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CL/tD7w/ 

• A) *7 


Department of 
Agriculture 

National 

Agricultural 

Statistics 

Service 


THE USE 
O F 

METEOROLOGICAL 
SATELLITE DATA 


Research and I N 

Applications 

Division ASSESSING CROP 


NASS Staff Report 
Number SRB-89-09 

August 1989 


CONDITION 

Wendell Wilson 


// 


ceived By: 
Indexing BrsWb 






/ -r- s 

Lxhe use of meteorological satellite data in assessing crop 

CONDITION by Wendell Wilson, Research and Applications Division, CNational 
Agricultural Statistics Service, U.S. Department of Agriculture,! NASS Staff Report No. 
SRB 89-09 . 


ABSTRACT 

In this pilot level research study, relationships between crop condition and polar orbiting 
meteorological satellite data were investigated for the 1984 com and soybean crops. The 
1984 forecasts and final estimates of com for grain and soybean yield per harvested acre 
were used as State level measures of crop condition. Regression analyses were employed 
to understand the State level relationships of a crop’s yield to its satellite vegetative index 
for ten States. The ten States are North Dakota, South Dakota, Minnesota, Iowa, Illinois, 
Indiana, Ohio, Kentucky, and Tennessee. Linear regression relationships for com and 
soybeans existed at the State level, with coefficients of determination (R 2 ’s) of .94 and .85 
for final yield, respectively. This methodology was applied during the 1988 crop season, 
under drought conditions. The indices were strongly correlated to the official Agricultural 
Statistics Board estimates throughout the com and soybean forecast season for 1988. 


KEY WORDS 

Meteorological satellite data, vegetative indices, crop conditions. 


Mr. Wilson took a position outside the Department of Agriculture when this paper was at a 
draft stage and hence the paper was not subject to the standard peer review process. The 
content of the draft has not been intentionally altered but the body (not the appendices) has 
been edited for brevity by Bruce Eklund and George Hanuschak. The report represents 
several years of extensive research effort by Mr. Wilson and thus is being documented. 
This paper is for limited distribution outside the U.S. Department of Agriculture. The 
views expressed herein are not necessarily those of the Agency (NASS), or the Department 
(USDA). 


ACKNOWLEDGEMENTS 

The author would like to acknowledge NASS research management for their support. The 
Meteorological Satellite data was provided by Bobby Spiers and Carl Gemazio of USDA’s 
Foreign Agricultural Service which was instrumental for this pilot research effort. 


l 


TABLE OF CONTENTS 


PAGE 

SUMMARY . vi 

INTRODUCTION. 1 

SOURCE AND DESCRIPTION OF DATA . 2 

Two Primary Data Types . 2 

Satellite Data . 2 

Agricultural Data. 3 

Other Data Sources . 3 

Data Variables Summary. 4 

OVERVIEW OF APPROACH USED . 4 

Overview Diagram. 4 

Utilize Options. 11 

The Study Area . 12 

RESULTS AT THE STATE, COUNTY, AND CROP REPORTING 
DISTRICT LEVEL . 14 

State Level Relationships. 14 

Agricultural Statistics Districts Satellite Generated Yield Results .... 14 

County Level Results. 20 

A More Thorough Examination Using Additional Performance 

Measures. 25 

Additional Performance Measures Summary. 28 

SOME COMMENTS ON ACCURACY AND USE OF THE DATA. 30 

A Closer Look at Satellite Generated County Com 

Yield Indications. 30 

Results Obtained by Applying the Irrigation Rule . 31 

CONCLUSIONS . 34 

RECOMMENDATIONS. 35 


ii 

























TABLE OF CONTENTS (CONTINUED) 


PAGE 


APPENDIX A 

Cloud Screening Bias Study. 37 

APPENDIX B 

Selection of Critical Periods with Satellite Vegetative 

Indexes Strongly Related to Com and Soybean Yields . 46 

APPENDIX C 

Statistical Analysis System Regression Output for Com and 

Soybean Models Based on EVI and NVI Vegetative Index Versions 

and Yield Versus NVI Plots. 67 

APPENDIX D 

Study Area and Individual State Performance Tables for Results 

at Various Levels for Com for Grain and Soybeans, and at the 

County Level for Com when Some Counties are Excluded by an 

Objective Rule or by Deletion of Obvious Outliers . 74 








LIST OF FIGURES 


PAGE, 

Figures 

Figure 1A Overview of Approach Used (Steps 1-4) . 5 

Figure IB Overview of Approach Used (Steps 5-7) . 9 

Figure 2 The Study Area with Grid Cell Centers. 13 

Figure 3 Com - State Level Yield vs Vegetative (EVI) Index. 15 

Figure 4 Soybean - State Level Yield vs Vegetative (EVI) Index. 16 

Figure 5 Com - District Yield vs Vegetative Index . 17 

Figure 6 Soybean - District Yield vs Vegetative Index . 18 

Figure 7 Com - County Yield vs Vegetative Index . 21 

Figure 8 Soybean - County Yield vs Vegetative Index . 22 

Figure 9 Residual of State Level Regression for Com. 23 

Figure 10 Residual of State Level Regression for Soybeans. 24 

Figure 11 Plot of County Level Com Yield vs Satellite Generated Estimates . . 29 

Figure 12 Plot of County Level Com Yield vs Satellite Generated Estimates 

with Outliers Excluded . 33 

Figure A-l Vegetative Index vs % of Good Pixels July 31 - August 23. 40 

Figure A-2 Modified Vegetative Index vs Good Pixels July 31 - August 23 . . . 41 

Figure A-3 Vegetative Index vs Good Pixels July 31 - September 1 . 42 

Figure A-4 Modified Vegetative Index vs Good Pixels July 31 - September 1 . . 43 

Figure B-l North Dakota Greenness Curves. 49 

Figure B-2 South Dakota Greenness Curves. 50 

Figure B-3 Minnesota Greenness Curves. 51 

Figure B-4 Iowa Greenness Curves. 52 

Figure B-5 Missouri Greenness Curves. 53 

Figure B-6 Illinois Greenness Curves. 54 

Figure B-7 Indiana Greenness Curves . 55 

Figure B-8 Ohio Greenness Curves. 56 

Figure B-9 Kentucky Greenness Curves . 57 

Figure B-10 Tennessee Greenness Curves. 58 

Figure B-ll Coefficient of Determination for Com Yield vs Vegetative 

Indexes for Short Periods. 62 

Figure B-l2 Coefficient of Determination for Com Yield vs Vegetative 

Indexes for Longer Periods. 63 

Figure B-13 Coefficient of Determination for Soybean Yield vs Vegetative 

Indexes for Short Period . 64 

Figure B-14 Coefficient of Determination for Soybean Yield vs Vegetative 

Indexes for Longer Periods. 65 

Figure C-l Com - State Level Yield vs Vegetative (NVI) Index. 70 

Figure C-2 Soybeans - State Level Yield vs Vegetative (NVI) Index. 71 


tv 

































LIST OF TABLES AND EXHIBITS 


PACE 

Tables 

Table 1 Relationships between Yields and Vegetative Indices . 25 

Table 2 Relationships between Yields and Vegetative Indices in Detail .... 27 

Table 3 Proportion of Com Acreage Irrigated in Outlier Counties. 31 

Table 4 Effects of Excluding Highly Irrigated Counties . 32 

Table A-l Coefficient of Determination for Certain Periods with Modified 

Vegetative Indexes as the Regressor. 45 

Table B-l Coefficient of Determination for Certain Periods with Modified 

Vegetative Indexes as the Regressor. 59 

Table B-2 Comparison of Coefficient of Determination between Vegetative 

Indices Weighted by Crop Reporting Districts and Counties. 66 

Table D-l Performance of Generated Estimates for Com. 75 

Table D-2 Performance of Generated Estimates for Soybeans . 76 

Table D-3 Performance of Generated Estimates for Com with Some 

Counties Excluded . 77 

Exhibits 

Exhibit C-l SAS Output for Regression of Com Yield on Vegetative Index 

(EVI) . 68 

Exhibit C-2 SAS Output for Regression of Soybean Yield on Vegetative Index 

(EVI) . 69 

Exhibit C-3 SAS Output for Regression of Com Yield on Vegetative Index 

(NVI) . 72 

Exhibit C-4 SAS Output for Regression of Soybean Yield on Vegetative Index 

(NVI) . 73 


v 















SUMMARY 


In this pilot level research study, relationships between crop condition and polar orbiting 
meteorological satellite data were investigated for the 1984 com and soybean crops. The 1984 
forecasts and final estimates of com for grain and soybean yield per harvested acre were used 
as State level measures of crop condition. NOAA-7 satellite data vegetative indexes were first 
aggregated to grid cells, averaged over time, weighted to counties and weighted by crop 
specific acreage weights to the State level. They were then used as the appropriate aggregate 
satellite derived crop condition index. Regression analyses were employed to understand the 
State level relationships of a crop’s yield to its satellite vegetative index for ten States. The 
ten States are North Dakota, South Dakota, Minnesota, Iowa, Illinois, Indiana, Ohio, Kentucky, 
and Tennessee. Linear regression relationships for com and soybeans existed at the State 
level, with coefficients of determination (R 2 ’s) of .94 and .85 for fincil yield, respectively. 

State level relationships were applied in generating county yield estimates to illustrate one of 
the applications possible from such a within-year study. Relationships with official county 
yields showed some decline from those at the State level. However, R 2 ’s were still .63 for 
com and .64 for soybeans with a relative standard deviation for both crops of about 16 
percent. By eliminating 31 of the 889 counties with a substantial proportion of their com 
irrigated, the com R 2 increased to .69 and the relative standard deviation dropped to 14.5 
percent. 

This methodology was applied during the 1988 crop season, under drought conditions. The 
indices were strongly correlated to the official Agricultural Statistics Board estimates 
throughout the com and soybean forecast season for 1988. The following maps demonstrate 
some of the input and output products for this study. 


vi 


VIN(Satellite Data) from July 28, 1988 



Vll 



































1984 SOYBEAN SATELLITE YIELDS 



U 

c 

CO 


C/> 


■ mmm 

o 



viii 


Yield Ranges (bushels) less than 29 29 to 34 I more than 34 

» / _ 62u2uiS£ui3 milrofimilSml 














THE USE OF METEOROLOGICAL SATELLITE DATA 
IN ASSESSING CROP CONDITION 
BY 

WENDELL W. WILSON 
INTRODUCTION 


This report will discuss research on the use of polar orbiting meteorological satellite data in 
assessing crop condition. In this report you will learn what is being done and hopefully, gain 
some appreciation for the potential of further research in this area and for applications arising 
from it. 

Estimates of com and soybean yields are produced at the State, agricultural statistics district 
and county levels for the ten State study area. The contiguous study area includes North 
Dakota, South Dakota, Minnesota, Iowa, Missouri, Illinois, Indiana, Ohio, Kentucky, and 
Tennessee. Data was examined for only a single year, in this case 1984. There are several 
reasons for restricting the study to a within-year approach. The primary reason is that, since 
the satellite platform and sensor configurations change fairly often, one would lack comparable 
satellite data for pooling over very many years. Other reasons involve the possibility of sensor 
calibration drift (even if the same sensor and platform are available) and the changing crop 
situation in different years. Even though some crop situation factors will vary between States 
within a given year, it is thought that maturity stage, mix of crop types, and various other 
factors may vary more substantially from year to year. 

Using a within-year approach does, however, impose certain limitations. There is no 
satisfactory method of using data from a single year to predict yields in another year. 
Innovative methods must be used within the year studied to produce other useful products. 
Some of these may provide improved local crop condition information of indirect use in 
producing improved current year crop yield forecasts and estimates. The application discussed 
in this report involves the use of State level yield to satellite data relationships in generating 
agricultural statistics district and county level yield estimate indications. 

Even though the current study is restricted to within a single year, it does not mean all hope 
of over-the-years analysis has been abandoned. Eventually, more years will exist with 
comparable satellite data. The frequent platfonn and sensor changes being experienced are, 
of course, designed to lead to superior vegetation monitoring. And, the current studies strong 
within-year relationships over States, portends the strong possibility of useful relationships over 
years for individual States or groups of States. 

A number of topics will be covered extensively in this report. They include the source and 
description of the data, an overview of the approach used, results at the State, county, and 
agricultural statistics district levels, and some observations on the use and accuracy of the 
county yield indications. The report also contains conclusion and recommendation sections, 
and a set of related appendices. 


SOURCE AND DESCRIPTION OF DATA 
Two Primary Types of Data 


This study primarily utilizes two types of data. One consists of data from the United States 
Department of Commerce, National Oceanic and Atmospheric Association (USDC/NOAA) 
polar orbiting satellite. The other consists of United States Department of Agriculture, 
National Agricultural Statistics Service (USDA/NASS) crop yield and acreage statistics. 


Satellite Data 

Satellite data used in this study was obtained by the NOAA-7 polar orbiting satellite. Because 
of the satellite’s orbit and sensor characteristics it senses a wide swath of the earth’s surface. 
Such a wide swath is associated with two important results. While it allows the satellite to 
image the same area twice a day (once in darkness, once in light), it requires that the spatial 
resolution be quite gross in comparison to other polar orbiters (notably the Landsat satellite). 
While the Landsat "sees" the same area on the earth’s surface every 16 days compared to once 
a day (in daylight, clouds permitting for both satellites), NOAA-7 can only spatially resolve 
1.1 kilometers (1100 meters) at nadir compared to about 60 meters for Landsat. The 
difference in spacial resolution translates into a picture element (pixel) size of about an acre 
for Landsat and around 300 acres for the polar orbiting meteorological satellites. So, the 
temporal resolution of the meteorological satellite offers improved opportunity to monitor such 
dynamic phenomena as crop condition, but the lack of spatial resolution means that monitoring 
can not be done for specific crops. There is no way that the NOAA satellites can "look at" 
individual com and soybean fields in this study area. 

The sensor used in this study (one of many on the spacecraft) is the Advanced Very High 
Resolution Radiometer (AVHRR). The NOAA-7 was equipped with the AVHRR/2 which has 
five channels in which visible or infrared imagery is sensed. Channel 1 (visible) and channel 
2 (near infrared) are used in computing the vegetative indexes used in this study, while some 
of the other channels are used to screen out imagery values effected by clouds. Channel 1 
is sensitive in the .55-.68 micron range and channel 2 goes from .72 to 1.00 microns. 

As part of Joint Remote Sensing Activities in the U.S. Department of Agriculture the Foreign 
Agricultural Service (USDA/FAS) has provided data to USDA/NASS to support this study. 
FAS receives ordered meteorological satellite data from USDC/NOAA and processes it. The 
FAS Image System (FASIS) is used to screen out satellite pixels that are either cloud covered 
or over water or have unacceptable reflectance values or that the algorithm eliminates for a 
number of other reasons. The (FASIS) grid cell summary program groups the data by 
geographically defined grid cells and computes summary statistics for each of them. Each grid 
cell, defined by a jth "row" and ith "column" location, is a 25 x 25 nautical mile square or 
about 28 3/4 statue miles on a side. The approximate center of each grid cell in longitude 
and latitude coordinates is available for each grid cell. The data reduction accomplished by 
USDA/FAS processing is of the order of about 1700 pixels to one grid cell for grid cells near 
nadir. A somewhat smaller data reduction for grid cells away from nadir occurs. 


