Modeling variations in soil moisture and crop yield for an irrigated alfalfa field in southwestern
Montana
by Daniel Bishop Harelson
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Agricultural Engineering
Montana State University
© Copyright by Daniel Bishop Harelson (1986)
Abstract:
The purpose of this study was to evaluate two computer models which can be used to predict variations
in soil moisture with time and space as well as crop yield. This evaluation was performed using data
from a sprinkler irrigated alfalfa field on the Montana State University Red Bluff Research Ranch.
FORTRAN models named SPAW and Plantgro were selected for evaluation because they differ
significantly in their random access memory requirements and because they were readily available.
Both models perform a water budget for a selected number of soil layers using pan evaporation to
estimate evapotranspiration. Crop yields are predicted using a linear relationship between potential
yield and the ratio of actual to potential transpiration. The models were calibrated using soil moisture
and yield data from 1979 while similar data from 1981 was used for testing. The results of this study
indicated that the SPAW model predicted soil moisture variations somewhat more acurately than the
Plantgro model. However, the Plantgro model predicted crop yield more accurately than the SPAW
model. Unfortunately, the results of this study were subject to doubt because model calibrations were
based on very limited data and the accuracy of some of these data was uncertain. More effective use of
the available data would eliminate some doubt and provide a more reasonable basis for evaluating the
models in terms of the accuracy of simulated results. MODELING VARIATIONS IN SOIL MOISTURE AND CROP YIELD FOR AN
IRRIGATED ALFALFA FIELD IN SOUTHWESTERN MONTANA
by
Daniel Bishop Harelson
A th e s is submitted in p a r t i a l fu lfillm e n t
o f the requirem ents fo r the degree
of
Master of Science
in
A g ricu ltu ral Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
March 1986
HZZZ/
Co p ^oL'
ii
APPROVAL
of a th e s is submitted by
Daniel Bishop Harelson
This th e s is has been read by each member of the th e s is committee
and has been found to be s a tis fa c to ry regarding content, English usage,
fo rm a t, c i t a t i o n s , b ib lio g r a p h ic s t y l e and consistency, and is ready
fo r submission to the College of Graduate Studies.
■? / j / / / T /
Date
'
Chairperson, G raduate Committee
Approved fo r the Major Department
Date
Head, Major Department
Approved fo r the College o f Graduate Studies
Date
uate D
<
Graduate
Dean
ill
'f
STATEMENT OF PERMISSION TO USE
In p r e s e n t i n g
th is
th e s is
in p a r t i a l f u f i l l m e n t o f th e
requirem ents fo r a m aster's degree a t Montana S ta te U niversity, I agree
t h a t th e L ib ra ry s h a l l make i t a v a i la b l e to b o rro w e rs under r u le s o f
the Library.
B rief quotations from t h is th e s is are allow able w ithout
sp ecial perm ission, provided th a t accurate acknowledgement of source i s
made.
P e rm issio n f o r e x te n s iv e q u o ta tio n from or reproduction of t h is
th e s is may be granted by my major p ro fesso r, or in h is absence, by the
d ire c to r of L ib ra rie s when, in the opinion of e ith e r, th e proposed use
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Any copying o r u se o f th e
m a te r ia l f o r f i n a n c i a l g a in s h a l l n o t be allo w ed w ith o u t my w r i t t e n
perm ission.
Date
V - <7- ^
iv
Acknowledgements
I
would lik e to g ra te fu lly acknowlege the a ssista n c e and guidance
p ro v id ed by my t h e s i s com m ittee composed o f Dr. Thomas L. Hanson,
Chairm an, Dr. W illiam E. L arsen and Dr. R ichard L. B ru stk e rn .
a d d itio n ,
In
I would lik e to express my ap p reciatio n to Pamela D iedrich
fo r generously sharing her programing e x p ertise.
V
TABLE OF CONTENTS
1. In tro d u c tio n .................................................................
I
Statement of Problem........................................
I
L ite ra tu re Review........................................................................................... 2
2. Background Inform ation..............................................
8
In tro d u c tio n .................. .............................................................................. • • 8
Spaw Model D escrip tio n ..................................................................
10
Plantgro Model D e s c r ip tio n ............................................................ 19
3. P rocedure.........................
25
A vailable D ata............ ....................................................
.25
Model C a lib ra tio n ................................................................
29
SPAW C a lib ra tio n ..................................................
32
Plantgro C a lib ra tio n ........................
38
Model T estin g ................................................................................................... 41
4. R esu lts................................
43
5. D iscussion......................................................
51
Data and Computational Requirements....................
51
A nalysis of R esults from the Red B luff Sim ulation........................... 52
Sources of Error in the Red B luff study..........................
54
Ease o f Model C alib ratio n and A pplication ........................................... 58
Suggested Program M odifications................................
62
Recommendations fo r a d d itio n a l work a t the Red B luff Ranch........ 63
6 . Conclusions........................................................................................................... 66
References C ite d ...............
Appendix A................................................
C lim atological D ata..........................
S o ils Data..................
Crop Data....................................................
Appendix B......................................
D escription of Program M odifications......................................
67
,71
72
75
79
82
83
vi
LIST OF TABLES
i
1. S o il percent sand and clay determined through
the SPAW model........................ ......................................................................
»33
2. Canopy and Phenology S u sce p ta b ility re la tio n s h ip s ...............................36
3. F ield Capacity and W ilting P oint as determined
from Plahtgro c a lib r a tio n ............................................
39
4. Values fo r the r a tio of p o te n tia l tra n s p ira tio n (PT)
to p o te n tia l ev apotranspiration (PET)....................................................... 40
5. SPAW model average percent e rro r in p redicted
s o il m oisture.....................
46
6 . Plantgro model average percent e rro r in p redicted
s o il m o istu re............ .....................................
46
7. Observed Y ield, SPAW Simulated crop w ater s tr e s s and
Plantgro Simulated y ie ld fo r the c a lib ra tio n year 1979.................... 50
8 . Observed y ie ld and y ie ld sim ulated by th e Spaw and
Plantgro models fo r the t e s t year 1981.....................................................50
9. P re c ip ita tio n data fo r 1979..............................................
72
10. P re c ip ita tio n data fo r 1980.........................................................................72
11. P re c ip ita tio n data fo r 1981...............
72
12. Pan
evaporation data fo r 1979......................................................................73
13. Pan
evaporation data fo r 1980............................................................... ...7 4
14. Pan
evaporation data fo r 1981..................
74
15. Soil te x tu re by quadrant and l a y e r ................................................... ....7 5
16. S oil m oisture holding capacity a t f ie ld capacity
and the w iltin g p o in t............................
75
17. Soil m oisture measurements by
quadrant fo r 1979...............................76.
18. Soil m oisture measurements by
quadrant fo r 1980............................... 77
19. S oil m oisture measurements by
quadrant fo r 1 9 8 1 ....;....................... 78
20. Harvest d a ta ....................................................................................................... 79
vii
LIST OF TABLES— continued
i
21. I r r ig a tio n data fo r quadrant I . . ...........
78
22. I r r ig a tio n data fo r quadrant 2 1.................................................................. 79
23. I r r ig a tio n data fo r quadrant 3 ........................................
24. I r r ig a tio n
79
data fo r quadrant 4 .................................................................... 80
viii
LIST OF FIGURES
1. Control volume fo r the SPAW and Plantgro models...................... ........... 9
2. SPAW model computational scheme.......................... ........................................11
3. Moisture S tre ss cu rv es.....................................................................................15
4. Plantgro model computational scheme.................. J ......................................20
5. Red B luff Research Ranch lo c a tio n .......... ................................................... 26
6 . Study s i t e p la n ...................................................................................................27
7. SPAW Crop
Canopy curve................................................................................... 34
8. SPAW Crop
Phenology curve............................................................................. 35
9. SPAW sim ulated S o il Moisture versus Time fo r the
c a lib ra tio n year and the t e s t y e a r............................................................ 44
10. Plantgro sim ulated S o il Moisture versus Time fo r
the c a lib ra tio n year and the t e s t y e a r...................................................45
11. SPAW model S tre ss versus Y ield.......... ........................................................ 48
12. Plantgro model Observed Yield versus Simulated
Y ield ....................................................................................................................4 9
ix
ABSTRACT
The purpose o f t h i s stu d y was to e v a lu a te two com puter m odels
which can be used to p re d ic t v a ria tio n s in s o il m oisture w ith tim e and
space as w ell as crop y ie ld . This evaluation was performed using data
from a s p r i n k l e r i r r i g a t e d a l f a l f a f i e l d on th e Montana S ta te
U n iv e rs ity Red B lu ff R esearch Ranch. FORTRAN 'm odels named SPAW and
Plantgro were selected fo r evaluation because they d i f f e r s ig n ific a n tly
in t h e i r random a c c e ss memory re q u ire m e n ts and because th ey were
rea d ily a v a ila b le . Both models perform a w ater budget fo r a selected
num ber o f s o i l l a y e r s u s in g pan e v a p o r a t i o n t o e s t i m a t e
e v a p o tr a n s p ir a tio n . Crop y i e l d s a r e p r e d i c t e d u s in g a l i n e a r
r e l a t i o n s h i p betw een p o t e n t i a l y ie ld and th e r a t i o o f a c tu a l to
p o te n tia l tr a n s p ira tio n .
The m odels w ere c a l i b r a t e d u sin g s o i l
m oisture and y ie ld d ata from 1979 w hile s im ila r data from 1981 was used
fo r te s tin g . The r e s u lts o f th is study indicated th a t the SPAW model
p re d ic te d s o i l m o is tu re v a r i a t i o n s somewhat more a c u ra te ly than the
Plantgro model. However, the Plantgro model predicted crop y ie ld more
a c c u r a te ly th an th e SPAW m odel. U n fo rtu n a te ly , th e r e s u l t s o f t h i s
study were su b je ct to doubt because model c a lib ra tio n s were based on
very lim ite d data and the' accuracy of some of these d ata was uncertain.
More e ffe c tiv e use of the a v a ila b le data would e lim in a te some doubt and
provide a more reasonable b a sis fo r evaluating the models in term s of
the accuracy of sim ulated re s u lts .
I
I
CHAPTER I
. INTRODUCTION
S o il w ater is an im portant q u a n tity in the hydrologic cycle since
i t i s a w a te r su p p ly f o r p l a n t s , in f lu e n c e s e ro s io n and ru n o ff and i s
p e rc o la te d
to g ro u n d w a te r r e s e r v o i r s .
The tim e and s p a t i a l
d is trib u tio n of s o il w ater w ithin the upper s o il
of
p ro file i s the r e s u lt
complex in te ra c tio n s between many v a ria b le s re la te d to cu rren t and
p ast occurences of w eather, crops and s o il conditions.
Computer models
have been developed to p ro v id e m ethods fo r q u a n tify in g i n t e r a c t i o n s
between these v a ria b le s so the tim e-depth d is trib u tio n of s o il w ater in
an a c tiv e s o il p ro file can be p redicted and re la te d to crop y ield .
Two
such computer models were examined in th is study using data co llected
from an i r r i g a t e d
a lfa lfa
fie ld
lo c a te d on th e
Montana S ta te
U niversity Red B luff Research Ranch 35 m iles west of Bozeman Montana.
Statem ent of Problem
1
The purpose of th is study was to compare and evaluate two computer
models which can be used to p re d ic t s o il m oisture and crop y ield.
The
models which were selected for study d iffe re d s ig n ific a n tly in th e ir
com putational requirem ents.
The acc u ra c y of p re d ic te d s o i l m o is tu re
and y ie ld v a lu e s , th e ease of c a l i b r a t i o n and a p p lic a tio n as w e ll as
i
com putational requirem ents were used to provide a b a sis fo r comparing
the models.
Stated in more sp e c ific term s, the o b jective of t h is study was to
evaluate two computer models fo r use in p red ictin g s o il m oisture and
hay production from an irrig a te d a lf a lf a fie ld .
2
To accomplish th is o b jec tiv e , i t was necessary to perform th is study in
the follow ing stages:
1. S elect models fo r study.
2. Analyze a v a ila b le data fo r the ir r ig a te d a lf a lf a f i e l d .
3. Make n e c e ssa ry m o d if ic a tio n s to th e m odels so t h a t they
would be com patible w ith an AT&T 6300 microcomputer.
4. C alib rate the models to sim ulate changes in the tim e-depth
d is trib u tio n of s o il m oisture.
5. T est th e c a p a c ity o f th e m odels to s im u la te changes in
s o il m oisture.
6 . C alib rate the models to sim ulate crop production.
7. T est th e c a p a c ity o f th e m odels to p r e d ic t crop produc­
tio n .
L ite ra tu re review
A larg e number of computer models are a v aila b le fo r the purpose of
sim ulating e v ap o tran sp iratio n and s o i l w a te r movement.
A monograph
p u b lish e d by th e Am erican S o c ie ty o f A g r ic u ltu r a l E n g in e ers (ASAE,
1982) in c lu d e s a c h a p te r o u tlin in g 75 m odels t h a t could be used f o r
!
th is purpose or re la te d purposes. Many of the models outlined in th is
p u b licatio n sim ulate processes in ad d itio n to s o il w ater movement and
crop production.
These processes include some or a l l of the follow ing;
flood ro uting, p re c ip ita tio n , snowmelt, i n f i l t r a t i o n ,
surface runoff,
chemical movement and erosion y ield.
A ta b le summarizing the processes sim ulated and the areas where
each model had been a p p lie d i s in c lu d e d in t h i s c h a p te r.
F ollow ing
th is ta b le are a b s tra c ts and references for each of the 75 models.
In
a d d itio n , a second ta b le in c lu d in g , r e fe re n c e s f o r m odels t h a t were
i
3
under development a t the time of p u b licatio n is incorporated in th is
chapter.
Another chapter ,which was p a rtic u la rly useful in th is study
d e a l t w ith th e c a l i b r a t i o n and t e s t i n g of h y d ro lo g ic m odels.
c h a p te rs in t h i s m onograph p r o v id e i n f o r m a t i o n
O ther
r e g a r d i n g th e
developm ent o f approaches fo r m odeling flood ro u tin g , p re c ip ita tio n ,
snowmelt, i n f i l t r a t i o n , surface runoff, e v ap o tran sp iratio n , subsurface
flow, chemical movement and erosion.
The SPAW (Saxton e t a l ., 1984) and P la n tg ro (R e tta and Hanks,
1980) models were examined in th is study because they d i f f e r in th e ir
c o m p u ta tio n a l re q u ire m e n ts by an o rd e r of m agnitude and th ey were
r e a d ily a v a ila b le .
In a d d itio n , th ey a re fre q u e n tly r e f e r e d to in
l i t e r a t u r e co n cern in g com puter m odeling o f s o i l m o is tu re and crop
y ie ld .
There a re o th e r com puter m odels (Kanemasu e t a l . ,
1976;
G o ld stie n e t a l . 1974) which a re d i r e c t l y com parable to th e SPAW and
Plantgro models in term s of the p red ic tio n s which are made.
One such
program i s th e PROSPER model developed a t th e Oak Ridge N a tio n a l
L ab o ra to ry in Tennesee (G o ld stie n e t a l . ,
1974).
T his program
c a l c u l a t e s e v a p o tr a n s p ir a tio n u sin g t h e com bin atio n e q u a tio n and
sim u lates liq u id w ater flow using netw ork e q u a tio n s .
U n fo rtu n a te ly ,
documentation for th is program could not be obtained w hile th is study
was in progress.
Considerable study has been devoted, to the SPAW model in the past.
The SPAW model has been c a lib ra te d and te s te d to sim ulate s o il m oisture
and crop y ie ld a t stu d y s i t e s in w e ste rn Iowa and c e n t r a l M isso u ri
( Sudar e t a l . , 1981).
Corn and soybean y i e l d s were exam ined a t th e s e
s i t e s and the r e s u lts showed th a t the SPAW model provided a p ra c tic a l
I
4
and accurate approach for assessing w ater s tre s s e ffe c ts on crop y ield .
An a d d itio n al study of the SPAW model te s te d the program fo r regional
a p p lic a tio n to corn a t 49 s i t e s in K ansas, M isso u ri, Iowa and South
Dakota (Saxton and Bluhm, 1982).
The r e s u l t s o f t h i s stu d y in d ic a te d
th a t some lo c a l c a lib ra tio n of the model was required
but th a t a fte r a
p a ra m e te r s e t was e s t a b l is h e d , crop y ie ld s could be p re d ic te d w ith
moderate to good accuracy.
The SPAW model has also been compared w ith the Stockle-Campbell
model (S to ck le, 1983) in term s of th e ir a b il i ty to p re d ic t w inter wheat
y ield s (Stockle and Saxton, 1984).
The model comparison was based on
w in ter wheat y ie ld s a t two s i t e s in Washington.
Prelim inary r e s u lts of
t h i s com parison in d ic a te d t h a t b oth m odels showed good p r e d ic tiv e
c a p a b il i ty and m ight be u s e f u l f o r p r a c t i c a l a p p lic a tio n s .
However
these r e s u lts were based on c a lib ra tio n data only and a d d itio n al work
was necessary before any firm conclussions could be drawn.
A dditional
work would in v o lv e t e s t i n g th e m odels u sin g in d ep e n d en t d a ta from
d if f e r e n t years and lo c a tio n s.
In p re v io u s work w ith th e P la n tg ro m odel, s e v e ra l v a r i a ti o n s of
i
the model have been studied. One study te s te d the a b il i ty of the model
to s im u la te corn dry m a tte r and g ra in y ie ld as w e ll as sorghum dry
m a tte r y ie ld (Hanks,
1974).
T his v e rs io n of th e P la n tg ro model
d i f f e r e d from th e one exam ined in t h i s stu d y in t h a t th e e n t i r e s o i l
p ro f ile was represented as a sin g le lay er and evaporation was sp ecified
u sin g a s in g le se a s o n a l v a lu e .
A lthough th e r e s u l t s o f t h i s study
showed r e la tiv e ly good p re d ic tiv e c a p a b ility , the model was not te s te d
5
using data which were independent of the c a lib ra tio n year.
