestimated yields in irrigated counties.
The errors of estimated total productions were −1.5% for corn and −0.6% for soybeans in 2011 and fall
within the acceptable ranges in other years. Note that the crop areas derived from the NASS CDL maps
may also contribute errors to our estimation of crop production here.
Table 4. Estimated and reported corn and soybean production for 12 states in the
Ye a r Corn Production Soybean Production
Estimated (Tg) Reported (Tg) Error Estimated (Tg) Reported (Tg) Error
2009 253.6 291.7 −13.04% 68.2 75.6 −9.74%
2010 268.1 276.3 −2.95% 73.9 77.7 −4.79%
2011 273.0 277.1 −1.49% 69.8 70.2 −0.56%
Remote Sens. 2013, 5 5938
5.1. Major Findings
We employed three key methods to estimate crop yields based on satellite data. First, there are clear
benefits to retrieving subpixel areas of different crop types and other vegetation based on land-cover
maps at a fine resolution. Although some studies concluded that coarse spatial resolution satellite data (0.05
degree or approximately 5.5 km) were advantageous over higher spatial resolution data for estimating the
yield because individual pixels will likely shift between crop types on a year-to-year basis , we
observed that a combination of fine and moderate resolution data was preferable for accurately
estimating yield because retrieving information related to crop types is essential to yield modeling.
Second, our analysis of corn and soybeans reveals that applying crop-type specific RUE values in the
PEMs is necessary to estimate crop yields properly. Global-scale PEMs mainly focus on quantifying
vegetation productivity for a general biome type . For example, the default RUE value in MOD17 is
the same for all crops and grasses [36,48]. However, it would be inappropriate to apply flat RUE values
to estimate the yields for different crops, especially for productive C4 plants such as corn.
Finally, it is necessary to deduct the GPP contributed by vegetation other than crops when estimating
the yield at the spatial resolution of MODIS. As illustrated, crop yields are likely to be overestimated
without such considerations when applying RUE values measured in field studies. Our findings are
consistent with other studies, which observed that the direct use of field-measured RUE values in
global-scale PEMs would result in an overestimated GPP .
5.2. Limitations and Future Improvements
Although we were able to adequately estimate crop yields over large geographical regions, some
limitations necessitate further improvements. Our algorithm is based on the assumption that the LAI of
other vegetation is relatively constant after mid-May. For much of the study area where corn and
soybeans are planted, this assumption is reasonable, and our model improved the estimated crop yields
as demonstrated. However, such an assumption is not entirely correct and does not hold for crops with
different phenological cycles such as winter wheat. It would be of interest to identify appropriate
solutions to modeling GPP by integrating MODIS data and fine-resolution land use maps.
There are also uncertainties related to irrigation practice and cloud cover. Although the MODIS
GPP/NPP algorithm considers the daily atmospheric water deficit , our study implies that it still
requires better parameterization for irrigated areas. Given the availability of time-series measurements
from the flux towers located in irrigated areas , we should be able to calibrate the production
efficiency models to improve yield estimation. Cloud cover is another factor that may influence the yield
estimation from remotely sensed data. Even though the fitting process can reduce the influence of
intermittent cloud-cover, the proposed method may not perform well in areas with persistent cloud
covers, which could result in large data gaps in the MODIS time series.
Remote Sens. 2013, 5 5939
This study proposes a production efficiency model-based algorithm for estimating crop yield in
the Midwestern US. The yield estimates have shown to agree well with the NASS survey data in
rainfed counties for both corn (R2 = 0.77; RMSE = 0.89 MT·ha−1) and soybeans (R2 = 0.66;
RMSE = 0.38 MT·ha−1). Different from previous studies, we found that the MODIS GPP algorithm was
capable of making reasonable yield estimates with certain considerations. Our analysis suggests using
field-measured RUE values instead of biome-wide RUE values in the production efficiency models
when estimating the yield for a specific crop type. Moreover, it is important to consider the productivity
contribution from other vegetation in mixed pixels. The proposed algorithm does not require a
retrospective analysis that constructs the empirical relationships between reported yields and remotely
sensed data, and it has the potential for monitoring crop yields over large areas. Future work on yield
estimation based on production efficiency models should focus on investigations that consider the
subpixel spatial heterogeneity and irrigation effects.
We thank Jie Wang, Xuecao Li, and Han Chen at Tsinghua University for data preparation. We also
thank the USGS and NASA for free data distribution. This study was partially funded by the China
Postdoctoral Science Foundation (No. 2013M540087) and National Science Foundation of China
(No. 41301445), and an international cooperation grant from Tsinghua University. RBM participation
was made possible by funding from NASA Earth Science Division.
Conflict of Interest
The authors declare no conflict of interest.
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