2 


The grid cell summary program provides the percentage of potential pixels in a grid cell’s area 
that are not screened out (% good), the proportion of good pixels that have vegetative indexes 
above the soil line (% green) and two grid cell vegetative index means. One of the vegetative 
indexes, the environmental vegetation index, (EVI), is the mean channel 2 value minus the 
mean channel 1 value for all good and green pixels within the grid cell. The other vegetative 
index is the so called "normalized" vegetative index (NVI). It is obtained by dividing EVI 
by the sum of the channel 1 and channel 2 means for the same set of pixels. Both of these 
vegetative indexes were explored in this study. Attempts were also made to create and use 
EVI’s and NVI’s adjusted to a 100% good "equivalent" based on a weak but positive 
relationship between the indexes and percent good. This study of the tendency of vegetative 
indexes to be biased lower when more cloud pixels are screened out (possibly because of 
cloud shadow or thin cloud effected pixels that remain) is reported in Appendix A. 

Agricultural Data 

The other primary type of data is in many respects the most important to this study. 
USDA/NASS State level yield estimates are used to calibrate the satellite data. These State 
level yield estimates (or forecasts, if they are used) are the product of indications from a 
collection of independent survey indications (see Scope and Methods) and the expert panel 
provided through the county estimates of acreage harvested for com for grain and soybeans 
at the county level for the previous year are used to weight the vegetative index means for 
counties to the State level. They are used in order to produce a State com vegetative index 
(when weighted by acres of com harvested for grain) and a soybean vegetative index (when 
weighted by acres harvested for soybeans). While these acreages for the study year (1984) 
would be the correct ones for reflecting that year’s actual county by county distribution of the 
crops, they would not be known until county estimates are made following the crop year. 
Therefore, the 1983 county acreage estimates are used to obtain crop specific vegetative 
indexes for the individual States. 


Other Data Sources 

County yield estimates for 1984 were of course, not used in the primary analysis. However, 
after satellite yield estimates were independently generated, the official USDA/NASS SSO 
county estimates were used retrospectively to evaluate the generated estimates’ estimated 
accuracy and potential use as an additional indication for making the county estimates. 
Another source was the U.S. Department of Interior, U.S. Geological Survey (USDI/USGS). 
They provided the approximate longitude and latitude coordinates for county centers. After 
their data was supplemented with USDA/NASS point estimates and edited, the locations were 
used in weighing grid cell vegetative indexes to produce county mean indexes based on the 
distance between each county center and the surrounding grid cell centers. The 1982 Census 
of Agriculture, from the U.S. Department of Commerce, Bureau of the Census (USDC/BOC), 
was used to identify counties which irrigate a large proportion of their com crop. This 
information was helpful in evaluating the situations in which satellite generated com yield 
indications would be of limited use. 


3 


Data Variables Summary 


To summarize the source and data variables used, primary and secondary variables are listed 
below. Secondary variables are those not used in the primary analysis. 


Source 

Primary 

Secondary 

USDC/NOAA 

NOAA-7 Satellite 

Channel 1&2 Values 

Values from other 
NOAA-7 channels 

US DA/FAS 

Grid cell vegetative 
indexes (EVI & NVI), 
latitude and longitude 

Grid cell % good, and % 
green 

USDA/NASS- 

ASB 

Final 1984 com for 
grain and soybean 
yield estimates for 

10 States 

August 1, September 1, 
October 1, and Novem¬ 
ber 1, 1984 yield fore¬ 
casts for the 10 States 

USDA/NASS- 

SSO’S 

1983 County estimates 
of acreage harvested 
for com for grain 
and soybeans 

1984 county estimates of 
com for grain and soy¬ 
bean yields per harvested 
acre 

USDI/USGS 

County center latitude 
and longitude 


USDC/BOC 


1982 Census of Agri- 


culture county estimates 
of number of farms and 
acres of total and 
irrigated com harvested 
for grain 


OVERVIEW OF THE APPROACH USED 
Overview Diagram 

Figure 1 is an overview diagram of the approach used in the primary analysis. Each step 
shown in the figure has a number, a brief description of what is being done, a description of 
the product at the end of that step and some symbolic notation. Each of the steps will be 
discussed rather thoroughly in this section. Topics involving analysis and selection of 
alternative procedures will be discussed briefly in this section and/or included in an appendix. 


4 





Figure 1A 

Overview of the Approach Used 
In the Primary Analysis 


Step 1 


Start 

with 

US DA/FAS 

Grid Cell Vegetative 

Index Means 

v ., 


Step 2 


Average 
for Critical 

Time Period 

Grid Cell Vegetative 

Index Period (may vary 
by crop) Means 

V, 


Step 3 


Map to 

County Level 

County Vegetative 

Index (may vary by crop) 

^mn -> (to Step 7) 


Step 4 


Create Crop 

Specific Weighted 

Average at State 

Level 

State 

Com _ 

Vegetative VC.„ 

Index 

State 

Soybean _ 

Vegetative VS. n 

Index 


(To Step 6) 


5 


Step 1 


In Step 1 the approach used starts with the USDA/FAS grid cell vegetative index means. 
In this study the use of both the EV1 and NVI indexes was explored. The symbol, V ijt , 
represents either index for a grid cell in the ith "column" and the jth "row" (see Figure 2 for 
coordinate system) that was derived from imagery obtained on day t. In the summer of 1984 
grid cell values were computed and retained by USDA/FAS for each day that the number of 
good pixels (% good) exceeded 50 percent. Therefore, values do not exist for days with 
complete or substantial cloud cover, but were usually available for clear or partly cloudy 
days. 


Step 2 

Step 2 involves obtaining the average vegetative index for a critical time period. The analysis 
that lead to the selection of critical periods for both crops is described more completely in 
Appendix B. 

Critical period selection basically involved two complementary methods. One method was to 
observe the seasonal pattern of grid cell vegetative indexes. It was desirable to identify a 
plateau in the index values. The plateau would occur after a period of "greening up" or 
perhaps following some "greenness" associated with pre-ripe small grain crops, but prior to 
the decline in "greenness" that accompanies fall and crop maturity. Such a plateau would 
provide observations on multiple dates when crop condition could be considered nearly stable. 
This would allow means to be created over the period which would mitigate some of the 
"noise" in the daily values. 

The other method involved testing the relationships of yields to average vegetative indexes 
over various length periods at the State level. The candidate period identified by the pattern 
of "greenness" analysis was broken down into cycles of approximately equal potential coverage 
of the entire study area. Each cycle’s (about eight days long) relationship to yield (forecasts 
for various dates and final estimates of each crop) was evaluated. Then, since a single cycle 
might have little or no data for some areas, and could provide unrepresentative data at the 
State level, adjoining cycles were combined and evaluated. Continuing in this manner, more 
adjoining cycles of coverage were combined until several very competitive periods were 
identified. These periods were made up of individual cycles, all of which had fairly strong 
relationships to the crop yield forecasts or estimates, and which when combined in groups of 
two achieved higher relationships as a result of more complete and representative State 
coverage. These periods were generally consistent with the "greenness" pattern method; 
however, some compromises were made by including a few observations near the end of small 
grains "greenness" or from the early stages of crop maturity. The average grid cell vegetative 
index for the critical period 


Vjj. = I V ijt / N,, where V,. 
t 


6 


is the mean vegetative index for ijth grid cell over the selected critical time period. The 
summation is over all available V ijt ’s within the period and N y is the number of those 
observations. For final yield estimates the period selected for com was July 31 through August 
23, 1984 and for soybeans it extended from July 31 through September 1. An earlier period 
would be closer to optimum for both crops when relationships to State level August 1 yield 
forecasts are considered. The optimum was quite flat around the several periods given the 
most consideration and selection of one over another would not alter results much. 


Step 3 

Step 3 maps grid cell mean vegetative indexes to the county level. In this case, the optimum 
mapping algorithm was also quite flat. The mapping criterion in this study was limited to the 
Euclidean distance between county and grid cell centers. Search radii limitations of 
approximately 20, 30, and 40 miles were investigated. Weights that declined linearly and 
exponentially were explored. Of these six combinations (three distance limitations by two 
weight decay rates), the exponential decay with a 30 mile search radius produced the strongest 
relationship to yield at the State level. However, all of the methods were very close at the 
State level and the exponential for 30 and 40 mile limits produced very highly correlated 
county vegetative indexes. Therefore, the method selected was a weighted average, where the 
weights were inversely proportional to the squared distance between the county and respective 
grid cell centers, with a search radius of 30 miles which was extended to 40 miles if no grid 
cell centers (with data) were within 30 miles. That is, 

V, = $ W,AW / S (1AW 


where V mn is the vegetative index for the mth county in the nth State, d 2 mnij is the squared 
distance from the center of the mnth county to the center of the ijth grid cell and both 
summations are over all grid cells within 30 miles of the county center (or within 40 miles 
if there are no observations within 30 miles). 

This algorithm, which can be termed the "extended 30 mile quadratic mapper", gives most of 
the weight to grid cells closest to the county center, limits the search radius to 30 miles in 
most cases and produces a vegetative index for most of the counties in the study area. Of 
the 916 counties, 908 had a vegetative index for the selected critical period for soybean final 
yield (July 31-September 1, 1984) and 905 had a value defined for the shorter com final yield 
period (July 31-August 23, 1984). 

Support for selecting the "extended 30 mile mapper" and examining the competing algorithms 
came in part from a study of 1983 official county yields. The difference in both com and 
soybean yields as a function of distances between county centers was reviewed. In general, 
the review suggested a maximum search radius of 40 miles (yields can become substantially 
different over greater distances) and a decay function greater than the linear rate, but often not 
quite a rapid as the distance squared. 


7 



Step 4 


Step 4 involves the creation of appropriate State level vegetative indexes. The county 
vegetative indexes are weighed to the State level just as one would do to obtain State average 
yields, if they were in fact known for each county. That is, weights are used based on the 
harvested acres which are equivalent to the same harvested acres used in the yield expression 
(production per acre harvested). Since this study is concerned with investigating what could 
actually be done, 1983 county harvested acreage estimates of com for grain (for com) and 
soybeans (for soybeans) are used as weights. A few counties in some States with nominal 
acreage are given a weight of zero (very close to their actual weight) because individual 
estimates are not made for those less important counties. 

The products resulting from this step are State crop specific (com for grain or soybeans) 
vegetative indexes. They are crop specific in the sense that county vegetative indexes were 
weighted together based on the relative density of the crop in different parts of the State. It 
is important to recognize the low spatial resolution of the meteorological satellite data. Since 
areas of the order of about 300 acres can be resolved spatially the V ijt ’s reflect something that 
may be thought of as "vegetative greenness". Therefore, the vegetative indexes reflect this 
general sensing of the scene and the State level com for grain and soybean vegetative indexes 
are only crops specific because they incorporate the varying importance of the crops in 
different counties. 

The equations for these State level indexes for com can be expressed as follows: 


vc.. = £ (C„„ V J / X c, 

and for soybeans 
vs; - Z (S ran VJ/I S M . 


Here, VC. n and VS. n are the mean crop specific vegetative indexes for com and soybeans, 
respectively, in the nth State. C mn and S mn are the 1983 (previous year) published harvested 
acreage estimates of the respective crop for the mth county in the nth State. The summation 
is over all counties in the State (m=l, 2, 3...) even though some of them may have a zero 
weight for either or both crops. 


8 




Figure IB 

Overview of the Approach Used 
In the Primary Analysis 


Step 5 


Obtain USDA/NASS 
Final State 
Yield Estimates 


Com 

Yield EC, 
Estimate 


Soybean 
Yield ES, 
Estimate 


Develop 

Calibration 

Equations 


Step 6 

Regression Parameter Estimates 


and Residuals 
Com 

EC. = £ + P TVC „) 
RC„ = EC. - EC. 


Soybeans 

es„=V5« 

RS n = ES n - ES n 


Produce County 
Yield Indications 


Step 7 

Satellite Generated 
County Yield Estimates 

Com 

EC,.. = ~ + E(V„.)-RC„ 


Soybeans 

ES,., A +3 (V m „)-RS„ 


9 






Step 5 


Step 5 involves obtaining the USDA/NASS final state com and soybean yield estimates. 
These estimates are, in many respects, the most important component in this study. There is 
no problem in obtaining the State level final yield estimates, they are published in January 
some time in advance of the date county yield indications would be needed. However, the 
timetable would be tighter for obtaining August 1 forecast yields for use in producing county 
or other local area potential yield variables. ITe symbols for the final yield estimates for the 
nth State are EC n and ES n for com for grain and soybeans, respectively. They are used as the 
dependent (calibration) variables in the next step. 


Step 6 

Developing the calibration equations constitutes the sixth step in the primary analysis. For the 
ten States in the study area each crop’s final yield estimate is regressed on its vegetative 
index. The level of each observation is the State, so that only ten data points are used in the 
analysis. To conserve degrees of freedom, to maintain the greatest simplicity consistent with 
objectives and to achieve parsimony, simple linear models are used. The products available 
at the completion of this step are the regression model parameters and residuals for individual 
States. The regression equations for com are: 

- A 

EC n = a + 6 VC. n , with residuals RC n = EC n - EC n ; 

— A 

for soybeans: ES n = ^ + 8 (VS. n ) with residuals RS n = ES n - ES n , 
where a, 6,, and 8 are regression intercept and slope parameters. 


Step 7 

In Step 7 the county yield indications are produced. These county yield indications or satellite 
generated yield estimates are the product available upon completion of the step. They are 
symbolically represented by EC mn and ES mn , the com for grain and soybean yield estimates for 
the mth county in the nth State. The county estimates are obtained by utilizing the 
relationship between the yield and vegetative index at the State level. That relationship is 
applied in mapping county vegetative indexes to county yields. In as much as the strength 
of the State level relationship supports belief in the phenomenon of the linear dependence of 
yield on the vegetative index, it may be reasonable to apply that relationship at another level 
of aggregation. 

The calibration equations are: 

A A 

EC™ = a + IS (V.J - RC„ and ES lnn =X+ 6 (V„j - RS„ 


10 



The State level residuals are subtracted from the mapping of county vegetative indexes to 
yields based on the ten State study area relationship. This has the desirable property of 
keeping the county yields in a State collectively consistent with the official State yield 
estimate. Intuitively, if the over or under estimate of the State yield is fairly uniform across 
a State then the adjustment would improve the county satellite generated estimates. A possible 
negative factor is that artificial yield differences along State boundaries might be introduced. 


Utilize Options 

One option is to produce theme map products (at the county level) which reveal where the 
crop is doing well and where it isn’t doing as well. Such map products can be useful to 
the ASB and SSO staffs. Map products showing the relative condition of crops in a spatial 
sense might also be provided to data users. 

Of course, one product to be utilized would be county yield indications. They would be used 
to provide improved crop statistics for county, agricultural statistics districts, and other groups 
of counties (drainage basins, marketing areas, etc.). A more speculative utilization would be 
the creation of supplemental variables for use in conducting more efficient yield surveys. Such 
supplemental variables would be produced in a manner similar to the county vegetative 
indexes. They would probably be for a more restricted search radius and would be designed 
to reflect the average crop condition in a local region around a sample farm or field, or for 
a group of sample units. If the correlation between the yield variable measured at the sample 
"point" and the neighboring area satellite generated crop condition variable were high enough, 
the satellite information could be used in a regression estimator, since the grand mean or 
average satellite variable value exists for the entire population. Of course, a sufficiently high 
correlation would permit other common uses of supplemental variables. These might include 
stratification or post-stratification (dependent on timing), unequal probability sampling and 
other uses of the supplemental information either in the sampling design or in the estimator. 


"Utilize Options" 


Map Products - Improved county, Agricultural 

Statistics District, and other local 
crop statistics 

Supplemental variable for more - Other possibilities 

efficient yield surveys 


11 


The Study Area 


The ten State study area of North Dakota, South Dakota, Minnesota, Iowa, Missouri, Illinois, 
Indiana, Ohio, Kentucky, and Tennessee is shown in Figure 2, along with the grid cell 
coordinate system. Showing the coordinate system with these States provides some idea of 
the magnitude of data available. The dots in the figures represent the approximate center of 
each grid cell. There are, for example, about 75 grid cell centers in Iowa. With about 1700 
pixels per grid cell (actually somewhat less because of cloud screening) and an average of four 
days of observation (actually more than four), Iowa would have in excess of half a million 
observation points during the critical period. 