A nother v a r i a ti o n o f th e P la n tg ro model was s tu d ie d u sin g th e
modified Penman equation to evaluate evap o tran sp iratio n over the course
o f the growing season (Nipah and Hanks, 1973).
This version d iffe re d
from the one studied here in the way evap o tran sp iratio n was evaluated
i
and in th e way th e movement o f s o i l m o is tu re was s im u la te d . S o il
m oisture movement was sim ulated using a f i n i t e d iffe re n c e form of the
Darcy equation for porous media flow.
to sim ulate crop y ield .
In ad d itio n , no attem pt was made
The r e s u lts of th is study in d icated th a t s o il
m o is tu re movement could be s im u la te d a c c u ra te ly a f t e r c a l i b r a t i o n .
However, the model was not te s te d using data which were independent of
the c a lib ra tio n data.
A v e rs io n o f th e P la n tg ro model has a ls o been used to sim u la te
s p rin g w heat g ra in y ie ld (Rassm ussan and Hanks, 1978).
G rain y ie ld s
w ere sim u la te d a t s e v e ra l s i t e s in Utah fo r s e v e ra l y e a rs .
These
s im u la tio n s p re d ic te d g ra in y ie ld w ith e r r o r s o f e ig h t to t h i r t y
p e rc e n t.
However, th e e r r o r of t h i r t y p e rc e n t was p re d ic te d f o r an
anomolous y e a r in te rm s .o f th e le n g th o f th e grow ing seaso n .
During
th is growing season, weather was warmer than normal and the planting
d a te was s i g n i f i c a n t l y
e a rlie r
th ah th e p la n tin g
d a te s
of th e
c a lib r a tio n years.
The SPAW and P la n tg ro m odels have a ls o been extended to p r e d ic t
s o lu b le ion movement and th e e f f e c t s o f s a l i n i t y on y ie ld .
The SPAW
model h a s ibeen m o d ified to s im u la te n i t r a t e n itro g e n movement and
d i s s i p a t i o n by c o n s id e rin g a d d itio n s ,
s u b tr a c tio n s ,
s to ra g e and
b io lo g ic a l conversions represented as a tim e d is trib u tio n (Saxton e t
6
a l.,
1977).
In t h i s
e x te n s io n o f th e SPAW m odel,
c o n s id e r e d in t'he c a l c u l a t i o n
of n itr a te
th e f a c t o r s
tr a n s p o r t in c lu d e ;
i n f i l t r a t i o n , s o i l w a te r r e d i s t r i b u t i o n , p e r c o la tio n , p la n t u p tak e , 1
fe rtiliz e r
a d d itio n ,
n itrific a tio n .
ra in fa ll
a d d itio n ,
m in e ra liz a tio n
and
A lthough n i t r a t e movement through d if f u s s io n was
sim ulated, the e ffe c ts of adsorption were not considered.
The P la n tg ro model has been extended to s im u la te th e e f f e c t s of
s a l i n i t y on crop y ie ld and s a l t movement w ith in th e s o i l p r o f i l e
(C h ild s and Hanks, 1975).
T h is e x te n s io n ta k e s in to c o n s id e ra tio n
e f f e c t s o f th e i r r i g a t i o n amount and s c h e d u lin g , i r r i g a t i o n w a te r
q u a lity , i n i t i a l s o il s a lin ity , crop type and uniform ity of irrig a tio n .
A decreased osmotic p o te n tia l was used to rep resen t s a lin ity e ffe c ts on
y ield .
Solute flow was modeled both in term s of bulk so lu tio n flow and
s o lu te d ifu s s io n .
The e f f e c t s o f a d s o r p t i o n a s w e l l a s s a l t
p re c ip ita tio n and d isso lu tio n were not represented.
In a d d itio n to th e in fo rm a tio n d e s c rib e d , two docum ents w ere
e s s e n t i a l to t h i s stu d y .
These docum ents a re th e u s e r 's m anuals f o r
th e SPAW (Saxton e t a l.,1 9 8 4 ) and P la n tg ro (R e tta and Hanks, 1980)
m odels.
The u s e r 's manual fo r th e SPAW model i s a p u b lic a tio n t h a t
covers in d e ta il every aspect of the operation of the SPAW model.
The
u s e r 's manual fo r th e P la n tg ro model i s a much s m a lle r p u b lic a tio n
w ith i n s u f f i c i e n t d e t a i l .
The u s e r 's manual f o r th e P la n tg ro model
was inadaquate because the u n its of measure used by the program are not
c le a rly s p e c ifie d .
A p aper t i t l e d
" E v a lu a tin g wash tub e v a p o ra tio n i r r i g a t i o n
7
s c h e d u lin g ” by
Hanson (1984)
p re v io u s stu d y of th e a l f a l f a
p ro v id ed u sefu l inform ation regarding
f i e l d a t th e Red B lu ff Ranch.
In
ad d itio n to discussing asp ects of ir r ig a tio n scheduling based on d ire c t
m easurem ents o f pan e v a p o ra tio n ,
t h i s paper p ro v id ed background
in fo rm a tio n on th e a l f a l f a f i e l d in q u e s tio n .
T h is in fo rm a tio n
in c lu d e d a summary o f y i e l d , s o i l s and e v a p o ra tio n d a ta a s w e ll as a
d e sc rip tio n of the methods and m a te ria ls used to p lan t the fie ld .
8
CHAPTER 2
BACKGROUND INFORMATION
I
The SPAW and Plantgro models are p re d ic tiv e accounting procedures
i
'
which produce a d aily w ater budget fo r s o il w ater w ithin sp e cified s o il
lay e rs.
These accounting procedures are governed by the major e ffe c ts
of w eather, crops and s o ils .
The primary purpose fo r developing these
models was to improve p re d ic tio n s of i n f i l t r a t i o n , runoff, erosion and
w ater q u a lity .
An equally, im portant reason fo r developing these models
was the assessm ent of a v a ila b le s o il m oisture throughout the growing
season fo r a g ric u ltu ra l crops.
A number of secondary o b jec tiv e s can be
approached th ro u g h th e a p p lic a tio n o f th e s e a c c o u n tin g p ro ce d u res.
These might include assesment of crop w ater s tre s s e ffe c ts on growth
and y i e l d , s o i l w a te r in f lu e n c e s on s o lu b le io n d i s t r i b u t i o n and th e
p erco latio n of s o il w ater fo r groundwater recharge.
While the SPAW and
P la n tg ro m odels w ere developed to r e p r e s e n t a complex p h y s ic a l and
b i o lo g ic a l sy stem , th e d a ta re q u ire m e n ts w ere r e s t r i c t e d to th o se
re a d ily av aila b le through normal sources.
The diagram in Figure I rep resen ts the control volume considered
by th e SPAW and P la n tg ro program s to compute e s tim a te s o f th e s o i l
w ater p r o file , actu al evap o tran sp iratio n and deep p erco latio n .
e stim ates of a l l of these
Daily
q u a n titie s are made by the models to produce
v e r t i c a l w a te r b u d g e t s .| In th e SPAW m odel, s o i l w a te r p r o f i l e s a re
e s tim a te d a t a maximum tim e .s te p o f one to fo u r h o u rs as re q u ire d to
m aintain com putational s t a b il i ty .
The s o il p ro file i s represented in
th e m odels by a s e le c te d number of la y e r s and d e p th s d esigned to
9
Precipitation
Evapotronspiratiorf
(E T )
Surface
Runoff (Q)
SOIL
Soil
Moisture
(Sm)
Percolation
(Re)
Figure I . Control volume for the SPAW and P lantgro models.
10
r e f l e c t th e average s o i l p r o f i l e over th e f i e l d or w a tersh e d being
m odeled.
Each la y e r may be a ssig n e d a unique s e t o f w a te r h o ld in g
c h a r a c t e r i s t i c s and, in th e case o f th e Spaw model, th e u n s a tu ra te d
hydraulic conductivity of the lay e rs can a lso be represented. The above
ground p o rtio n of; th e - c o n tr o l volume i s assumed to be a u n ifo rm ly
d is trib u te d p la n t!canopy.
SPAW model d e scrip tio n
The general com putational scheme used in the SPAW model is shown
in
F ig u re
2.
In
th is
c o m p u ta tio n a l
ev ap o tran sp iratio n i s determ ined independently
estim ate of a ctu a l ev apotranspiration.
th e a c t u a l e v a p o t r a n s p i r a t i o n
schem e,
p o te n tia l
and then reduced to an
Susequent c a l c u l a t i o n s d iv id e
i n t o components o f in te r c e p tio n
e v a p o ra tio n , s o i l w a te r e v a p o ra tio n and p la n t t r a n s p i r a t i o n .
A fte r
su b tra ctin g the actu al evap o tran sp iratio n from e x is tin g s o il m oisture
by s o i l l a y e r s , d a ily i n f i l t r a t i o n i s added.
re d is trib u te d based on a Darcian equation.
Then, s o i l w a te r i s
A b r ie f d e sc rip tio n of each
element considered in th is com putational scheme follow s.
P o te n tia l evap o tran sp iratio n
The p o te n tia l ev apotranspiration may be obtained from a v a rie ty of
m e te o ro lo g ic a l m ethods. . As p re s e n te d ,
th e SPAW model e s tim a te s
p o t e n t i a l e v a p o tr a n s p ir a tio n from m easured or e s tim a te d d a ily pan
e v a p o ra tio n .
The pan ,e v a p o ra tio n r a t e s a re reduced by a m onthly pan
c o e ffic ie n t to become e stim ates of p o te n tia l evapotranspiration. .
In terc ep tio n
. "
• J •"
'
'
_
_
I n te r c e p tio n of w a te r by th e crop canopy i s s im u la te d u sin g
a s to r a g e d e v ic e w ith a maximum c a p a c ity r e p r e s e n tin g p o t e n t i a l
11
♦
ROTENTtML E T
\
INTERCEPTION
,#«**""*#**##*##**
CM NO Rr
suscERT/etLtrr
E VM R O R MT IO N
T-Mt e« r€A*
UNUSCO CNCNOT
% r»ANsrcw
»• CANONT
R O T E NTIML
TNJNSRtRM TlO N
SO'L vMOiST
^<N 0L 00<A t
MCTUML S O U
E VMRORM TION
OTH ER
EN ER GY S I N K S
S tA T f
% •# CANONT
RHENOLOGICML
SU SCERTIBlLlTr
AOOT O'STNiiuTiON. %
% AVAIL. SOIL MOIST
MCTUML
rtCLO
TRANS RtRM TION
SU SC E R T lB IU TT
SOU
ACTUAL
N O !S T U R E R E O t S T R i B u r i O N
ET
Figure 2. SPAW model computational scheme
12
in te rc e p tio n .
.
The p o te n tia l ev apotranspiration value i s reduced by the
amount of in te rc e p tio n before tra n s p ira tio n and s o il w ater evaporation
are computed.
1
Crop canopy
B ecau se
s o la r
ra d ia tio n
p la y s
a m a jo r
ro le
in
c a u s in g
tra n s p ira tio n , the SPAW program uses crop canopy as an in d ic a to r of the
proportion of t h e ip o te n tia l evap o tran sp iratio n th a t w ill be considered
as tra n s p ira tio n from the crop canopy.
Crop canopy i s expressed as an
annual tim e graph of the percentage of shaded s o il.
Values vary from
z ero f o r b a re s o i l s to a lm o st 1.00 f o r dense c an o p ies.
Crop re s id u e s
a re t r e a t e d as canopy cover because th ey p ro v id e s o i l shading which
a ffe c ts evaporation from the s o il.
The in a b ility of crop residues to
tra n s p ire i s accounted fo r in the model by considering p la n t phenology.
For dry s o i l c o n d itio n s w ith a p a r t i a l canopy, th e r e i s some
p o rtio n of the energy a v a ila b le for p o te n tia l evap o tran sp iratio n which
i s n o t used f o r w a te r e v a p o ra tio n .
a d ja c e n t a i r and th e canopy.
Unused energy h e a ts th e s o i l , th e
As a r e s u l t , th e canopy has a second
so u rce o f energy in a d d itio n to d i r e c t l y in te r c e p te d energy.
rep resen t t h is e ffe c t,
To
a lin e a r re la tio n sh ip of canopy versus percent
unused energy i s in c o rp o ra te d i n t o th e SPAW model.
When th e canopy
reaches six ty percent, a l l unused energy is captured by the canopy and
i t becomes p a rt of the energy a v a ila b le fo r p o te n tia l tra n s p ira tio n .
P lan t phenology
A second annual tim e graph of a phonological fa c to r i s included in
th e SPAW model as a d i r e c t m o d ifie r o f th e crop canopy’s a b i l i t y to
13
tra n s p ire .
At t im e s d u r in g th e y e a r when th e can o p y i s n o t
tra n s p irin g , the phenological fa c to r tak es on a value o f zero.
As the
proportion of the crop canopy tra n s p irin g in cre ases, the value of t h is
fa c to r approaches 1.0.
Soil w ater evaporation
In th e SPAW program , a t h in upper boundary la y e r i s in c lu d e d in
the s o il p ro f ile increm entation.
This la y e r has a l l of the functions
o f th e o th e r la y e r s e x c e p t p la n t r o o ts a re no t p re s e n t. In a d d itio n ,
w a te r can be r e a d ily e v a p o r a te d from
t h i s b o u n d a ry l a y e r and
e v a p o ra tio n i s l im i te d only by p o te n tia l evapo t r anspi r a t i on.
Upward
w a te r movement from th e second la y e r i n t o th e e v a p o ra tiv e boundary
la y e r i s estim ated by a Darcian equation using a sm all fra c tio n
of the
unsaturated hydraulic conductivity fo r the cu rren t s o il w ater content
o f th e second la y e r .
The c o n d u c tiv ity re d u c tio n r e p r e s e n ts th e f a c t
t h a t e v a p o ra tio n i s by vapor flow r a t h e r than l iq u i d flow and th e
e ffe c tiv e conductivity i s sev eral magnitudes le s s.
Water uptake by p la n t ro o ts
A sim ple d e sc rip tio n of a w ater e x tra c tio n p a tte rn w ith depth was
programed in to the SPAW model.
For se lec te d d ates the percent of w ater
to be a b stra c te d from each s o il lay e r i s entered.
Each d is trib u tio n i s
a p p lie d to su cceed in g d a te s _ u n til a new d i s t r i b u t i o n i s s p e c if ie d to
r e f l e c t r o o t developm ent.
The e n te re d w ater e x tra c tio n d is trib u tio n
assumes th a t w ater i s re a d ily and equally av aila b le in a l l s o il lay e rs.
Any w a te r s t r e s s due to s o i l d ry in g i s c o n sid e re d in th e crop w a te r
s tr e s s r e la tio n s h ip .
Crop w ater s tr e s s
As th e w a te r supply to a p la n t becomes l i m i t e d , p h y s ic a l and
b io lo g i c a l c o n tr o ls beg in to l i m i t th e r a t e o f t r a n s p i r a t i o n .
To
acco u n t f o r t h i s e f f e c t , s e v e ra l c u rv e s r e p r e s e n tin g th e r a t i o o f
a ctu a l to p o te n tia l evap o tran sp iratio n (AT/PT) v e rsu s p la n t a v a ila b le
m oisture and p o te n tia l evap o tran sp iratio n have been programed in to the
SPAW model.
Several curves, shown in Figure 3, are included because a
p lan t i s more lik e ly to a tt a i n a la rg e r proportion of a lower p o te n tia l
e v a p o tra n s p ira tio n
ra te
e v a p o tr a n s p ir a tio n r a t e .
th a n
it
is
a
h ig h e r
p o te n tia l
In th e m odel, th e program ed c u rv es a re
applied to each s o il lay e r independently and the a ctu a l tra n s p ira tio n
i s a m u ltip le fu n c tio n .o f the canopy, phenology and ro o t d is trib u tio n .
A fter estim atin g the d a ily p la n t a c tu a l t r a n s p i r a t i o n , th e SPAW
program fu rth e r estim ates the magnitude of water s tr e s s as (I-(AT/PT)).
This value i s then used to c a lc u la te s tr e s s e ffe c ts on canopy growth,
p h en o lo g ic developm ent and y ie ld .
S t r e s s e f f e c t s on canopy and
phenology are used to derive the p lan t s ta tu s and adjustm ents are made
to p la n t d e s c r i p t o r s (canopy and phenology) fo r c a l c u l a t i o n s on th e
subsequent day. These adjustm ents are such th a t prolonged w ater s tre s s
w ill sev erly lim it p lan t growth or even cause p lan t death.
The c a p a b il i ty to e s tim a te how th e d a ily crop w a te r s t r e s s i s
in te g ra te d throughout the growing season to r e s u lt in a f in a l y ield was
a ls o in c o rp o ra te d i n to th e model.
To r e p r e s e n t th e r e l a t i v e w a te r
s t r e s s s u s c e p t a b i l i t y in tim e and among c ro p s , y ie ld s u s c e p t a b i l i t y
Actual / Potential Transpiration
.3 m m
PET =
2 .5 m m
6 .3 m m
1 0 .2
mm
A. Normal canopy development
B. Declining rate of
canopy development
C. No development
1 7 .8 m m
Available Soil Moisture (% of m a x im u m )
Figure 3 . SPAW model m oisture s tr e s s curves
16
re la tio n s h ip s for p a rtic u la r crops must be developed and entered in to
th e program .
Y ield re d u c tio n due to s t r e s s on a p a r t i c u l a r day i s
calcu late d as the product of the w ater s tr e s s on th a t day and a fa c to r
rep resen tin g the su s c e p ta b ility of the crop to s tre s s on the same day.
The program provides r e la tiv e s tre s s in d ices which become meaningful
only a f te r they are c o rre la te d w ith observed y ie ld s from the study s i t e
or the region to derive a y ield su s c e p ta b ility re la tio n sh ip .
Actual ev ap o tran sp iratio n
An e stim ate of a ctu a l ev ap o tran sp iratio n i s obtained by adding the
components of in te rce p ted w ater evaporation, s o il w ater evaporation and
p la n t tra n s p ira tio n .
