An assessment of pre- and within-season remotely sensed variables for

forecasting corn and soybean yields in the United States

David M. Johnson ⁎

United States Department of Agriculture, National Agricultural Statistics Service, 3251 Old Lee Highway, suite 305, Fairfax, VA 22030, United States

article info abstract

Article history:

Received 15 July 2013

Received in revised form 24 October 2013

Accepted 26 October 2013

Available online 22 November 2013

Keywords:

Crop yield forecasting

Corn

Soybeans

Precipitation

NDVI

Land surface temperature

MODIS

Regression tree modeling

Four timely and broadly available remotely sensed datasets were assessed for inclusion into county-level corn

and soybean yield forecasting efforts focused on the Corn Belt region of the central United States (US). Those

datasets were the (1) Normalized Difference Vegetation Index (NDVI) as derived from the Terra satellite's

Moderate Resolution Imaging Spectroradiometer (MODIS), (2) daytime and (3) nighttime land surface temperature (LST) as derived from Aqua satellite's MODIS, and (4) precipitation from the National Weather

Service (NWS) Nexrad-based gridded data product. The originating MODIS data utilized were the globally

produced 8-day, clear sky composited science products (MOD09Q1 and MYD11A2), while the US-wide NWS

data were manipulated to mesh with the MODIS imagery both spatially and temporally by regridding and

summing the otherwise daily measurements. The crop growing seasons of 2006–2011 were analyzed with

each year bounded by 32 8-day periods from mid-February through late October. Land cover classifications

known as the Cropland Data Layer as produced annually by the National Agricultural Statistics Service (NASS)

were used to isolate the input dataset pixels as to corn and soybeans for each of the corresponding years. The

relevant pixels were then averaged by crop and time period to produce a county-level estimate of NDVI, the

LSTs, and precipitation. They in turn were related to official annual NASS county level yield statistics. For the

Corn Belt region as a whole, both corn and soybean yields were found to be positively correlated with NDVI

in the middle of the summer and negatively correlated to daytime LST at that same time. Nighttime LST and

precipitation showed no correlations to yield, regardless of the time prior or during the growing season. There

was also slight suggestion of low NDVI and high daytime LST in the spring being positively related to final yields,

again for both crops. Taking only NDVI and daytime LST as inputs from the 2006–2011 dataset, regression treebased models were built and county-level, within-sample coefficients of determination (R2

) of 0.93 were found

for both crops. Limiting the models by systematically removing late season data showed the model performance

to remain strong even at mid-season and still viable even earlier. Finally, the derived models were used to predict

out-of-sample for the 2012 season, which ended up having an anomalous drought. Yet, the county-level results

compared reasonably well against official statistics with R2 = 0.77 for corn and 0.71 for soybeans. The rootmean-square errors were 1.26 and 0.42 metric tons per hectare, respectively.

© 2013 Elsevier Inc. All rights reserved.

1. Introduction

1.1. Crop yield statistics

Accurate and timely estimation of local and regional crop yield

statistics is important for a variety of reasons. On the macroeconomics

level they allow societies to understand the food and fiber supply

which in turn helps the demand side plan for and better utilize the finite

crop resources. In the most developed countries this is manifested

through futures contract markets which are most efficient and fair for

price discovery when transparent and current statistics are available.

Local, direct to consumer markets work similarly in that statistics help

both parties understand the value of the crop. From a management

standpoint, yield information gives a farmer a baseline of what is

typically expected to be produced and thus can be used to best establish

risk, insurance premiums or the value of input costs. Established yield

information also highlights the impact to crops from natural events

such as severe weather or changing climatic conditions. Likewise,

regional yield statistics help quantify how strategies such as planting

methodologies, irrigation, fertilizer and pesticide use are playing

out in aggregation and can identify regions that are chronically

underperforming, or have a “yield gap.”

The United States Department of Agriculture (USDA) spends considerable effort in determining United States (US) crop yields in service

to the agricultural community. The statistical arm of the USDA, the

National Agricultural Statistics Service (NASS), conducts two large

panel surveys (USDA, 2012) that are annually ongoing throughout the

growing season (USDA, 2010) to establish state- and national-level

yield estimates. The first is known as the Agricultural Yield Survey

Remote Sensing of Environment 141 (2014) 116–128

⁎ Tel.: +1 703 877 8000x169.

E-mail address: dave.johnson@nass.usda.gov.

0034-4257/$ – see front matter © 2013 Elsevier Inc. All rights reserved.

http://dx.doi.org/10.1016/j.rse.2013.10.027

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which is based on a maintained “list frame” of farmers and the

results are directly reliant on the information they provide. Each year

thousands of those farmers are randomly selected, contacted monthly

by phone during the growing season and asked to report expected

yields for their crops grown. Information from all those sampled

is then combined and summarized to derive a set of regional yield

“indications.” Run in parallel is the Objective Yield Survey which derives

an independent set of indications through biophysical crop measurements. For it, hundreds of small plots are randomly sampled from fields

throughout the major growing areas and visited by an enumerator a few

times during the crop season. Attributes collected include plant counts

per unit area, grain size, grain weight, etc. The information from all

of the plot-level data is ultimately aggregated into a model to derive

this second set of yield indications. The Objective Yield Survey is more

limited in scope over the Agricultural Yield Survey in that it only focuses

on the dominant commodity crops like corn, soybeans, wheat, potatoes

and cotton. Ultimately, the results from both surveys, along with any

relevant ancillary information, are analyzed by the NASS Agricultural

Statistics Board (ASB) to establish the monthly published yield forecasts.

After the season is complete late in the fall, an additional widely cast

survey is undertaken which documents agricultural production statistics down to the county-level. For it questionnaires are sent to a much

larger sample of producers asking for responses on many agricultural

facets of their operation including estimates of their crop yields. Finally,

these county-level statistics are assessed and published to reconcile

with the previously established ASB national- and state-level yields.

Any further independent, error assessable and cost effective measures of crop yield indications that can be provided to the ASB are

welcome. Real-time measuring of crop yields from remote sensing technologies has been promoted as a feasible methodology but has been

fairly limited in implementation (Allen, Hanuschak, & Craig, 2002;

Baruth, Royer, Klisch, & Genovese, 2008; Reynolds et al., 2000; Rojas,

2007). Reasons for lack of uptake are likely many but probably lead by

a perception that results are not being seen as accurate, timely, or objective enough. Furthermore, remote sensing estimation of crop yields

has potentially been hindered due to the unknown availability, cost

and capacity of future imagery data combined with the highly specialized nature of the work for which it may be hard to find skilled and

experienced labor.

In terms of US crop statistics themselves, corn and soybeans are the

two largest commodities grown by land area and the planted acreage

has steadily expanded in reach by about 25% over the last couple of

decades (USDA/NASS Quick Stats). Yield trends for these crops have

been increasing at a similar rate but see more relative variability year

to year. Corn and soybeans from the US are high value and significant

commodities on global export markets and of late they have been

volatile in pricing. This suggests, at least in part, that the true amount

produced has not been fully understood at all times.

1.2. Remote sensing of crop yields

Monitoring crops via satellite remote sensing is not a new idea or

one in which there is a lack of research. Funk and Budde (2009) showed

a summary of the work in a variety of sensor, location, and crop type

contexts. Gallego, Carfagna, and Baruth (2010) also presented a history

targeted specifically to crop production estimation. Even with all

this aggregated work, assimilating the results to summarize to a best

practice is confounding because the research has targeted different

ecoregions of the globe, does not use the exact same type of input

datasets or has varying methodologies. Furthermore, the specific crop

type of focus has varied across the studies making the outcomes further

difficult to compare. However, in general there has been more emphasis

on corn, soybeans and wheat. Reasons why these three crops in particular have been the most studied are unknown but likely because

they are found wide spread and in large quantities geographically. An

alternative reason could be that there has been found better remote

sensing yield estimation success with them versus other potential

crops (and failures tend not to get published).

