A model based on multiple regression was developed to estimate soybean yields for the seven soybean-growing states of Brazil. The meteorological data of these seven states were pooled and the years 1975 to 1980 were used to model since there was no technological trend in the yields during these years. Predictor variables were derived from monthly total precipitation and monthly average temperature

Callis, S. L.

Sakamoto, C.

English

NASA Technical Reports Server

YM-N4-04455 
J S C  18907 t 
.* 
A Joir:t Program for 
Agriculture and 
Resources Inventory 
Surveys Through 
Aerospace - 
Remote Sensing 
Yield Wocit:. Development JANUARY 16, 1984 
3P.r.Z 1 L SOYBEAN Y I E U )  COVARIANCE MODEL 
( E $ 4 -  10 134)  bE,Ai,IL S b Y t E A h  Y I E L D  C L V A E I M ~ C L  hdk-2  1922 
H(;XL (Natio:.al cceh1.i~ aria A t a o s p h e r i c  
A d m l c i s t r a t l o ~ ~ )  25  p .;L i i 3 i / E k  A 0 1  LSLL 02C Llnc id s 
3 G O l i . 4  
SUSAN L ,  CALL1 S 
CLARENCE SAKAMOTO 
USDA/NOAA 
C I A  /MODEL RANCH 
b ROO 1 200 ? %  E ERA BUIG 
fog CHERAY STREE! OLUMBIA, MO 65201 
Lyndon B. Johnson Space Center 
Houston. Texas 77Q58 
https://ntrs.nasa.gov/search.jsp?R=19840013854 2020-03-20T23:59:26+00:00Z
JSC Form 1424 (Rrv N m  75) 
'For salo bv the Nat~onal Technical Information Smlce. Spcngfield. Virginia 22161 
3. R m p a t ' s  Catalog No. 
5. Report Date 
January 16, 1984 
6. f'erformlng Organlratcon Code 
8. Performcng 0rganczat:m Rcpat No. 
10. Work Unct No. 
11. Contract or Grant No. 
13. Type of Repon and Percod Covered 
14. Sponsoring A- code 
1. Report No. 
\IM-N4-04455, ;SC 18907 
NASA - JSC 
2. Gowrnment Accesscon No. 
4. Tctle and Subtctle 
B r a z i l  5ovbean Y ie l  d Covariance Model 
7. Author(s1 
Susan L. C a l l i s  and Clarence Sakamoto 
9. Perforrncng Organlation hbme and Address 
USDCjNOAA 
CIAD/Model s Branch 
Room 200, Federal Bldg, 608 Cherry S t -  
Columbia, MO 65201 
12. Sponsor~ng Agency Name and Address 
Na t ions l  Aeronautics and Space Admin i s t r a t i  on 
Lyndon B. Johnson Space Center 
Houston, TX 77058 
IS. Supplementary Notes 
16. Abmm 
A model based on m u l t i p l e  regress ion was developed t o  es t imate  soybean y i e l d s  f o r  t h e  
seven soybean-growing s t a t e s  o f  B r a z i l .  The meteoro log ica l  data o f  these seven s ta tes  
were "pooled" and t h e  years 1975 t o  1980 were used t o  model s ince the re  was no 
techno log ica l  t rend  i n  the  y i e l d s  du r ing  these years. P r e d i c t o r  va r iab les  were 
der ived from monthly t o t a l  p r e c i p i t a t i o n  and monthly aversge temperature. 
17. Key Words (Suqgsstsd by Authu(s1) 
Mu1 t i p 1  e regress i o n  ana lys i s  
P red ic to r  va r iab les  
'8. D~sn~butcon Statement 
19. ~ s c w ~ t y  a m l f .  (of thk myor*' 
Unc lass i f i ed  
1 A 
21. No. of Papss 
I 2 4 
20. Secur~ty Classif. (of thls psg) 
Unc lass i f i ed  
22. Rice' 
BRAZIL SOYBEAN Y I E L  D COVARIANCE MODEL 
Susan L. C a l l i s  
and 
C l  arence Sakamoto 
AISC Models Branch 
January 16, 1984 
I NTRODUCTI ON 
The put-pose o f  t h i s  study was t o  se lec t  weather va r iab les  t h a t  could be 
used t o  estimate the soybean y i e l d s  f o r  t he  country of B raz i l .  Soybean produc- 