I n f i lt r a t i o n
The Spaw model e stim ates a d a ily i n f i l t r a t i o n value fo r each day
th a t has p re c ip ita tio n by one of two methods.
I f measured d a ily runoff
data are a v a ila b le and c o rre c tly associated w ith a p re c ip ita tio n event,
they are entered and i n f i l t r a t i o n i s computed as p re c ip ita tio n minus
r u n o f f and i n te r c e p t io n .
I f m easured d a ta a re no t a v a i l a b l e , th e n a
d a ily e s tim a te o f ru n o ff i s made by a m o d ified v e rs io n o f th e S o il
Conservation Service curve number method.
The SCS curve number method e stim ate s runoff based on a s e rie s of
c u rv e s w hich in d ic a te th e p e rc e n ta g e o f p r e c i p i t a t i o n w hich becomes
ru n o ff.
A p a r t i c u l a r cu rv e i s s e le c te d f o r use based on ta b u la te d
values fo r various s o il and crop combinations.
The standard SCS method
was modified in the SPAW model to u t i l i z e predicted e stim a te s of crop
canopy and s o il m oisture.
D aily i n f i l t r a t i o n amounts e n ter and move through the s o il p ro file
17
in stan tan eously
in the Spaw model.
I n f i l t r a t i n g w ater i s added to the
upper s o il la y e rs w ithout exceeding th e ir sa tu ra tio n capacity.
Water
i s cascaded to d eep er la y e r s u n t i l ad aq u ate s to ra g e i s a v a ila b le fo r
the i n f i l t r a t e d w ater.
All fu rth e r re d is trib u tio n of w ater i s done by
the Darcian m oisture re d is trib u tio n ro u tin e.
S o il w ater re d is trib u tio n
A sim p lifie d Darcian equation of w ater flow between s o il layers
was included in the SPAW program to evaluate s o il w ater re d is trib u tio n .
The Darcy equation in f i n i t e d ifferen c e form is :
(h(&)+ AZ)
q=K ( 9 )-------------------- (At)
AZ
w here;
q
i s th e e s tim a te d v o lu m e tric w a te r flow p er u n i t a re a p e r
tim e s te p a c ro ss la y e r boundaries (cm3/cm2/hr)
K(e) i s the mean u n sa tu rated h y d rau lic condu ctiv ity of the two
l a y e r s b e in g c o n s i d e r e d .
T h ese c o n d u c t i v i t i e s a r e
fu n ctio n s of the re s p e c tiv e la y e r w ater contents (cm /hr).
A(9) i s th e m a tr ic p o t e n t i a l head d i f f e r e n c e betw een th e two
la y e rs being considered as a fu n ctio n of th e ir re s p e c tiv e
w ater c o n ten ts (cm).
AZ
At
is the distance between the midpoints of the layers being
considered (cm).
i s the tim e increm ent (hr).
Many p r e s s u r e
and c o n d u c t i v i t y
v e r s u s m o i s t u r e c o n te n t
re la tio n sh ip s were summarized from l i t e r a t u r e and c la s s if ie d by s o il
t e x t u r e to p ro v id e a s e r i e s o f average r e l a ti o n s h i p s f o r e s tim a tin g
these when no others are a v ailab le.
However, there are input options
to provide measured s o il water c h a ra c te ris tic data to the program or
pressure and conductivity re la tio n sh ip s can be c alcu lated em p irically
18
by th e model.
E m p iric a lly c a lc u la te d p re s s u re and c o n d u c tiv ity
re la tio n s h ip s are a function of s o il te x tu re and s o il m oisture.
These
r e l a t i o n s h i p s a re d e s c rib e d in a paper soon to be p u b lis h e d in th e
S o il Science Society of America Journal (Saxton e t a l. 1986)
Summary o f data requirem ents fo r the SPAW model
Weather data
D aily p r e c i p i t a t i o n and i r r i g a t i o n amounts (cm).
D aily r u n o f f - e i t h e r observed or e s tim a te d
using the modified SCS curve number method.
by th e model
Daily p o te n tia l ev ap o tran sp ira tio n -th e model i s now programed
to use d a ily pan e v a p o ra tio n and monthly pan c o e ffic ie n ts.
Crop data
Dates of p lanting and harvest.
Crop canopy- e s tim a te d s o i l shading percentage fo r selected
d ates which d efine a crop canopy curve.
Canopy suscept a b i l i t y - v a l u e s
e ff e c ts on crop growth.
t o r e p r e s e n t w a te r s t r e s s
Crop p h e n o lo g y -v a lu e s from 0.0 to 1.0 w hich d e s c rib e th e
p ro p o rtio n o f th e canopy a b le to t r a n s p i r e on s e le c te d
d a te s . These v a lu e s and th e c o rre sp o n d in g d a te s d e s c rib e a
crop phenology curve.
Phenology s u s c e p t a b i li t y - v a l u e s to r e p r e s e n t w a te r s t r e s s
e ffe c ts on crop phenology.
P lant w ater e x tra c tio n p attern -v a lu e s for each s o il layer for
s e le c te d d a te s which r e f l e c t th e ex p ected w a te r w ith d ra w a l
p e rc e n ta g e by th e crop i f w a te r were r e a d ily and e q u a lly
a v aila b le throughout the s o il p ro file .
P la n t m o is tu re s t r e s s c u rv e s -v a lu e s describing the av aila b le
s o i l w a te r and e v a p o ra tiv e demand e f f e c t s on th e r a t i o o f
a ctu a l to p o te n tia l p lan t tra n s p ira tio n .
Yield su sc e p tab ilty -v a lu e s d escribing the r e la tiv e sig n ific an c e
of w ater s tr e s s to y ie ld throughout the crop growth period.
19
S o ils data
In c re m e n ta tio n d e p th s
a p p ro p r ia te s o i l w a te r
Curves can be s e le c te d
sp e cified or calcu lated
r e p r e s e n tin g th e s o i l p r o f i l e and
c h a r a c t e r i s t i c c u rv e s f o r each la y e r .
from s ta n d a rd program ed c u rv e s, u se r
by the program.
Observed volum etric s o il m oisture values for each s o il layer on
e a c h d a te e n t e r e d .
Used f o r i n i t i a l i z a t i o n , o r m odel
c a lib ra tio n and v e rific a tio n .
Summary of output presented by the SPAW model
D a ily and a c c u m u la te d v a lu e s o f P o t e n t i a l and a c t u a l
evapotra n sp ira tio n , tra n s p ira tio n and s o il w ater evaporation as
w ell as p re c ip ita tio n , ir r ig a tio n runoff and drainage.
Daily s o il m oisture values by s o il layer.
V alues fo r d a ily and accum ulated crop w a te r s t r e s s and y ie ld
reduction.
Plantero model d e sc rip tio n
A sim p lifie d version of the flow c h a rt for the Plantgro model is
shown in Figure 4.
in to
its
This model operates by s p l i tt i n g ev apotranspiration
c o m p o n e n ts o f e v a p o r a t i o n from th e s o i l s u rfa c e and
tra n s p ira tio n from p lan ts.
a lin e a r
re la tio n s h ip
Crop production is then p red icted based on
b e tw e e n t r a n s p i r a t i o n and y ie ld .
Since
evaporation from the s o il surface does not co ntribute to p lan t growth,
it
is
n o t in c lu d e d in th e p ro d u c tio n r e l a ti o n s h i p .
e stim atio n i s based on an equation having the form;
Dry m atter yield=P(AT/PT)
where;
P ro d u c tio n
20
Input plant, weather
and soils data
Is stage ol growth
in energy units?
Convert duration ol stage
as a traction ol season
Oid rain
or irrigation occur?
Oislribute the added water
into soil root zone profile.
Store excess water
as drainage.
Compute and remove water
Irom profile Dy transpiration
Compute and remove water
by evaporation Irom top layer
day equal to end ot a
stage ol growth?
Compute relative transpiration
at end ol stage
Increm ent day Dy I
day greater man last
_ day ol season? _
Compute relative dry matter
and gram yields
Figure 4. Plantgro model computational scheme
21
P i s th e p o t e n t i a l dry m a tte r y ie ld
lim itin g .
if
w a te r i s
not
AT i s the accumulated seasonal actu al tra n s p ira tio n .
PT i s the accumulated seasonal p o te n tia l tra n s p ira tio n .
In a d d itio n to p r e d ic tin g dry m a tte r y ie ld , th e P la n tg ro model
a ls o h as th e a b i l i t y to p r e d i c t g ra in p ro d u c tio n .
G rain y ie ld i s
p r e d ic te d based on a r e l a t i o n s h i p w hich acc o u n ts f o r th e v ary in g
sig n ific an c e of m oisture s tr e s s during d iffe re n t growth stages.
This
re la tio n s h ip i s s im ila r to th a t used to p re d ic t dry m atter y ie ld except
the r a tio of actu al to p o te n tia l tra n s p ira tio n i s c alc u la te d fo r each
stage o f growth and ra ise d to an appropriate power.
Grain prodution i s
assumed to be the product of these r a tio s each raise d to a power.
Each
r a tio i s ra ise d to a power which rep resen ts the r e la tiv e sig n ific an c e
of m oisture s tre s s during the corresponding stage of growth.
P o te n tia l evap o tran sp iratio n i s determ ined in the Plantgro model
by m u ltip lying observed pan evaporation by a seasonal pan c o e ffic ie n t.
Daily values of pan evaporation or average values fo r sev eral days may
be supplied to the model.
its
P o te n tia l evap o tran sp iratio n i s s p l i t in to
c o m p o n e n ts o f p o t e n t i a l
s o il
e v a p o ra tio n
and p o t e n t i a l
tra n s p ira tio n using the follow ing equations;
PT=Kt(PET)
PE=Ks(PET)=(I-Kt)(PET)
where;
PT
PE
PET
Kt
Ks
<
i s p o te n tia l tra n s p ira tio n on a given day.
i s p o te n tia l s o il evaporation on a given day.
i s p o te n tia l ev apotranspiration on a given day.
i s the proportion of the PET th a t could be tra n sp ire d .
i s the proportion of the PET th a t could evaporate from
the s o i l .
22
The p ro p o rtio n f a c t o r s Kt and Ks a re d e fin e d by a p l o t o f Kt v a lu e s
versus tim e.
In the version of the Plantgro model Used in th is study,
lin e a r segments were used to jo in values of K t,a t the begining and end
of each stage of crop growth.
Actual tra n s p ira tio n i s determined in the Plantgro model based on
th e amount o f a v a ila b le w a te r in th e s o i l p r o f i l e and th e fo llo w in g
re la tio n s h ip s ;
AT=PT i f SWS/AW i s g re a te r than b
AT=PT(SWS/(AWxb)) i f ,SWS i s le s s than b
where;
AT
PT
SWS
AW
b
i s a ctu al tra n s p ira tio n .
i s p o te n tia l tra n s p ira tio n .
i s the amount of a v a ila b le s o il w ater in the ro o t zone.
i s the amount of a v aila b le w ater in the ro o t zone when
the ro o t zone i s a t f ie ld cap acity .
i s the fra c tio n of a v a ila b le w ater a t . f i e l d capacity below
which tra n s p ira tio n w ill be lim ite d .
A ctu al e v a p o ra tio n from th e s o i l (AE) i s e s tim a te d based on th e
p o t e n t i a l s o i l e v a p o ra tio n (PE) and th e le n g th o f tim e ( t) in days
since the l a s t ir r ig a tio n or p re c ip ita tio n event using the equation;
AE=PEZf5
When ra in or an ir r ig a tio n occurs on the day under consideration
by th e m odel, th e to p la y e r of s o i l i s f i l l e d to f i e l d c a p a c ity f i r s t
and i f th e r e i s any e x c e ss, th e n ex t la y e r i s . f i l l e d .
I f th e amount
of w ater added exceeds the w ater holding capacity of the ro o t zone a t
f i e l d c a p a c ity , th e e x c e ss i s l o s t a s deep p e rc o la tio n .
The depth of
the ro o t zone i s estim ated by the model based on a lin e a r re la tio n sh ip
betw een th e depth of th e ro o t zone a t m a tu r ity and th e p ro p o rtio n o f
the season th a t has elapsed.
Water i s withdrawn by
tra n s p ira tio n from
23
the s o il lay ers th a t contain roots.
Evaporation only occurs from the
to p s o i l la y e r and t h i s la y e r i s allo w ed to lo s e w a te r below th e
w i l ti n g p o in t to a s p e c if ie d a i r dry m o is tu re c o n te n t.
W ater fo r
t r a n s p i r a t i o n i s w ithdraw n from th e s o i l la y e r w ith th e h ig h e s t
m oisture content.
I f the amount of w ater required fo r tra n s p ira tio n on
a given day i s g r e a t e r th an th e amount o f a v a ila b le w a te r in th e s o i l
lay e r w ith the highest s o il m oisture, the d ifferen ce is removed from
the lay e r w ith the next highest s o il m oisture.
With the exception of
the top lay e r, the m oisture content of the s o il lay e rs i s not allowed
to drop below the w iltin g poin t m oisture content.
U nlike th e SPAW m odel, th e P la n tg ro model does n o t account f o r
surface runoff or in te rc e p tio n .
A summary of the data requirem ents fo r
the Plantgro model follow s.
Summary o f Plantaro data requirem ents
Weather Data
P re c ip ita tio n date and amount.
Pan e v a p o ra tio n d a te and amount. The pan e v a p o ra tio n amount
can be d a ily values or average values fo r a number of days.
Crop Data
Season length in days.
Length of each stage of crop growth in days or energy u n its.
Values fo r the proportion of the p o te n tia l evap o tran sp iratio n
made up o f p o t e n t i a l t r a n s p i r a t i o n a t th e b e g in in g o f each
stage of growth.
Date when the maximum rooting depth i s reached.
Dates and amounts of ir r ig a tio n .
.
24
S o ils Data
Thickness of each s o il la y e r to be considered.
V o lu m etric m o is tu re c o n te n t o f each s o i l la y e r when i t i s a t
f ie ld capacity (decimal percent).
V o lu m etric m o is tu re c o n te n t o f each s o i l la y e r when i t i s a t
the permanent w iltin g po in t (decimal percent).
E stim a te d a v a ila b le m o is tu re in each s o i l la y e r a t th e
begining of the computation period (decimal percent).
Measured s o il m oisture values
c a lib ra tio n and v e rific a tio n .
fo r
i n it i a l i z a t i o n and model
Summary o f output presented by the P lantero model
D aily and accum ulated v a lu e s f o r p o t e n t i a l and a c tu a l evapotra n s p ira tio n , tra n s p ira tio n and s o i l w ater evaporation as w ell
as ir r ig a tio n , p re c ip ita tio n and drainage.
Daily s o il m oistures by s o il lay e r.
Values fo r the r a t i o of a ctu a l to p o te n tia l tra n s p ira tio n , open
s o il w ater storage and occupied s o il w ater storage.
V alues f o r th e g ra in p ro d u c tio n fu n c tio n a t th e end o f each
stage of growth.
25
CHAPTER 3
PROCEDURE
A vailable Data
The SPAW and Plantgro models were c a lib ra te d and te s te d using data
c o lle c te d from an ir r ig a te d a lf a lf a f ie ld located on the Montana S ta te
U n iv e rs ity
Red B lu ff R esearch Ranch.
The Red B lu ff Ranch i s
a p p ro x im a te ly 56 k ilo m e te r s (35 m ile s) w e st o f Bozeman Montana on
Highway 84 as shown in F ig u re 5.
The a l f a l f a f i e l d has a le g a l
d e sc rip tio n of SW 1/4, NE 1/4 Sec. 12 T2S, RIW and covers approxim ately
16 h ectares (36 acres).
The- f ie ld i s located on a south facing slope
a t an elev atio n of 1490 m eters (4880 f t .) and i s ir r ig a te d by a center
p iv o t s p r i n k l e r system .
The f i e l d was p la n te d w ith a l f a l f a a t th e
b e g in in g of th e 1978 grow ing season (Hanson, 1984) and d a ta from th e
year 1979 was used to c a lib ra te the models.
Data from 1981 was used to
t e s t the a b il i ty of the models to sim ulate s o il m oisture and crop y ield
fo r periods other than the c a lib ra tio n period.
The year 1979 was used
fo r c a lib ra tin g the models because a g re a te r number of s o il m oisture
m easurem ents w ere made d u rin g t h a t y e a r than d u rin g 1981.
Although
d a ta from 1980 was a v a i la b l e , i t was n o t used in t h i s stu d y because a
r e la tiv e ly sm all number of s o il m oisture measurements were made during
th a t year.
However, these data are included in Appendix A.
The d a ta c o lle c te d d u rin g each o f th e s e y e a rs concerned s o i l
c o n d itio n s , crop s t a t u s and w eath er c o n d itio n s .
For each q u a d ra n t
shown in F ig u re 6, s o i l sam ples r e p r e s e n tin g 30 c e n tim e te r (I fo o t)
increm ents in the s o il p ro file were taken a t three lo c a tio n s to a depth
26
T2S
RIW
Sections
...HP—.
12 I 7
I
I
I
Scale ~ 4"= t mile
Figure 5 . Red B luff Research Ranch lo ca tio n
27
Yield Sample Stations
Neutron Probe Stations
Quadrant 4
Quadrant 3
Quadrant 2
Tower Wheel TrocM
Evaporation Tub
Quadrant I
I
N
Figure 6. Study site plan
I Weather Station
28
o f 90 c e n tim e te r s (3 f e e t ) .
T e x tu ra l a n a ly s is o f th e s e sam ples
in d icated a re la tiv e ly uniform s o il p ro file w ith a s i l t y clay loam or
s i l t loam tex tu re.
S oil m oisture measurements were a lso made fo r each
of these samples a t ten sio n s of -.3 bars (f ie ld capacity) and -15 bars
( w i l ti n g point).
In a d d itio n ,
s o i l m o is tu re m easurem ents w ere made a t th re e
l o c a ti o n s in each q u a d ra n t u sin g a n e u tro n probe on s e v e r a l d a te s
during each of the growing seasons considered (1979 and 1981).