Regardless of crop being investigated, a common and central

theme of this type of remote sensing research involves the reduction

of the sensor's multispectral channels into a single metric known

as the Normalized Difference Vegetation Index (NDVI), analyzing its

response throughout the crop growing season and then relating it

again to in situ collected crop information. NDVI is calculated from the

red and near-infrared (NIR) spectral channels as

NDVI 1⁄4 ð Þ NIR–red =ð Þ NIR þ red :

NDVI exploits the large difference seen between the red and NIR

bands for heavily vegetated land cover types and has been shown to

be strongly correlated with plant productivity in both in situ (Hatfield,

1983; Shanahan et al., 2001; Viña et al., 2004) and remote sensing

applications (Basnyat, McConkey, Lafond, Moulin, & Pelcat, 2004;

Tucker, 1979). NDVI is often preferred over the independent use of the

red and NIR channel in that it simplifies data analysis into a single metric

while at the same time it is a normalization which helps to reduce

data errors due to poor viewing geometry or hazy atmospherics. The

normalization also allows for easier comparison across different sensors.

Many sensors with the ability to provide NDVI have been utilized

throughout the past few decades. Long-term, ubiquitous, and freely

available US satellite assets are reviewed here. The program with the

longest lineage is that of the Advanced Very High Resolution Radiometer (AVHRR) sensor. Variants of it have been aboard over a dozen operational polar orbiter meteorological satellites that were first launched in

the late 1970s. The last was placed into orbit in 2009. AVHRR is decently

suited from monitoring vegetation dynamics given its daily revisit rate

and reasonable spatial resolve of a little over 1 km which is fine enough

for monitoring relatively homogenous crop areas. Assessment of AVHRR

NDVI phenology and the general relation local crop yields has been

performed (Ferencz et al., 2004; Maselli & Rembold, 2001) in addition

to analysis targeted toward the specific commodities of corn, soybeans

or wheat (Benedetti & Rossini, 1993; Hays & Decker, 1996; Mkhabela,

Mkhabela, & Mashinini, 2005; Salazar, Kogan, & Roytman, 2007; Wall,

Larocque, & Léger, 2008). Modeling results have been shown reasonable

for all but there are limitations on the yield estimation precision. Errors

may be a function of the native coarse pixel size of AVHRR, which is

larger than most fields even in heavily mechanized agricultural regions,

or due to the sensor itself which may not be able to provide adequate

spectral information with low noise.

Technology has progressed and a newer and more sophisticated

sensor called the Moderate Resolution Imaging Spectroradiometer

(MODIS) improves on AVHRR (Fensholt & Sandholt, 2005; Huete

et al., 2002) particularly in terms of spectral response, spatial resolution,

and having more emphasis placed on land related observations (Justice

et al., 2002). MODIS is aboard two earth science research oriented

satellites, Terra and Aqua, which were launched in 1999 and 2002,

respectively. MODIS carries a total of 36 spectral bands with most

having a nadir ground resolution of about 1 km, which is similar to

AVHRR. However, two of the key bands for land observations, the red

and NIR, have a much finer resolution of about 250 m. MODIS derived

crop and productivity yield work has again often relied on NDVI phenology with a focus on wheat (Becker-Reshef, Vermote, Lindeman, &

Justice, 2010; Mkhabela, Bullock, Raj, Wang, & Yang, 2011; Reeves,

Zhao, & Running, 2005) and corn or soybeans (Bolton & Friedl, 2013;

Doraiswamy et al., 2004; Doraiswamy et al., 2005; Funk & Budde,

2009; Guindin-Garcia, Gitelson, Arkebauer, Shanahan, & Weiss, 2012;

Sakamoto, Gitelson, & Arkebauer, 2013). Yield research which use

MODIS data have proven better results than those that use AVHRR

data. There are no identical MODIS follow-on mission planned but

a similar meteorology focused polar orbiting sensor called the Visible

Infrared Imaging Radiometer Suite (VIIRS) program has begun. A prototype VIIRS instrument was launched in 2011 aboard a satellite platform

D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128 117
named Suomi National Polar-orbiting Partnership. VIIRS was ultimately

designed to replace the AVHRR program but has characteristics more

similar to MODIS.

Improving on spatial resolution further are the Landsat series of

earth observation satellites. They have also provided an opportunity

for assessing crop yields from space. Landsat has carried a few optical

and thermal sensor variants since the first launch in 1972 with steady

performance and calibration improvements on successive missions to

the present. The original sensor was the Multispectral Scanner (MSS)

which had four or five spectral channels and a spatial resolution of

about 60 m. More contemporary Landsats have carried variants of a

sensor called Thematic Mapper (TM). It has even more spectral bands

than the MSS and a ground sample resolution of 30 m. The eighth

Landsat mission, having eleven bands, was launched early in 2013.

While the spatial resolution from all Landsat sensors is vastly superior

to AVHRR and MODIS, Landsat has been hindered for use in monitoring

crop yields given its relatively narrow swath of about 185 km which

provides a temporal revisit rate of only 16 days. This severely limits

the number of observations within a typical growing season, particularly when factoring in the likelihood of clouds. However, yield and productivity work utilizing TM data have been prototyped for different

crop types (Doraiswamy, Moulin, Cook, & Stern, 2003; Gitelson et al.,

2012; Liu et al., 2010; Lobell, Ortiz-Monasterio, Asner, Naylor, & Falcon,

2005) and it has been shown possible, albeit for relatively small analysis

areas only.

Weather variables have had a much longer history of use for understanding crop yields compared to NDVI which was spawned from multispectral remote sensing technologies. Temperature and precipitation

are the ubiquitous choice for yield predictor variables. Ample, and too

lengthy to list, research going back a century ago has shown the negative correlation of heat and positive correlation to precipitation for

corn yields (Smith, 1914; Wallace, 1920). More recent analysis has

been increasingly sophisticated and refined (Kauffman & Snell, 1997;

Lee, Phil Kenkel, & Brorsen, 2013; Tannura, Irwin, & Good, 2008) as

more detailed climate and weather datasets in addition to wide-scale

and historical yield validation information have become available.

Most recent analysis is also integrating future climate variability into

crop models (Dixon, Hollinger, Garcia, & Tirupattur, 1994; Schlenker &

Roberts, 2009). Ultimately, all work converges around the notion that

too much summer heat reduces crop yields while decent rainfall

amounts help increase it.

While there has been a lot of agro-meteorology research, little of it

has used remotely sensed datasets as input for predicting crop yields.

But now, unlike in the past, there exists the ability to collect spatially

detailed proxy parameters for agro-meteorology variables via remote

sensing. Land surface temperature (LST) is a similar, but not exactly

the same, measurement as more commonly collected air temperature.

The two variables are strongly related, though, with LST having larger

temperature extremes and being locally dependent on the land cover

type (Mildrexler, Zhao, & Running, 2011; Prihodko & Goward, 1997;

Wan, 2008). In terms of satellite LST and the relation to yield no

known direct research has been done. However, there have been related

studies that have used LST to monitor agricultural drought (Feddema &

Egbert, 2005; Patel, Parida, Venus, Saha, & Dadhwal, 2012). Some have

also integrated NDVI alongside LST for the analysis (Goetz, 1997;

Prasad, Chai, Singh, & Kafatos, 2006; Wan, Wang, & Li, 2004).

Research using remotely sensing derived precipitation in the context

of agricultural yields would also seem prudent given that rainfall rates

can vary dramatically by location, and thus interpolated measurements

from the limited weather stations may not be providing sufficient

spatial detail. To counter this problem, a dedicated satellite for measuring rainfall amounts was indeed developed called the Tropical Rainfall

Measuring Mission (TRMM). Unfortunately, its steeply inclined polar

orbit around the earth is only focused on the equatorial Tropics and

thus it provides no imagery farther than 35° north and south. So,

TRMM can only monitor the southern portion of the US and thus misses

the Corn Belt, and most other major growing areas around the globe,

completely. Within the US however there is an alternative option.