The study area States have a few characteristics in common. They are all important 
agricultural States with a significant part of their land area in crops. Com and soybean 
production is important enough throughout the area that county yield estimates are produced 
and published for each of the States. Most of the remaining common factors are associated 
with the fact that they are contiguous. From north to south they can exhibit substantial 
diversity in crop development and maturity stages. Not only are there differences in crop 
stages, but the variability in development stage (by necessity) is much more restricted in the 
North. From West to East, or perhaps from Northwest to Southeast, substantial differences 
prevail. The natural woodland vegetation in the East is very different from the prairies in the 
West. The low rainfall, low humidity, and fallowing practices of the west are about as 
dissimilar as can be found within a contiguous area of this size from those of the East and 
Southeast. 

Many of these factors (both the similar and dissimilar ones) affect the vegetative information 
that can be obtained from satellites, particularly from those with such a low spatial resolution 
as the meteorological satellites. The wide mix of natural cover types and crops would 
logically make one question whether the satellite data could possibly measure crop condition 
in a consistent way for these States. If one should find a strong relationship between crop 
yields and satellite vegetative indexes for such a dissimilar group of States, then it may not 
be too unreasonable to hope that the same satellite data will also provide useful crop condition 
information for agricultural reporting districts and counties (which can be quite dissimilar) 
within these States. 


12 


Figure 2 

TEN STATE STUDY AREA 
Grid Cell Coordinate System and Approximate 
Location of Cell Centers 



13 
































RESULTS AT THE STATE, COUNTY, AND 
AGRICULTURAL STATISTICS DISTRICTS LEVEL 


State Level Relationships 

A plot of relationships between the final yield estimate and each crop’s vegetative index is 
shown in Figures 3 and 4 for com for grain and soybeans, respectively. 

A _ 

The regression equation line for com, EC n = -16.25 + 1.60 VC. n 

is shown in Figure 3. The model explains a highly significant amount of variability in yields 
between the States and has a coefficient of determination (R 2 ) of .94. Individual State data 
are plotted with the letter in the postal abbreviation underlined in Figure 2. Iowa, Missouri, 
Illinois, and Ohio are denoted by the second letter, while the other six use the first. 

A _ 

The regression line for soybeans, ES n = -9.05 + 0.53 VS. n , 

and the State data points are displayed in Figure 4. The soybean model explains a highly 
significant 85 percent (R 2 =.85) of the yield variability for the ten States. 

The statistical software package (SAS) regression output for the com and soybean models is 
included in Appendix C. 

The com and soybean models just presented used EVI as the vegetative index for both crops. 
The NYI version was very competitive for com, but had lower slightly explanatory power for 
the yield of both crops. 

The EVI version was selected, based on its performance for soybeans, so that the same version 
could be used for both crops. The greater effective range of the EVI variable was also 
thought to provide better discrimination at the county level for the wider com yield range. 
Plots analogous to those in Figures 3 and 4 and corresponding SAS regression analyses are 
shown for NVI in Appendix C. 


Agricultural Statistics Districts Satellite Generated Yield Results 

After the State equations and residuals were employed in generating county yield indications, 
the counties in each agricultural statistics districts were weighted together by their 1983 
acreage weights to produce district means. The agricultural statistics districts level results are 
shown for com and soybeans in figures 5 and 6, respectively. The ordinate is the official 
yield of the crop as published in USDA/NASS SSO bulletins and included in the Agency’s 
crops data base. The abscissa is the mean district satellite generated yield for counties with 
published acreage for the previous year. So, even if county estimates agreed completely, 
district estimates could differ because the relative importance of counties for the crop changed 
from 1983 to 1984 or the omission of minor counties distorted the satellite generated yield 
mean. 


14 


Drn w K! r > ~ n ~ ^ *1 o 


Figure 3 

CORN FOR GRAIN - STATE LEVEL 
Official Final Yield Estimate (bushels per acre) 
Versus 

Corn Vegetative Index 
(EVI Version) 


120 ♦ 


110 ♦ 


100 


90 ♦ 


SO ♦ 


Model: N=10, R 2 =.94, 



60 ♦ 

5-0 


• 

55 


60 


65 


70 


75 


80 


85 


CORN VEGETATIVE INDEX 


15 




Of , W H K! 


Figure 4 

SOYBEANS STATE LEVEL 
Official Final Yield Estimate (bushels per acre) 
Versus 

Soybean Vegetative Index 
(EVI Version) 


Model: N=10, R 2 =.85, 
lBS o =-9.05+0.53 VS. n 

H 


35 ♦ 



-•*.-♦--+-+-+-♦-♦--+•--♦ 4.--♦ 

56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 

SOYBEAN VEGETATIVE INDEX 


16 







orB M >< r > 


Figure 5 

CORN FOR GRAIN - AGRICULTURAL STATISTICS DISTRICTS LEVEL 
Official Yield Estimate (bushels per acre) 

Versus 

Satellite Generated 

Corn Yield Estimate (bushels per acre) 


N=84, R 2 =.75 


150 ♦ 
• 
i 
i 

140 ♦ 

I 

I 

I 

130 ♦ 

I 

I 

Q 120 ♦ 

f ; 
F no ♦ 

I 

I 

C ioo ♦ 

I 

I 

90 ♦ 

I 
I 
I 

80 ♦ 

70 ♦ 

I 
I 
I 

60 ♦ 

50 ♦ 

40 ♦ 

I 
I 

30 ♦ 

I 
l 
I 

20 ♦ 



- — ♦- --*-*---*■-♦- * - * -♦- * ~ 

20 30 40 50 60 70 80 90 100 110 120 130 140 150 

SATELLITE GENERATED CORN YIELD 


17 




O P* H H ^ 


Figure 6 

SOY BEANS - AGRICULTURAL STATISTICS DISTRICTS LEVEL 
Official \ ield Estimate (bushels per acre) 

Versus 

Satellite Generated 

4 5 ♦ Soybean Yield Estimate (bushels per acre) 


40 ♦ 


35 ♦ 


30 * 


25 ♦ 


20 ♦ 


15 


10 ♦ 


5 ♦ 


5 


N=76, R 2 =.74 



— -—>—--+ --- ♦- 

10 15 20 25 30 35 40 


45 


SATELLITE GENERATED SOYBEAN YIELD 


18 




For com, all 84 agricultural statistics districts in the study area (six in Kentucky and 
Tennessee, nine in each of the others) had both official and satellite generated mean yields. 
The R 2 between means from these different sources was .75, explaining three-fourths of the 
district to district yield variability. The line shown in Figure 5 is the one-to-one line of 
perfect agreement. The "State postal one letter code" is used to identify districts in each 
State. The three underestimated outlier "S’s" are the western South Dakota districts. The 
far outlier is the Southwest district. Note that the other "S" districts are near the one-to-one 
line. The "M" outlier, with yield substantially overestimated by the satellite source, is the 
three county district in Northeast Minnesota. Since only one of the three counties had a 1984 
published com yield that data point really represents a single county (St. Louis County). 
Although, the "M" is not such an extreme outlier when considered as a single county, it is 
still a substantial overestimate. Actually, St. Louis county is very large. One would not be 
surprised to find that the vegetative index, mapped from surrounding grid cells towards the 
county center, failed to represent where the county’s 300 acres of com harvested for grain 
were in 1984. 

For soybeans, both variables were available for 76 of the 84 districts. So, even though 
soybean satellite generated yield estimates were available for counties in additional districts 
(they can be generated even where the crop isn’t grown), the lack of weights (1983 harvested 
soybean acreage estimates for individual counties) prevented their aggregation for some 
districts. The explanatory power at the district levels was about the same for soybeans as 
it was for com (R 2 =.74). 

The soybean plot in Figure 6 also shows some outliers. These include some districts near 
those that were outliers for com and may involve small acreages of soybeans grown in locally 
advantageous areas within those districts. Another factor that should be considered is the 
range of vegetative index and yield data used in fitting the State level models. The models 
will, of course, perform linear extrapolations beyond the lowest and highest values when they 
are applied at the county and agricultural statistics districts levels. The State level model 
predicted yields express the range of vegetative indexes in terms of the yield of the two 
crops. These values ranged from 67 to 119 bushels for com and 21 to 35 bushels for 
soybeans. The soybean official and satellite generated yield relationships (see Figure 6) 
appear to split into two groups when extrapolating below 21 bushels. Of course, the "yield 
ceiling" near the top end of the scale makes extrapolations above 119 (for com) and 35 (for 
soybeans) bushels less of a concern than the greater extrapolations on the opposite end of the 
generated yield scale. 


19 


County Level Results 


County level results are shown graphically in Figures 7 and 8. The ordinate is the official 
county yield as published in USDA/NASS SSO bulletins and included in the NASS 
Headquarters’ crops data base. If an individual county crop yield is not published (because 
of no acreage, low acreage, or to avoid disclosure of individual operations) then it is excluded 
from Figures 7 and 8. The abscissa is the result of mapping county vegetative indexes into 
com and soybean yields as was described in Step 7 on Page 14. For com for grain, the 
average yield of the mth county in the nth State is given by: 

A 

EC mn = -16.25 + 1.60 V mn - RC n . 

For soybeans the equation for expressing county vegetative indexes obtained over the July 31 
through September 1, 1984 critical period as yield is 

A 

ES mn = -9.05 + 0.53 V™ - RS n . 

The residuals of each crop for the ten States are displayed in Figures 9 and 10. The maps 
reveal some large adjoining State residual shifts which could lead to substantial yield 
differences between nearby counties with similar vegetative indexes. The agricultural statistics 
districts referred to earlier are shown in Figure 9. Some appreciation for the varying size 
and orientation of counties can be obtained from observing their boundaries in Figure 10. 

County com yields are plotted in Figure 7 for the 889 of the 916 counties that have both 
official and satellite generated com yields. Official com yields were published for all but 17 
counties in the area. As mentioned earlier, 11 of the 916 counties do not have a vegetative 
index for the com period (and thus no satellite generated yield). The strength of relationships 
has declined somewhat, dropping from an R 2 of .75 at the district level to .63 for counties. 
The spread of the com data around the one-to-one line shows large underestimates for some 
South Dakota, North Dakota, and Missouri counties. The selected letter from the postal 
abbreviation is again used to identify the State a county comes from; however, when looking 
at the plotted data for so many points it is important to realize that much of the data is 
hidden near the one-to-one line. Thus, one should not get the mistaken impression that the 
proportion of outliers is as large as it may appear from the plot. A substantial number of 
the overestimates are below the State level satellite generated yield range (below 67 bushels). 
Likewise, it is true that most overestimates are above the State level range (greater than 119 
bushels). More will be said about the accuracy of the data and the outliers in the next 
section of this report. 

The soybean yields from both sources are available for 756 counties. All of the 160 
"missing" counties did not have a published soybean yield for 1984. The eight counties 
without a satellite generated yield were among those without published yields. In fact, the 
160 counties have very few soybean acres, so that those plotted are the ones to examine in 
considering the value of the satellite generated estimates. As in the case of com, the strength 
of soybean relationships declined as the aggregation level was lowered. However, the decline 
in the strength of the soybean relationship was less than for com; stating at a lower State 
level but being essentially the same as com at the district and county levels. 


20 


Figure 7 

CORN FOR GRAIN - COUNTY LEVEL 
Official Yield Estimate (bushels per acre) 
Versus 

Satellite Generated 

Corn Yield Estimate (bushels per acre) 


O 

F 

F 

I 

C 

I 

A 

L 

Y 

I 

E 

L 

D 


150 ♦ 

i 

i 

i 

140 ♦ 

I 

■ 

no * 

• 

i 

i 

120 ♦ 
i 
i 
i 

1 10 ♦ 

I 

I 

I 

100 ♦ 

I 

I 

90 ♦ 

l 

i 

i 

80 * 

70 ♦ 

I 

I 

l 

60 ♦ 

50 ♦ 

i 

l 

l 

40 ♦ 

30 ♦ 

I 

I 

I 

20 ♦ 


N=889, R 2 =.63 


M 


M LL I I 

AMA L LLH MH /HH 
A A LLLIILI/TM IH 
MO AAA IIIALUmi 1 
A M HOML LLAAIAAA M HHI 
OK OLAAAAIM/ALAHHH 


H AHMIILALH AAAAcULAL 
A HIMAIALAAA^AAALH 

T LAILHK AL^fAA ALIA 
L TM L LIIAXLHAiA AA IALI 
MMLIKIIKL KAKIAAKAH AA 
H T TTOO HLALKLA/AKAIKLH ALLM 
SO T IT MLMMLITAA/lTLKKA A 

TT T KTOOLT LKKSrf K I LLI M I 
) O T T O T T KLLKAKK AL AKLK 
O OO MOMOKK MKKML K TA 

N T T T TLM76KKAMKKAL K 
0 0 T MT O^KTKK KKKA K 

0/ MM 0 K TM L 
0 KSK AL KL A T 
A ML KM KL K K 
ON L L 

OOSMO T 00 LLM 
SO OMOO A M A A 
0 M 

N M 0 0 M 

NH/H S OM 0 

0 


-♦-♦-♦-♦---*-+- 4 --♦-- 4 ----*--* - 

20 30 40 50 60 70 80 90 100 110 120 130 140 150 


SATELLITE GENERATED CORN YIELD 


21 




Figure 8 

SOYBEANS - COUNTY LEVEL 
Official Yield Estimate (bushels per acre) 
Versus 

Satellite Generated 

Soybean Y ield Estimate (bushels per acre) 


45 ♦ 


40 «■ 


o 

F 

F 

I 

C 

I 

A 

L 

Y 

I 

E 

L 

D 


35 ♦ 


30 ♦ 


25 ♦ 


20 ♦ 


15 ♦ 


10 ♦ 


5 ♦ 


N=756, R 2 =.64 


I LI 
L I 
LMLL IIAMILLI 
H AA IL LI! 
L LH LMAHH 
AHA L IL/ 

HAH A AHA 
M LHLL/ 
LALLILLLAA, 

AAI 

K MHL k. 


TT 

S TTT 
TMSMT S 
M M 


TO OILK LLILMAIi 
T KALIIKOIAKAK 
T OKMKXITLIMI 
T TO MMTTLLLKK, 

I 

0 L L L *KK ALAKK 
LL LKX A A TM K 



10 


15 


■ - * - 
30 


40 


20 


25 


35 


45 


SATELLITE GENERATED SOYBEAN YIELD 


22 




Figure 9 

RESIDUAL OF THE STATE LEVEL REGRESSION 

of the 

Corn For Grain Yield 
on the Corn Vegetative Index 
agricultural statistics districts are shown 



23 

































Figure 10 

RESIDUAL OF THE STATE LEVEL REGRESSION 
of Soybean Yield 
on the Soybean Vegetative Index 
county boundaries are shown 


Soybog^Residual Legend 


„ ES 
n n 



24 







































































































































Table 1 summarizes the number of units and strength of relationships at each level of 
aggregation. The more moderate decline in R 2, s for soybeans may relate to a less systematic 
pattern in the county and agricultural statistics districts outliers than was the case for com. 
The number of extreme outlier counties beyond both the lower (21 bushels) and upper (35 
bushels) ends of the State level range appears less than it was for com. However, there are 
more outliers within the range (most with the satellite values underestimating official yields) 
and there is generally a greater spread in the data. 


TABLE 1. Strength 17 of relationships between average yields (official estimates) and satellite 
vegetative indexes or satellite generated yield estimate indications at the State, district, and 
county levels, 1984, ten State study area. 