These
s o i l m o is tu re m easurem ents w ere made in 30 c e n tim e te r (I fo o t)
in c re m e n ts to a dep th o f 150 c e n tim e te r s (5 f e e t) on each d a te .
The
average of the th ree measurements made a t each increm ent of depth in
each quadrant was used to rep resen t the s o il m oisture d is trib u tio n for
a q u a d ra n t on a p a r t i c u l a r d a te .
These average v a lu e s w ere used to
c a lib r a te and t e s t the models.
Data regarding the s ta tu s of the a lf a lf a crop included the dates
when h arv ests began, when h arv e sts were completed as w ell as the y ie ld
of a lf a lf a produced from each harvest in each quadrant.
In ad dition,
data concerning the approximate date and amount of each ir r ig a tio n were
a ls o a v a ila b le .
S ince as many as s e v e r a l days e la p se d betw een th e
b e g in in g and end o f an i r r i g a t i o n , i t was n e c e ssa ry to e s tim a te th e
d a te each q u a d ra n t re c ie v e d a given i r r i g a t i o n .
These d a te s w ere
e s tim a te d based on th e rec o rd ed t r a v e l speed o f th e c e n te r p iv o t.
However, the date a p a rtic u la r quadrant recieved an ir r ig a tio n could be
in e r r o r by a day or two s in c e th e s t a r t i n g p o in t o f th e c e n te r p iv o t
fo r
each ir r ig a tio n could not always be determined p re c ise ly from the
a v a ila b le d a ta .
29
Data concerning the weather a t the s i t e included p re c ip ita tio n and
pan e v a p o ra tio n .
P r e c i p i t a t i o n was m easured u sin g a re c o rd in g r a in
gage w hile pan evaporation was measured using a standard Weater Bureau
four fo o t evaporation pan.
In some cases, pan evaporation values fo r a
s in g le day were re c o rd e d and where p o s s ib le , th e s e v a lu e s w ere used.
In other cases, accumulated pan evaporation values were recorded fo r a
period of several days.
In these cases, average d a ily pan evaporation
values were determined by dividing the accumulated pan evaporation by
th e number o f days over which i t was accum ulated.
A summary of
p r e c i p i t a t i o n and pan e v a p o ra tio n d a ta a s w e ll as th e o th e r d a ta
described in t h is sectio n can be found in Appendix A.
Model c a lib ra tio n
For computer models to be u sefu l in a p a rtic u la r s itu a tio n , they
m u st be c a l i b r a t e d t o r e p r e s e n t t h a t s i t u a t i o n .
T hrough th e
c a l i b r a t i o n p ro ce d u re, modeled r e s u l t s a re made to m atch observed
r e s u lts as clo sely and c o n sista n tly as i s ju s tif ie d by the precisio n of
o b serv ed d a ta and th e in te n d e d use o f th e modeled r e s u l t s .
The
c a lib ra tio n process re q u ire s a procedure to evaluate the success of a
given c a lib ra tio n and another procedure to ad ju st param eter estim ates
fo r the next c a lib ra tio n .
The c rite r io n fo r judging the adequacy of a
giv en c a l i b r a t i o n may be s u b je c tiv e judgem ent or some s t a t i s t i c
selected to r e f le c t how w ell sim ulated values match observed values.
The adjustm ent of param eters may be performed in sev eral ways; i t may
be based on a s u b je c tiv e judgem ent o f w hat p a ra m eter changes seem
l i k e l y to be d e s i r a b l e , a s e t o f r u l e s d e riv e d from a s e n s i t i v i t y
30
a n a ly s is o f th e p a ra m e te rs or a s y s te m a tic v a r i a t i o n o f p a ra m e te rs
(ASAE,1983).
A sin g le s t a t i s t i c was selec te d fo r measuring how w ell the modeled
s o i l m oisture p ro file matched the observed s o il m oisture p ro file .
The
s t a t i s t i c used was th e sum o f th e sq u ared d e v ia tio n s o f modeled s o i l
m o is tu re v a lu e s from observed v a lu e s.
s t a t i s t i c in d ic a te a b e tte r match.
was used in two ways:
procedure,
The sum of the squared d eviations
In th e e a r ly s ta g e s o f th e c a l i b r a t i o n
d eviations of modeled from observed s o il m oisture for the
e n tire s o il p ro file were used.
procedure,
S m a lle r v a lu e s fo r t h i s
In the l a t e r stages of the c a lib ra tio n
d ev iatio n s of modeled from observed values fo r individual
s o i l l a y e r s w ere used.
D e v ia tio n s f o r th e e n t i r e s o i l p r o f i l e w ere
used as a measure of how w ell the n et movement of w ater in to and out of
th e s o i l p r o f i l e was b ein g m odeled.
D e v ia tio n s f o r in d iv id u a l s o i l
lay e rs were used as a measure of how w ell w ater movement between s o il
la y e rs was being modeled.
P aram eter e s tim a te s f o r th e m odels exam ined in t h i s stu d y were
adjusted using two procedures.
A fter i n i t i a l param eter e stim ate s fo r
th e model bein g c a l i b r a t e d w ere made, th e model was run.
model ru n ,
From t h i s
th e s im u la te d change in t o t a l s o i l m o is tu re betw een
o b s e rv a tio n d a te s was compared to th e observed change in t o t a l s o i l
m o is tu re betw een th e s e d a te s .
Based on t h i s co m p ariso n , i t was
p o ssib le to id e n tify periods when the sim ulated ev ap o tran sp iratio n was
e ith e r too high or too low.
p a ra m e te rs
w ere
a d ju s te d
A fter id e n tify in g these periods, several
to
e ith e r
in c re a s e
e v a p o tr a n s p ir a tio n d u rin g th e a p p ro p r ia te p e rio d s .
or
d e c re a se
When s e v e ra l
31
c a lib ra tio n runs had been completed, appropriate param eter adjustm ents
w ere no lo n g e r obvious and i t was n e c e ssa ry to. use th e second
c a lib r a tio n procedure.
In the second c a lib ra tio n procedure, a sin g le param eter value was
a d ju s te d s l i g h t l y and th e model was ru n .
I f t h i s a d ju s tm e n t reduced
th e sum o f th e squared d e v ia tio n s , th e a d ju s te d p a ra m e te r v alu e was
recorded, the param eter was returned to i t s o rig in a l value and a second
param eter value was adjusted fo r the next model run.
o f th e f i r s t
I f the adjustm ent
p a ra m e te r d id n o t reduce th e sum o f th e
squared
d ev iatio n s, a d d itio n al adjustm ents were performed u n til the sum of the
sq u ared d e v ia tio n s
was reduced.
At t h i s p o in t, th e p a ra m e te r was
re tu rn e d to i t s o r i g i n a l v alu e and a second p a ra m e te r v alu e was
adjusted fo r t h e ■next model run.
This process was continued u n til a l l
p a ra m e te r v a lu e s had been a d ju s te d and re tu rn e d to t h e i r o r i g in a l
v a lu e s.
When t h i s had been acco m p lish e d , a l l p a ra m e te r v a lu e s w ere
sim ultaneously s e t to the adjusted values which had reduced the sum of
th e sq u ared d e v ia tio n s .
T his e n t i r e p ro c e ss was re p e a te d u n t i l th e
sim u lta n e o u s a d ju s tm e n t o f p a ra m e te rs no lo n g e r s i g n i f i c a n t l y (10
p e rc e n t re d u c tio n ) red u ced th e sum o f th e s q u a re d d e v i a t i o n s .
P aram e te r v a lu e s w ere a d ju s te d i n d iv id u a lly and re tu r n e d to t h e i r
o r i g in a l v a lu e s to p re v e n t some p a ra m e te rs from b e in g over a d ju s te d
w hile o th ers would be under adjusted.
A fte r th e m odels had been c a l i b r a t e d to s im u la te v a r i a t i o n s in
s o il m oisture, they were c a lib ra te d to model crop y ie ld .
Since y ie ld
m easurem ents were a v a ila b le f o r b o th o f two h a r v e s ts d u rin g th e
32
c a l i b r a t i o n y e a r (1979) and th e t e s t y e ar (1981), y ie ld c a l i b r a t i o n s
were based on two sim ulation periods fo r each quadrant.
Sim ulations of
each q u a d ra n t f o r y ie ld c a l i b r a t i o n were possible only because y ield
measurements by quadrant were a v aila b le.
The f i r s t sim ulation period
used fo r y ie ld c a lib ra tio n represented the tim e from the f i r s t of June
u n til the begining of the f i r s t harv est.
The second sim ulation period
represented the tim e from the begining of the f i r s t h arv est u n til the
b e g in in g o f th e second h a rv e s t.
The f i r s t o f June was used as th e
s t a r t i n g d a te f o r th e f i r s t s im u la tio n p e rio d b ecause i t was n o t
p o s s ib le to c a l i b r a t e th e m odels p r i o r to t h i s d a te due to a la c k o f
s o il m oisture measurements during the c a lib ra tio n year.
S ince th e SPAW and P la n tg ro m odels u t i l i z e somewhat d i f f e r e n t
p a ra m e te rs , a more d e ta il e d d e s c r ip tio n of the c a lib ra tio n procedure
fo r each model follow s.
SPAW c a lib ra tio n
The o p e ra tio n o f th e SPAW model i s governed by th e v a lu e s o f
s e v e r a l s o i l , crop and w e ath e r p a ra m e te rs .
S o il c o n d u c tiv ity and
te n s io n c u rv e s w ere d e fin e d u sin g th e e m p iric a l r e l a t i o n s a lre a d y
b r ie f ly mentioned.
These re la tio n s are dependent on the percentages of
sand and clay in a s o il.
Table I contains values fo r these percentages
in each s o i l la y e r as d ete rm in e d th ro u g h th e c a l i b r a t i o n p ro ced u re.
Based on th e v a lu e s in t h i s t a b l e and
sta n d a rd s o i l c l a s s i f i c a t i o n
c rite ria
a l l o f th e s o i l l a y e r s a r e
(D onahue e t
a l . , 19 7 8 ),
c la s s if ie d as s i l t y clay loams or s i l t loams.
These c la s s if ic a tio n s
correspond r e la tiv e ly w ell w ith the s o il te x tu re s determ ined from f ie ld
measurements.
33
TABLE I . Percent sand and clay determined
through the SPAW c a lib ra tio n
s o il lay e r
depth
(cm)
I
2
3
4
5
0-30
30-60
60-90
90-120
120-150
percent
sand
clay
26
26
24
24
24
18
19
21
22
22
_______________________________-__________
Crop p a ra m e te rs in c lu d e crop canopy, crop phenology, canopy
s u s c e p t a b i l i t y , p h e n o lo g ic a l s u s c e p t a b i l i t y as w e ll as crop r o o t
d i s t r i b u t i o n , crop w a te r s t r e s s and y ie ld s u s c e p t a b i l i t y .
The crop
canopy curve d e riv e d th ro u g h th e c a l i b r a t i o n p ro ce d u re i s shown in
Figure 7 w hile Figure 8 shows the corresponding crop phenology curve.
As shown by Figure 7, crop canopy in cre ases lin e a rly from the begining
o f th e season to th e b e g in in g o f th e f i r s t h a rv e s t.
Between th e
b e g in in g and end o f th e f i r s t h a r v e s t , c ro p c an o p y d e c r e a s e s
d ram a tic ally to r e f l e c t the e ffe c ts of c u ttin g , windrowing, baling and
rem oval o f h a rv e s te d a l f a l f a .
From th e end o f th e f i r s t h a rv e s t,
canopy a g ain in c r e a s e s l i n e a r l y u n t i l th e b e g in in g o f th e second
c u ttin g where canopy again d eclin es ra p id ly due to h arvesting.
As shown by Figure 8, crop phenology remains r e la tiv e ly constant
before the f i r s t h arv est and between the end of the f i r s t harvest and
the begining of the second.
However, rapid changes in the proportion
o f the canopy tra n s p irin g occur during harv est periods.
Although cut
a lf a lf a making up windrows and b ales would c o n trib u te to crop canopy,
P ercent Cover
J u lia n D a te
Figure 7 . SPAW model crop canopy curve
Phenology
I
150
170
190
210
J u lia n D a t e
Figure 8. SPAW model crop phenology curve
230
250
36
i t would n o t be a b le to t r a n s p i r e and remove w a te r from th e s o i l
p ro file .
T his i n a b i l i t y to t r a n s p i r e was r e f l e c t e d by a d e c lin e in
phenology u n til the m id-point of each harvest.
From the m id-point of
each h a r v e s t, th e p ro p o rtio n o f th e crop canopy t r a n s p i r i n g would
increase since only a c tiv e ly growing a lf a lf a would have been l e f t on
the f ie ld as harvested m a te ria l was removed.
T able 2 in c lu d e s v a lu e s used in th e canopy s u s c e p t a b i l i t y and
phenology s u s c e p t a b i l i t y r e l a t i o n s h i p s .
The r a t i o s o f a c tu a l to
p o t e n t i a l e v a p o tr a n s p ir a tio n (AET/PET) were s e le c te d based on a
p re v io u s a p p lic a tio n o f th e SPAW model to th e s im u la tio n o f corn in
e aste rn Washington (Saxton e t a l., 1984).
I n i t i a l e stim ate s of canopy
grow th and re d u c tio n in phenology w ere made based on t h i s p re v io u s
a p p lic a tio n ,
however, these values were s lig h tly a lte re d during the
c a lib ra tio n procedure.
Table 2. Canopy and Phenology su s c e p ta b ility
re la tio n sh ip s
AET/PET
( cm/cm)
Canopy
Growth
(dec. %)
Phenology
Reduction
(dec. %)
0.00
0.20
0.50
0.70
0.80
1.00
1.00
1.00
1.00
0.90
0.60
0.00
0.000
0.000
0.000
0.000
0.002
0.010
A c o n s ta n t r o o t d i s t r i b u t i o n th ro u g h th e grow ing season was
assumed fo r th is model ap p lica tio n since the a lf a lf a f ie ld in question
was planted a f u l l year before the c a lib ra tio n year.
Based on reported
37
v a lu e s (Bolta n , 1962), i t was assum ed t h a t th e m a jo r ity o f th e r o o ts
would be found in th e f i r s t 30 c e n tim e te r s (I fo o t) o f d e p th .
I t was
f u r t h e r assumed t h a t r o o ts below 120 c e n tim e te r s (4 f e e t ) would be
in s ig n ific a n t.
Some v a ria tio n in the proportion of ro o ts in each s o il
la y e r over th e c o u rse o f th e grow ing seaso n was exam ined f o r th e
c a l i b r a t i o n y e a r.
However, th e s e v a r i a t i o n s d id n o t s i g n i f i c a n t l y
improve the c a lib ra tio n .
The follow ing ro o t d is trib u tio n was based on
th e s t a te d a ssu m p tio n s and th e c a l i b r a t i o n p ro ce d u re: 0 to 30 cm (I
f t . ) , 75 p e rc e n t o f th e r o o t system ; 30 to 60 cm (2 f t . ) , 15 p e rc e n t;
60 to 90 cm (3 f t . ) 5 p e rc e n t and 90 to 120 cm (4 f t . ) , 5 p e rc e n t.
Although the crop w ater s tr e s s re la tio n sh ip s lig h tly a ffe c ts the
sim u latio n of s o il m oisture v a ria tio n s through i t s influence on canopy
growth and crop phenology, i t s primary purpose i s to provide an index
w hich can be r e l a t e d to y ie ld .
For t h i s re a so n , th e pre-program ed
m oisture s tr e s s curves were not adjusted u n til the SPAW model had been
c a l i b r a t e d to s im u la te v a r i a t i o n s in s o i l m o is tu re over th e e n t i r e
growing season.
When t h i s had been accomplished, two p o rtio n s of the
growing season designed to rep resen t the p o rtions of the season which
would a f f e c t y ie ld from e i t h e r th e f i r s t or second h a rv e s t were
sim ulated sep arately .
Based on two sim u latio n s fo r each quadrant, the
m oisture s tr e s s curves were adjusted u n til low sim ulated s tr e s s values
could be c o rre la te d w ith high measured y ie ld s and high sim ulated s tre s s
values could be c o rre la te d w ith low measured y ield s.
Since m oisture
s tr e s s only s lig h tly a ffe c ts the sim ulation of s o il m oisture v a ria tio n ,
th e SPAW model was n o t r e c a l i b r a t e d to model s o i l m o is tu re changes
38
a f te r i t was c a lib ra te d to model m oisture s tre s s .
The SPAW model c a lc u la te s the amount of y ie ld reduction based on a
fu n c tio n o f m o is tu re s t r e s s and y ie ld s u s c e p t a b i l i t y .
Time did n o t
a llo w f o r th e c a l i b r a t i o n o f th e y ie ld s u s c e p t a b i l i t y r e l a ti o n s h i p .
However, th is param eter could be c a lib ra te d by e x tra p o la tin g the y ield
versus m oisture s tr e s s re la tio n s h ip to e stim ate the y ie ld th a t could be
ex p ected i f th e r e w ere no m o is tu re s t r e s s .
Based on t h i s v alu e o f
p o t e n t i a l y ie ld and m easured y ie ld v a lu e s , th e y ie ld s u s c e p t a b i l i t y
param eter could be c a lib ra te d . The o b jec tiv e of th is c a lib ra tio n would
be to s im u la te re d u c tio n s in y i e l d c o rre sp o n d in g t o th e d if f e r e n c e
between the p o te n tia l y ie ld and the measured y ield .
Since recorded values for. pan evaporation and p re c ip ita tio n were
a v a i la b l e , o n ly pan c o e f f i c i e n t s w ere c a l ib r a t e d to d e fin e w e ath e r
c o n d itio n s .
S ince rec o rd ed s o i l m o istu re values were a v a ila b le only
f o r th e m onths o f June th ro u g h S eptem ber, pan c o e f f i c i e n t s w ere
c a l i b r a t e d only f o r th e s e m onths.