The National Weather Service (NWS) part of the National Oceanic and

Atmospheric Administration (NOAA) operates a ground based remotely

sensed dataset with coverage being provided by a large array of Doppler

radars from which precipitation can be estimated (Seo, 1998). Up to this

point few applications of the data beyond pure rainfall and hydrological

monitoring have been published. Reason why are unknown but are

likely a combination of it being a new dataset and one that is not

obviously available to those in the remote sensing community.

It could also be seen as providing too much spatial and temporal

information that is not obvious how to exploit.

1.3. Objective

This applied-leaning research here attempts to provide an increased

understanding of the corn and soybean production in the US through

two primary objectives:

1. To firmly understand the relationship between US county-level average

corn and soybean yields versus relatively common variables collected

throughout the entire crop growing season via remote sensing. The

variables assessed were a time series of the NDVI as derived by the

Terra MODIS sensor, daytime and nighttime LST as derived by

the Aqua MODIS sensor and precipitation estimates produced from

the NWS Nexrad Doppler weather radar system. The Aqua LST and

Nexrad precipitation datasets were both considered novel in regard

to what has been researched previously for predicting crop yields.

Also, equal importance to corn and soybeans was given whereas in

many studies only a single crop type is analyzed.

2. To build a county-level yield forecasting model, from those remotely

sensed variables deemed important, that is not only accurate but also

timely and relatively simple to run in an operational environment. A

large and robust cross-sectional panel of historical county-level

yield information from NASS was used as the basis of the forecasting

and implemented with regression tree, machine learning software.

Rulequest Cubist was chosen for the modeling solution and is viewed

as both pragmatic and unique.

2. Materials and methods

2.1. Study area

The crop yield work focused on 12 states which sit in the central and

north US and are known collectively as the Corn Belt (Fig. 1). They are

Arkansas, Illinois, Indiana, Iowa, Kansas, Minnesota, Missouri, Nebraska,

North Dakota, Ohio, South Dakota and Wisconsin. The states make up

over 75% of the US corn and soybean production and thus are focused

upon by the NASS Objective and Agricultural Yield Surveys in making

national crop production estimates. Note, corn does not include

Arkansas or North Dakota in the Objective Yield Survey and soybean

does not include Wisconsin. The 12 states are geographically contiguous, relatively flat and level, and have very fertile soils. Winters are

usually cold and snowy and summers warm and humid. Prior to

transitioning to wide-scale farming in the middle and late 1800 s

the area was covered by native tall grasses. Most of the states are now

dominated by the two crops of soybeans and corn which are often

rotated symbiotically in the same field alternatively from year to year.

The states towards the west, ebbing into the drier Great Plains, do

however have a higher diversity of crop types and in particular small

grains crops like wheat and barley. Recent and overall trends have

shown corn and soybeans to be slowly accounting for more and more

of the cropland area and reducing the area of other crops (USDA/

NASS, Quick Stats).

118 D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128
2.2. Datasets

Four grid-based, map referenced datasets were explored in terms of

their relationship to county level crop yields and for possible inclusion

into corn and soybean yield forecasting models. They were:

1. NDVI — calculated from the 8-day composited surface reflectance

bands product (Vermote, Kotchenova, & Ray, 2011) from the Terra

MODIS sensor (termed MOD09Q1),

2. Daytime LST — produced from the 8-day composited thermal product

(Wan, 2007) from the Aqua MODIS sensor (termed MYD11A2),

3. Nighttime LST — also produced from the 8-day composited Aqua

thermal MODIS sensor, and

4. Precipitation — derived from the NOAA/NWS Nexrad ground based

system (Seo, 1998; Seo, Breidenbach, & Johnson, 1999).

These particular variables were chosen for several reasons. First

and foremost, they all are suggestive of being related to crop yields via

simple conventional wisdom and more importantly, agronomy type

research. Secondly, each of the datasets is spatially detailed and allows

for modeling at relatively fine geographic scales approaching, particularly for NDVI, the crop field level. As incorporated here the NDVI

resolution is about 250 m, the LST is 1 km, and the precipitation is

4 km (6.25, 100, and 1600 ha, respectively). Temporal revisit times

are also high with all of these products as raw input data for each

are collected daily. On any given date cloud cover impacts the quality

of imagery collected from satellites and thus MODIS composite products

which pick the “best of” pixels over an eight day period are distributed

to end users helping simplify data management and processing. The

precipitation dataset used is also produced and distributed daily but

not impacted by cloud cover due to the penetrating ability of radar.

Composited precipitation type products are also produced but

they are accumulation periods of a week or month and not exactly

in alignment with MODIS datasets. Thirdly, each of the datasets has a

reasonable history depth. Terra data collection goes back to the year

2000 and Aqua 2002. These start years were soon after the launch of

each satellite. The NWS precipitation product archive began in 2005.

All products have a finite lifespan but it is believed that each of these

dataset will continue to be at least available into the near future. For

MODIS, while it is aging, at the time of writing there is no sense that

the sensor is about to fail or be shut off, and even if one platform does

fail the other can be considered a backup. Furthermore, for MODIS the

VIIRS sensor is considered a replacement. More VIIRS sensors are

planned for the operational Joint Polar Satellite System so whatever

is learned about yield forecasting from MODIS will likely be directly

applicable for years to come. And finally, and perhaps most importantly,

all four of these datasets are provided free of charge and accessible

immediately via the Internet. They each have little lag time from

collection to distribution. The last point is particularly critical if trying

to forecast yields in an operational and time sensitive environment.

The respective Terra and Aqua satellite from which the MODIS

data were chosen was done for purposeful reasons. Terra was used for

NDVI because its approximately 10:30 a.m. overpass time is thought

to provide the most optimal time for observing surface reflectance

versus Aqua which is at 1:30 p.m. and more likely on average to have

encountered afternoon clouds. Conversely, Aqua was chosen for LST

observations instead of Terra because the daytime overpass of 1:30 p.m.

aligns closer in time with the maximum daytime temperature. Likewise,

the Aqua nighttime temperature product was also chosen over Terra's

because it would be more representative of the low temperature point

of the diurnal cycle. Both daytime high and nighttime low temperatures

are often talked about in terms of crop yield impacts, albeit usually

anecdotally, so it was desirable to include a proxy for both. The 8-day

composited products were chosen as a compromise over single day

observations or even longer compositing time windows. Furthermore,

the 8-day compositing period is seen as usually sufficient time in which

to have obtained at least one clear sky observation, in the Corn Belt at

least, for inclusion into the mosaic.

All of the MODIS MOD09Q1 and MYD11A2 data were obtained via

File Transfer Protocol (FTP) over the Internet from the Land Process

Distributed Active Archive Center (LP DAAC). The MODIS data is global

in nature and distributed by standardized five degree by five degree

“tiles.” Six tiles were needed to cover the entire Corn Belt region of

interest and consisted of “horizontal/vertical” referenced tiles 9/4, 9/5,

10/4, 10/5, 11/4 and 11/5. Thirty-four time periods of the 8-day data

Fig. 1. Distribution of corn and soybean within the US as depicted from the 2012 USDA Cropland Data Layer. Deeply shaded states are those that were used in analysis.

D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128 119
were pulled for the years 2006 through 2012. The start time of the first

composite for each year was February 10th, or day-of-year (DOY) 41.

The start date of the final annual composite acquired was November

1st which equals DOY 305. The entire data series time window was

seen as more than comprehensive enough not only to cover the Corn

Belt crop growing season, which is typically from May to October, but

also allowed for spring pre-season information to be investigated. The

MODIS raw files were obtained natively in the Hierarchical Data Format.