LEVEL 

N 

CORN FOR GRAIN 

R 2 R 

SOYBEANS 

N R 2 

R 








STATE 

10 

.94 

.97(.87, .99) 

10 

.85 

.92(.69, .98) 

DISTRICT 

84 

.75 

.87(.81, .91) 

76 

.74 

.86(,79, .91) 

COUNTY 

889 

.63 

.80(.78, .82) 

756 

.64 

.80(.77, .82) 


1/ Strength of relationships are expressed in terms of the coefficient of determination (R 2 ) and 
correlation coefficient (R) for the number of observations (N) available at each level. The 
95 percent confidence interval for the population correlation coefficient is shown in 
parentheses. 


A More Thorough Examination Using Additional Performance Measures 
Looking at results in tenns of correlation or regression relationships alone can be misleading. 
A more thorough examination of the results is presented in the next table. Information from 
Table 1 is included in this table since it does tell something about how the satellite generated 
yield indications (and satellite vegetative indexes) correspond to the official estimates. If the 
satellite generated yield indications were to be used only to proportionally distribute official 
State mean yields around each State, then the relationship statistics would provide essentially 
all of the information on their accuracy. However, if the individual county point estimates 
provided by the satellite generated yields (and those from other sources, also) are to be used 
directly in setting individual estimates, another set of performance or accuracy measures may 
be appropriate. Before specifically discussing these other measures of performance, it may 
be important to discuss the role of official estimates in the assessments. 


25 


Official estimates, at any level, are not infallible or immune from error. As was discussed 
previously, com and soybean final mean State yield estimates for the States in this study are 
quite accurate. They provide the best knowledge available on the actual average yield for 
a State. County mean yield estimates are generally not as accurate as State level yields. 
Since the official county estimates are used in evaluating the performance of the yield 
indications, this reservation on accuracy should be kept in mind. For example, suppose we 
got the extremely unlikely outcome of the county R 2 s in Table 1 being equal to one. Then 
we could use the satellite generated yield indications to duplicate the yield estimates currently 
produced resulting in no real gain at all! Of course, if the R 2, s were quite low (or zero, or 
not significantly different from zero), we would also be disappointed because the official 
county yield estimates do correspond to something approximating actual yields. The same 
kinds of statements could also be made for the other performance measurements (to be 
discussed next). Perfect results as measured against official estimates would not be very 
useful. Nor would poor results as measured by these statistics show much promise for the 
use of satellite generated yield estimates. 

The additional performance measurements are based on the mean square error and its 
components, variance and bias squared. The appropriate roots in the original units (bushels 
per acre) and a relative error are also included in Table 2. The mean square error is the sum 
of the squared differences between the satellite generated yield indications or predicted values 
and the official yields, divided by the number of observations. For example, the study area 
wide mean square error for county com yields can be expressed as: 


MSE = 1/N KEC™ - EC mn ) 2 , 


The summation is over all counties for which both variables are defined (N=889, in this 
case) and EC^, is the 1984 official mean com yield for the mth county in the nth State 
(previously not defined since it was not used in the primary analysis). Since the mean square 
error can be separated into variance (VAR) and bias components, these measures are shown 
along with the root mean square error (RMSE), standard deviation (ST DEV), and the 
standard deviation relative to the mean official yield (RSD). 

The MSE reflects collectively the accuracy of the individual satellite generated county yields 
when considering the official county yields as "truth". The variance reflects the precision of 
these new yield indications when the bias is adjusted out. The variance may be a more 
appropriate measure in this application because the counties are given equal weight in this 
analysis. While equal weights are appropriate if one wants to be accurate in all counties, 
applying the yield indication to individual counties with varying acreages should result in a 
nearly zero effective bias at the State and higher aggregation levels. Thus, the variance is 
more indicative of the TABLE 2. 


26 


Performance measures" at the State, district, and county levels for satellite generated yield 
estimate indications obtained by considering official estimates as "truth", 1984, ten State study 
area. 

TABLE 2 

LEVEL N R 2 R MSE VAR BIAS* RMSE ST DEVRSD v 

(bushels/acre) 2 .bushels/acre— % 

CORN FOR GRAIN 


STATE 

10 

.94 

.97 

26.66 

26.66 

0.00 

5.16 

5.16 

5.3 

DISTRICT 

84 

.75 

.87 

181.40 

178.76 

-1.63 

13.47 

13.37 

13.7 

COUNTY 

889 

.63 

.80 

249.31 

248.69 

-0.79 

15.79 

15.77 

16.2 





SOYBEANS 





STATE 

10 

.85 

.92 

5.17 

5.17 

0.00 

2.27 

2.27 

7.9 

DISTRICT 

76 

.74 

.86 

15.93 

14.98 

-0.97 

3.99 

3.87 

13.4 

COUNTY 

756 

.64 

.80 

22.07 

21.02 

-1.03 

4.70 

4.58 

15.8 


1/ The performance measures are discussed at length in the text. 

2/ The bias at the district and county level would be very close to zero for a harvested acreage 
weighted mean. However, all counties (districts) were given equal weight in this analysis. 

3/ RSD is the standard deviation relative to the mean (equal weights) com for grain (97.6 
BU./A) and soybean (28.9 BU./A) yields for the ten States. 

equally weighted accuracy and precision for individual counties when the resulting bias is 
essentially zero. An essentially zero bias would occur because the acreage estimates 
(supported by other data) are constrained to agree with the previously estimated total State 
acreage harvested and the satellite generated county yields are likewise constrained 
(individually adjusted by the State level residual) to collectively be consistent with mean State 
yield per acre. These measurements in terms of bushels per acre squared may be thought of 
as being analogous to an exponential loss function. That is, a loss function in which to miss 
by zero bushels "hurts" zero, one "hurts" one, two "hurts" four, three "hurts" nine, and so on. 


27 



The bias, RMSE and ST DEV are presented in bushels per acre. The bias is positive if the 
equally weighted county official yields tend to be overestimated by the satellite generated 
yields. However, there is a little more that needs to be said about interpreting the bias in 
this situation. Overestimates suggest that a tendency exists to overestimate the yield for 
counties with lower acreages (within State) since the weighted bias would be closer to zero. 
In this case, it would appear that the more important counties or areas of a State would tend 
to be underestimated. In the opposite situation, when the equally weighted bias presented in 
Table 2 is negative, satellite generated yield indications tend to be too low for all counties, 
tend to be too low to a greater extent for lower acreage counties, and tend to be 
overestimates for the higher acreage counties. The RMSE and ST DEV are the square roots 
of the MSE and VAR, respectively. Because of the bias handling characteristics arising 
from the county estimation techniques used, the standard deviation is more applicable. To 
understand its relative value and to consider the performance for both crops it is expressed 
relative to the mean yield for the study area. The relative standard deviation is the ST DEV 
divided by the mean (equal weights) yield for the ten States (multiplied by 100 and expressed 
as a percent). 


Additional Performance Measures Summary 

The bias at the State level is zero as a result of the regression least squares fit and 
consequently the MSE and VAR, and the RMSE and ST DEV are equal. Attention may be 
focused on the ST DEV and the RSD (other than the correlation or regression statistics) to 
understand the performance of the satellite generated yield indications when considering the 
official statistics as truth. The standard deviation performance level for com drops from a 
little more than five bushels at the state level to around 13 bushels at the district level and 
then to nearly 16 bushels at the county level. For soybeans, the State to district to county 
decline in performance as measured by the standard deviation is from two and one fourth, 
to nearly four, to a little more than four and one-half bushels. The relative standard 
deviations for the crops are essentially the same at the district and county levels (near 13.5 
and 16 percent, respectively). However, the satellite data corresponds more closely for com 
at the State level with a RSD of just over five percent as compared to nearly eight percent 
for soybeans. 

Tables, similar to Table 2, which also show the com for grain and soybean performance for 
each State were prepared. They are included in Appendix D. An examination of these tables 
will suggest, performance is not good for some States. However, in many respects, these 
satellite generated yield estimates should be considered pilot or experimented in nature. Just 
as would be done in considering other yield indications, the satellite indications should be 
further evaluated, and some experience acquired their statistical value. 


28 




150 ♦ 

I 

140 ♦ 

130 ♦ 

I 

I 

120 ♦ 
l 

110 ♦ 

100 + 

I 

90 ♦ 

80 * 
l 

70 ♦ 

I 

I 

I 

60 ♦ 

I 

I 

I 

50 ♦ 

I 

I 

40 ♦ 

I 

I 

I 

30 ♦ 

) 

I 

I 

20 ♦ 

» 


Figure 11 

CORN FOR GRAIN - COUNTY LEVEL 
Official Yield Estimate (bushels per acre) 
Versus 

Satellite Generated 

Corn Yield Estimate (bushels per acre) 
With 


OUTLIERS CIRCLED 



—+ - ♦ — - ♦ - ♦-+-—♦- -------- - 

20 30 40 50 60 70 80 90 100 110 120 130 140 150 


SATELLITE GENERATED CORN YIELD 


29 



SOME COMMENTS ON ACCURACY AND USE OF THE DATA 
A Closer Look at Satellite Generated County Corn Yield Indications 


In beginning a discussion of accuracy and use of the data, a closer look at the com for grain 
satellite generated yield indications may be helpful. In Figure 11, the same plot of the 
county level com data is shown that was previously presented in Figure 7. Individual outliers 
are circled (and encircled). They will be given further consideration in hopes of 
understanding some characteristics about those counties which may explain why the satellite 
generated yield indications performed poorly. The group of encircled counties totals 11 (one 
data point represents two South Dakota counties). Understanding why the actual yields, as 
approximated fairly well (one can assume) by the official estimates, were substantially 
underestimated by the satellite generated yields is not difficult for these 11 counties. The 
vegetative conditions of western South Dakota and North Dakota were quite poor in 1984 (as 
they usually are relative to the entire ten State area) and a fairly small proportion of the 
region is in crops. Since region wide and county by county vegetation is sparse (to some 
the area can appear quite bleak), vegetative indexes are low. This, of course, results in low 
satellite generated com yield estimates (less than 50 bushels per acre for these counties). So, 
why are the actual (and official) com yields so high? Most of the com acreage is irrigated. 
In addition to irrigation lifting com yields much higher, the low irrigated and other crop 
acreage keeps their effect on the vegetative indexes to a minimum. The crop areas 
(particularly the irrigated ones) simply do not cover enough of the land to have much effect 
on average values from the satellite data. 

It may be desirable to objectively identify types of counties and characterize the usefulness 
of the satellite generated indications for each category. Such an attempt was made for 
counties which have a substantial proportion of their com acres irrigated. However, irrigation 
statistics are not available for all ten States in 1984. Therefore, in order to objectively group 
all study area counties of the type encountered in this problem a more complete data set was 
needed. The 1982 Census of Agriculture provides such a data source. The number of farms 
with com harvested for grain is provided for all farms and for those with some of the crop 
irrigated. 


30 


TABLE 3. Com harvested for grain: Total acreage, proportion irrigated and average yields 
(official and satellite generated), 1984, selected 1 counties. 

(ARD) 

CROP 

REPORTING TOTAL PROPORTION AVERAGE YIELD 
COUNTY DISTRICT ACREAGE IRRIGATED 27 OFFICIAL SAT. GENERATED 

% .bushels/acre. 


SULLY 

5 

43,900 

42 

77 

35 

BUTTE 

1 

12,500 

92 

100 

24 

TODD 

8 

11,400 

65 

98 

43 

BUFFALO 

5 

7,600 

53 

98 

48 

LYMAN 

8 

6,800 

50 

92 

36 

FALL RIVER 

7 

4,600 

— 

118 

31 

BENNETT 

7 

3,600 

72 

107 

36 

STANLEY 

4 

2,000 

— 

93 

36 

MEADE 

4 

1,000 

— 

79 

29 

SHANNON 

7 

200 

— 

75 

31 

MCKENZIE 

4 

200 

100 

101 

33 


1/ The selected counties are the encircled outliers in Figure 11. All are Western South Dakota 
counties, except for McKenzie (which is located in West Central North Dakota). 

2/ Fall River, Stanley, Meade and Shannon irrigated acreages were not published separately. 
Published district data shows 87 percent of the 9,400 acres in district 7 (Southwest South 
Dakota) and 40 percent of the 7,200 acres in district 4 (West Central South Dakota) being 
irrigated in 1984. 

Total and irrigated acres of com harvested for grain are available for most counties. In the 
few counties where 1982 acreage is not provided, (to avoid disclosing information on the few 
operations involved) the proportion of farms with irrigated com provides a basis for judging 
the importance of irrigation. Using data such as that provided by the Census of Agriculture 
also allows identification of groups of counties before the satellite yield estimates are 
generated or the official estimates are produced. 


Results Obtained by Applying the Irrigation Rule 

An attempt was made to learn the impact of objectively eliminating a group of counties with 
substantial proportions of irrigated com. After trying several alternatives, it was decided to 
exclude those which irrigated more than 30 percent of their com harvested for grain acreage. 
Basically, the 30 percent cut off eliminated the more obvious outliers without excluding as 
many additional counties as lower proportions would. However, to eliminate the 11 outliers 
listed in Table 3 satellite generated com yield indications were effectively discarded for 20 
additional counties. The resulting plot of the surviving official/satellite generated county yield 


31 










pairs are shown in Figure 12. In Appendix D the com for grain performance measures (like 
those shown in Table 2) are presented when the 31 counties are excluded. The appendix 
table shows the performance for the ten State area and individual States when the objective 
rule is applied. There are notable improvements for some of the States. 

In Table 4 some comparative values have been excerpted from the county level com for grain 
performance tables in Appendix D. They are presented in terms of the number of counties 
covered and benefits of using the Census of Agriculture irrigation data to objectively reject 
use of the satellite yield indications for some counties. 

TABLE 4. Number of counties covered and gains 17 of excluding counties based on more than 
30 percent of com harvested for grain being irrigated in 1982, 1984, ten State study area, 
selected county level com for grain performance measures. 

APPLICATION COST GAINS 

AREA N R 2 RSD(%) 

—(ALL COUNTIES/EXCLUSION RULE APPLIED)— 


TEN STATES 

889/858 

.63/.69 

16.2/14.5 

NORTH DAKOTA 

47/ 40 

291.69 

22.2/12.0 

SOUTH DAKOTA 

62/ 49 

.04/. 78 

36.4/12.8 

MINNESOTA 

81/ 78 

.56/. 59 

15.1/14.7 

MISSOURI 

114/107 

.30/. 19 

21.0/21.3 

ILLINOIS 

102/101 

.3 8/. 3 8 

12.5/12.6 


/ Number of counties covered and gains are measured when the objective exclusion rule is 
applied to counties with a substantial proportion of their com for grain irrigated against the 
alternative of not excluding any of the 889 counties for which satellite generated and official 
yield data exists. 

One could have looked at other criteria for grouping counties (for both com and soybeans) 
into various categories of usefulness. For example, counties with little soybean acreage could 
have been identified where that acreage possibly is restricted to more advantageous local areas 
within the counties. One could also have identified counties with few crop acres, where 
vegetative conditions, and thus satellite derived yield estimates, for the entire county could 
be quite different than for the crop area within the county. Perhaps, areas with substantial 
woodland could be grouped into some type of performance category. Many possibilities could 
have been attempted; however, a fairly simple one was employed. It’s application 
demonstrated that eliminating some obvious outliers (ones that could be detected even without 
knowledge of the official estimates because they are clearly too low) could improve the 
relational and accuracy performance measures somewhat. 