C a lib r a tio n o f th e p a ra m e te rs
d esig n ed to su p p ly v a lu e s f o r m is sin g e v a p o ra tio n d a ta was n o t
attem pted in t h i s study.
P lantero c a lib ra tio n
P la n tg ro c a l i b r a t i o n p a ra m e te rs r e p r e s e n tin g s o i l c o n d itio n s
in c lu d e th e m o is tu re c o n te n t a t f i e l d c a p a c ity , a t th e w i l ti n g p o in t
and th e a i r dry m o is tu re c o n te n t o f th e upper s o i l la y e r .
In itia l
e s tim a te s o f th e m o is tu re c o n te n t a t f i e l d c a p a c ity and th e w i l ti n g
p o in t were made based on measured values (Appendix A). These measured
values were adjusted through ,the c a l i b r a t i o n pro ced u re to o b ta in th e
values shown in Table 3.
An a i r dry m oisture content of th ree percent
39
by volume was d e riv e d th ro u g h th e c a l i b r a t i o n p ro ce d u re based on an
assumed i n i t i a l value of fiv e percent.
Table 3. F ield capacity and w iltin g poin t as
determined from Plantgro c a lib ra tio n
S o il la y e r
I
2
3
4
5
F ie ld c a p a c ity
(% v o l.)
w i l ti n g p o in t
(% v o l.)
16.0
15.5
15.4
15.3
15.7
7.6
7.6
7.1
7.0
7.4
The p a ra m e te rs w hich d e s c rib e crop c o n d itio n s in c lu d e th e
p ro p o rtio n o f th e p o t e n t i a l e v a p o tr a n s p ir a tio n made up by p o t e n t i a l
t r a n s p i r a t i o n a t th e b e g in n in g and end o f each s ta g e o f grow th, th e
s o i l m o is tu re c o n te n t below which t r a n s p i r a t i o n w i l l be l im ite d by
m oisture s tr e s s as w ell as the depth and tim ing of rooting.
The length
of each stage of growth was selec te d to r e f l e c t the follow ing periods:
Stage I from the beginning of the sim ulation period to the beginning of
th e f i r s t h a rv e s t; S tage 2 from th e b e g in n in g o f th e f i r s t h a rv e s t to
the end of the f i r s t h arv est; Stage 3 from the end of the f i r s t harvest
to th e b e g in n in g o f th e second h a rv e s t; S tage 4 from th e b eg in n in g o f
th e second h a rv e s t to th e end o f th e second h a rv e s t and S tage 5 from
\
the end of the second h arv est to the end of the sim ulation period.
The v a lu e s c o r r e s p o n d in g t o t h e p r o p o r t i o n o f p o t e n t i a l
ev ap o tran sp iratio n made up by p o te n tia l tra n s p ira tio n a t the beginning
and end o f each o f th e s e s ta g e s can be found in T able 4.
I t was
assumed t h a t t r a n s p i r a t i o n would be l i m i t e d when th e s o i l m o is tu re
40
dropped below f i f t y p e rc e n t o f th e a v a i la b l e m o is tu re c o n te n t T h is
i n i t i a l e s tim a te was s l i g h t l y r e f i n e d
th ro u g h t h e c a l i b r a t i o n
procedure.
Table 4. Values fo r the r a t i o of p o te n tia l
tra n s p ira tio n (PT) to p o te n tia l
e v ap o tran sp iratio n (PET).
Stage of .
Growth
I
2
3
4
5
*
(PT)Z(PET)
begining
end
0.56
0.86
0.17
0.83
0.14
0.86
0.17
0.83
0.14
0.23
The P la n tg ro model assum es a uniform ro o t d i s t r i b u t i o n t h a t
in creases lin e a rly in depth from the beginning of the season u n til i t
reaches a maximum depth on' a p a rtic u la r date.
Since th e a lf a lf a f ie ld
in question was planted a f u l l year p rio r to the f i r s t year sim ulated
(Hanson, 1984), i t was assum ed t h a t th e r o o t d i s t r i b u t i o n would have
reached i t s maximum before the beginning of the sim ulation periods.
To
rep re se n t t h is assumption, i t was sp e c ifie d in the P lantgro input f i l e s
t h a t th e maximum r o o tin g dep th was reach ed on th e f i r s t day o f th e
grow ing seaso n .
A maximum r o o tin g d ep th o f 150 cm (5 f t . ) was
sp e c ifie d by d e fa u lt because the model assumes th a t only the portion of.
the s o il p ro file containing ro o ts i s being sim ulated.
A f t e r th e P l a n t g r o m odel had b een c a l i b r a t e d to s im u la te
v a ria tio n s in s o il m oisture, i t was c a lib ra te d to sim u late y ield .
As
w ith the SPAW model, the growing season was sim ulated in two p ortions
41
to rep resen t the fra c tio n s of the season which would a ff e c t y ield from
e ith e r the f i r s t or second harv est.
The Plantgro model sim u lates y ie ld
based on a l i n e a r r e l a t i o n s h i p betw een th e p o t e n t i a l y ie ld and th e
r a t i o of a c tu a l tra n s p ira tio n to p o te n tia l tra n s p ira tio n .
To c a lib ra te
f o r y i e l d , th e v a lu e o f th e p o t e n t i a l y ie ld was a d ju s te d to m inim ize
th e sum o f th e squared d e v ia tio n s o f sim u la te d y i e l d s from observed
y ie ld s f o r a l l fo u r q u a d ra n ts.
S ince sim u la te d s o i l m o is tu re s a re
in d ep e n d en t o f th e v a lu e o f th e p o t e n t i a l y i e l d , th e s im u la tio n o f
v a r i a t i o n s in s o i l m o is tu re was u n a ffe c te d by th e c a l i b r a t i o n f o r
y ie ld .
A s in g le pan c o e f f i c i e n t f o r th e e n t i r e s im u la tio n p e rio d was
d e te rm in e d in th e c a l i b r a t i o n p ro c e d u re .
T his was th e o nly w eath er
param eter which was adjusted.
Model te s tin g
The a b il i ty of each model to sim ulate changes in s o il m oisture was
te s te d in two phases.
A fter each model was c a lib ra te d fo r each of the
four f i e l d quadrants using data from 1979,
each quadrant c a lib ra tio n
was te s te d using data from the other th re e quadrants.
The purpose of
t h i s p h a se o f t e s t i n g was t o d e te r m in e i f s e p a r a t e q u a d ra n t
c a lib ra tio n s modeled the e n tire f ie ld b e tte r than a sin g le c a lib ra tio n .
T h is d e te rm in a tio n was based on th e sum o f th e sq u ared d e v ia tio n s
sim ulated using each c a lib ra tio n on i t s corresponding quadrant and each
c a l i b r a t i o n on a l l q u a d ra n ts.
The r e s u l t s o f th e f i r s t phase of
te s tin g in d icated th a t separate c a lib ra tio n s for each quadrant did not
n e c e s s a r ily produce b e t t e r r e s u l t s th an a sin g le c a lib ra tio n for a l l
quadrants.
The c a lib ra tio n which produced th e b e s t r e s u l t s (minimum
42
sum o f th e squared d e v ia tio n s ) f o r th e e n t i r e f i e l d was used in th e
second phase of te s tin g .
In th is phase, data from 1981 was sim ulated
f o r each q u a d ra n t u sin g both m odels.
From th e s e s im u la tio n s , th e
av erag e p e rc e n t d e v ia tio n f o r a l l fo u r q u a d ra n ts o f sim u la te d from
observed s o i l m o is tu re s w ere c a lc u la te d f o r each l a y e r in th e s o i l
p ro file .
Based on th e s e e r r o r s and p l o ts o f observed and sim u la te d
s o i l m o is tu re v e rs e s tim e , i t was p o s s ib le to e v a lu a te each model in
term s of the.accuracy of predicted s o il m oistures.
The SPAW and P la n tg ro m odels w ere a ls o e v a lu a te d based on t h e i r
capacity to sim ulate crop y ie ld fo r periods other than the c a lib ra tio n
period.
The 1981 growing season was sim ulated in two p o rtio n s which
w ere d esig n ed to r e p r e s e n t th e f r a c t i o n s o f th e seaso n t h a t would
a f f e c t y ie ld s from e i t h e r th e f i r s t or second h a r v e s t.
When each
p o r tio n o f th e 1981 grow ing season had been s im u la te d f o r a l l fo u r
quadrants,
the y ie ld values p redicted by each model were compared to
corresponding observed y ie ld v a lu e s.
The m odels were th e n e v a lu a te d
based on th e a cc u ra c y o f th e p r e d ic te d y ie ld v a lu e s .
In a d d itio n to
th e acc u ra c y o f p re d ic te d s o i l m o is tu re s and y i e l d s , th e SPAW and
Plantgro models were a lso evaluated based on th e ir d ata, com putational
and c a lib ra tio n requirem ents.
»v.
43
CHAPTER
>i
RESULTS
Figures 9 and 10
show p lo ts of s o il m oisture verses tim e fo r each
of the fiv e s o il la y e rs sim ulated in th is study.
Figure 9 shows p lo ts
derived using the SPAW model and measured s o il m oisture values.
The
g rap h s on th e l e f t s id e o f F ig u re 9 w ere d e riv e d u sin g d a ta from th e
c a lib ra tio n year 1979.
The graphs on the r ig h t side of Figure 9
show
p lo ts derived using the 1979 c a lib ra tio n of the SPAW model and observed
p re c ip ita tio n , ir r ig a tio n and evaporation data from the t e s t year 1981.
Observed s o i l m o is tu re v a lu e s a re shown a s i s o l a t e d p o in ts in th e s e
p l o t s and in th e p l o ts shown in F ig u re 10.
F ig u re 10 i s s i m i l a r to
Figure 9 except the p lo ts shown were obtained by applying the Plantgro
m odel.
A lthough th e p l o ts shown in F ig u re s 9 and 10 r e p r e s e n t th e
r e s u l t s from one q u a d ra n t o n ly , s i m i l a r p l o t s w ere o b ta in e d f o r th e
oth er th re e quadrants.
T ab les 5 and 6 in c lu d e v a lu e s f o r th e average p e rc e n t e r r o r in
s o il m oisture values sim ulated by the SPAW and Plantgro models.
The
values in these ta b le s were calcu late d by averaging the r e la tiv e e rro rs
o f sim u la te d s o i l m o is tu re v a lu e s when compared to m easured s o i l
m oisture values fo r a l l four quadrants.
Average e rro r fig u re s for the
c a lib ra tio n year were used to to r e f l e c t how p rec ise ly each model can
be c a lib ra te d .
Figures rep resen tin g the t e s t year are designed to show
how accu rately each program can sim ulate s o il m oisture during periods
independent of the c a lib ra tio n period.
44
PERCENT MOISTURE (VOL.)
one Toot
two foot
two foot
th re e foot
th re e foot
four foot
four foot
five fo o t
Figure 9. SPAW model simulated soil moisture versus time for the
calibration year (left) and the test year (right).
<45
one
foot
one
foot
PERCENT MOISTURE (V O L )
two foot
t h r e e foot
foui
fOvt
JUUAN £>ATC
Figure
t h r e e f oot
JULIAN OATt
10. Plantgro simulated soil moisture versus time for the
calibration year (left) and the test year (right).
46
T able 5. SPAW model av erag e p e rc e n t e r r o r in
p redicted s o il m oistures
S o il Layer
I
2
3
4
5
p ro file average
C alib ratio n
Year (1979)
Test
Year (1981)
11.1
7.9
4.1
3.3
3.2
5.9
18.0
15.2
8.2
4.7
4.4
10.1
Table 6. Plantgro model average percent e rro r in
pred icted s o il m oistures
S oil Layer
I
2
3
4
5
p ro file average
C alib ratio n
Year (1979)
Test
Year (1981)
10.8
4.7
8.1
10.3
16.8
10.1
21.5
12.0
14.8
15.5
15.3
15.8
Based on th e v a lu e s f o r 1979 in T ab les 5 and 6, i t i s a p p a re n t
t h a t th e SPAW model can be c a l i b r a t e d to s im u la te th e e n t i r e s o i l
p r o f ile more p rec ise ly than the Plantgro model.
show th a t,
The fig u re s fo r 1981
in th is a p p lic a tio n , the SPAW model re p re se n ts independent
d a ta more a c c u ra te ly fo r th e e n t i r e s o i l p r o f i l e th a n th e P la n tg ro
m odel.
However, 1979 v a lu e s show t h a t th e P la n tg ro model produced a
c a l i b r a t i o n fo r s im u la tin g m o is tu re changes in th e upper two s o i l
la y e rs th a t was somewhat more p recise than the SPAW model c a lib ra tio n .
In a d d itio n , the d ifferen c e in the accuracy of s o il m oistures predicted
47
by each model d u rin g th e t e s t y e a r f o r th e upper two s o i l la y e r s was
r e l a t i v e l y s m a ll.
S ince m o is tu re in th e upper s o i l l a y e r s i s more
im p o rta n t in te rm s o f a p l a n t 's w a te r supply th an m o is tu re in lo w er
l a y e r s , th e s i m i l a r i t y o f th e r e s u l t s produced by each model f o r th e
upper s o il la y e rs should be considered in an evaluation of the models.
Figure 11 shows g rap h ically th e r e s u l t s o f th e SPAW c a l i b r a t i o n
f o r y ie ld s im u la tio n w h ile F ig u re 12 shows s i m i l a r r e s u l t s f o r th e
P la n tg ro m odel.
As can be seen from th e s e f i g u r e s ,
b o th m odels
sim u late crop y ie ld fo r the c a lib ra tio n year re la tiv e ly w ell.
A lin e a r
reg ressio n of crop w ater s tr e s s and y ie ld data from SPAW sim ulations
produced th e l i n e shown in F ig u re 12 w ith an r squared v a lu e of 0.92.
A lin e a r reg ressio n of observed y ield data and y ie ld data sim ulated by
the Plantgro model produced an r squared value of 0.97.
Observed y ield
values and crop w ater s tr e s s values sim ulated by the SPAW model fo r the
c a l i b r a t i o n y e ar can be found in T able 7 along w ith y ie ld v a lu e s
sim ulated by the Plantgro model fo r the c a lib ra tio n year.
F ig u re s 11 and 12 as w e ll as th e v a lu e s in T able 8 in d ic a t e t h a t
n e ith e r model sim ulates crop y ie ld very a ccu rately fo r the t e s t year of
1981.
Table 8 contains values fo r observed y ie ld , the y ie ld sim ulated
by each model as w ell as the r e la tiv e e rro r in y ield values sim ulated
by each m odel.
The v a lu e s in t h i s t a b l e in d ic a te t h a t th e P la n tg ro
model s im u la te d y ie ld f o r th e t e s t y e a r b e t t e r th an th e SPAW model.
However, th e e r r o r s a s s o c ia te d w ith b o th m odels a re l a r g e enough to
make y ie ld s im u la tio n s by e i t h e r model f o r th e t e s t y e a r o f d o u b tfu l
v alu e.
S i m u l a t e d Yield ( t o n s / a c r e )
1st
2nd
le t
2nd
0
4
6
IZ
16
Figure 11. SPAW model s tr e s s versus y ield
20
1979
1979
1981
1981
24
1 st 7 9
S im u la ted Yield ( t o n / a c r e )
2nd 7 9
2nd 81
Figure 12. Plantgro model observed y ield versus sim ulated yield
50
T able 7. O bserved■y i e l d , SPAW s im u la te d cro p w a te r s t r e s s and
Plantgro sim ulated y ie ld fo r the c a lib ra tio n year 1979.
Sim ulation
1
2
3
4
•••
Observed
Yield
(to n /a cre )
SPAW Simulated
Water S tre ss
(index)
T ts
2.14
2.03
2.09
Plantgro Simulated
Crop Yield
(to n /a cre )
6761
5.21
6.26
6.25
•••••■
T M
...........
5
1.51
16.79
6
1.31
18.07
7
1.33
17.17
8
1.43
15.59
SPAW YIELD=-0.06(STRESS)+2.36
Plantgro Y ield= I.00(obs. y ie ld )-0.01
~
2.09
2.00
2.16
....
1.47
1.38
1.39
1.38
r 2=0.92
r2=0.97
T able 8. Observed y ie ld and y ie ld s im u la te d by th e SPAW and
Plantgro models for the t e s t year 1981.
Sim ulation
observed y ield
(to n s/ac re)
I
2
3
4
2.67
2.53
2.77
2.98
sim ulated y ie ld
(to n s/a c re )
SPAW Plantgro
• • O
5
6
7
8
2.42
- 2.54
1.88
2.09
2.14
2.14
2.10
2.02
2.05
1.97
2.17
2.50
9 « • «
9 9 9 9
r e la tiv e
e rro r (%)
SPAW Plantgro
1.06
2.19
1.59
2.29
2.25
1.77
1.43
2.03
average re la tiv e e rro r
20
15
24
32
23
22
22
16
56
37
20
32
30
10
10
6
3
. 14
S im u la tio n v a lu e s one th ro u g h fo u r in T ables 7 and 8 a re y ie ld
d a ta f o r th e f i r s t h a rv e s t o f 1979 or 1981 w h ile v a lu e s f i v e through
e ig h t are fo r the second harvest.
Since the SPAW model provides s tr e s s
v a lu e s r a t h e r th an y ie ld v a lu e s , th e SPAW s im u la te d y ie ld v a lu e s in
T able 8 w ere d e te rm in e d from F ig u re 11.
51
CHAPTER 5
DISCUSSION
The purpose of t h is chapter i s to evaluate the SPAW and Plantgro
m odels in te rm s o f t h e i r d a ta and c o m p u ta tio n a l re q u ire m e n ts , th e
r e s u l t s o f t h e i r a p p lic a tio n a t th e Red B lu ff Ranch and so u rc e s o f
e r r o r in t h i s stu d y .
The e ase o f c a l i b r a t i o n
and a p p lic a tio n ,
p o te n tia l program improvements as w ell as p o te n tia l fu tu re a p p lica tio n
to the Red B luff area w ill also be examined.