The “Collect 5” version was used.

The NOAA/NWS data were also obtained via Internet FTP but from

the NWS Advanced Hydrologic Prediction Service website. Because the

rainfall data were to be aggregated to the same 8-day schedule as

MODIS, all the daily data from February 10th through November 8th

were gathered. The same 2006–2011 years were spanned. The NWS information was natively in Environment Systems Research Institute's

(ESRI) Shapefile vector format in a standardized and regularized point

grid of approximately 4 km in spacing. The Shapefile data were provided

by the NWS in “compressed”.zip format.

The dependent variable for which the remote sensed dataset

would ultimately be compared came from annual county-level corn

and soybean yields as published by the USDA NASS. The data were

downloaded from the Internet in tabular form from the USDA/NASS

Quick Stats website. An annual average yield for each county, for

both corn and soybeans, across the Corn Belt, years 2006–2011, was

ultimately gathered. There are roughly 1000 counties in the region so

with seven years of data a large amount of data points resulted. A handful of the counties did not contain data in certain or all years because

they failed to meet NASS publication standards of having a sufficient

number of farmers or large enough response rate. This typically means

there was very little or none of that crop produced in that particular

county and any estimate would have been unreliable.

Finally, land cover “masks” depicting crop areas were obtained.

NASS produces a robust annual land cover classification over the US

called the Cropland Data Layer (CDL). The first US wide coverage was

developed in 2009 (Johnson & Mueller, 2010) and has continued annually since (Boryan, Yang, Mueller, & Craig, 2011). Year 2008 was completed retrospectively for the nation and for the Corn Belt area CDL

classifications exist in the years 2006 and 2007 as well. CDL accuracies

for corn and soybean fields are particularly strong and thus can act as

an excellent proxy for ground validation data. All of the CDL information

was obtained over the 12 state region from 2006 to present. The 2006

start year of the CDLs also drove the starting point for inclusion of the

MODIS and precipitation datasets even though they both exist farther

back in time. The CDLs were ultimately used to isolate only the relevant

areas of corn and soybeans from the MODIS and precipitation data.

2.3. Data preparation

A consistent grid-based reference frame was first established in

which all of the data products used would harmoniously nest. The

MODIS-based “250 meter” sinusoidal equal area map projection was

chosen. Selecting this coordinate system minimized the overall amount

of data processing needed since the majority of the data used was from

MODIS. It also avoided any resampling caused degradation of the

MODIS data since it would not have to undergo a map reprojection. Of

note, while the MODIS data are labeled as 250 m in resolution

they are more precisely 231.66 and indeed that spacing is what was

used. The generalized 250 m, and multiples of it, nomenclature will be

continued here.

With the reference grid established, a 250 m resolution raster-based

mask file for each state (again, Arkansas, Illinois, Indiana, Iowa, Kansas,

Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, and

Wisconsin) was created to define which pixels were within a particular

state's border. All boundary definitions were derived from ESRI's Data

and Maps Detailed Counties Shapefile (dtl_cnty.shp) by first converting

the vector file into the sinusoidal projection and then determining

which 250 m reference grid cell belonged to what state. A majority

area rule was used to assign pixels that were split by two or more states.

Each final state mask was ultimately aligned spatially with the MODIS

reference grid and stored in 1-bit Earth Resources Data Analysis System

(ERDAS) Imagine format with pixels coded zero defined as residing

outside the state border and those coded one being inside.

Similarly and in conjunction, 250 m pixel identifications grids were

developed by state to define which county each pixel best fit. Grid cells

were assigned to their Federal Information Processing Standard (FIPS)

codes which typically are ordered alphabetically by county name

starting at a value of one and increasing by odd numbers only. The

ESRI County Shapefile was again used as input. The output however

was in 16-bit format to account for FIPS values that could range above

255.

Corn and soybean masks were next developed, by state and year,

from the available CDL 2006–2011 annual information. These masks

were developed to provide a means to isolate corn or soybean areas

from the MODIS and precipitation data (Kastens et al., 2005). A four

step process was used to tailor the information from each 30 or 56 m

CDL into something appropriate at the 250 m level. The first step was

to reproject the raw CDL grids from their native Albers equal-area

conic projection to that of the MODIS sinusoidal. The output grid cell

size was kept the same as the input (thus, either 30 or 56 m). Next,

the number of crop of interest pixels from the CDL that were contained

within each 250 m pixel grid cell was calculated. The total possible was

also established. Depending on the CDL pixel size, and the vertical and

horizontal alignment of it versus the 250 m grid, the maximum counts

possible could vary between 16 and 49. Next, the total corn (or soybean)

counts in each MODIS grid cell were divided by the maximum possible

to give an areal proportion. Finally, that proportion information was

compared to a threshold of 0.9 to establish whether the 250 m cell

contained enough of the crop of interest. This 90 percent threshold

value was subjectively determined but was felt to be a good compromise between the possibility of excluding too many pixels, because of

noise or minor cover type mixing, yet conservative enough to be robust.

The final corn and soybean masks for each state were a 1-bit formatted

file where a value of one equaled at least 90% of the MODIS-scaled pixel

to be containing corn (or soybeans) as a cover type while a value of zero

was less than 90%. In the end, each of the state-level mask grids had

minimally thousands of pixels declared as corn or soybeans and most

counties within them hundreds of pixels. This was deemed more than

sufficient to build a high quality sample for intersection against the

NDVI, LST and precipitation datasets.

With the state, county and yearly corn and soybean masks all

in place, next the remotely sensed data was managed. For the MODIS

surface reflectance data (MOD09Q1) each of the 6 Hierarchical Data

Format (HDF) tiles comprising the Corn Belt per 8-day time step were

successively mosaicked into a single HDF file. Next, the red and nearinfrared channels (HDF bands 0 and 1, respectively) were extracted

and stored in ERDAS Imagine format. Finally, the NDVI was calculated

for each entire image mosaic. All data management was kept in the

original 16-bit scaled by 10,000 format and thus the output NDVI was

also scaled. There were ultimately 34 NDVI mosaic images per year

created and thus a grand total of 204 over the six years from 2006

through 2011.

Next all of the corresponding MODIS LST datasets were ingested. The

processing used was very similar as to the surface reflectance data in

that each date of six tiles were first read and mosaicked. However,

after combining the tiles, it was HDF layers 0 and 4 that were imported

into ERDAS Imagine format. Those particular bands corresponded to the

daytime and nighttime information, respectively. No further processing

was then done and thus temperatures were left in their native, scaled by

50 K, 16-bit and 1 km spatial resolution, format. In total there were 204

images for both the daytime and nighttime LST information.

Through subjective observation of the MODIS composite imagery it

was noticed that there were often times when the 8-day window was

120 D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128
not long enough to assure noise free pixels. The errors tended to be

more pronounced in the early or later periods of the growing season

and in more northerly locations. It was also concluded that for both

NDVI and LST when noise occurred it usually erred in the negative

direction. These findings were consistent with what would result

when periods of prolonged clouds or haze or even standing snow or

water existed. Many methods for minimizing noise within remotely

sensed time series data have been proposed and used to smooth the

data. They range from simple to sophisticated and include analysis

methods like least squares (Jönsson & Eklundh, 2004), harmonics

(Moody & Johnson, 2001) or wavelets (Galford et al., 2008). Choosing

a best method is not always straightforward (Hird & McDermid, 2008)

and a disadvantage of them all is they usually perform best when a

true periodic length of data is available. For many applications this

may not be an issue. But, if trying to analyze and forecast crop yields

in the middle of the season, the full time series of the current year

will not be available, or in itself will need to be modeled. Furthermore,

potential outlier or unusual data needs to be scrutinized carefully for

any smoothing methods for fear of imputing additional error into the

time series.