32 




o r m ~ kj r > ~ o ^ ^ o 


Figure 12 

CORN FOR GRAIN - COUNTY LEVEL 
Official Yield Estimate (bushels per acre) 
Versus 

Satellite Generated 

Corn Yield Estimate (bushels per acre) 
with 

SOME COUNTIES OBJECTIVELY ELIMINATED 


150 ♦ 

I 

140 ♦ 

I 

I 

130 ♦ 

l 

120 ♦ 

110 ♦ 

100 ♦ 

90 * 

I 

l 

I 

30 ♦ 

I 

70 ♦ 

I 

I 

60 ♦ 

I 

I 

50 ♦ 

I 

I 

40 ♦ 

I 

30 ♦ 

I 

I 

I 

20 ♦ 


AHA 

A A 

MH AAA I UAL 
M BOML LLAAI 


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L LLH MH /HH 
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M HHI 


0 M 


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n AHMIILALH AAAA/XAAL H T 
A HIMAIALAA^AAAALM HL T 

T LAILHK ALLCAA ALIA 
4 TM L LIIAKLHAKA AA IALI H K 
MMLIKIIKL KJ^IAAKAH AA H 
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7T MLM LITAA/TTLKKA A 
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0 M 0 
i 0 0 0 


-♦---♦-* 

20 30 40 50 


60 


70 


80 


90 


100 


no 120 130 140 150 


SATELLITE GENERATED CORN YIELD 


33 


CONCLUSION 


In conclusion, it has been shown that at the State level within a single year satellite derived 
vegetative index variables are statistically correlated to com and soybean yields. An 
application of such strong State level within-year relationship has been illustrated and the 
possibility of other applications suggested. The methods employed in aggregating the satellite 
data to obtain the appropriate State crop specific vegetative indexes have been presented in 
sufficient detail to facilitate duplication or to allow research on alternative techniques. 

The application of generating satellite com for grain and soybean county yield indications 
shows promise. Satellite vegetative index values by themselves could have been used to 
provide infonnation on relative crop condition. The calibration and verification of their 
explanatory power at the State level within the year of application, however, provides the 
important assurance that (at least at the State level) they are strongly related to yield. The 
nature of the relationship of satellite data (from a particular satellite, recorded by a specific 
sensor, constructed as a defined vegetative index, aggregated to a specific area (grid cell) in 
a certain way, averaged over a selected time period, mapped to counties by a specified 
algorithm and weighted to the State level by available or constructed county crop weights) 
to official crop yield estimates (arising from a certain type of crop year, rate of development, 
mix of crops, condition of other vegetation, etc.) can be measured at the State level for a 
broad spectrum of important agricultural States and applied to individual counties or groups 
of counties such as agricultural statistics districts. 

These conclusions are based on a single year, 1984. The study should be repeated for 
additional years, with similar although different meteorological satellites, sensors, crop 
development patterns, crop mixes, and other characteristics. 

The application of satellite generated yield forecasts for agricultural statistics districts and 
counties should continue to have high priority. This has been conducted for the 1988 yield 
forecasts with similar (actually higher correlations than 1984) results. Recall that 1988 was 
a severe drought year for com and soybeans in these States. This type of method, perhaps 
in combination with early season objective yield and daily ground weather observation data 
models could be the only foreseeable improvement in methodology for early season crop yield 
forecasting. 

There are several other possible areas that could be explored. They involve changes in the 
way the data are summarized for the grid cells. Currently this is an FAS function. Any 
changes in the processing system would involve FAS agreement and/or a greater role by 
NASS in this area. The potential changes involve altering the data screening and averaging 
or summarization procedures. One possible improvement would be to compute grid cell 
averages only for pixels with a vegetative index above a certain threshold. That is, the 
current fixed threshold (at the so called soil line) would need to be adjusted to a higher 
(perhaps variable level) so that the vegetative index reflects conditions similar to that of crops 
in good enough condition to justify a harvest. Similar changes might also be required to 
investigate crop condition assessment methods for other crops, such as wheat or cotton. 
Other changes might involve those effecting the cloud cover and screening bias problem 
discussed in Appendix A. Still other changes might call for smaller grid cell sizes or flexible 


34 


locations. This might be particularly important to the generation of useful supplemental 
variables for improved yield survey efficiencies. 

Another group of potential future research efforts could be applied to many of the methods 
presented in this report. Averaging grid cell vegetative indexes over time by employing a 
functional fit similar to that employed by Boatwright could be considered. The benefits of 
conducting a manual or automated edit of the daily grid cell vegetative index values could 
be investigated. Employing a flexible crop stage indicator, or crop calendar, to shift the 
critical period by local areas could be explored. This attempt to tie the critical period more 
directly to crop progress would require additional data and impose the burden that the critical 
period specifying algorithm give equivalent results for all areas. 

Many of the other steps in the primary analysis could be considered for modification. 
Kriging theory (spatial estimation) could be employed to find more optimum ways of mapping 
grid cell means to counties, perhaps with differential decay functions in various directions for 
different areas and crop seasons. Ways of modifying the State level residual adjustment could 
be investigated that avoid artificial differences near State borders and which would potentially 
improve the accuracy of county estimates. 


RECOMMENDATIONS 

The application of satellite generated yield forecasts for agricultural statistics districts and 
counties should continue to have high priority. This has been conducted for the 1988 yield 
forecasts with similar (actually higher correlations than 1984) results. 

There are several other possible areas that could be explored. They involve changes in the 
way the data are summarized for the grid cells. Currently this is an FAS function. Any 
changes in the processing system would involve FAS agreement and/or a greater role by 
NASS in this area. The potential changes involve altering the data screening and averaging 
or summarization procedures. One possible improvement would be to compute grid cell 
averages only for pixels with a vegetative index above a certain threshold. That is, the 
current fixed threshold (at the so called soil line) would need to be adjusted to a higher 
(perhaps variable level) so that the vegetative index reflects conditions similar to that of crops 
in good enough condition to justify a harvest. Similar changes might also be required to 
investigate crop condition assessment methods for other crops, such as wheat or cotton. 
Other changes might involve those effecting the cloud cover and screening bias problem 
discussed in Appendix A. Still other changes might call for smaller grid cell sizes or flexible 
locations. This might be particularly important to the generation of useful supplemental 
variables for improved yield survey efficiencies. 


35 


Another group of potential future research efforts could be applied to many of the methods 
presented in this report. Averaging grid cell vegetative indexes over time by employing a 
functional fit similar to that employed by Boatwright could be considered. The benefits of 
conducting a manual or automated edit of the daily grid cell vegetative index values could 
be investigated. Employing a flexible crop stage indicator, or crop calendar, to shift the 
critical period more directly to crop progress would require additional data and impose the 
burden that the critical period specifying algorithm give equivalent results for all areas. 

Many of the other steps in the primary analysis could be considered for modification. 
Kriging theory (spatial estimation) could be employed to find more nearly optimal ways of 
mapping grid cell means to counties, perhaps with differential decay functions in various 
direction for different area and crop seasons. Ways of modifying the state level residual 
adjustment could be investigated that avoid artificial differences near state borders and which 
would potentially improve the accuracy of county estimates. 


36 


APPENDIX A 


CLOUD SCREENING 
BIAS 
STUDY 


37 


A cloud screening bias study was conducted because there was a tendency for vegetative 
index values to average lower when a larger portion of a grid cell’s pixels were screened 
out. Also, the amount of satellite data was sparse enough in some areas that merely 
discarding potentially biased data was not an attractive alternative. The approach taken in 
this study was to learn more about the nature of the bias. The idea, based on this 
knowledge, was to conclude either that the bias could be safely ignored or adjust for it in 
some satisfactory way. 

It was speculated that vegetative index mean grid cell values (for both the EVI and NVI 
versions) were lower when more pixels were screened out. This was confirmed in an earlier 
exploratory study. State means were lower for grid cells with up to 50 percent of their pixels 
screened out as opposed to a maximum of 25 percent. This downward bias might result 
because of the kinds of pixels remaining when others are screened out. Pixels associated with 
those removed may contain haze, thin clouds or cloud shadows, all of which tend to depress 
index values. Based on visual satellite image observations the author was tempted to 
conclude that the bias was greater when scattered clouds were present. Vegetative index 
values for grid cells observed near the same date seemed to be altered less when the images 
showed solid cloud masses or definitive fronts rather than scattered clouds. Thus, it could 
have been hypothesized that the amount of bias was some function of cloud boundary length, 
but that was beyond the scope of this study. 

Instead, the overall relationship of the vegetative indexes to the percentage of pixels not 
screened out was examined. Such an examination is shown for EVI in Figure A-l. This 
analysis was performed for grid cells in a coordinate system rectangle around the study area 
(i th from 210 to 260 and j th from 340 to 390). The analysis and Figure include available 
daily data over the period from July 31 through August 23, 1984 (the selected com period). 
The model regressing EVI on the percentage of pixels not screened out (GDPIX or % good) 
is, of course, highly significant in all respects. This results because of the large number of 
observations N=2338), even though the R 2 is only .12. 

Since regional patterns of cloudiness, cloud types and index levels could cause spurious 
relationships between EVI and GDPIX, some additional analyses were completed. The model 
of dependence of EVI on GDPIX was looked at both by regions and with the i th and j ith 
coordinates included as co-variables. Another type of analysis was motivated by another 
consideration. The only true test for this dependence would be to apply the full range of 
treatments (proportions screened out) to each daily observation. This controlled study is, of 
course, impossible (only one proportion is realized for each daily grid cell observation). In 
lieu of this "ideal" test, the next best thing was attempted. The regression relationship was 
computed for each grid cell over the available daily data, and mean intercepts and slope 
parameters computed for the entirevarea. This eliminated grid cells with fewer than three 
daily observations from the analysis (since the regression could not be computed for them). 
Grid cell’s with defined regression parameters were weighted together in proportion to their 
degrees of freedom (with some extreme parameter estimates edited out) to produce aggregate 
estimates. 


38 


While the various analyses employed (by regions, with coordinate system co-variables and 
aggregation of individual grid cell relationships) did reveal some variation between individual 
grid cells and between regions, they generally supported the overall slope parameter estimate 
(0.46). As shown below, only the model slope parameter would be involved in attempting 
to satisfactorily adjust the EVI’s. 

To adjust the EVI’s to the value they would be presumed to have for "clear skies" (or no 
pixels screened out), one can visualize lifting the line (denoted by asterisks in Figure A-l) 
by the left end until the slope is zero and maintaining the observations the same residual 
distance from the line. That is, the modified EVI (MDEVI) should be; 

MDEVT=EVI 100 + Residuals 

where EVI 100 is the EVI for GDPIX=100 and the residuals are those from the regression 
model (EVI = £= + p GDPIX). Substituting in the above equation it is seen that, 

MDEVI = [ £ + 3 (100)] + (EVI - EVI) A 

= £ + 0 (100) + EVI - [ ~ + 0 (GDPIX)] 

= ~ + j^(100) + EVI - £ - (3 (GDPIX) 

= EVI + p (100 - GDPIX). 

This is the intuitively pleasing result that the modified EVI’s are just the original EVI values 
plus a constant add on amount ( 0 ) for each percent of pixels screened out. 

Results of applying this adjustment for the selected com period are shown in Figure A-2. 

Here, MDEVI = EVI + 0.46 (100-GDPIX). As verified by the fitted line the overall bias 

has been eliminated. However, one can note some values along the periphery which appear 
to have been adjusted too much. The lower periphery shows no EVI’s (modified or not) near 
the soil line for the lower GDPIX values and the top shows some values much larger than 
the usual maximum. These observations may arise from grid cells where the screening 
procedure worked well, even though many pixels were screened out, and unbiased or less 
biased values were adjusted too much. Of course if that is the case , then other grid cell 
daily observations for which the bias was greater may not have been adjusted enough. This 
tendency for some individual adjustments to be inappropriate may be an indication that the 
model of dependence on GDPIX provides an incomplete explanation of the bias. 

Figures A-3 and A-4 show the EVI and MDEVI relationships with GDPIX, respectively, for 
the selected soybeans period (July 31 - September 1, 1984). A variety of analyses, again, 
support the value of the slope parameter estimate given by the overall model ( 0= 0.42), but 
indicate considerable variation in adjusting individual daily grid cell vegetative indexes. 

Table A-l shows the matrix of R 2 values for relationships of the August 1 and October 1 
forecasts and the final yield estimates for the com and soybean crops to the modified 
vegetative index (MDEVI) state means for each of 36 varying length periods. The individual 
daily grid cell MDEVI’s were computer based on the regression slope derived for that 
individual time period (from the start of the "FROM" period through the ending date of the 
"THRU" period). Then the predicted values (MDEVI’s) were averaged over the period and 
aggregated to the state level as described in Appendix B (by Crop Reporting Districts, rather 
than countries). 


39 


Figure A-l 

Environmental Vegetative Index (EVI) 
Versus 

Percentage of Good Pixels (GDPIX) 

For Available Daily Grid Cell Observations 
In And Around The Ten State Study Area, 
July 31-August 23, 1984 (Selected Com Period) 


Plot of PREDICT*GDPIX 
Plot of £VI*GDPIX 


125 


100 


75 


50 


25 


Symbol used is * 

Legend: A = 1 obs, B = 2 obs, etc. 


Model: N=2338 R 2 = .12 


A 


EVI = 27.39 + 0.46-GDPIX 


A A 


A A 


1 A 

A 8 


A A A 

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A AAA AA A 

AA A A B A A A 

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50 


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70 


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100 


40 


















Figure A-2 

Modified (To 100% Good Equivalent) 
Environmental Vegetative Index (MDEVI) 
Versus 

Percentage of Good Pixels (GDPIX) 


For Available Daily Grid Cell Observations 
In And Around The Ten State Study Area, 
July 31-August 23, 1984 (Selected Com Period) 


Plot of PREDICT*GDPIX 
l2f Plot o£ MDEVPGDPIX 


Symbol used is * 

Legend: A = 1 obs, B = 2 obs, etc. 


100 


TS 


AAA A A 

A 

A A 

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41 










Figure A-3 

Environmental Vegetative Index (EVI) 
Versus 

Percentage of Good Pixels (GDPIX) 

For Available Daily Grid Cell Observations 
In And Around The Ten State Study Area, 

July 31-September 1, 1984 (Selected Soybean Period) 


Plot of PREDICT*GDPIX 
l2J Plot o/ EVI*GDPIX 


100 


75 


SO 


25 


Symbol used is * 

Legend: A = 1 obs, B = 2 obs, etc. 

Model: N = 2922 R 2 = .13 
A 

EVI = 29.33 + 0.42 GDPIX 


A A 


A A 
A A AJ 


A A 


1 A 

A B 


A Al 

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L 

AX 


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BBAA CAA ••••••••BABA ACACAADAABBCCCACCCAAACACC A ABBAAAC 

AA«**«***»*BAAA D B AAA BC BABBBA ABAC1BBSAADB BA A B CA 
•»* AABABACDBBAADCBABABBAPBAAXBDAIAA CM* A A C AA A 
C AAABA BAC C C AB B AACAC CABABACDCB8 K AB A A AA C A AAB A 
A BCA AA BC A A 1C ABAA ABCACABAAC DBSCBAB1 AA BAi 

AAC ABCBAAAB OACACAABCBABB CCCCAA CA A BA ABA ACSADT 
AAM AA MABADABAA BSDBBBDBBDM ABACA1AC M AA BAA1A ICC 

BAD* AA ADCCA BMBBAD DAM CC A CA ABCAB AA A AA M A AA AAAAAAP 
BBA ADB8BSAB C AACA AB CQAAA BABSA BA AA A A BBBAABAA DCS 
A AAM CCDBAAABAC91ABDC CABBBAC ABB8ABAM ABAA ABBAACAC 

BA A A CACAACAABABB D9D0 AAB AABDC BBA A A AAA A BA A 
A B AAC AA AAD* AAAA B A AA A • A 

A A B A 1 AAAA A 


A A 


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50 


70 


00 


100 


42 
















Figure A-4 

Modified (To 100% Good Equivalent) 
Environmental Vegetative Index (MDEVI) 
Versus 

Percentage of Good Pixels (GDPIX) 


For Available Grid Cell Observations 
In And Around The Ten State Study Area, 

July 31-September 1, 1984 (Selected Soybean Period) 


12 $ Plotiof PREDICT*GDPIX 
Plot 'of MDEVPGDPIX 


Symbol used is * 

Legend: A = 1 obs, B = 2 obs, etc. 