Data and Computational Requirements
Although the SPAW model is much more elab o rate than the Plantgro
m odel, th e re q u ire m e n ts o f b oth m odels f o r m easured d a ta a re v ery
s im ila r.
Each model r e q u ir e s d a ily v a lu e s o f p r e c i p i t a t i o n and
i r r i g a t i o n a s w e ll a s m easured e v a p o ra tio n .
In a d d it i o n , m easured
v a lu e s o f s o i l m o is tu re a re n e c e ssa ry f o r c a l i b r a t i o n purposes.
A dditional measured data such as th o se d e fin in g s o i l c h a r a c t e r i s t i c s
a re h e lp f u l in o b ta in in g i n i t i a l p a ra m e te r e s tim a te s , how ever, a l l
oth er input data can be defined through the c a lib ra tio n procedure and
su b jectiv e judgement.
Subjective judgement i s necessary to determine
i f p a ra m e te r v a lu e s a r r iv e d a t th ro u g h th e c a l i b r a t i o n pro ced u re
r e a l i s t i c a l l y rep resen t the physical s itu a tio n .
S ince th e SPAW model i s more e la b o r a te th an th e P la n tg ro m odel,
i t s c o m p u ta tio n a l re q u ire m e n ts a re correspondingly g re a te r. The SPAW
model re q u ire s a computer w ith approxim ately 132 k ilo b y te s of random
access memory (RAM) in ad d itio n to the memory required by the operating
system of the computer.
The operating systems of most microcomputers
52
do n o t r e q u ir e more th an ab o u t 40 k ilo b y te s o f random a c c e ss memory
w h ile many o p e ra tin g sy stem s r e q u ir e l e s s th an t h i s amount (Adams,
1986).
In c o n t r a s t ,
th e P la n tg ro model r e q u ir e s o nly about 10
k ilo b y tes of RAM in ad d itio n to memory required by the operating system
o f the microcomputer.
Analysis o f r e s u lts from th e Red B luff sim ulation
The r e s u lts of th is study in d ic ate d th a t the SPAW model sim ulated
s o il m oisture in the e n tire s o il p r o f ile somewhat more p re c ise ly and
accu rately than the Plantgro model.
However, the SPAW model produced
much b e tte r r e s u lts fo r the lower th re e s o il lay e rs w hile both models
produced comparable r e s u lts fo r the upper two s o il la y e rs.
Although
th e s im u la te d s o i l m o is tu re s f o r th e upper two s o i l la y e r s w ere
comparable fo r both models, these r e s u lts could be m isleading.
These
r e s u lts might be m isleading because, based on other a p p lic a tio n s of the
SPAW model (Saxton and Bluhm, 1982; Sudar e t . a l . , 1981) i t a p p e a rs
t h a t a d d it i o n a l c a l i b r a t i o n o f th e SPAW model co u ld pro b ab ly be
performed to improve the p recisio n and accuracy of the sim ulation of
the upper two s o il lay e rs.
A d d itio n a l c a l i b r a t i o n o f th e P la n tg ro model would probably not
s ig n ific a n tly improve the p recisio n or accuracy of the sim ulation of
any of the s o il lay e rs.
The lim ite d improvement i s p red icted because
th ere are a sm aller number of c a lib ra tio n param eters and the values of
th e s e p a ra m e te rs w ere th o ro u g h ly exam ined d u rin g th e c a l i b r a t i o n
p ro c e ss .
However, th e SPAW model in c lu d e s a much l a r g e r number o f
c a lib ra tio n
p a ra m e te rs and tim e
d id
n o t allo w
f o r a com plete
examination of a l l r e a l i s t i c a l l y p o ssib le combinations of c a lib ra tio n
53
param eter values.
The r e s u l t s o f t h i s stu d y in te rm s o f s im u la tin g v a r i a ti o n s in
s o i l m o is tu re m ight be m is le a d in g in a n o th e r way due to th e model
te s tin g procedure used.
In the f i r s t phase of the te s tin g procedure,
s e p e r a t e c a l i b r a t i o n s f o r e a c h q u a d r a n t w ere t e s t e d .
T hese
c a lib ra tio n s were te s te d a g ain st data fo r a l l of the quadrants for both
the c a lib ra tio n and the t e s t year.
Based on th is i n i t i a l te s tin g , the
c a l i b r a t i o n w hich produced th e b e s t s im u la tio n s o f a l l d a ta was
s e le c te d f o r f u r t h e r stu d y .
T his p o r tio n o f th e t e s t i n g pro ced u re
produced biased r e s u lts because, in another s itu a tio n , i t might not be
p o ssib le to obtain more than one independent c a lib ra tio n .
B e tte r c a l i b r a t i o n s f o r both m odels could p ro b ab ly have been
o b ta in e d in t h i s stu d y i f th e a v a ila b le d a ta had been used more
e ffe c tiv e ly .
Data from 1980 was a v a i la b l e , how ever,
i t was n o t
u t i l i z e d and c a l i b r a t i o n s w ere made based on only one y e a r o f d a ta ,
the f i r s t phase of te s tin g showed th a t seperate c a lib ra tio n s fo r each
q u a d ra n t w ere u n n e ce ssa ry . C a lib r a tio n s based on d a ta from a l l fo u r
quadrants fo r two years would probably have been b e tte r than those th a t
w ere t e s te d .
Model c a l i b r a t i o n s a r r iv e d a t on t h i s b a s i s would have
been superior to those obtained since flaw s in the c a lib ra tio n s caused
by p e c u lia r itie s in data fo r a p a rtic u la r year and e rro rs in p a rtic u la r
f ie ld measurements would have been reduced.
In a d d itio n , data from the
t h i r d y e a r o f a v a ila b le d a ta could s t i l l have been used f o r t e s t i n g
purposes.
In term s of y ie ld p red ic tio n , the r e s u lts of t h is study show th a t
54
both models can be c a lib ra te d to sim ulate y ield re la tiv e ly p rec ise ly
during the c a lib ra tio n year.
However, the r e s u lts a lso in d ic ate d th a t
the models did not sim ulate y ie ld data from n o n -ca lib ra tio n years very
a c c u r a te ly .
Y ield d a ta f o r a n o n - c a lib r a tio n y e ar w ere p ro b ab ly n o t
v ery a c c u ra te because th e y ie ld c a l i b r a t i o n s w ere based on a very
l im i te d amount o f d a ta and a l l o f th e s e d a ta w ere from a s in g le y e a r.
Reducing the e ffe c ts of c a lib ra tio n flaw s by using data from a number
o f years to produce average c a l i b r a t i o n s would p ro b ab ly in c re a s e th e
accuracy of n o n -ca lib ra tio n year y ie ld sim ulations.
.
Sources o f e rro r in the Red B luff study
In a d d itio n to im perfect c a lib ra tio n s , th ere were other probable
sources of e rro r in ,the r e s u lts of th is study.
In some cases sp e c ific
so u rc e s o f e r r o r could be a s s o c ia te d w ith e i t h e r one model or th e
other.
In oth er cases, sources of e rro r were id e n tic a l fo r both models
and th e s e e r r o r s did n o t a f f e c t th e model com parison based on th e
p r e c is io n and accu racy o f m odeled s o i l m o is tu re r e s u l t s .
However,
e r r o r s found in only one o f th e m odels could have a f f e c te d the,
comparison of the models based on the p recisio n and accuracy of modeled
r e s u lts .
In the a p p lic a tio n of the SPAW model, e rro r was introduced by the
c a lib ra tio n of the crop w ater s tre s s re la tio n sh ip .
However, th is e rro r
i s not re fle c te d by the s o il m oisture versus tim e p lo ts and the average
e r r o r v a lu e s p re s e n te d in th e r e s u l t s s e c tio n o f t h i s document.
Because the SPAW model was not re c a lib ra te d to sim ulate v a ria tio n s in
s o il m oisture a f te r i t was c a lib ra te d to sim ulate crop w ater s tre s s ,
the param eter values presented here could probably be improved.
The
55
e f f e c t o f th e c a l i b r a t i o n f o r crop w a te r s t r e s s s im u la tio n i s n o t
r e f l e c t e d in th e s o i l m o is tu re v esu s tim e p l o ts o r th e av erag e e r r o r
fig u res because th is inform ation was generated p rio r to c a lib ra tin g the
s tr e s s function.
Although c a lib ra tin g the m oisture s tr e s s re la tio n sh ip
p ro b ab ly reduced th e a c c u ra c y and p r e c is io n o f th e c a l i b r a t i o n
presented here, i t seems reasonable to assume th a t re c a lib ra tio n fo r
s o il m oisture would retu rn the p recisio n and accuracy of the sim ulated
s o il m oisture r e s u lts to le v e ls comparable to those presented.
The major source of e rro r found in s o il m oisture values sim ulated
by th e P la n tg ro model was caused by th e way in w hich th e r o o t
d i s t r i b u t i o n was s p e c if ie d .
There was no p ro v is io n in th e P la n tg ro
model fo r specifying a maximum rooting depth other than the f u l l depth
o f th e s o i l p r o f i l e being s im u la te d .
The f a c t t h a t a uniform ro o t
d is trib u tio n extending throughout the s o il p ro file was assumed probably
accounts fo r the wide flu c tu a tio n s in s o il m oisture values sim ulated
f o r th e lo w e r s o i l la y e r s .
Observed f l u c t u a t i o n s in th e low er s o i l
la y e rs were very moderate and the assumed ro o t d is tr ib u tio n probably
a cc o u n ts f o r th e m a jo r ity o f th e e r r o r in r e s u l t s f o r th e s e s o i l
la y e rs .
A second, though minor, source of e rro r found in the Plantgro model
b u t n o t p r e s e n t in th e SPAW model was caused by th e f a i l u r e of th e
P la n tg ro model to acco u n t f o r i n te r c e p t io n .
As i t w as, th e P la n tg ro
model acco u n ted f o r i n te r c e p t io n i n d i r e c t l y by u sin g e x a g e ra te d
param eter values.
However, accounting fo r in te rc e p tio n d ire c tly would
have two advantages.
Parameter values would be more r e a l i s t i c because
56
i t would not be necessary to exagerate them to account fo r in te rc e p tio n
and accounting fo r in te rc e p tio n would add another c a lib ra tio n param eter
which co uld be a d ju s te d .
An a d d itio n a l c a l i b r a t i o n p a ra m e te r would
probably in crease the p rec isio n w ith which the Plantgro model could be
c a l ib r a t e d .
A lthough th e a d d itio n o f a c a l i b r a t i o n p a ra m e te r would
increase the tim e required to c a lib ra te the model, th is tim e increase
would probably be in s ig n ific a n t.
The most s ig n ific a n t source of e rro r common to both models fo r the
t e s t y e a r was in tro d u c e d by th e t e s t i n g
p ro ce d u re.
E rro r was
in tro d u c e d by th e t e s t i n g p ro ce d u re because May 20 was used as th e
s t a r t i n g d a te f o r th e s im u la tio n s o f th e t e s t y e a r.
T his d a te was
se lec te d because the f i r s t s e t of s o il m oisture measurements were made
on May 20 d u rin g th e t e s t y e a r.
E rro r was in tro d u c e d i n to th e t e s t
y e ar s im u la tio n s because th e m odels w ere no t c a l i b r a t e d f o r p e rio d s
p rio r to June f i r s t .
The models were not c a lib ra te d fo r periods p rio r
to June f i r s t because s o il m oisture measurements were not made before
th e f i r s t o f June d u rin g th e c a l i b r a t i o n p e rio d .
The e f f e c t o f t h i s
source o f e rro r on the comparison of the models was probably not very
s ig n ific a n t since the period from May 20 to June f i r s t rep re se n ts only
a sm all fra c tio n of the t o ta l sim ulation period fo r the t e s t year (May
2 0 -S e p t. 2).
Measured data in the form of s o il m oisture values, the tim ing and
amount of ir r ig a tio n s and pan evaporation values were a lso sources of
p o t e n t i a l e r r o r common to both m odels.
There were th r e e so u rc e s o f
p o te n tia l e rro r asso ciated w ith the s o il m oisture values, however, two
o f th e s e so u rc e s o f e r r o r would be found in any model stu d y o f t h i s
57
ty p e .
S o il m o is tu re m easurem ents w ere made u sin g a n e u tro n probe.
U nfortunately, s o il m oistures measured using th is p a rtic u la r probe did
not always agree w ell w ith corresponding s o il m oisture values measured
g r a v i m e t r i c a ll y . Since s o i l m o is tu re m easurem ents made u sin g th e
neutron probe were checked g ra v im e tric a lly only o ccasionally, th ere was
some doubt as to th e ir accuracy.
E r r o r s a s s o c i a t e d w ith r e p r e s s e n t i n g an a re a u sin g p o in t
measurements would be p resen t in any study of th is type.
Average s o il
m oisture values were determined based on th ree measurements fo r each
q u a d ra n t, how ever, th e s e p o in t m easurem ents may o r may n o t have
a c c u r a te ly r e f l e c t e d m o is tu re c o n d itio n s in an e n t i r e q u a d ra n t.
In
ad d itio n , s o il m oistures measured using a neutron probe were converted
from a w eight b a sis to a volum etric b a sis using point measurements of
s o i l b u lk d e n s ity . Here a g a in th e r e was some q u e s tio n a s to th e
accu racy o f e x tr a p o la tin g p o in t m easurem ents to r e p r e s e n t th e bulk
d en sity in an e n tire quadrant.
Data concerning ir r ig a tio n s could have introduced e rro r in to the
s im u la tio n s in th r e e ways.
Due to a la c k o f d a ta , i t was n o t alw ays
p o ssib le to determ ine the p recise date a p a rtic u la r quadrant received a
given i r r i g a t i o n .
Some e r r o r could be a t t r i b u t e d to t h i s so u rc e ,
however, the tim ing of a l l ir r ig a tio n s was known accu ra tely w ithin a
day or tw o.
A second so u rc e o f p o s s ib le e r r o r in i r r i g a t i o n d a ta was
th e assu m p tio n t h a t i r r i g a t i o n w a te r was a p p lie d u n ifo rm ly over a
p a rtic u la r quadrant.
Since a l l ir r ig a tio n systems are im perfect, th is
source of e rro r would be present in any modeling s itu a tio n where w ater
58
i s a p p lie d by an i r r i g a t i o n system .
A lthough th e SPAW model d id
acco u n t f o r i n t e r c e p t i o n , a t h i r d so u rce o f e r r o r was in tro d u c e d by
f a i l i n g to acc o u n t f o r i r r i g a t i o n l o s s e s due to f a c t o r s such as wind
d r i f t and spray evaporation.
E rrors introduced by pan evaporation measurements were caused by
u n c e r ta in ty in th e tim e d i s t r i b u t i o n o f e v a p o ra tio n .
In some c a s e s ,
e v a p o ra tio n m easurem ents were re c o rd e d f o r p e rio d s o f up to s e v e ra l
days.
An a rith m e tic average of these measurements was used to a rriv e
a t d a ily e v a p o ra tio n v a lu e s f o r p e rio d s when d a ily v a lu e s were not
re c o rd e d .
I f d a ily m easurem ents o f e v a p o ra tio n had been used, some
e rro r would probably have been elim inated.
However, e rro rs introduced
by averaging evaporation measurements were probably not as s ig n ific a n t
as those introduced by u n c e rta in tie s in s o il m oisture measurements and
the tim ing of ir r ig a tio n s .
Ease o f Model C alib ratio n and A pplication
The SPAW and Plantgro models sim ulate the same physical processes
b u t each model has ad v an tag es over th e o th e r in te rm s o f t h e i r
c a lib ra tio n .
Based on the sim ulations performed here, the SPAW model
produced r e s u lts th a t were somewhat more accurate than those produced
by the Plantgro model.
However, considerably more tim e and e ff o r t was
re q u ire d to c a l i b r a t e th e SPAW model ( s ix m inute run tim e ) th an was
required to c a lib ra te the Plantgro model (45 second run tim e).
Adding
to th e tim e and e f f o r t re q u ire d to c a l i b r a t e th e SPAW model was th e
fa c t th a t the SPAW model includes a much la rg e r number of param eters
which required c a lib ra tio n .
The la rg e number of c a lib ra tio n param eters incorporated in to the
59
SPAW model was b oth an advantage and a d isa d v a n ta g e .
A more p r e c is e
c a lib ra tio n of the SPAW model was p ossible because th ere were a la rg e
number of c a lib ra tio n param eters which could be fin e tuned.
This 'fin e
tuning* was accomplished by a lte rin g param eters which the SPAW model i s
l e s s s e n s i t i v e to a f t e r a good rough c a l i b r a t i o n was o b ta in e d by
a d ju s tin g s e n s i t i v e p a ra m e te rs .
The la r g e number o f c a l i b r a t i o n
p a ra m e te rs found in th e SPAW model was a d isa d v a n ta g e in t h a t th e
o v e ra ll e ff e c ts of some param eter changes were not always obvious.
It
to o k a g r e a t d e a l o f tim e to d e te rm in e w hich p a ra m e te r changes w ere
a p p ro p r ia te because a d d it i o n a l model ru n s w ere re q u ir e d to t e s t
in ap p ro p riate param eter a lte ra tio n s .
In c o n tra st, the Plantgro model has a r e la tiv e ly sm all number of
p a ra m e te rs w hich was a ls o b oth an advantage and a d isa d v a n ta g e . A
l im i te d number o f c a l i b r a t i o n p a ra m e te rs was an ad v an tag e in t h a t a
c a lib ra tio n th a t had l i t t l e p o te n tia l fo r improvement was arriv ed a t in
a r e l a t i v e l y s h o r t p e rio d o f tim e .
In a d d itio n , even i f a p p ro p ria te
param eter changes were not obvious, p o te n tia l changes in a l l param eters
could be examined w ithout spending an excessive amount of tim e w aiting
fo r computed r e s u lts .
Although r e s u lts from the Plantgrp model were
s e n s itiv e to changes in d iffe r e n t param eters to varying degrees, the
l im i te d number o f c a l i b r a t i o n p a ra m e te rs was a d isa d v a n ta g e in t h a t
th ey d id n o t a llo w f o r a g r e a t d e a l o f 'f i n e tuning* in a c a l i b r a t i o n .