Thus, here only a simple and mild error checking of the data was

employed to help minimize the effects of the typically lower error

values. To do so, each pixel within the time series was compared to

the pixel one composite date prior and one date after. If that middle

value was lower than both, it was deemed to be bad. It was then

corrected by taking the simple average of that prior and subsequent

pixel. The only caveat is the first and last images in each year's time

series were not able to be error checked since they are at the ends of

the time series. But, this is why 34 time steps were downloaded per

year when ultimately only the central 32 would be used for direct analysis. This simple error checking method was sufficient to improve the

data in the vast majority of cases yet not so extreme as to be altering

perfectly good pixels.

Next, the precipitation information was ingested to harmonize with

the MODIS time series data. The native format of the rainfall data was

markedly different from the MODIS since it was stored as vector points.

So, an independent series of steps was taken to prepare the data. First,

the data were grouped by 8-day intervals in the same time windows

as for each of the 8-day MODIS composites and added together to derive

an accumulated 8-day precipitation at each vector point. These 8-day

accumulated precipitation files were each then projected to the

MODIS sinusoidal projection. Finally, the values were interpolated

from vector points to raster-based cells via an inverse distance

weighting methodology. Ultimately, a four km grid (more closely

3706 m) with floating point values of rainfall measured in inches was

a result. An output value of zero meant no rainfall during the 8-day

period. The precipitation output grid was established so that the 1 km

LST and 250 m NDVI data nested perfectly to the four km precipitation

pixels. No temporal error checking or smoothing of the precipitation

data was undertaken.

2.4. Data integration

With the 8-day composited NDVI, daytime and nighttime LST, and

accumulated precipitation information in place alongside the reference

masks, a final step was performed to determine the time series of

county-level averages for both corn and soybeans. In summary, the 32

8-day periods, spanning from mid-February to late October, for each

variable were “stacked” into one file and then intersected, by county,

state, and crop mask for each of the years. Global mean statistics were

then calculated for the pertinent pixels within each county for all of

the 32 time periods. The result was a 32 value long vector containing

county-level averages for NDVI, daytime and nighttime LST, and precipitation over only the corn and soybean areas. So in total, for each county

and for each year 128 variables were derived.

After all the vectors were derived, they were combined and managed into a table in which each row in the database pertained to a particular year and county. A state identifier, county identifier, and year

were affixed. Most important, the NASS published county-level average

yield values (reported in the US customary bushels per acre for units) to

be used as the independent variable were also added to each record.

A few counties did not have any crop pixels to analyze so those were

ultimately dropped. Counties that were shown to have crop pixels but

no corresponding NASS yield were also dropped. Also, Arkansas and

North Dakota counties were not included in the corn dataset since

they were not part of the NASS Objective Yield survey region. Wisconsin

was excluded from the soybeans list for the same reason. The resulting

corn and soybean tables had 4824 and 4693 records, respectively.

3. Results

Having the corn and soybean databases built, simple exploration to

determine what dependencies existed between each variable by date

and the crop yields was undertaken. The Pearson product-moment

correlation coefficient (r) was used for this and the results for the entire

combined Corn Belt region over all of the years are shown in Fig. 2a for

corn and Fig. 2b for soybeans. Both corn and soybeans showed similar

relationships and patterns. For corn the strongest correlations came

positively from NDVI peaking during the first week of August

(r = 0.73). A simple linear regression of NDVI versus yield at that

date gave a R2 = 0.54. An exponential regression was tighter with

an R2 = 0.63. There was a continuous and smooth correlation relationship going forward or backward from that time but it progressively weakened. Inversely, daytime LST showed a good negative

correlation to corn yields. It was also optimized during early August

(r = −0.58) and steadily weakened in both time directions. A

linear regression at the most negative correlation point yielded an

R2 = 0.33 while again an exponential regression was better

with R2 = 0.53. Soybean NDVI and daytime LST peak correlation

responses were a week later and slightly less (r = 0.70, R2 = 0.49

and r = −0.51, R2 = 0.26). The scatterplots during the peak correlation time for NDVI and daytime LST, corn and soybeans, are shown

in Fig. 3a, b, c and d.

Another noticeable, albeit weak feature, was the inverse relationship

of NDVI to yields during spring. There was also some suggestion of

positive spring daytime LST relating to better yields. The nighttime LST

however showed very little correlation to crop yield regardless of the

time of the season or crop but there was possibly some minor suggestion of being consistently negative throughout. Precipitation also

showed little to no relationship with corn or soybean yield and with

equal distribution along the zero line throughout the 32 period time

window.

The corn and soybean datasets were further analyzed for NDVI and

daytime LST correlation coefficient response by dividing them into subgroups. The first stratification was done by state. In summary, each state

had a similar response to the average and varied mainly by degree. Thus,

all state's corn peaked at or around early August with most having r

greater than 0.70. Missouri, Indiana and Ohio were somewhat weaker

with peak r = 0.53, 0.46 and 0.39, respectively. Likewise, the corn

daytime LST relationships by state were all consistently inverse to

yield. Those peak magnitudes were somewhat more widely spread

ranging though and varied from −0.29 (Kansas) to −0.83 (South

Dakota). For soybeans the state responses were also all similar in shape

to the overall average. NDVI in Indiana had the lowest correlation but

was still 0.46. Minnesota was the highest with r = 0.83 and all states

peaked at or around the middle of August. Daytime LST for soybeans

for each states was also consistent and inverted for each state and ranged

more weakly from −0.22 (Nebraska) to −0.64 (Illinois and Missouri).

A second stratification methodology was performed but by year

instead. Like by state, the results showed for both crops that each

stratum followed a similar summer pattern to the combined average,

D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128 121
regardless of year. For corn the NDVI to yield correlation still peaked

mid-summer for all strata on or just around the July 28–August 4th

composite. Year 2011 saw the highest peak correlation with r = 0.81

and 2008 with the lowest equal to 0.64. Also closely consistent

was the inverted response of daytime LST. However, in years 2009

and 2010 daytime LST peaked an 8-day period earlier during the July

20–27th and in 2008 it was a period later than the average. For soybeans

the peaks all occurred in August and most centered with the overall

average. For NDVI the peaks were fairly consistent and ranged from

0.67 for 2008 and 0.77 for 2010. For LST the relationships were also

clustered in August but weaker with 2009 notably lower than the rest

with only −0.24. Overall, the strength and weakness years for soybeans

were the same as that for corn.

4. Discussion

4.1. Yield relationships to remote sensing variables

The positive mid-summer NDVI to yield relationship for both corn

and soybeans was not surprising and expected given past research by

others. The results here simply reinforce the fact and fine tune the

knowledge that early August NDVI is the very best relationship for

understanding corn yields from MODIS NDVI and about a week later is

the optimal time for understanding soybean yields. From the scatterplot

there is suggestion that the values are saturating and the best regression

fit is non-linear. The mild inverse relationship to NDVI shown around

the late April period is perhaps more interesting and new knowledge.

More of an unknown going into this work was the relationship of the

LST variables since most agronomy type research involves simple air

temperature instead of land surface temperatures. Furthermore, the

limited LST research has involved the morning overpass of the MODIS

sensor from the Terra satellite instead of the afternoon overpass of

Aqua which confounds the question. The early afternoon daytime LST

was clearly inversely related mid-summer in this study for corn and

just slightly less for soybeans. This is consistent with agronomy work

that suggests that as temperatures get overly warm plant productivity

begins to suffer, particularly for corn. It was expected that there would

also be found a relationship between the nighttime LST and crop yields

given, albeit anecdotal, information that plants prefer a cooling off

period during the evening. However, nothing of the sort was proven

here. With either the daytime or nighttime temperature case it needs

to be noted that the relationships shown here would not necessarily

reflect what might be found if using more traditional air temperatures

instead. Also, since the LST information is natively at 1 km resolution

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Corn -Correlation Coefficient(r)

8-day composite window dates

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NDVI Precipitation Nighttime LST Daytime LST

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Fig. 2. Corn (a. upper) and soybeans (b. lower) remotely sensed variable correlation by date.