t i o n  i n  Brazi 1 had i t s  incep t ion  i n  t he  s t a t e  of R io  Grande do Sul where 
soybeans were f i r s t  p lanted i n  r o t a t i o n  w i t h  wheat. Present ly,  soybeans a re  
planted i n  seven southern states:  R io  Grande do Sul, Santa Catarina, Parana, 
Sao Paulo, Mato Grosso, Goias and Minas Gerais. This means t h a t  a v a r i e t y  o f  
growing condi t ions are covered i n  t h i s  extensive area. F igure 1 i s  a map o f  
t he  soybean-growi ng areas of Brazi  1. 
The northern pa r t  o f  t h e  soybean area, i nc l ud ing  t he  s ta tes o f  Mato Grosso, 
Goias, and Minas Gerais, a re  character ized by a "wet-arad-dry" c l ima te  w i t h  a d r y  
season o f  two or  more months. The r e s t  of t he  area i s  subt rop ica l  humid w i t h  
r e l a t i v e l y  abundant r a i n f a l l  which i s  we1 l - d i  s t r i  buted throughout t h e  year bu t  
w i t h  s l i g h t l y  more r a i n f a l l  i n  t he  warm months. Summers are hot and w in te rs  
r e l a t i v e l y  mild. Temperatures i n  t h e  summer are above 400C i n  t he  p l a i n s  o f  
R io  Grande do Sul when warm a i r  masses penetrate t h e  plains.  Southern Sao 
Paulo i s  t he  northern l i m i t  f o r  f r o s t  occurrence. 
The soybean growing season begins w i t h  p l a n t i n g  i n  October and November and 
runs through A p r i l  and May when harvest s ta r ts .  
METHOD 
Mu1 t i p l e  regression ana lys is  o f  y i e l d  w i t h  se lected agroc l imat ic  ind ices  
was used t c  der i ve  a su i t ab l e  model. The f i r s t  approach taken was t o  develop a 
model f o r  each state. However, l a ck  o f  data f o r  several s ta tes  posed a problem 
and no su i t ab l e  models were derived. Therefore, i t  was decided t o  c rea te  a 
covariance model whereby a l l  t h e  ava i l ab l e  data a re  combined t o  ob ta in  a model 
f o r  the  country. 
ORIGINAL PAGE C9 
9F POOR QUALITY 
Figure 1. Soybean-proving a r e a  of B r a z i l .  
(Pitcher, 1971) 
Since moisture stress was considered a prime determinant o f  y ie ld ,  the 
index P-PET (p rec ip i t a t i on  m i  nus potent ia l  evapotranspiration) was used i n  the 
regressions. 
The regression equation i s :  
A 
Y = U + BID + B2RDFNi + B3(P-PET)i + E 
where 
A 
Y = Estimated y ie ld ,  
a = Constant, 
B j  = Coef f ic ients of the variables j = 1 - 3, 
D = Dummy var iable t o  adjust each state 's  y i e l d  t o  a base y i e l d  set by 
Rio Grande's do Sul 's y ie ld ,  
RDFNi = Deviat ion from normal o f  t o t a l  p rec ip i t a t i on  f o r  month i , 
P-PET1 = P rec ip i t a t i on  minus PET f o r  month i , and 
E = Unexplained e r ro r  
I n  developing the model, various procedures o f  the S t a t i s t i c a l  Analysis 
System (SAS I n s t i t u t e  Inc., 1979) were used. The procedures used and the 
operations performed w i t h  each are summarized i n  t he  Appendix. The .elected 
model had the highest R~ and included variables s i g n i f i c a n t  a t  (o r  close t o )  
the 10 per cent leve l  and agronomically meaningful. 
DATA 
The Braz i l  crop data f o r  1961 t h r u  1977 were obtained from the  Foreign 
Agr icu l tura l  Service (Sam Ruff, personal communication, 1982). The data were 