From experience gained through working w ith the SPAW and Plantgro
m odels, i t was p o s s ib le to draw some g e n e ra l c o n c lu s s io n s re g a rd in g
t h e i r s e n s i t i v i t y to v a rio u s p a ra m e te r v a lu e s.
The s o i l m o is tu re
60
r e s u l t s s im u la te d by th e SPAW model w ere e x tre m e ly s e n s i t i v e to pan
c o e f f i c i e n t v a lu e s used to reduce m easured e v a p o ra tio n to p o t e n t i a l
evapotranspiration..
This model was r e la tiv e ly s e n s itiv e to changes in
crop canopy, crop phenology and maximum in te rc e p tio n values in term s of
m odeling w a te r movement i n to and o u t o f th e e n t i r e s o i l p r o f i l e .
In
term s of modeling the movement of w ater w ith in the s o il p r o f ile , the
SPAW model was m ost s e n s i t i v e to p a ra m e te rs t h a t d e s c rib e th e s o i l
c h a ra c te ris tic s
(p e rc e n t
sand and c la y
in
th is
d i s t r i b u t i o n o f p la n t r o o ts w ith in th e s o i l p r o f i l e .
stu d y )
and th e
The SPAW model
was l e a s t s e n s i t i v e to v a r i a t i o n s in p a ra m e te rs d e s c r ib in g canopy
s u s c e p t a b i l i t y , phenology s u s c e p t a b i l i t y and th e cro p w a te r s t r e s s
curves.
The Plantgro model was most s e n s itiv e to v a ria tio n s in the value
of the pan c o e ffic ie n t.
The next most s ig n ific a n t param eter in term s
o f the s e n s itiv ity of modeled r e s u lts was th e param eter which describes
the r a tio of p o te n tia l tr a n s p ir a tio n to p o t e n t i a l e v a p o tr a n s p ir a tio n
during each stage of crop growth.
The Plantgro model was not a ffected
as much by changes in th e p a ra m e te rs w hich d e s c rib e th e m o is tu re
content of each s o il lay er a t f ie ld capacity and a t the w iltin g point.
However, th e r e s u l t s from th e P la n tg ro model were s t i l l r e l a t i v e l y
se n s itiv e to changes in the param eters describing the a b il i ty of a s o il
to h o ld m o is tu re a t f i e l d c a p a c ity and th e w i l t i n g p o in t.
The
Plantgro model was le a s t a ffe c te d by changes in the param eters which
describe the a i r dry m oisture content of the upper most s o i l lay er and
the e ff e c ts of m oisture s tr e s s on tra n s p ira tio n .
The SPAW and Plantgro models d if f e r in th e ir ease of a p p lic a tio n
61
in a number of resp ects.
Because the SPAW model i s much more elaborate
th an th e P la n tg ro m odel, i t took a g r e a t d e a l more tim e to become
fa m ilia r w ith i t s lo g ic and stru c tu re .
I t was more d i f f i c u l t to make
program changes in the SPAW model than i t was to reprogram the Plantgro
model.
The c o m p lex ity o f th e SPAW model a ls o made i t d i f f i c u l t to
a n tic ip a te the e ffe c ts of the v a ria tio n of some c a lib ra tio n param eter
values.
This was p a rtic u la rly tru e of param eter values asso c iated w ith
th e e f f e c t s o f m o is tu re s t r e s s (canopy s u s c e p t a b i l i t y , phenology
su s c e p ta b ility and th e m oisture s tr e s s curves).
Although the Plantgro model was r e la tiv e ly easy to understand and
modify, improvement in term s of i t s ease of a p p lic a tio n could be made.
The input f i l e required by the Plahtgro model was very stru c tu re d and
in fle x ib le in comparison to the input f i l e required by the SPAW model.
Input f i l e s not produced s p e c ific a lly fo r use w ith the Plantgro model
would r e q u ir e m ajor m o d if ic a tio n s b e fo re th ey co u ld be used.
T his
fa c to r would be im portant i f th ere were a la rg e amount of p re c ip ita tio n
and e v a p o ra tio n d a ta in e x i s t i n g f i l e s .
The f l e x a b i l i t y o f th e SPAW
model input stru c tu re would allow e x is tin g
f i l e s to be incorporated
i n to SPAW in p u t f i l e s w ith l i t t l e or no m o d ific a tio n .
In a d d itio n ,
since th ere was no provision fo r ex p lanitory remarks in the Plantgro
input f i l e s , they were d i f f i c u l t to read and understand.
The r e la tiv e in f le x a b ility of the Plantgro input stru c tu re became
very apparent when input f i l e s were modified to c a lib ra te the model for
s im u la tin g y ie ld .
When th e model was c a l ib r a t e d and t e s t e d f o r
sim u latin g y ie ld , each growing season was modeled in two p ortions.
In
62
the Plantgro model, a l l ir r ig a tio n , p re c ip ita tio n and evaporation data
w ere re fe re n c e d in tim e to th e f i r s t day o f th e s im u la tio n p e rio d .
When th e f i r s t day o f th e s im u la tio n p e rio d was changed, i t became
n e c e ssa ry t o a l t e r a g r e a t d e a l o f d a ta to r e f l e c t t h i s change.
c o n tr a s t ,
In
a new s t a r t i n g d a te f o r a s im u la tio n p e rio d could be
sp e c ifie d fo r the SPAW model by changing one value in i t s input f i l e .
Program M odifications
Program m o d if ic a tio n s to th e SPAW model should be d esig n ed to
in c r e a s e th e e ase o f model a p p li c a t io n in s e v e r a l ways.
The m ost
obvious need in the SPAW model i s a means to reduce the tim e and e ff o r t
re q u ire d to c a l i b r a t e th e m odel.
A c a l i b r a t i o n r o u tin e w hich would
s y s t e m a t i c a l l y a d j u s t p a r a m e t e r s and e v a lu a te th e e f f e c t s o f
a d ju s tm e n ts could be w r i t t e n to make th e model s e l f c a l i b r a t i n g .
A lthough a c a l i b r a t i o n r o u tin e would reduce th e tim e and e f f o r t
re q u ire d to c a l i b r a t e th e SPAW m odel, i t would a ls o s i g n i f i c a n t l y
in c re a s e th e random a c c e ss memory (RAM) re q u ire m e n t o f th e program .
Supplying pan c o e ffic ie n ts as in p u t d a ta would s l i g h t l y d e c re a se th e
tim e and e f f o r t required to c a lib ra te the model when pan c o e ffic ie n ts
a re used as c a l i b r a t i o n p a ra m e te rs . A s e p e ra te keyword to supply
ir r ig a tio n data might be b e n e fic ia l since i t would allow the program to
presen t ir r ig a tio n data as such in i t s output.
M o d ific a tio n s could be made to th e P la n tg ro model w hich would
in c r e a s e i t s e ase o f a p p lic a tio n and co u ld p o t e n t i a l l y im prove i t s
a b ility to sim ulate v a ria tio n s in s o il m oisture.
S im ila rly to the SPAW
model, a c a lib ra tio n ro u tin e which would decrease the lab o r required to
63
c a lib ra te
I
th e model could be developed.
R edesigning th e in p u t
s t r u c t u r e to u t i l i z e keywords would make th e P la n tg ro model more
f l e x i b l e and would a llo w
d a ta w ith v a ry in g fo rm a ts to be used.
Allowing fo r ex p lanitory remarks in th is input stru c tu re would help to
make in p u t f i l e s more re a d a b le .
re f e r e n c e d a ta to a d a te
I t would a ls o be d e s ir a b le to
t h a t would n o t be s u b je c t to
change.
Modifying the program so th a t a maximum rooting depth oth er than the
f u l l th ic k n e s s of th e s o i l p r o f i l e could be s p e c i f i e d would be
d e sira b le .
Reprograming the model so th a t w ater could be removed from
several s o il lay e rs based on the proportion of the root system in each
la y e r would probably be b e tte r than the programed procedure.
Recommendations fo r a d d itio n a l work a t th e Red B luff Research Ranch
In a d d itio n to making th e program m o d ific a tio n s d e s c rib e d ,
p e rfo rm in g some a d d itio n a l work u sin g d a ta from th e Red B lu ff Ranch
w ould be d e s i r a b l e .
T h is a d d i t i o n a l w ork w ould im p ro v e th e
c a l i b r a t i o n s f o r s o i l m o is tu re and y ie ld s im u la tio n .
Im proving th e
c a lib ra tio n s fo r s o il m oisture sim ulation would probably improve the
c a lib ra tio n s fo r p r e d ic tin g y ie ld
in d ire c tly .
Im p ro v in g th e
c a l i b r a t i o n s f o r y ie ld s im u la tio n d i r e c t l y would p ro v id e a more
reasonable b a sis fo r te s tin g the a b il i ty of the models to p re d ic t y ie ld
from n o n -ca lib ra tio n years.
In a d d itio n , work to c a lib ra te functions
in the SPAW model which were not examined in th is study would increase
the v e r s i t i l i t y of the model.
The c a lib ra tio n s fo r s o il m oisture sim ulation should be improved
by r e c a l i b r a t i n g th e m odels based on d a ta from a t l e a s t two o f th e
64
th r e e y e a rs o f a v a ila b le d a ta and d a ta from a l l fo u r q u a d ra n ts.
C alib ratio n
u sin g d a ta from 1979 and 1981 would be s u p e rio r t o
c a lib ra tio n using data from 1979 and 1980 or 1980 and 1981.
Using data
from 1979 and 1981 would be su p erio r since a re la tiv e ly sm all number of
s o i l m o is tu re m easurem ents w ere made d u rin g 1980 and d a ta from 1981
would extend the c a lib ra tio n period in to May.
Although a sm all number
o f s o il m oisture measurements were made during 1980, an adequate number
were made to t e s t the a b il i ty of the models to sim ulate v a ria tio n s in
s o i l m o is tu re .
I f a d d itio n a l d a ta a re c o lle c te d in th e f u tu r e , any
fu rth e r c a lib ra tio n of the models should be based on as many measured
values of s o il m oisture as possible.
The c a lib ra tio n s fo r y ie ld sim u latio n obtained in t h i s study were
v ery poor s in c e th ey were based on y ie ld d a ta from o nly one y e a r.
B asing c a l i b r a t i o n s fo r y ie ld s im u la tio n on a l l a v a ila b le y ield data
would a lm o st c e r t a i n l y im prove th e s e c a l i b r a t i o n s .
However, th e s e
c a lib ra tio n s would be su b je ct to doubt since they would s t i l l be based
on a v ery l im i te d amount o f d a ta .
Y ield c a l i b r a t i o n s f o r th e SPAW
model in o th e r s tu d ie s have been based on d a ta from 9 to 12 y e a rs
(Sudar e t a l . ,
1981; Saxton and Bluhm, 1982).
T his s u g g e s ts t h a t
a d d itio n a l data should be c o llec ted to obtain a c a lib ra tio n fo r the Red
B lu ff. Ranch.
A d d itio n a l c o ll e c t io n o f s o i l m o is tu re d a ta would
p ro b ab ly n o t be n e c e ssa ry s in c e y ie ld c a lib ra tio n could be performed
w ithout a d d itio n a l s o il m oisture c a lib ra tio n .
C alib ratio n using data
from o th er s i t e s would a lso be d e sira b le .
The SPAW model in c lu d e s two o p tio n s t h a t were n o t c a l i b r a t e d i n
65
th is
stu d y .
The f i r s t
o f th e s e
o p tio n s was th e fu n c tio n which
c a l c u l a t e s th e amount o f y ie ld re d u c tio n w hich would be caused by a
g iv en l e v e l o f cro p w a te r s t r e s s .
C a lib r a tin g t h i s f u n c tio n a f t e r a
good c a lib ra tio n fo r y ie ld sim ulation has been obtained would allow the
SPAW model to be used fo r evaluating a v a rie ty of ir r ig a tio n scenarios
a t the Red B luff Ranch in term s of y ie ld and cost.
Although th is type
o f e v a lu a tio n could be perform ed w ith o u t c a l i b r a t i n g th e y ie ld
r e d u c tio n f u n c tio n , i t would r e q u ir e more e f f o r t on th e p a r t o f th e
modeler.
The second f u n tio n o f th e SPAW model n o t exam ined in t h i s stu d y
/
su p p lies approximate values fo r m issing evaporation data.
C alib ratin g
t h i s o p tio n would a llo w th e a p p li c a t io n o f th e SPAW model to s i t e s
where m easured e v a p o ra tio n d a ta a re n o t a v a ila b le .
E xtending th e
a p p lica tio n of the SPAW model to s i t e s where measured evaporation data
are not a v a ila b le would allow the evalu atio n of d iff e r e n t ir r ig a tio n
p ra c tic e s a t these s ite s .
However, some re c a lib ra tio n of the model to
r e f l e c t s o il conditions a t the s i t e would be d e sirab le.
In ad d itio n ,
i t would be extrem ely im portant fo r c lim a tic conditions a t a s i t e where
m easured e v a p o ra tio n d a ta w ere n o t a v a ila b le to be v ery s i m i l a r to
those a t th e Red B luff Ranch.
66
CHAPTER 6
CtMCLUSHMS
Both th e SPAW and th e P la n tg ro m odels show p rom ise in term s o f
t h e i r a b i l i t y to p r e d ic t s o i l m o is tu re d i s t r i b u t i o n s and crop y ie ld .
However, th e r e s u l t s o f t h i s stu d y should be i n te r p e r e te d w ith c a re
s in c e th e c a l i b r a t i o n s t e s t e d w ere based on very l i m i t e d d a ta .
In
a d d itio n , th e re was some doubt as to the accuracy of s o il m oisture and
irrig a tio n
d a ta u se d t o c a l i b r a t e and t e s t t h e m o d e ls.
The
c a lib ra tio n s te s te d here could alm ost c e rta in ly be improved by using
the a v a ila b le data more e ffe c tiv e ly .
The SPAW model acc o u n ts f o r th e f a c t o r s a f f e c t i n g v a r i a ti o n s in
s o il m oisture more comprehensively than the Plantgro model.
However,
the SPAW model a lso req u ire s a computer w ith considerably more random
access memory.
In a d d itio n , the SPAW model takes more tim e to become
f a m i l i a r w ith and i t i s more d i f f i c u l t to reprogram th e model.
In
c o n tr a s t , th e P la n tg ro can be f u l l y u n d ersto o d w ith in a r e l a t i v e l y
s h o r t p e rio d o f tim e .
However, th e r e i s room f o r im provem ent in th e
way th e P la n tg ro model a c c o u n ts f o r some f a c t o r s a f f e c t i n g s o i l
m oisture v a ria tio n s.
67
I
References C ited
>
.
68
Adams, Tom 1986. P e rso n a l c o m u n ica tio n . Program S p e c i a l i s t I I ,
Computing S ervices, Montana S ta te U niversity. Bozeman MT 59717.
ASAE monograph, 1983. Hydrologic modeling of sm all w atersheds. American
Society of A g ricu ltu ral Engineers. St. Joseph MI.
B o lta n , J. L., 1962. A lf a lf a ; B otanyr C u ltiv a tio n and U t i l i z a t i o n .
In te rsc ien c e P ublishers Inc. New York, NY. p 165-167.
C h ild s , S. W., J. R. G ille y and W. E. S p l i n t e r , 1977. "A s i m l i f i e d
model o f corn growth under m oisture s tre s s " . T ransactions o f the ASAE.
Vol. 20; No. 5, p 858-865.
C h ild s , S. W., and R. J. Hanks, 1975. Model to p r e d i c t th e e f f e c t s o f
s o i l s a l i n i t y on crop grow th. S o il S c i. Soc. Am. Proc. 39: p 617-622.
Donahue, R. L., R. W. M ille r , and J. C. S h ic k lu n a . 1978. S o i l s i An
indroduotion to s o ils and p la n t growth. Fourth Ed. P ren tice-H all Inc.,
Englewood C lif f s , NJ p51.
G o ld stie n R. A., J. B. Mankin and R. J. Luxmore, 1974. D ocum entation
fo r PROSPER: A model of a tm o sp h e ric -so il-p la n t w ater flow. EDFB-IBP73-9. Oak Ridge N ational Laboratory, Oak Ridge TN.
Hanks, R. J., 1974. Model fo r p re d ic tin g p la n t growth as influenced by
ev ap o tran sp iratio n and s o il w ater. Agron. J. 66:660-665
Hanson, T. L., 1984. " E v a lu a tin g wash tu b e v a p o ra tio n pan i r r i g a t i o n
scheduling". Montana AgResearch. Montana S ta te U niversity, Bozeman MT.
1(2) p 1-5.
K a n e m a su , E. T ., L. R. S to n e a n d W. L. P o w e r s , 1 9 7 6 .
"E vapotranspiration model te s te d f o r f o r soybean and sorghum ”. Agron.
J. 68(4): p757-761.
Nimah, M. N. and R. J. Hanks, 1973. Model fo r e s tim a tin g s o i l w a te r
and atm ospheric re la tio n s . S oil Sci. Soc. of Am. Proc. 37 P 522-532
Rasmussen, V. P. and R. J. Hanks. 1978. S p rin g w heat y i e l d model f o r
lim ite d m oisture conditions. Agron. J. 70:940
R e tta , A. and R. J. Hanks, 1980. Manual f o r u sin g Model P la n tg r o . Utah
A g ricu ltu ral Research Report 48. Utah S ta te U niversity, Logan, UT. 13p
Saxton, K. E., W. J. Raw ls, J. S. Romberger and R. I . P apendick, 1986.
E stim ating generalized s o i l w ater c h a r a c te r is tic s from te x tu re . W ill be
p u b lish e d in th e S o il S c i. Soc. o f Am. J ., 50
Saxton K. E., G. E. Schuman and R. E. B u rw e ll, 1977. M odeling n i t r a t e
d is p e r s io n and movement in f e r t i l i z e d s o i l s . S o il S c i. Soc. Am. J .,
41(2)p 265-271.