122 D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128
there is a potential that finer resolution data would reduce pixel mixing

of the land cover types and thus further improve the relationships.

The results of the lack of any sort of relationship between precipitation and yields were more surprising and perplexing because it is conventional wisdom that crops need rainfall to thrive. The reasons that

no relationships were found, regardless of time of year, could be

many. First, there are certainly areas, particularly in Nebraska and Kansas, that are heavily reliant on irrigation and thus regardless whether

rain occurs or not the corn and soybean crops can still have adequate

moisture. Second, the NWS rainfall grids are effectively a model of the

rainfall amounts derived from radar reflectivity data and may not in

fact be overly accurate even though they appear reasonable. Third,

it could just be that rainfall during the season is not as helpful to yield

production as it might seem. Perhaps soil moisture is built up over a

longer time period and at sufficient depths that the plants can still

reach and utilize it even during times of minimal rainfall.

Finally, precipitation comes in different severities, types, and duration and likely some are more beneficial than others. For example, a

slow but steady rainfall over a long period like days or weeks may

have better impact on plant health and yields than that from a quick

but intense storm lasting only hours or minutes long. Those strongest

of storms could also result in hail which if large enough outright could

destroy the crop. The accumulated 8-day period was likely not time

specific enough to capture the intensity attribute. On the flipside

it could be speculated that longer accumulation periods are needed to

develop a relationship to yields. This is something that was actually

tested. The precipitation data were explored more intensively by recursively combining the original 32 values by multiples of 2 to further

accumulate the data. In other words, a variety of 16-day, 32-day, 64-day

and 128-day accumulated grids were formed. These types of snapshots

provided something more akin to more commonly used monthly or

seasonal totals. However, regardless of what periodic window was tried,

no better relationships were found.

While the mid-season NDVI and daytime LST relationships are

obviously strongest, the suggestion of a pre-season indicator of crop

yield via the inverse NDVI in late April is particularly compelling. It is

reinforced, even though weak, because it occurs over many dates

which reduces the likelihood that it is just noise. Why this inverse

pre-season relationship exists is not immediately intuitive but an explanation could be that low NDVI tends to occur in damp soils with little

Fig. 3. Relationship between NDVI and daytime LST and crop yield at the point of peak of correlation. NDVI corn (a. upper left), daytime LST corn (b. upper right), NDVI soybeans (c. lower left),

and daytime LST soybeans (d. lower right).

D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128 123
vegetation present and thus those are the areas which will lean toward

having better yields as the season progresses. Likewise, there may also

be a very slight suggestion that warm spring land surface temperatures

are helpful to crop yields. This could possibly be explained by reason

knowing that warm spring temperatures provide earlier and better

planting conditions which should improve the yield outcomes. These

leading season indicators are tantalizing and could be seen as extremely

important predictors for crop yields that potentially could be used, at

least minimally, to nudge yield forecasts up or down from a trend line.

Finally, the stratifying of databases by state and by year was done to

understand if there were dominant dependencies based on geography

within the Corn Belt or certain years. In all cases the individual state

or year levels followed the overall trend of being peaked for NDVI in

early August, and inversed for daytime LST, for corn. Soybeans peaked

a period or two later than but otherwise each state and year followed

the over trends. These results suggest that the NDVI and daytime LST

relationships to crop yield are similar throughout the widespread Corn

Belt area in addition to over each of the six years studied. This ultimately

bolsters the idea that a singular model across time and space integrating

all of the county-level information is appropriate.

4.2. Forecast application of the remote sensing variables

Armed with a better understanding of what variables are correlated

with crop yields, the next objective was to put them into practice for

forecasting. Many types of modeling options exist but in this context it

was decided to use a tool called Rulequest Cubist and allow it to “data

mine” for the best ways relate the historical county-level input variables

to crop yields. Cubist is a machine learning tool which autonomously

derives best fitting piecewise linear models used to predict a continuous

outcome variable (Quinlan, 1993). It has the ability to analyze the

input data for “nearest neighbor” relationships and can run iteratively

multiple times to form ensemble or “committee” models. Furthermore,

it is clever in that is has a built in multi-fold cross-validation ability to

self-test the models it has created. Finally, Cubist also provided output

so a user can assess the rules set for importance of which dependent

variables are used most. Decision tree type models have been used for

remote sensing of agriculture applications but have tended to be toward

crop type mapping (Chang, Hansen, Pittman, Carroll, & DiMiceli, 2007;

Friedl & Brodley, 1997) versus crop yield mapping (Lobell et al., 2005).

Only NDVI and daytime LST were used going forward for modeling

efforts since both nighttime LST and precipitation provided little correlation to yield regardless of the time of season or crop type. However,

the entire time series of NDVI and daytime LST were used even though

it was acknowledged that some dates, particularly early and late in the

season, had likely no value. It was fully anticipated that with more information than from just the single optimal dates, as summarized earlier,

the modeling efforts would improve due to the accumulation of information over the season, but it was not obvious exactly which dates to

include to maximize the information gain. So, a liberal stance was

taken to include all which was bolstered by the knowledge that decision

tree analysis has the inherent ability to ignore, or prune, input data that

is not useful, or might even be harmful, compared to other modeling

methodologies.

By omitting nighttime LST and precipitation, the data tables where

effectively halved in terms of the number of data fields before letting

Cubist assess them. To reiterate, at this point each record contained

variables for state, county, year, along with the seasonal 32 NDVI values

and 32 daytime LST values. Corn and soybeans were run separately.

Since Cubist has a few input parameters for tweaking its models,

many trial-and-error runs of the software were performed in an

attempt to determine its most effective and parsimonious use. Eventually, the method settled upon was letting Cubist use “instances”

while limiting it to a single rule set with a “committee” model of five

iterations. A 10-fold cross-validation was done to assess the model but

this option ignored when the final rule-set model was built.

The county-level yield model results using all of the data gave a selfreported cross-fold validation R2 of 0.93 for both corn and soybeans. The

average absolute error at the county-level was self-reported 0.50 -

metric tons per hectare for corn and 0.17 for soybeans. Interestingly,

allowing Cubist to derive a more sophisticated model with multiple

rules instead of a single one showed little performance gain. Thus the

simplest was used to make the results more interpretable and reduce

the potential for model over-fitting. Using Cubist's instances option instead of rules mode did provide significantly better results. The iterative

committee models also improved the results noticeably. The derived

rules for both the soybean and corn models tended to rely most heavily

on the mid-summer variables for both NDVI and daytime LST. This

is reassuring and expected given that they were known to have the strongest correlations with yields. Some time periods and/or variable types

were not used at all, particularly those early or late in the season. Finally,

some variables were indeed used, such as during the green-up and senescence times, but had a small coefficient in the resulting model so are

viewed more as tweaking the overall results rather than driving it.

The initial Cubist runs incorporated the whole years' worth of data.

However, the corn and soybean models were also tested to understand

the performance when withholding the data available towards year

end. This would mimic the scenario when trying to forecast crop yields

mid-season. So, R2 assessments of the models were calculated by

systematically removing end of year data. Surprisingly, the models still

derived an R2 = 0.93 when only provided with information up through

the middle of August. Subsequent reduction of the end of year data

finally started to impact the models but the decrease in the R2 was not

overly dramatic. For example, in early July the cross-validated R2 for

corn and soybeans 0.90 translating to absolute error averages about

20% greater than with having the full season's information. This ability

to derive reasonable mid-season yields is heartening and suggests that

even without a full years' worth of data there is yet enough information

in the time series data to forecast accurately.