100 


7$ 


A 44 


4 

C 


44 44 M 4 


♦ 4 4 


SO 


:414 4 4 44 4 

• Aft 44 4 14 M4 


4 

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41 I 
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4 m CM 


• 4 

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IS * . . / 

4 14 4 4 4 

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» 4 I'S 4 C 4 

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4 4444 41 1 44 C144C4 0 441 411 

AD 44 4 14 M4 1 4 4AAA4A1A CA AJUl M44 4 1W-- KAAAMDkk 

. CA/C 4 4 441 4 1 CA 444 4144 1 CCAA 14 414BA14A14 1 4 4444*w— 

1411141 44 AC ^ * A AlAAMADl^AAlAAAA 4^ 1ACAMA 4 II 

• CM****** c*c**^ba»»*oiawux*a»*c»c » * g***** **?,^ tauS 

i 414 44 UCIAAIA BAC 1441 C 1 D114AAAC41 

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jaS^S A1C* KSJiSaIaDAACIM^ 44 ^ 


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^SSSTSTJ^JSS, 3 


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4 


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4 4 4 


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k ■ aamvataIAIA 4 • *4 


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4 444 4 4 WAA1W 
4 4 44 1 


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44 4 4444 444 
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4 4 


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so 


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101 


43 






Comparison between Table A-l and the analogous table for EVI’s (unmodified) in Appendix 
B indicates the improvement, lack of change or deterioration in state level relationship 
strength for each period, and forecast or estimate month. These comparisons provide some 
insight to the success or failure of the attempt to modify the EYl’s. 

The results are not very encouraging in that adjusting for this bias does not make all the 
relationships stronger or even result in improvement for a majority of them. Perhaps the 
most important result is that the strength of the stronger relationships does not differ much 
between the unmodified and modified indexes. These R 2 ’s are as similar as they are 
primarily because grid cells are averaged over enough daily observations for the best periods. 
The tendency of the adjustment for such periods to average out to something like a constant 
is an argument for not making any adjustment. The hope is that enough days of data exist 
in the selected periods so that the bias is "averaged out" for many of the grid cells. 

Ignoring the bias was the course chosen in this study. Perhaps discarding data below some 
percent good threshold could be considered as a way of minimizing the bias without loosing 
too much data. However, the very linear relationship of the 1984 data does not suggest such 
a threshold. The bias study provides some basis for not attempting to make the adjustment 
and suggests an approach for appraising the same problem in other years. A more complete 
understanding of the bias can best be used to support developing improved screening 
capabilities. This use would directly address the problem, rather than using information 
obtained to merely to adjust "noisy" data values in a "noisy" manner. 


44 


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45 


TABLE Al. Coefficient of determination (R ) between modified vegetative indexes (MDEVI vemoo), averaged over the "FROM" through the "THRU" period, with the 
August 1 and October 1 yield forecasts and the final yield estimate, corn for grain and soy bean a, ten state study area, 1984 








APPENDIX B 


SELECTION OF CRITICAL PERIODS 
WITH 

SATELLITE VEGETATIVE INDEXES 
STRONGLY RELATED TO 
CORN AND SOYBEAN YIELDS 


3 


46 


The selection of critical time periods to average satellite vegetative indexes for useful 
relationships to com and soybean yields is motivated by two concepts. One concept is that 
a time period exists when general vegetative conditions are indicative of the suitability of the 
environment during the critical yield determining part of the respective crop’s life. The other 
concept is that averaging multiple vegetative index values over a period of time should 
mitigate some of the "noise" in the daily values. 

Critical period selection involved two complementary methods. One approach was to observe 
the seasonal pattern of grid cell vegetative indexes. It was desirable to identify a relatively 
consistent period of index values or what might be regarded as a "greenness plateau." Such 
a "plateau" would occur after a period of "greening up," or perhaps following some 
"greenness" associated with pre-ripe small grain crops (or other earlier vegetation), but prior 
to the "greenness decline" that eventually accompanies the approaching fall season. The 
"plateau period" would provide observations on multiple dates when general vegetative 
conditions could be considered essentially stable. Conceptually each vegetative index value 
within the period, no matter how "noisy," would provide information on these stable 
conditions. So, taking an average over the period would reduce the "noise" around a common 
value. 

The other method examined the strength of relationships between various yield forecasts and 
estimates to vegetative index values created for various time periods during the summer of 
1984. Grid cell means were created for each time period and aggregated (by equal weights 
to the Crop Reporting Districts then by crop specific district weights) to the state level so 
that the relationships could be appraised for the entire ten state area. Eight short periods 
from July 8 through September 9, 1984, were examined. Each of these approximately eight 
day periods was long enough to provide fairly uniform coverage of the entire study area; 
however, within state coverage was often incomplete and could result in unrepresentative data 
at the state level. Examination of these short periods was limited to determining if there was 
any information on a crop’s yield from the vegetative indexes in each time interval. 
Adjoining periods were then combined by twos, threes and so on, so that data 
representiveness was improved and the strength of relationships could be considered when 
more index values are averaged. Several very competitive longer periods were identified 
using this method. Each of these periods was composed of short periods which individually 
demonstrated some relationship to crop yields and which when combined with adjoining short 
periods achieved strong relationships. 

The seasonal pattern of grid cell vegetative index values was observed in many different 
ways. Because there are over 1000 grid cells in and around the study area not all could be 
looked at individually, nor is that advisable. Since a single interval is to be selected for each 
crop over the entire area, one does not want the selection tailored too much for an individual 
grid cell or local area. However, one would not like the period selected to cause serious 
misrepresentations of the respective crop’s actual condition for very many areas. 


47 


Figures B-l through B-10 provide some idea of the vegetative indexes for individual grid 
cells. The figures show the functional lines of the "greenness curve" for three grid cells in 
each state. The function is merely the straight line between daily environmental vegetative 
index (EVI) values available from July through September 1984. The grid cells in the figures 
were chosen to (1) be from different areas of each state, (2) provide an illustration of the 
different patterns found in the ten state area and (3) have enough separation so three could 
be shown. The grid cells are from the western, central and eastern parts of each state. The 
western grid cell "greenness curve" is denoted by an asterisk (*), the central one by an at 
sign (@) and the eastern most one by a plus sign (+). Patterns shown in the figures include 
curves "greening up," those "plateauing" after passing through an earlier "small grains 
greenness" period and some with very little data (which also, unfortunately, is illustrative of 
patterns present in the area). 


48 


Figure B-l 

North Dakota Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 
(DAY) 


KVILIMB ! 
120 ♦ 


For Three North Dakota Grid Cells 
I-Jth Coordinates Symbol 
219,345 * 

225,347 @ 

226,352 + 


110 


100 ♦ 


to ♦ 


to 


70 


60 


SO 


40 


♦ 

♦♦♦♦♦ 

♦♦ ♦♦ 


#♦♦♦ 


♦ ♦ 




♦♦♦♦♦ 


UIUI 


♦ 

-♦« 


July 


August September 


49 











Figure B-2 

South Dakota Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 


For Three South Dakota Grid Cells 
I-Jth Coordinates Symbol 


17ILIH1 : 
120 ♦ 


110 


100 


•0 


80 


70 


•0 


so 


40 


JO 


♦♦ 


♦♦♦♦ 


♦♦♦♦ 


♦♦♦ 

♦ 


«• 


220.356 

224.356 

227.356 


@ 

+ 


♦♦♦♦♦ 

♦♦♦♦ ♦♦♦ 


♦♦ 


♦♦♦ 


««**«*«* 


•*«* 








July 


August September 


50 







KVILIMI 

120 


110 


100 


90 


80 


70 


•0 


90 


40 


30 


Figure B-3 

Minnesota Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 


For Three Minnesota Grid Cells 
I-Jth Coordinates Symbol 
228,359 * 

231,356 <a> 

235,352 + 


♦♦♦ 

♦♦♦♦ 

♦♦♦ 


♦♦ 


♦♦ 


♦♦ 

« 


«* 


• •••• 

**« M« 

• •• 




♦ ♦ 

♦ ♦♦ 
♦ 


♦ ♦ 

♦ ♦ 


• • 


1 • 

• • 

t 

• » 

• • 

► t 

♦ • 

t 

♦ 9 




July 


August 


September 


51 








Figure B-4 

Iowa Greenness Curves 

Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 

For Three Iowa Grid Cells 
I-Jth Coordinates Symbol 


228,367 * 

IVILIM* : 234,366 @ 

120 ; 235,362 + 



l 

— w' ~ 




1 

i 

♦4 




1 

« 

♦4 ♦ 




I 

» 

♦ ♦ ! 



110 

♦ 

♦4 ♦ 




1 

1 

♦4 ♦ 




1 

» 

♦ ♦ ; 


• 


• 

( 

♦ 4 ♦ 


• 


1 

1 

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8 

100 

♦ 

♦♦ ; 


8 


1 

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8 


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1 

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44 

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48 

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30 

• 

• 

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8 

8 

8 

6 


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July August September 


52 









Figure B-5 

Missouri Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 


For Three Missouri Grid Cells 
I-Jth Coordinates Symbol 


KVILItfl : 
120 ♦ 


110 


100 


90 


90 


70 


90 


SO 


40 


♦♦♦♦ 
♦♦ ♦ 


♦♦ 

♦ 


♦ 

♦♦ 


♦♦ 


227,377 

230,375 

236,379 


@ 

+ 


♦♦♦ 


♦♦♦♦ 

♦♦ 


« 

•a ** 

• • 


•* 


aa 

aa 

aa 

aa 

999999 
99 9 






July 


August 


September 


53 







Figure B-6 

Illinois Greenness Curves 

Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 


For Three Illinois Grid Cells 
I-Jth Coordinates Symbol 


IVItlW 


235,373 


120 

♦ 


• 

238,372 @ 


l 

1 

i 

1 


I 

i 

1 

i 

1 

241,371 + 

110 

« 

♦ 


• 

• 

• 

1 



1 


• 



1 

i 

• 

1 



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t : 



« 

• 

• 

i 

• 

100 

♦ 


♦ •: 

I 


1 

I 


pgi 

• 


1 

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t t: 



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« 

• ♦ 

i 

i 

♦ ♦ ♦ •# 


( 

i 

« ♦ 

• 

*“t ♦ • 

90 

♦ 

• 

i 

i 

♦* 


1 

* 

« f* ♦•*« 

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♦« ♦ 


i 

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♦ | 

*-• ♦♦ 


I 

i 

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* ♦♦♦♦♦# ♦ 


1 

t 

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i 

t * 

80 

♦ 

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i 


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i 

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1 


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• • • 

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♦ 


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• 

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l 

l 


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50 

♦ 


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m 


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• 


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• 

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40 

♦ 


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1 

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1 

1 

ft 


1 

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1 

e 

nm 

% 

30 

1 

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♦ 


• 

• 

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0 

i 

• 

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July 


August September 


54 









iviLitfi : 
120 ♦ 


110 ♦ 


100 ♦ 

• 

I 

I 

I 

• 

90 ♦ 

I 

I 

I 

I 

80 ♦ 


70 ♦ 


•0 ♦ 

• 

I 

I 

I 

I 

50 ♦ 

. ! 

♦ 

so ♦ 


Figure B-7 

Indiana Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 
(DAY) 


For Three Indiana Grid Cells 
I-Jth Coordinates Svmbol 

243,375 

* 

244,372 

@ 

246,370 

+ 


• • 
M t 
t • 
t 

M 

• ♦ ♦ 

M 

t ♦ ♦ 

*4 ♦ 

f*» ♦ 

«*« 

»» ♦ 

«* 

♦♦♦ 

♦ ♦♦♦ *** 


t 

• t • 

• MM 

• ft 

• • ♦ M t 

t ♦♦♦♦ t t 

• t ♦♦♦♦ f 

t • ♦♦ ♦ • 

t ♦ ♦♦ t 

• ♦ ♦ t 


♦ ♦♦ 
♦ ♦ 

♦ 


• • 


** 


«• • 
•• 


• * 


•• 

« 


♦ • 

♦ • 

♦ t 

♦ • 

♦ • 

♦♦ 




t ♦♦ 

t 


July 


August September 


55 








Figure B-8 

Ohio Greenness Curves 

Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 
(DAY) 

For Three Ohio Grid Cells 
I-Jth Coordinates Symbol 


KVILIMI 

1 9A 

1 

1 


228,373 

* 

1 4 U 

• 


252,375 

@ 


• 

• 

1 

i 


254,371 

+ 

no 

1 

i 

♦ 

l 

l 




100 

« 

1 

• 

♦ 

1 

• 

1 



« 

• 


1 

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t 


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1 

• 

l 

*> 

♦ 


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1 


• 

» 

• 

aaa 

a 


! 

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ta 

aa 


1 

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aaa Q ***« 


aa 


( 

« 

sea ssa 


a 

80 

♦ 

ease 


aa 


1 

m 


a 


1 

• 



♦ ♦♦♦♦ a; 


« 

i 



♦♦ aa 

70 

♦ 


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♦♦ ! • 


• 

• 



4884 ♦♦| a 


l 



♦♦ aa 


l 

• 



;♦♦ as 


« 

i 



♦♦ a 

80 

♦ 



♦♦ a 


• 



♦♦aa 


1 

1 



♦♦♦a 


1 

• 



a 


1 

» 



♦♦ 

50 

♦ 



; ♦ 


1 

l 



; ♦♦♦ 


I 



♦♦ 


I 

1 

• 



• ♦ 

8 

40 

♦ 

1 

• 

1 

• 



• 

1 

• 

• 

1 

• 

• 

30 

1 

• 

1 

• 

♦ 



1 

• 

• 

I 

1 

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July 

August 

September 


♦- 


56 









I7ILIMI : 
120 * 


no 


100 


90 


80 


70 


10 


50 


40 


SO 




Figure B-9 

Kentucky Greenness Curves 
Vegetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 
(DAY) 

For Three Kentucky Grid Cells 
I-Jth Coordinates Symbol 

237,380 * 

• 241,378 @ 

247,379 + 


« 

0 • 




♦ ♦« 
♦ 

«♦ 

* 


t 


«* 


♦♦♦♦♦♦♦ ♦♦ 

♦ ♦ ♦♦ 


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♦♦ 


♦ ♦ 




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♦ ♦♦ 

♦ ♦♦ 

♦♦ 


♦♦ 

♦♦ 


♦♦ 


** 


♦ t 

♦♦ M 
♦♦ • 

♦♦♦ •• 

♦ t 

♦♦ M 
♦♦ t 
♦ 


July 


August 


September 














IVILIK1 : 
120 ♦ 


110 ♦ 


100 ♦ 


90 


80 ♦ 

I 


70 ♦ 


80 ♦ 


50 ♦ 

.. ! 

i 


30 ♦ 

-♦ 


Figure B-10 

Tennessee Greenness Curves 
egetation Index Functional Values - EVI Version 
(EVILINE) 

Versus 

Days in July - September 1984 

(DAY) 

For Three Tennessee Grid Cells 
I-Jth C oordinates Symbol 

: 235,383 * 

; 244,385 @ 

248,384 + 


**** 

■** «*• 


*«* 

•«« 

** 


••; 
*• 



♦ 

♦♦♦ 

♦ 


♦♦♦♦♦♦ m 


♦♦♦♦♦ 


♦♦♦♦♦ 

♦ 


♦ 

♦ 

♦ 


♦♦ 


* August 


September 


58 


♦ 4 









s! 