recorded w i th  year o f  y i e l d  as year o f  harvest, so the  weather in f luencing 
the crop occurred during year-1. 
Meteorological data from 1975 through 1980 were used t o  model because 
there i s  no apparent trend i n  the y i e l d  data during t h i s  period. Table 1 1 i s t s  
- ORIGINAL PAGE M' 
OF POOR QUALITY 
a Montes Cleros 
Figure 2. Location of Meteorological Stations Used to Derive 
Data Sets for the Brazil Soybean Model. 
STATE 
-
Goias 
Mato Grosso 
Minas Gerais 
Parana 
METEOROLOGICAL S TAT1 OK 
Bras i l i a /Cruze i ro  
Goiania 
Ponta Pora 
Pres  Prudente 
Foz do Iguacu 
Montes Claros 
Araxa 
Londrina 
Santa  Branca 
Foz do Iguacu 
Por to  Uniao 
Rio Grande do Sul Ij u i  
Veranopolis 
Farroupi iha  
Sao B ~ r j a  
Passo Fundo 
J u l i o  de Cas t i lhas  
Santa  Maria 
Santa  Ca ta r ina  
Sao Paulo 
Por to  Uniao 
Sao Joaquim 
Vacaria 
Pindorama 
Ribei ro  Pre to  
Mococa 
Bauru 
Jau  
Limeira 
Camp i n a s  
Monte Alegre do S u l  
T i e t e  
Sao Pa7:lo 
Jundiqr  
Table 1. Meteorological  S t a t i o n s  Used t o  Derive Data S e t s  
f o r  the  B r a z i l  Soybean Model. 
t h e  s t a t i ons  used t o  der i ve  t he  meteorological  da ta  se t  f o r  each state.  
F igure 2 shows the l oca t i on  of each s ta t ion .  The seven s ta tes  o f  R io  Grande 
- 1 
do Sul, Santa Catarina, Parana, Sao Paulo, Mato Grosso, Goias, and Minas Gerais i 
8 
were included i n  the covariance model. 
1 
PROCEDURES , 
. The o r i g i n a l  va r iab les  used i n  t h e  regress ion equat ion included "dummy 
- .  
v a r i  ables" f o r  s i x  o f  t he  seven s ta tes  (Rio  Grande do Sul was t h e  excep t i r k  . ; 
Thit "durnmy var iab les"  ad jus t  t h e  con t r i bu t i ons  t o  y i e l d  o f  each o f  t he  s ta tes  t 
t o  a base y i e l d  which, i n  t h i s  case, i s  Rio  Grande do Su l ' s  y i e l d .  Weather 
va r iab les  selected r e f l e c t e d  ava i l ab l e  no i s t u re  f o r  t h e  months December through 
March. The var iab les  which were s i g n i f i c a n t  a t  t he  10 per cent l e v e l  were t h e  
"dummy var iab les"  f o r  Sao Paulo, Parana, and Santa Catar ina and t h e  P-PET fo r  
January and February (see the  Appendix f o r  a  d e f i n i t i o n  o f  P-PET). The coef- 
f i c i e n t  f o r  the  Santa Catar ina "dummy var iab le "  was negative, i nd i ca t i ng '  i t s  
y i e l d  was below t h a t  o f  t h e  norm set  by R io  Grande do Sul; t h e  c o e f f i c i e n t s  
f o r  t he  o ther  dummy var iab les  were pos i t i ve .  The c o e f f i c i e n t s  f o r  January and 
February P-PET were pos i t i ve ,  i n d i c a t i n g  a  need f o r  mois ture du r i ng  those 
c r i t i c a l  months. The s t a t i s t i c s  o f  t h e  selected model a re  summarized i n  Table 2. I 
TEST RESULTS ! 
A j a ckkn i f e  t e s t  was run on t h e  f i n a l  model. I n  t h i s  tes t ,  a  year was 
e l im ina ted  from the  crop data and t he  model was used t o  p r e d i c t  t h a t  year 's  
y i e l d .  This process was done f o r  each successive year  beginning w i t h  1975. 
The t e s t  had t o  be run separately on each state.  The r e s u l t s  a re  p r i n t ed  on 
Tables 3 through 9 and p l o t t e d  on Figures 3 through 9. 
APPEND I X
Def in i t ion  o f  Variables 