4.3. Validation of forecasting

Cubist's self-assessment tools are useful for understanding the

performance of its models but it is not a true out-of-sample validation.

So, to fully test the implications of the remote sensed corn and soybean

forecasting rules, they were run against the MODIS data collected for

2012 and results compared to the NASS 2012 published county-level

yields. This assessment was undertaken by first downloading the 2012

NDVI data from Terra and daytime LST data from Aqua and managed

in the exact same manner as for the 2006–2011datasets. Likewise, the

2012 CDL data were also gathered and processed to create the corn

and soybean masks and then were used to extract the county-level

NDVI and daytime LST averages for 2012.

Next, an executable, called Cubistsam.exe provided with the

Cubist software, was run to easily implement the previously derived,

full-season rules against the new predictor data. The final result was

an estimated yield for each county based solely on the MODIS data. Of

note, several 2012 images early and late in the season were very noisy

beyond what could be error checked and thus were excluded as

the model inputs. They were the first eight NDVI and last three NDVI

periods and the first ten and last three daytime LSTs. Effectively

what was left was the data spanning the middle of May through early

October. Also, all modeling work here was completed prior to the official

release of those numbers so as to avoid retrospect altering of the model

to, perhaps, tune results.

Fig. 4a shows the relationship between the modeled yields for corn

and what NASS ultimately published. Each point represents a county

in the Corn Belt region. Fig. 4b shows the same for soybeans. For corn

the relationship between the county-level predicted and published

years gave a good R2 = 0.77 and a root-mean-square error (RMSE) of

1.26 metric tons per hectare. The linear regression relationship was

y = 0.96x + 0.27. Because the slope was close to one there not much

124 D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128
suggestion of bias to the estimates dependent on the magnitude of yield.

However, there is some visual evidence by way of increased scatter that

the model is less accurate on the low yielding counties. The soybean

results were also good but not as strong as for corn. The soybean

regression gave an R2 = 0.71, RMSE = 0.42 metric tons per hectare,

and a linear model equation of y = 0.81x + 0.48. The slope was not

as close one as hoped and showed that remote sensing tended to

underestimate on the low end and overestimate on the high. Because

the R2 is lower than it was for corn the soybean model is not as precise

overall.

It was expected for both crops that the modeled results would have a

tighter relationship to the final NASS yield given the self-reported R2

performance of Cubist at 0.93. Three explanations to the decrease are

hypothesized. The first, and perhaps the most obvious, is that Cubist is

simply overestimating how powerful it is. The program is ultimately

proprietary and complicated and it is not externally obvious how it

is constructing its results. However, even if it is indeed overstating its

usefulness it is still believed valid to use comparative results to understand the utility of different models' parameters and input variables.

Secondly, it is recognized that the time series of input data variables

which are input into Cubist are not purely independent. For example,

NDVI from successive time period is usually similar and one would be

a good predictor for a previous or successor value because it usually

does not vary much from one 8-day period to the next. And in addition

to the temporal autocorrelation there are likely spatial autocorrelation

effects too. This overall lack of date independence is usually considered

a violation of purely statistical type modeling and may be coming into

play here as well.

Finally, and perhaps most importantly, 2012 turned out to be an

outlier year in terms of US weather in the Corn Belt where the bulk of

crop production exists. The area underwent what was considered the

biggest agricultural drought since at least 1988 due to unusually

prolonged heat and dryness which occurred directly in the middle of

the summer. Final yields for corn were far under trend expectations

across the region and most depressed in non-irrigated southern and

western parts of the Corn Belt region. On average they were down

about 16% from 2011 and 25% from the record high set in 2009 — this

when usual year to year yield variability tends to be less than 10%.

Ultimately, corn yields were the lowest since 1995 which is remarkable

considering the improved seed varieties and planting and management

techniques that have progressed since. Soybean yields were also negatively impacted in 2012 although to a lesser extent since they are

more heat tolerant to begin with and late season rains helped spare

the crop. They were down over 5% from 2011 and 10% from the record

high set in 2009. Still 2012 was the lowest soybean yield since 2003.

So, both the corn and soybean models here having been derived from

relatively good to excellent 2006–2011 data had to extrapolate to a

certain extent its results for 2012. It is believed that any modeling

efforts which purely relied on contemporary datasets like this would

have struggled to properly predict 2012 values given that they were

unusually low on average.

A second, albeit subjective, validation was also performed to understand the utility of the remote sensing estimates. It was done by creating

2012 yield maps at the 250 m MODIS resolution. Fig. 5a shows the studied corn states and Fig. 5b the soybeans. They were created in ERDAS

Imagine by calculating for each pixel a yield from the final decision

tree model equation against the time series of the 2012 MODIS data.

The original 30 m resolution 2012 CDLs were also integrated to better

mask cartographically the pertinent field areas for each crop. The map

results were particularly interesting because they begin to show

the spatial heterogeneity that occurs even across a county. At the finest

scale and in the most homogeneous of pixels one can attempt to

estimate a field-level yield. Unfortunately, no field-level in situ information is known to be widely available in order to fully understand the

accuracy of the maps. However, the patterns look reasonable and certainly highlight the known lower yielding areas, particularly those toward

the south and west. The maps also reinforce the irrigated areas common

throughout Nebraska which ultimately maintained good yields in 2012.

A final assessment of the practicality of the model was to recursively

perform hindcasting for each of the years 2006–2011. In other words

2006–2010 and 2012 were used to predict for 2011, then 2006–2009

and 2011–2012 to predict for 2010, then 2006–2008 and 2010–2012

to predict for 2009, and so on for each of the individual years back to

2006. This is hypothetical because one would never have future

data to predict for the current but it does allow for more out-ofsample validation trials to help increase the understanding of the

model performance. It also provides evidence of the model accuracy

beyond trying to predict for the anomalous 2012 drought year.

y = 0.9623x + 0.2691

R2 = 0.7737

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Fig. 4. 2012 corn (a. upper) and soybeans (b. lower) county-level remote sensing forecasted

yields versus NASS published.

D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128 125
Results showing RMSE (metric tons per hectare), R2

, model regression line slope and intercept (again, metric tons per hectare) for each of

the scenarios are shown in Table 1. For corn the best R2 was for the year

2012 but RMSE was tied for worst in 2012, along with 2007. Overall, no

years for corn were shown to be a real under or over outlier in terms

model performance. A notable consistency though was the model

slope always being less than one. This suggests that the model is always

prone to underestimating on the low end and/or overestimating on the

high. For soybeans the overall results and implications were similar

with slopes also always less than one. RMSE and R2 were also fairly

stable across analysis years for soybeans although 2008 only had an R2

of 0.47. Its RMSE of 0.41 was relatively average though so in general

not of much concern. In terms of an average coefficient of determination

the corn models outperformed the soybean models with R2 = 0.70

versus 0.65. Average model slope was closer to one for corn as well

(0.83 versus 0.77). In summary, the hindcasting results reinforce

that the modeling efforts are strong for both crops but with corn being

somewhat more robust.

4.4. Modeling for 2013

With the 2012 data now in hand, it was deemed constructive to test

the overall models by including it into the pool of 2006–2011 data. It

was believed that having the preponderance of low 2012 data points

should only help for future forecasting efforts. Indeed once added,

correlations to yields for the 2006–2012 increased the NDVI and

daytime LST relationships further. For corn the NDVI peak correlation

r was still found to be the first week of August and increased to 0.78

from 0.73. The inverted peak daytime LST relationship increased to an

r of −0.60 from −0.58. Similarly the updated soybean relationship

also increased with r = 0.73, from 0.70, for middle August NDVI and

−0.56 from −0.51 for the same date daytime LST. Additionally, the

modest pre-season inverse NDVI relationship strengthened for both

crops going from −0.33 to −0.39 for corn and −0.29 to −0.34 for soybeans. But, any early season positive daytime LST to yield relationship

became even weaker and thus it is truly not believed to be useful as

a yield predictor for either crop. Finally, updating of the Cubist rules to

include the 2012 data showed the self-reported full-season R2 to

increase to 0.95 for corn and 0.94 for soybeans. It was 0.93 for

both previously. Since 2012 was an unusually low year for yields, the

inclusion of that data has now resulted in even stronger models for

the future.