(o) 

1/6-K/» 

S/15-23 

(F) 

(a) 

H-tfi 

7/3I-*/7 

0>) 

7/24-30 

<Q 

7/16-23 

(B) 

7/1-15 

(A) 


E?l 

E?l 

EM 

EM 

EM 

EM 

EM 

251 

is is is 

is is is 

fa is is 

t 5 * 

£ 3 S 

fa fa is 

fa s c 

16 

.74 

.74 

51 a is 

5! 3 S 

2 3J S 

fe fe 8 

£ U >d 

fi n a 

fa fa fa 

fa fa fa 

is is t 

s is * 

5 8 iS 

fa is is 

fa fa fa 

a d e 

•d <« — 

fa fa fa 


JS 

.74 

.74 

si is is 

.92 

.76 

.74 

8 fa is 

test 

V U '"d 
-d — vO 

fa fa fa 


•S 

.92 

.93 

sis 

is is is 

is is is 

is is is 

01 bo S 

Ui a» « 



.74 

69 

.70 

‘*4 *«4 **4 

^ ui >o 

S Vi m 

■d Ov *d 

^ « 

* * *- 

fa fa 3 

3 $ fa 



*4 

.95 

.94 

is is fa 

« » 
u* * O 

is is 3 

OB OD 

*4 U 0* 




.72 

.74 

.76 

8 8 51 

4 • bi 

^ u* 

3 2 5 

fa fa 51 




is t fa 

8 is 3 

s i s 

fa fa fa 





Vnl '*4 j* 

* * G* 

a fa fa 

fa 8 fa 

fa fa 3 






3 

o 

a: 

V 

V 



.7* 

.90 

.91 

3 3 3 

fa s s 

3 fa fa 

.6* 

.73 

.74 

.76 

.73 

.72 



fa 3 fa fa fa fa 
fa fa fa fa 5 fa 





59 


i 


i§ 


vO 


TABLE B-l. Cod&ieDt o i determination (R ) betwee n vegetative indexes (EVI vcrnon), aver ag e d over the "FROM" through the THRU" period, with the Aligns) 1 nd 
October 1 yield forecasts and die final yield eatimam. corn for grain and soybeans, ten «a«e rtudy area, 19*4 







Table B-l shows the matrix of R 2 values for potential relationships of the August 1 and 
October 1 com and soybean yield forecasts and the final yield estimates for the two crops 
to vegetative index means for 36 different periods. Relationship strength for the September 
1 and November 1 yield forecasts was also investigated. Since the patterns for these 
additional forecasts were similar to those presented, they are omitted from the table. The 
coefficients of determination shown on the diagonal (for each month and crop) indicate which 
of the short periods have some relationship to the yield forecasts or estimates. Coverage can 
be quite incomplete for such short time intervals. For some of these periods whole Crop 
Reporting Districts were not represented. Moving just off the diagonal, one can see the 
results of combining two adjoining short periods. For example, when the July 16-23 and July 
24-30 periods are combined the final yield estimate for com attains and R 2 of .67 compared 
to .13 for the earlier period. This type of situation indicates that the July 16-23 period may 
have some marginal information on com condition even though the R 2 for that period alone 
is quite small. On the other hand, final com R 2 ’s are already fairly high for the August 8- 
14 and August 15-23 individual periods (.71 and .87, respectively). They reach .90 for the 
combined 16 day August 8-23 period. 

Many patterns can be observed from the table. Most of them have rational explanations. 
Some of these patterns and explanations are: 


Pattern 
Explanation - 


Pattern 
Explanation - 


Pattern 


Explanation - 


Earlier periods have stronger relationships to the August 1 forecasts. 
The forecasts were made based on survey data and knowledge of 
conditions around August 1 and would be more likely to differ from 
conditions longer after that date. 

Soybean R 2 ’s are often lower than those for com. 

The critical period is longer for soybeans than it is for com (particularly 
over this study area) so that general vegetative conditions in any period 
are not as indicative of the soybean yield determining environment. 
Longer periods that are composed of selected individual periods (those 
with some individual relationship to crop yields, which also form 
adjoining periods with fairly strong relationships) have similar strength 
relationships. 

Means change very little as data is added or deleted as long as the 
means come from fairly long periods with enough observations, and as 
long as the periods added or deleted have strong and similar 
relationships. 


Figures B-ll and B-12 illustrate the selection of periods based on the strength of relationships 
between the vegetative index and the final com for grain yield estimate. Figure B-ll shows 
the com R 2 ’s for individual short periods and for all adjoining two period combinations. 
The periods are labeled A through H from the first period, 7/8-15 (A), through the last 
period, 9/2-9 (H). Thus, period D-E denotes periods D (the Fourth one) and E (the fifth one) 
taken together or July 31 through August 14. From this figure it can be seen that 
individually periods C through G show some explanatory power for final com yield, although 
vegetative indexes from periods E and G are not as strongly related. By examining the two 
period combination R 2 ’s, it can be concluded that periods C-D through G-H exhibit strong 
relationships. This implies that data from periods C through H have a strong relationship to 


60 


com yield. However, because individually the H period vegetative index mean had such a 
weak relationship, only C through G (July 24-September 1) will be given further 
consideration. All the three through eight period combinations that start and end within the 
C through G interval (thus, five periods is the maximum in this case) are shown in figure 
B-12. Three periods (D-F, C-F, and D-G) have an R 2 of .93 for the final com yield to mean 
vegetative index relationship. Two others (C-G and C-E) are at .92. 

The same type of analysis is shown for soybeans in figures B-13 and B-14. Individual short 
periods with some explanatory information on soybean final yield appear to be C, D, E, F 
and possibly G. The two period combinations confinn the value of vegetative index 
information from the first four of these periods (C-F) and suggest that period G (August 24- 
September 1) may help explain State level variability in soybean yields. Periods A, B and 
H individually showed no relationship to soybean final yield estimates and even when 
combined with some more strongly related individual periods (C and G) failed to attain very 
large R 2 ’s. All of the three period and up combinations which start and end within C through 
G (July 24-September 1) are shown in Figure B-14. 


61 


Figure B-ll 

Coefficient of Determination 


of the 

Corn for Grain Final Yield Estimate 
with the 


Mean Vegetative Index - EVI Version (CORNRSQ) 
Over Individual Short Periods 
and Adjoining Two Period Combinations 


Symbol is value of NOCOMB 

OORKRSS ; 


1 0 

1 

1 

♦ 

1 


• 

• 

• 

• 

• 

a 


0 9 

1 

1 

• 

+ 


• 

• 

• 

a 

• 

> 

C-0 


1 

1 

1 


• 

• 

1 

1 

o. a 

♦ 

1 

1 


• 

• 

• 

• 

i 


0 7 

♦ 

1 

B-C 

• 

• 

• 

• 

• 



1 


t 

4 


o a 

• 

1 

♦ 

1 


1 

• 

• 

• 

1 

< 


0.5 

1 

• 

♦ 

• 

1 


• 

1 

* 

1 

• 

1 

1 


0 4 

1 

« 

• 

♦ 

• 

• 


• 

• 

• 

1 

a 

i 

• 

0 


0.3 

• 

1 

• 

♦ 

A-l t 

a 

a 

a 

a 

a 



1 

» 


a 

a 

• 


0 2 

1 

• 

♦ 

• 

• 


a 

a 

a 

a 

a 

a 


0.1 

• 

1 

• 

♦ 

1 

I 

a 

a 

a 

a 

a 

a 

9 



• 

:i 

i 


a 

a 

a 

a 


0 0 

• 

♦ 


a 

a 

a 



A 

1 

C 

D 


D-.E 


* 

> 


E-F 


F»G 


S-H 


1 




1 


♦ 


♦ 


t r o ■ 




62 














Figure B-12 

Coefficient of Determination 
of the 

Corn for Grain Final Yield Estimate 
with the 

Mean Vegetative Index - EVI Version (CORNRSQ) 
Over Adjoining Periods of Three or More 
Short Periods Within the Restricted Internal (C-G) 


Symbol is value of NOCOMB 


C0RNRS4 
0 93 






♦ 


C-F 0-6 

D-F 


♦ 


0 92 


♦ > 



C-G 

» - ■ 






0.91 


0 90 ♦ 

C 


0 


> 

I 



T 


■S 

a 


mioo 

63 









Figure B-13 

Coefficient of Determination 
of the 

Soybean Final Yield Estimate 
with the 

Mean Vegetative Index - EVI Version (SOYBRSQ) 
Over Individual Short Periods 
and Adjoining Two Period Combinations 


Symbol is value of NOCOMB 

SOYBJttS 


0.7* 

• 

• 

♦ 

0.79 

♦ 

0.74 

♦ 

0.72 

♦ 

0 70 

♦ 

0 99 

♦ 

0 99 

♦ 

0 94 

♦ 

0 92 

♦ 

0 90 

♦ 

0 SI 

♦ 

0 56 

♦ 

0 54 

♦ 

0 52 

♦ 

0 50 

♦ 

0 49 

♦ 

0. 46 

♦ 

0 44 

♦ 

0.42 

♦ 

0 40 

♦ 

0 36 

♦ 

0 36 

♦ 

0 34 

♦ 

0 32 

♦ 

0.30 

♦ 

0 26 

♦ 

0 26 

♦ 

0 24 

♦I— 

0 22 

♦ 

0 20 

♦ 

0.16 

♦ 

0 16 

♦ 

0 14 

♦ 

0. 12 

♦ 

0 10 

♦ 

0 08 

♦1 

0 06 

♦ 

1 


s-c 


A-l 


D-E 


E-F 


F-S 


C-D 


- »« 

A 


C 


»♦« 

t 


»♦« 

r 


pnioo 

64 














Figure B-14 

Coefficient of Determination 
of the 

Soybean Final Yield Estimate 
with the 

Mean Vegetative Index - EVI Version (SOYBRSQ) 
Over Adjoining Periods of Three or More 
Short Periods Within the Restricted Internal (C-G) 


Symbol is value of NOCOMB 


S0YBRS4 
0 90 


O.Tf 


0 79 


0 77 


0.76 


0.75 


0.74 


0-6 


D-F 


£-6 


C-F 



100 


65 


♦ 9 











Four of the periods with the strongest relationships to the final yield estimate for both the 
com and soybean crops were subsequently evaluated by deriving the state mean vegetative 
index in the manner shown in Figure 1. The mean grid cell indexes for each of these 
periods were mapped to counties and then aggregated by previous year acreage county 
weights to the state level. This produced higher R 2 ’s for some periods than the previous 
analysis and probably reflects the more appropriate and detailed weighting of where the 
crops are within states and within Crop Reporting Districts. The comparison results are 
shown in Table B-2. 

TABLE B-2. Comparison of coefficients of determination (R 2 ’s) between crop yield estimates 
and mean vegetative indexes when state mean vegetative indexes are weighted via Crop 
Reporting Districts (CRD’s) or via Counties, by selected periods, 1984, Ten State Study Area. 



Com 

- R 2 ’s 

Soybean - R 2, s 

Period 

CRD 

Countv 

CRD 

Countv 

D-F (7/31-8/2) 

.93 

.941 

.79 

.775 

D-G (7/31-9/1) 

.93 

.926 

.80 

.847 

C-F (7/24-8/23) 

.93 

.908 

.77 

.770 

C-G (7/24-9/1) 

.92 

.893 

.76 

.806 


It appears to be fairly important to include available vegetative index values from the nine 
day period of August 24 through September 1 (period G) for soybeans, but to exclude them 
in developing the com for grain final estimate. This may reflect the fact that the yield 
determining period generally ends earlier of com than soybeans, so that general conditions 
some time after the critical com period ends provides less information on the environment 
for that crop. Table B-2 also suggests that it is best to exclude period C (July 24-30) for 
both crop’s final yield. This may be related to some of the earlier "greenness" (as seen in 
Figures B-l through B-10) still present during the later part of July. This "greenness" may 
not be directly associated with environmental conditions effecting com and soybean yields as 
expressed by general vegetative conditions somewhat later than when the critical periods for 
the crops began. 

Again, the critical periods selected for relating final yield estimates to mean vegetative 
indexes at the state level are July 31 - August 23 for com and July 31 - September 1, for 
soybeans. Weighting via Crop Reporting Districts, as discussed in this Appendix, is 
preferable for shorter periods when county coverage would be very incomplete. However, 
a somewhat larger set of the longer periods (than reported here) might be effectively 
evaluated when state vegetative index means are derived via county mapping and weights. 


66 








APPENDIX C 


STATISTICAL ANALYSIS SYSTEM REGRESSION 
OUTPUT FOR CORN AND SOYBEAN MODELS BASED ON 
EVI AND NVI VEGETATIVE INDEX VERSIONS AND YIELD VERSUS 

NVI PLOTS 


67 


EXHIBIT C-l 

STATISTICAL ANALYSIS SYSTEM OUTPUT 
Regression of Final Corn for Grain Yield (CYDFN) 

on (he 

EVI Version of the Corn for Grain 
Vegetative Index (EQMECI9) 


SAS 


Model: MODEL1 

Dep Variable: CYDFN 

Analrsia of Variance 




Sum cf 

Mean 



Source 

DF 

Squares 

Square F Value 

Prob>F 


M'-'del 

1 3401.14850 3401.14850 127.592 

0 0001 


Error 

8 

213 25150 

26 65644 



C Total 

9 3614.40000 




Root 

MSE 

5 16299 

R-Square 0.9410 



Dep M 

ean 

97 60000 

Adj R-Sq 0.9336 



C V 


5.28995 




Parameter 

Estiaatts 






Parameter 

Standard T 

for HO: 


Variable 

DF 

Estimate 

Error Parameter^ 

Prob > :t: 

INTERCEP 

1 

-16.250967 

10.21055398 

-1.592 

0.1501 

EQMECI9 

1 

1 600619 

0 14170205 

11.296 

0.0001 



Predict 




Obs 

CYDFN 

Value 




1 

112.0 

118.9 




2 

114 0 

114.9 




3 

117.0 

119.2 




4 

100.0 

93.4393 




5 

107.0 

103 8 




6 

80.0000 

85 4765 




7 

66.0000 

66 8332 




6 

118.0 

113 5 




9 

67.0000 

71 . 1318 




10 

95.0 

88.7733 





Sum of Squared Residuals 213.2515 

Predicted kesid SS (Press) 315 3164 


68 


Exhibit C-2 

STATISTICAL ANALYSIS SYSTEM OUTPUT 
Regression of Final Soybean Yield (SYDFN) 
on the 

EVI Version of the Soybean 
Vegetative Index (EQMESIO) 


SAS 

Model: M0DEL1 

Dep Variable: SYDFN 

Analysis of Variance 





Sun of Mean 


Source 

DF 

Squares Square F Value Prob>F 

Model 

1 

2 

29 

53774 229 53774 44 

396 0 0002 

Error 

8 


41 

.36226 5 17028 


C Total 

9 

270 

.90000 


Root 

MSE 


2 

27383 R-Square 0 

8473 

Dep Mean 


28 

90000 Adj R-Sq 0 

8282 

C. v 



7 

86791 


Parameter 

Estimates 







Parameter Standard 

T for HO: 

Variable 

DF 


Estimate Error 

Parameter=0 

INTERCEP 


1 


-9 049912 5 74082661 

-1.576 

EQMESIO 


1 


0.528877 0 07937515 

6 663 





Predict 


Obs 

SYDFN 


Vaiue 


1 

31 

5000 


34.3013 


2 

32 

0000 


31 8967 


3 

34 

5000 


34 8049 


4 

29 

0000 


26 6335 


5 

33 

0000 


30 3580 


6 

20 

5000 


24.2815 


7 

23 

0000 


21 2933 


8 

36 

5000 


34 9618 


9 

23 

0000 


23 4398 


10 

26 

0000 


27.0290 



Sum of Squared Residuals 41 3623 

Predicted Resid SS (Press) 64 2779 


> ;t; 

. 1536 
0002 


69 


or m w k< r > ~ n ^ ^ ^ o 


Figure C-l 


CORN FOR GRAIN - STATE LEVEL 
Official Yield Estimate (bushels per acre) 

Versus 

Corn Vegetative Index 
(NVI Version) 


120 ♦ 


ino ♦ 


80 


70 


60 ♦ 


26 


Model: N=10, R 2 = 94, 
EC =-31,59+3.53 VC. a 



- ♦- ---4 -*---♦ - ------- -* - 

28 30 32 34 36 38 40 42 44 


CORN VEGETATIVE INDEX 


70 




o r n « *< 


Figure C-2 

SOYBEANS - STATE LEVEL 
Official Final Yield Estimate (bushels per acre) 

Versus 

Soybean Vegetative Index 
(NVI Version) 


40 ♦ 

I 

I 

1 Model: N=10, R 2 =.75, 

! ES n =-7.26+0.96 VS. n 


H 


35 ♦ 


30 ♦ 


25 ♦ 


20 ♦ 



- + --- ♦ - ♦-♦-*- * 

28 29 30 31 32 33 34 35 38 





38 39 40 41 42 43 44 


SOYBEAN VEGETATIVE INDEX 


71 





Exhibit C-3 
SAS OUTPUT 

Regression of Final Corn for Grain Yield (CYDFN) 

on the 

NYI Version of the Corn lur Grain 
Vegetative Index (EQMNCI9) 


SAS 

Model: MODEL1 

Dep Variable: CYDFN 


Analysis of Variance 




Sum of 

Mean 


Source 

DF 

Squares 

Square 

F Value 

Model 

1 

3391 49534 

3391 49534 

121.720 

Error 

8 

222 90466 

27.86308 


C Total 

9 

3614.40000 



Root 

MSE 

5 27855 

R-Square 

0.9383 

Dep 

Mean 

97.60000 

Adj R-Sq 

0.9306 

C V. 