P-PET, p rec ip i t a t i on  minus potent ia l  evapotranspiration, i s  an index used 
t o  measure the amount o f  moisture avai lab le f o r  p lant  growth. Potent ia l  
evapotranspiration i s determi ned by the procedure devel oped by Thornthwai t e  
(1948) which uses only temperature: 
PET = 
\ A /  
where I = Heat index, which i s the  sum o f  the 12 monthly i ndices i . 
T = Monthly temperature i n  OC,  and 
a = An empir ical  exponent, 6.75 x 10-713 - 7.71 x  10'512 + 1.79 x  10'21 
The durat ion o f  day1 i g h t  i s  used t o  adjust  po ten t ia l  evapotranspiration as a 
por t ion o f  12 hours. 
S t a t i s t i c a l  Analysis System Procedures Used 
PROC CORR 
PROC PLOT 
PROC STEPW I SE 
PROC STEPWISE FORWARD 
PROC STEPW I SE BACKWARD 
Computes cor re la t ion  coe f f i c i en ts  between 
variables, inc lud ing  Pearson product-moment 
and weighted proca.ct-moment corre lat ion.  
Graphs one var iable against another, producing 
a p r i n t e r  p lot .  
Provides f i v e  methods f o r  stepwi se regression. 
Stepwi se i s  useful  when select ing variables t o  
be included i n  a regression model from a 
co l  l ec t i on  o f  independent variables. 
Begins by f ind ing  the  one-variable model t ha t  
produces the highest ~ 2 .  For each o f  the other 
independent variables, FORWARD calculates F- 
s t a t i s t i c s  r e f l e c t i n g  the  cont r ibu t ion  t o  the 
model i f  the var iable were t o  be included. 
Begins by ca lcu la t ing  s t a t i s t i c s  fo r  a model 
inc luding a l l  the independent variables. The 
variables are deleted from the  model one by 
one u n t i l  a l l  the remaining variables produce 
F -s ta t i s t i cs  s ign i f i can t  a t  the .10 level.  
PRO6 STEPW I S E  STEPW I SE 
PHUC STEPWISE MAXK 
PROC PETM 
PROC ZINDEX 
The stepwise method i s  a modi f icat ion of the 
forward select ion technique, d i f f e r i n g  i n  
t h a t  var iables a1 ready i n  the  model do not 
necessari ly stay there. Af ter  a variable i s  
added (as i n  the forward select ion method) the 
stepwise method looks a t  a11 tne variables 
alreaay lncluaea i n  the  moael and oeletes any 
var iable tha t  does not  produce an F-statistic 
s ign i f i can t  a t  the .10 level. Only a f te r  t n i s  
check i s  made and the  necessary delet ions 
accomplished can another var iable be added t o  
the  model. 
(Maxlmum K 2  imp ~vement) Unl ike the three 
techniques above, t h i s  method does not s e t t l e  
on a s ingle method. Instead i t  looks f o r  the 
"best' two-variable model, the  "best" three 
var iab le  model, and so for th.  
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ca lcu la te  Thornthwai t e ' s  po ten t ia l  evapo- 
t ranspi  r a t i o n  f o r  each month. 
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(begi ning moisture i n  surface layer),  
AWCS (avai lab le water capacity i n  surface 
layer) ,  SU (beginning moisture i n  the 
underlying 1 ayer ) , and AWCU (avai 1 able water 
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Palmer's SON moisture budget, drought index 
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Brazil soybean yield covariance model

Abstract

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