5. Conclusions

In summary, this work was undertaken to substantiate the use of

four timely and spatially detailed remotely sensed datasets for inclusion

into county-level corn and soybean yield forecasting models for use

across the US Corn Belt. Those datasets tested were NDVI, daytime LST

and nighttime LST as collected from the space-borne MODIS sensors

and precipitation as derived from the ground-based NWS Nexrad

weather monitoring system. All datasets were assessed as 8-day

composited products chosen as a compromise between data processing

simplicity and retention of sufficient temporal detail. A large and robust

cross-sectional panel of county-level data from NASS spanning the years

2006 through 2011 was used to verify the explanatory power throughout the spring and summer of each input dataset. Detailed land cover

information helped isolate within the datasets the corn and soybean

areas.

NDVI was found to be strongly and positively correlated with both

corn and soybean yields throughout the summer and most dramatically

in early August. Also, and unexpectedly, there was a suggestion that

early season NDVI is negatively correlated to crop yields, albeit weakly.

Daytime LST strongly mirrored NDVI and was found to be negatively

correlated with yields for both crops throughout the summer season

and peaking in early to mid-August. Nighttime LST and precipitation

were also investigated but showed to have no correlation to corn or

soybean yields regardless of the seasonality. Not finding a precipitation

to yield relationship was particularly surprising.

Using the full time series of NDVI and daytime LST variables for

inclusion into a decision rule-based predictive model gave very good

results (R2 = 0.93) for both corn and soybeans as ascertained through

the self-reported, cross-validation diagnostics of Cubist software.

Dates of the strongest correlation in August were shown to most heavily

used by the models as expected. Removal of data from mid-August and

later degraded the model little suggesting that yield forecasting results

in early August are nearly as robust as would be after the season has

completed. Furthermore, forecasts even earlier in the season are possible with model precision dropping steadily into the spring to where

the error is about double. This may still be useful in certain applications.

Out-of-sample validation of the model with a full season's worth of

2012 NDVI and daytime LST remote sensing input data against the

2012 published county estimates was calculated and showed corn

performing good with an R2 = 0.77 and soybeans, somewhat less so,

with an R2 = 0.71. These correlations were lower than was suggested

by model cross validation but 2012 turned out to be an anomalous

Fig. 5. Corn (a. upper) and soybean (b. lower) remotely sensed pixel-level forecast yield map.

126 D.M. Johnson / Remote Sensing of Environment 141 (2014) 116–128
yield year in which to forecast for due to a large and deep drought which

lowered yields, some dramatically, across most of the study region.

Thus, much of the model error may have been a result of trying to

predict what would eventually become outlier events. Hindcasting the

individual years 2006–2011 showed similar results to that of 2012. All

the results taken together show the modeling efforts to be robust for

both crops but with corn performing somewhat better on average.

While the focus on this paper has been the forecasting of countylevel corn and soybean yields, the ability to derive broader estimates

at the state- and national-level was also a strong motivation for

this work. Those results were not shown but were indeed constructed

by weighting each county by typical harvested area statistic to come

up with a state and then regional estimate. Those estimates ultimately

corresponded with even greater accuracy against the official 2012

NASS estimates. Finally and perhaps most importantly, was the strong

desire to derive timely and objective early and mid-season yield

estimates at these state- and national-levels. The Cubist modeling

methodology employed appears flexible and robust even when a full

season's worth of data is not yet available for input.

Moving forward, Collect 6 version of the MODIS data archive is

currently under construction and should provide the final and most

revised history for the dataset. It is said to be modestly improved in

terms of data precision and stability over time (Wang et al., 2012) and

thus hoped to fine tune the crop yield modeling further when released.

In the end, after both MODIS sensors are finally retired, this type of work

will undoubtedly transition to VIIRS. Exploration of that dataset

will need to be undertaken when a reasonable history of data has

been collected. The good LST relationships found from Aqua MODIS

should be bolstered by the fact that the VIIRS instruments will also

be in afternoon orbits. Analogous NDVI work utilizing the Aqua sensor

instead of only Terra should also be tested before VIIRS is deemed operational to better understand if it shows markedly different results.

Conversely, Terra LST could also be analyzed, for completeness, but

since there is no future morning LST sensor there is little incentive to test.

Finally, this work focused only on corn and soybeans as grown in the

Corn Belt region of the US and it was predicated on having detailed crop

specific land cover information in which to best isolate the relevant

areas from the input remote sensing datasets. In most settings this information does not exist with the same spatial detail or timeliness. However, anecdotal testing here suggests that using more generalized masks

for cropland cover (Johnson, 2013) can still be effective for modeling

corn and soybean yields although the model precision does decrease.

Also, and regardless of the detail of land cover information available, it

is not directly evident whether the results found here can be assumed

to work or extrapolated to other crops or areas. But given the clear

seasonal relationship of both corn and soybeans to NDVI and daytime

LST it is believed that, minimally, functionally related crops in similar

style growing regimes should indeed respond similarly.

Acknowledgments

The MODIS MOD09Q1 and MYD11A2 data were obtained through

the online Data Pool at the NASA Land Processes Distributed Active

Archive Center (LP DAAC), USGS/Earth Resources Observation and

Science (EROS) Center, Sioux Falls, South Dakota (https://lpdaac.usgs.

gov/get_data). The precipitation data were obtained through the National Oceanic and Atmospheric Administration's, National Weather Service,

Advanced Hydrologic Prediction Service, Silver Spring, Maryland (http://

water.weather.gov/precip/download). The NASS CDL land cover classifications were available through CropScape (http://nassgeodata.gmu.edu/

CropScape). Historical county-level corn and soybean yield information

was obtained via USDA/NASS, Quick Stats (http://www.nass.usda.gov/

Quick_Stats).

Software used for the data analysis included ArcGIS (Environmental

Systems Research Institute 2011, ArcGIS Desktop: Release 10. Redlands,

CA. http://www.esri.com), ERDAS Imagine (Intergraph Corporation part

of Hexagon 2011, ERDAS Imagine versions 9.1 and 2011. Huntsville, AL.

http://geospatial.intergraph.com/), R (R Development Core Team 2010,

R version 2.12.1. Vienna, Austria. http://www.R-project.org/) and Cubist

(Rulequest 2012, Cubist version 2.08. St. Ives, NSW, Australia. http://

www.rulequest.com). All are copyrighted. The MODIS Reprojection

Tool was also used (NASA, MRT version 4.0 and 4.1., LP DAAC, https://

lpdaac.usgs.gov/tools/modis_reprojection_tool). The use of any or all

of these software tools here does not constitute an endorsement for or

against.

Thank you to coworker Karla Koudelka, mathematical statistician,

for assessing and providing further suggestions to the methodology,

double checking of the datasets and substantive review of this manuscript. Thanks to other peers, particularly Richard Mueller, within the

NASS Spatial Analysis Research Section whom also provided lengthy

comments, feedback and suggestions. And finally, thanks to Varun

Kshirsagar, economist and friend, for providing the initial suggestion

of using multi-year county-level data to vastly increase the sample

size and thus modeling robustness.

Note

Since the initial submission of this manuscript, soybean yield values

were adjusted by NASS for the 2011 crop season. The average countylevel change was up fractionally by 0.02 metric tons per hectare, or

less than 1%. The analysis was rerun using the updated 2011 numbers

but found to be insignificant on the results so the initial 2006–2011

dataset was kept as the basis for this work. NASS corn yield estimates

did not change.

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