5 40835 




Parameter Estimates 


Variable 

DF 

Parameter 

Estimate 

Standard 

Error 

T for HO: 
Parameter^ 

INTERCEP 

1 

-31.585946 

11 82776820 

-2.670 

EQMNCI9 

1 

3.5342C7 

0 32033987 

11.033 


Obs 

CYDFN 

Predict 

Value 

1 

112 0 

117 3 

2 

114 0 

112 2 

3 

117 0 

119 1 

4 

100 0 

95 1 

5 

107 0 

106 1 

6 

80 0<000 

87.4483 

7 

66 0000 

62 7135 

8 

118.0 

114 0 

9 

67.0000 

73.4120 

10 

95.0 

68.6963 


Sam of Squared Residuals 222 9047 

Predicted Resid SS (Press) 350 6414 


> :t: 

.0283 
. 0001 


72 





Exhibit C-4 
SAS OUTPUT 

Regression of Final Soybean Yield (SYDFN) 
on the 

NVI Version of the Soybean 
Vegetative Index (EQMNSIO) 


SAS 


Model: MODEL1 

Dep Variable: SYDFN 


Analysis of Variance 


Source DF 


Sum of 
Squares 


Mean 

Square 


F Value Prob>F 


Model 
Error 
C Total 


1 204 19806 204.19806 

8 66 70194 8.33774 

9 270 90000 


24.491 0.0011 


Root MSE 
Dep Mean 

C V 


2 88751 R-Square 

28 90000 Adj R-Sq 

9 99140 


0 7538 
0.7230 


Parameter Estimates 


Variable 

DF 

Parameter 

Estimate 

Standard 

Error 

T for HO: 

Parameter^ 

Prob > : T : 

INTERCI? 

1 

-7.256920 

7.36300969 

-0 986 

0.3532 

EQMNSIO 

1 

0.963342 

0.19466091 

4.949 

0 0011 


Obs 

SYDFN 

Predict 

Value 

1 

31 5000 

34 8035 

2 

32 0000 

31 8288 

3 

34 5000 

34 6043 

4 

29 0000 

27 8062 

5 

33 0000 

30 6260 

6 

20 5000 

25.0374 

7 

23 0000 

20 2372 

8 

36 5000 

32.4040 

9 

23 0000 

24 6185 

10 

26 0000 

27.0342 


Sum of Squared Residuals 66.7019 

Predicted Resid SS (Press) 115.7222 


73 


APPENDIX D 


STUDY AREA AND INDIVIDUAL STATE PERFORMANCE 
TABLES FOR RESULTS AT VARIOUS LEVELS FOR CORN FOR GRAIN 
AND SOYBEANS, AND AT THE COUNTY LEVEL FOR CORN WHEN 
SOME COUNTIES ARE EXCLUDED BY AN OBJECTIVE RULE 
OR BY DELETION OF OBVIOUS OUTLIERS 


0 


74 


TABLE D-l. Performance measures at the State, district and county levels for satellite generated com 
for grain yield estimate indications obtained by considering official estimates as "truth”, 1984, ten State 
study area and individual States. 


APPLICATION 


AREA 

N 

R 2 

R 

MSE 

VAR 

BIAS" 

RMSE 

ST.DEV. RSD 





(bushels/acre) 2 

.bushels/acre- 


% 





STATE LEVEL 





TEN STATES 

10 

.94 

.97 

26.66 

26.66 

0.00 

5.16 

5.16 

5.3 




DISTRICT LEVEL 





TEN STATES 

84 

.75 

.87 

181.40 

178.76 

-1.63 

13.47 

13.37 

13.7 

NORTH DAKOTA 

9 

.84 

.92 

34.42 

34.03 

-0.62 

5.87 

5.83 

8.8 

SOUTH DAKOTA 

9 

.03 

-.20 

934.08 

638.17 

-17.20 

30.56 

25.26 

37.7 

MINNESOTA 

9 

.80 

.90 

181.70 

158.94 

4.77 

13.48 

12.61 

11.8 

IOWA 

9 

.44 

.66 

75.89 

75.52 

0.61 

8.71 

8.69 

7.8 

MISSOURI 

9 

.56 

.75 

130.81 

118.67 

-3.48 

11.44 

10.89 

13.6 

ILLINOIS 

9 

.76 

.87 

38.68 

38.05 

0.80 

6.22 

6.17 

5.4 

INDIANA 

9 

.64 

.80 

31.58 

31.28 

-0.54 

5.62 

5.59 

4.8 

OHIO 

9 

.75 

.83 

86.32 

67.81 

-4.30 

9.29 

8.23 

7.0 

KENTUCKY 

6 

.30 

.55 

57.39 

37.96 

4.41 

7.58 

6.16 

6.2 

TENNESSEE 

6 

.72 

.85 

211.97 

204.18 

2.79 

14.56 

14.29 

15.0 





COUNTY LEVEL 





TEN STATES 

889 

.63 

.80 

249.31 

248.69 

-0.79 

15.79 

15.77 

16.2 

NORTH DAKOTA 

47 

.29 

.54 

217.80 

215.51 

-1.51 

14.76 

14.68 

22.2 

SOUTH DAKOTA 

62 

.04 

.18 

683.58 

594.04 

-9.46 

26.15 

24.37 

36.4 

MINNESOTA 

81 

.56 

.75 

261.26 

260.86 

0.63 

16.16 

16.15 

15.1 

IOWA 

99 

.27 

.52 

178.70 

177.14 

1.25 

13.37 

13.31 

11.9 

MISSOURI 

114 

.30 

.54 

292.16 

283.18 

-3.00 

17.09 

16.83 

21.0 

ILLINOIS 

102 

.38 

.62 

204.80 

203.86 

0.97 

14.31 

14.28 

12.5 

INDIANA 

92 

.46 

.67 

97.28 

96.43 

-0.92 

9.86 

9.82 

8.4 

OHIO 

86 

.42 

.65 

160.92 

151.35 

-3.09 

12.69 

12.30 

10.4 

KENTUCKY 

113 

.15 

.39 

177.06 

145.54 

5.61 

13.31 

12.06 

12.1 

TENNESSEE 

93 

.09 

.29 

356.70 

348.96 

-2.78 

18.89 

18.68 

19.7 


The bias at the district and county level would be very close to zero for a harvested acreage 
weighted mean. However, all counties (districts) were given equal weight in this analysis. 


RSD is the standard deviation relative to the mean (equal weights) com for grain yield (97.6 
BU./A) for the ten States and to the final yield estimate for individual States. 


75 




TABLE D-2. Performance measures at the State, county, and district levels for satellite generated 
soybean yield estimate indications obtained by considering official estimates as "truth", 1984, ten State 
study area and individual States. 


APPLICATION 

AREA 

RSD 2 " 

N 

R 2 

R 

MSE 

VAR 

BIAS 1 ' 

RMSE 

ST.DEV. 






(bushels/acre) 2 

.bushels/acre 


% 





STATE LEVEL 





TEN STATES 

10 

.85 

.92 

5.17 

5.17 

0.00 

2.27 

2.27 

5.3 




DISTRICT LEVEL 





TEN STATES 

76 

.74 

.86 

15.93 

14.98 

-0.97 

3.99 

3.87 

13.4 

NORTH DAKOTA 

6 

.78 

.88 

9.23 

9.10 

0.36 

3.04 

3.02 

13.1 

SOUTH DAKOTA 

7 

.01 

.08 

89.74 

41.29 

-6.96 

9.47 

6.43 

28.0 

MINNESOTA 

7 

.81 

.90 

14.38 

12.97 

-1.19 

3.79 

3.60 

10.9 

IOWA 

9 

.77 

.88 

5.79 

5.79 

0.09 

2.41 

2.41 

7.7 

MISSOURI 

9 

.52 

.72 

14.30 

14.27 

-0.17 

3.78 

3.78 

18.4 

ILLINOIS 

9 

.61 

.78 

6.98 

6.90 

0.28 

2.64 

2.63 

8.2 

INDIANA 

9 

.73 

.86 

3.56 

3.46 

-0.32 

1.89 

1.86 

5.4 

OHIO 

8 

.71 

.85 

6.83 

4.88 

-1.40 

2.61 

2.21 

6.1 

KENTUCKY 

6 

.06 

.24 

6.13 

6.12 

-0.09 

2.48 

2.47 

8.5 

TENNESSEE 

6 

.43 

.65 

9.85 

8.71 

-1.07 

3.14 

2.95 

11.3 





COUNTY LEVEL 





TEN STATES 

756 

.64 

.80 

22.07 

21.02 

-1.03 

4.70 

4.58 

15.8 

NORTH DAKOTA 

28 

.59 

.77 

10.49 

10.08 

0.64 

3.24 

3.18 

13.8 

SOUTH DAKOTA 

36 

.00 

.04 

50.47 

36.47 

-3.74 

7.10 

6.04 

26.3 

MINNESOTA 

76 

.56 

.75 

25.15 

23.16 

-1.41 

5.01 

4.81 

14.6 

IOWA 

99 

.36 

.60 

16.23 

16.16 

-0.26 

4.03 

4.02 

12.8 

MISSOURI 

95 

.23 

.48 

29.37 

28.76 

-0.78 

5.42 

5.36 

26.1 

ILLINOIS 

102 

.35 

.59 

18.94 

18.89 

-0.21 

4.35 

4.35 

13.6 

INDIANA 

92 

.57 

.75 

10.46 

10.05 

-0.64 

3.23 

3.17 

9.2 

OHIO 

68 

.34 

.58 

16.02 

13.64 

-1.54 

4.00 

3.69 

10.1 

KENTUCKY 

81 

.11 

.33 

13.31 

13.29 

-0.15 

3.65 

3.65 

12.6 

TENNESSEE 

79 

.02 

.13 

40.57 

30.11 

-3.23 

6.37 

5.49 

21.1 


- The bias at the district and county level would be very close to zero for a harvested acreage weighted 
mean. However, all counties (districts) were given equal weight in this analysis. 


- RSD is the standard deviation relative to the mean (equal weights) soybean yield (28.9 BU./A) for 
the ten States and to the final yield estimate for individual States. 


76 




TABLE D-3. Performance measures at the county level for satellite generated com for grain yield 
estimate indications obtained by considering official estimates as "truth" when data for some counties 
are excluded based on two different criteria, 1984, ten State area, and individual States. 


APPLICATION 

AREA N R 2 R MSE VAR BIAS RMSE ST.DEV. RSD 1 ' 

(bushels/acre) 2 .bushels/acre- % 

COUNTY LEVEL 


31 Counties Excluded by Irrigation Rule 


TEN STATES 

858 

.69 

.83 

200.74 

200.66 

0.28 

14.17 

14.17 

14.5 

NORTH DAKOTA 

40 

.69 

.83 

66.95 

63.01 

1.98 

8.18 

7.94 

12.0 

SOUTH DAKOTA 

49 

.78 

.88 

76.13 

73.81 

1.52 

8.73 

8.59 

12.8 

MINNESOTA 

78 

.59 

.77 

250.90 

248.91 

1.41 

15.84 

15.78 

14.7 

IOWA 

99 

.27 

.52 

178.70 

177.14 

1.25 

13.37 

13.31 

11.9 

MISSOURI 

107 

.19 

.43 

297.05 

290.28 

-2.60 

17.24 

17.01 

21.3 

ILLINOIS 

101 

.38 

.62 

206.08 

204.96 

1.06 

14.36 

14.32 

12.6 

INDIANA 

92 

.46 

.67 

97.28 

96.43 

-0.92 

9.86 

9.82 

8.4 

OHIO 

86 

.42 

.65 

160.92 

151.35 

-3.09 

12.69 

12.30 

10.4 

KENTUCKY 

113 

.15 

.39 

177.06 

145.54 

5.61 

13.31 

12.06 

12.1 

TENNESSEE 

93 

.09 

.29 

356.70 

348.96 

-2.78 

18.89 

18.68 

19.7 


COUNTY LEVEL 

11 Obvious Outlier Counties Excluded 


TEN STATES 

878 

.68 

.83 

205.46 

205.46 

-0.05 

14.33 

14.33 

14.7 

NORTH DAKOTA 

46 

.50 

.70 

123.00 

123.00 

-0.08 

11.09 

11.09 

16.8 

SOUTH DAKOTA 

52 

.67 

.82 

109.93 

109.93 

0.06 

10.48 

10.48 

15.6 

MINNESOTA 

81 

.56 

.75 

261.26 

260.86 

0.63 

16.16 

16.15 

15.1 

IOWA 

99 

.27 

.52 

178.70 

177.14 

1.25 

13.37 

13.31 

11.9 

MISSOURI 

114 

.30 

.54 

292.16 

283.18 

-3.00 

17.09 

16.83 

21.0 

ILLINOIS 

102 

.38 

.62 

204.80 

203.86 

0.97 

14.31 

14.28 

12.5 

INDIANA 

92 

.46 

.67 

97.28 

96.43 

-0.92 

9.86 

9.82 

8.4 

OHIO 

86 

.42 

.65 

160.92 

151.35 

-3.09 

12.69 

12.30 

10.4 

KENTUCKY 

113 

.15 

.39 

177.06 

145.54 

5.61 

13.31 

12.06 

12.1 

TENNESSEE 

93 

.09 

.29 

356.70 

348.96 

-2.78 

18.89 

18.68 

19.7 


V RSD is the standard deviation relative to the mean (equal weights) com for grain yield (97.6 
BU./A) for the ten States and to the final yield estimate for individual States (with all counties 
with the crop included therein). 


77 


U. S. C0«ERNI"£NT PRINTING OF F I CE :1 98 9-24 1 -859 : 00279/NASS