69
S a x to n , K. E ., H. P. Jo h n so n and R. H. Shaw. 1974. M o d e lin g
e v a p o tr a n s p ir a tio n and s o i l m o is tu re . T rans. Am. Soc. A gric. E ngr.,
17(4) p 673-677.
Saxton, K. E., P. F. Brooks, R. Richmond. 1984. U sers m anual f o r SPAW-A
s o il- p la n t-a ir-w a te r model (D raft copy o f A ugust, 1984). USDA-SEA-AR,
Washington S ta te U niversity, Pullman WA.
Saxton, K. E., G. C. Bluhm, 1982. "R egional p r e d ic tio n o f crop w a te r
s tr e s s b y .s o il w ater budgets and c lim a tic demand". T ransactions of the
American S o c ie ty o f A g r ic u ltu r a l E n g in e e rs. Vol. 25; No. I , p 105-110
and 115.
S to c k le , C. 0 ., 1983. M odeling w a te r s t r e s s e f f e c t s on crop grow th.
M. S. th e s is . Washington S ta te U niversity, Pullman.
Stockle C. 0. and K. E. Saxton, 1984. Modeling w ater s tr e s s e ffe c ts on
w in ter wheat: c a lib ra tio n phase. Paper presented a t the 1984 P a c ific
N orthw est R egional m eeting o f th e Am erican S o c ie ty o f A g r ic u ltu r a l
Engineers. Paper no. 84-202
Sudar, R. A., K. E. Saxton, R. G. Spomer; 1981. "A p r e d i c ti v e model o f
w a te r s t r e s s in corn and soybeans". T ra n s a c tio n s o f th e Am erican
so ciety of A g ricu ltu ral Engineers. Vol. 24; No. I, p 97-102;
)
70
APPENDICES
i
APPENDIX A
C lim atological, S o ils and Crop Data
72
Clirnatoloepcal d ata
Table 9. P re c ip ita tio n data fo r 1979
d ate
depth
(cm)
(in )
date
depth
(cm)
(in )
date
depth
(cm)
(in )
6/6
6/17
6/18
6/19
6/25
0.89
0.30
4.06
0.56
0.15
6/26
7/23
7/28
8/12
8/15
0.28
0.41
0.51
0.18
0.89
8/24
8/25
8/28
0.61
0.20
0.25
0.35
0.12
1.60
0.22
0.06
0.11
0.16
0.20
0.07
0.35
0.24
0.08
0.10
Table 10. P re c ip ita tio n data fo r 1980
date
depth
(cm)
(in )
date
depth
(cm)
(in )
date
depth
(cm)
(in )
6/11
6/15
6/18
0.38
0.89
0.25
6/20
6/23
7/2
0.51
1.27
0.51
7/3
8/1
8/13
1.02
0.13
0.13
0.15
0.35
0.10
0.20
0.50
0.20
0.40
0.05
0,05
Table 11. P re c ip ita tio n data for 1981
d ate
depth
(cm)
(in )
date
depth
(cm)
(in )
date
depth
(cm)
(in )
5/21
5/22
5/23
5/31
6/1
6/3
6/6
3.18
2.41
0.15
0.25
0.13
1.07
0.66
6/7
6/8
6/12
6/13
6/14
7/6
7/7
0.15
0.05
0.38
2.67
0.41
1.52
0.38
0.06
0.02
0.15
1.05
0.16
0.60
0.15
7/11
7/17
7/18
8/4
8/19
8/20
0.64
0.38
1.68
0.64
0.20
0.13
1.25
0.95
0.06
0.10
0.05
0.42
0.26
I
0.25
0.15
0.66
0.25
0.08
0.05
73
Table 12. Pan evaporation data fo r 1979
s ta rt
to ta l
d a te (cm) (in )
average
(cm) (in )
s ta rt
d a te
t o ta l
(cm) (in )
6/11
6/12
6/14
6/15
6/16
6/17
6/20
6/23
6/26
6/27
6/28
6/29
6/30
7/03
7/04
7/06
7/07
7/10
7/11
7/12
7/16
7/17
7/18
7/19
7/20
7/21
7/22
7/23
0.84 0.33
1.19 0.47
1.32 0.52
0.53 0.21
0.69 0.27
0.64 0.25
0.53 0.21
0.61 0.24
0.86 0.34
0.48 0.19
0.56 0.22
0.74 0.29
1.04 0.41
0.43 0.17
0.66 0.26
0.71 0.28
0.89 0.35
0.86 0.34
0.97 0.38
0.69 0.27
0.91 - 0.36
0.64 0.25
0.61 0.24
1.45 0.57
0.76 0.30
0.66 0.26
0.89 0.35
0.13 0.05
7/24
7/26
7/27
7/28
7/31
8/02
8/03
8/04
8/07
8/08
8/09
8/10
8/11
8/14
8/16
8/17
8/18
8/21
8/22
8/23
8/24
8/25
8/26
8/28
8/30
9/01
9/05
1.57 0.62
0.69 0.27
0.64 0.25
1.68 0.66
1.73 0.68
0.56 0.22
0.86 0.34
1.37 0.54
0.74 0.29
1.91 0.75
0.36 0.14
0.91 0.36
1.60 0.63
0.60 0.25
0.53 0.21
0.51 0.20
1.37 0.54
0.38 0.15
0.15 0.06
0.71 0.28
0.66 0.26
0.51 0.20
0.60 0.24
1.22 0.48
0.97 0.38
3.30 1.30
0.71 0.28
0.84
1.19
1.32
0.53
0.69
1.93
1.60
1.83
0.86
0.48
0.56
0.74
3.12
0.43
1.32
0.71
2.67
0.86
0.97
2.72
0.91
0.64
0.61
1.45
0.76
0.66
0.89
0.13
0.33
0.47
0.52
0.21
0.27
0.76
0.63
0.72
0.34
0.19
0.22
0.29
1.23
0.17
0.52
0.28
1.05
0.34
0.38
1.07
0.36
0.25
0.24
0.57
0.30
0.26
0.35
0.05
average
(cm) (in )
0.79
0.69
0.64
0.56
0.86
0.56
0.86
0.69
0.74
1.91
0.36
0.91
0.53
0.30
0.53
0.51
0.46
0.38
0.15
0.71
0.66
0.51
0.30
0.61
0.48
0.84
0.36
0.31
0.27
0.25
0.22
0.34
0.22
0.34
0.27
0.29
0.75
0.14
0.36
0.21
0.12
0.21
0.20
0.18
0.15
0.06
0.28
0.26
0.20
0.12
0.24
0.19
0.33
0.14
74
Table 13. Pan evaporation data fo r 1980
s ta rt
d ate
to ta l
(cm) (in )
6/11 0.81
6/13 2.03
6/17 1.98
6/20 1.85
6/24 2.06
6/27 1.42
7/01 3.81
7/08 0.91
7/10 0.91
7/11 2.36
7/14 0.30
7/15 1.42
7/17 1.57
0.32
0.80
0.78
0.73
0.81
0.56
1.50
0.36
0.36
0.93
0.12
0.55
0.62
average
(cm) (in )
s ta rt
d ate
t o ta l
(cm) (in )
0.16
0.20
0.26
0.18
0.27
0.14
0.21
0.18
0.36
0.31
0.12
0.28
0.31
7/19
7/22
7/24
7/26
7/29
7/31
8/01
8/02
8/05
8/08
8/09
8/11
8/12
2.06
1.98
1.68
2.13
2.59
0.69
0.81
2.82
1.80
0.76
1.78
0.74
1.32
0.41
0.51
0.66
0.46
0.69
0.36
0.53
0.46
0.91
0.79
0.30
0.71
0.79
Table 14. Pan evaporation data
s ta rt
date
to ta l
(cm) (in )
5/28
2.59
0.56
6/04
2.18
6/06
2.64
6/08
6/18
3.51
6/26
1.27
3.43
6/27
0.71
7/01
1.42
7/02
3.05
7/04
7/07 ■ 1.68
0.33
7/09
1.88
7/10
2.04
7/12
1.68
7/14
0.66
7/16
4.72
7/17
7/22
0.91
1.22
6/02
1.02
0.22
0.86
1.04
1.38
0.50
1.35
0.28
0.56
1.20
0.66
0.13
0.74
0.80
0.66
0.26
1.86
0.36
0.48
average
(cm) (in )
0.51
0.28
1.09
0.26
0.43
1.27
0.86
0.71
0.71
1.02
0.84
0.33
0.94
1.02
0.84
0.66
0.94
0.91
0.61
0.20
0.11
0.43
0.10
0.17
0.50
0.34
0.28
0.28
0.40
0.33
0.13
0.37
0.40
0.33
0.26
0.37
0.36
0.24
0.81
0.78
0.66
0.84
1.02
0.27
0.32
1.11
0.71
0.30
0.70
0.29
0.52
average
(cm) (in )
0.69
0.99
0.84
0.71
1.30
0.69
0.81
0.94
0.61
0.76
0.89
0.74
0.66
0.27
0.39
0.33
0.28
0.51
0.27
0.32
0.37
0.24
0.30
0.35
0.29
0.26
1981
s ta rt
date
t o ta l
(cm) (in )
7/23
7/24
7725
7/28
7/29
7/31
8/01
8/06
8/07
8/08
8/11
8/13
8/15
8/18
8/20
8/26
8/29
9/01
0.76
0.58
1.24
0.89
1.78
0.61
3.73
0.66
0.66
2.46
1.55
1.37
2.46
1.47
3.84
2.79
2.59
1.96
0.30
0.23
0.49
0.35
0.70
0.24
1.47
0.26
0.26
0.97
0.61
0.54
0.97
0.58
1.51
1.10
1.02
0.77
average
(cm) (in )
0.76
0.58
0.41
0.89
0.89
0.61
0.74
0.66
0.66
0.81
0.76
0.69
0.81
0.74
0.64
0.94
0.86
0.99
0.30
0.23
0.16
0.35
0.35
0.24
0.29
0.26 ,
0.26
0.32
0.30
0.27
0.32
0.29
0.25
0.37
0.34
0.39
75
S o ils Data
Table 15. S oil te x tu re by quadrant and la y e r
Quadrant
0-3Ocm
(I fo ot)
depth
30-60cm
(2 foot)
I
2
3
4
SCL
SCL
CL
SCL
SCL
LS
SCL
SL
60-90cm
(3 foot)
.
SCL
SCL
LS
LS
Table 16. S o il m oisture holding capacity a t F ield Capacity and
the permanent W ilting po in t
Quadrant
I
2 .
3
4
0-30cm
(I fo o t)
WP
FC
6.4
8.0
5.8
7.6
11.9
14.1
10.7
14.5
depth
30-6Ocm
(2 fo o t)
WP
FC
6.5
6.2
5.6
6.6
13.0
15.4
11.9
15.9
60-90cm
(3 fo o t)
WP
FC
6.0
6.4
5.1
6.5
12.8
14.6
11.4
12.9
76
Table 17. S o il m oisture measurements by quadrant (% v o l . ) fo r 1979
30-60cm
(2 foot)
depth
60-90cm
(3 foot)
90-120cm
(4 fo o t)
I 20-150cm
(5 foot)
Date
quad
0-30cm
(I foot)
6/01
6/18
6/22
7/06
7/26
8/01
8/16
8/31
9/06
I
I.
I
I
I
I
I
I
I
13.2
21.6
17.9
16.2
20.7
18.6
16.9
15.&
14.6
13.4
15.3
15.9
14.9
15.3
15.0
14.4
14.3
14.2
12.7
13.7
14.5
13.8
13.6
13.6
13.6
13.5
13.4
12.7
13.8
14.2
14.0
13.7
13.7
13.7
13.7
13.6
12.6
13.5
13.9
13.7
13.5
13.5
13.5
13.5
13.5
6/01
6/18
6/22
7/06
7/26
8/01
8/16
8/31
9/06
2
2
2
2
2
2
2
2
2
13.9
15.7
16.6
15.0
16.7
16.1
14.7
13.0
12.1
13.8
14.6
15.7
14.7
15.0
15.2
14.6
14.3
14.1
12.9
13.5
14.1
13.6
13.4
13.6
13.5
13.4
13.3
12.7
13.3
13.3
13.3
13.2
13.2
13.2
13.2
13.2
12.7
13.3
13.3
13.3
13.2
13.2
13.2
13.2
13.2
6/01
3
6/18 . 3
6/22
3
7/06
3
7/26
3
8/01
3
8/16
3
3
8/31
9/06
3
13.2
16.3
17.0
15.4
16.3
15.2
14.8
12.8
12.4
13.6
14.2
15.5
14.4
14.7
14.9
14.2
13.9
13.8
12.8
13.4
14.1
13.7
13.4
13.8
13.4
13.3
13.3
12.8
13.4
13.6
13.6
13.3
13.4
13.4
13.3
13.3
12.8
13.5
13.6
13.6
13.5
13.4
13.5
13.4
13.4
4
4
4
4
4
4
4
4
4
13.0
18.2
16.3
15.3
17.6
16.1
13.6
12.6
12.1
13.6
14.9
15.4
14.3
15.0
15.0
14.0
13.8
13.7
12.9
13.6
14.3
13.6
13.3
13.8
13.4
13.3 .
13.3
12.8
13.4
14.1
13.8
13.4
13.4
13.3
13.3
13.2
12.8
13.4
13.7
13.6
13.4
13.4
13.4
13.3
13.3
6/01
6/18
6/22
7/06
7/26
8/01
8/16
8/31
9/06
.
77
I
Table 18. S o il m oisture measurements by quadrant (% vol) fo r 1980
0-3Ocm
(I foot)
30-6Ocrn
(2 foot)
depth
60-90cm
(3 foot)
I
I
I
I
13.7
14.8
15.8
17.4
13.7
14.2
14.2
14.3
13.1
13.4
13.4
13.4
13.0
13.6
13.5
13.5
12.9
13.4
13.4
13.4
6/11
7/10
7/21
8/12
2 .
2
2
2
12.8
13.2
14.4
14.1
13.8
14.2
14.3
14.2
13.2
13.4
13.4
13.4
12.8
13.1
13.3
13.1
12.8
13.1
13.1
13.2
6/11
7/10
7/21
8/12
3
3
3
3
11.3
12.3
14.4
13.1
13.1
13.8
13.8
13.9
12.7
13.2
13.4
13.3
12.7
13.3
13.3
13.3
12.7
13.4
13.5
13.4
6/11
7/10
7/21
8/12
4
4
4
4
12.2
12.5
13.7
17.0
13.6
13.7
13.9
13.9
13.1
13.2
13.3
13.3
13.1
13.3
13.3
13.3
12.9
13.3
13.3
13.3
date
quad
6/11
7/10
7/21
8/12
(
90-120cm
(4 fo o t)
I20-I50cm
(5 foot)
78
Table 19. S oil m oisture measurements by quadrant (S v o l.) fo r 1981
O-SOcm
(I foot)
90-120cm
(4 fo o t)
I20-150cm
(5 foot)
quad
5/20
6/17
7/01
7/16
8/06
8/17
9/02
I
I
I.
I
I .
I
I
21.1
20.6
16.4
20.9
21.6
18.2
15.1
15.8
15.5
14.2
15.1
15.7
14.7
14.0
14.6
14.1
13.4
13.5
14.2
13.6
13.3
14.4
13.9
13.6
13.6
14.0
13.8
13.5
14.0
13.6
13.5
13.6
13.7
13.5
13.4
6/17
7/01
7/16
8/06
8/17
9/02
2
2
2
2
2
2
19.5
14.7
17.9
19.4
16.1
13.6
15.7
14.5
14.5
15.6
14.7
14.1
14.1
13.4
13.5
13.8
13.5
13.3
13.4
13.3
13.2
13.2
13.2
13.1
13.4
13.3
13.2
13.2
13.2
13.1
6/17
7/01
7/16
8/06
8/17
9/02
3
3
3
3
3
3
17.7
13.2
19.1
18.5
17.4
13.4
. 15.3
14.0
14.2
15.7
14.5
13.8
14.0
13.4
13.4
14.3
13.7
13.3
13.8
13.4
13.4
14.0
13.7
13.3
13.8
13.6
13.4
13.7
13.6
13.4
6/17
7/01
7/16
8/06
8/16
9/02
4
4
4
4
4
4
17.4
12.8
16.8
18.3
17.0
12.7
15.1
13.6
15.0
15.5
14.8
13.8
13.7
13.3
13.4
14.5
13.7
13.2
13.6
13.3
13.2
14.3
13.8
13.3
13.5
13,3
13.4
14.0
13.6
13.3
.
SO-SOcm
(2 fo o t)
depth
60-90cm
(3 fo o t)
date
'
79
Crop Data
Table 20. Harvest Data
Year
1979
1980
1981
Harvest
I
2
I
2
I
2
begin
date
end
date
7/05
8/28
7/01
8/21
6/30
8/20
7/17
9/06
7/10
8/30
7/09
9/03
I
2.14
1.31
2.21
1.54
2.53
2.54
.
Yield by quadrant
(to n s/a c re )
2
3
1.78
1.51
2.12
1.43
2.67
2.42
2.09
1.43
2.54
1.49
2.98
2.09
4
2.03
1.33
2.18
1.35
2.77
1,88
I r r ig a tio n Data
Table 21. I r r ig a tio n data fo r quadrant I
Year 1979
date
depth
(cm) (in )
6/04
6/06
6/14
6/19
6/27
7/17
7/19
7/21
7/23
7/26
8/02
8/09
8/13
8/20
8/22
8/24
0.58
2.92
2.18
2.82
2.74
1.52
1.52
1.50
2.82
2.87
2.79
0.74
0.74
0.74
0.71
1.45
0.23
1.15
0.86
1.11
1.08
0.60
0.60
0.59
1.11
1.13
1.10
0.29
0.29
0.29
0.28
0.57
1980
1981
date
depth
(cm) (in )
d ate
depth
(cm) (in )
7/10
7/12
.7/16
7/22
7/23
7/24
7/26
7/28
7/29
7/31
8/05
8/08
8/09
8/11
1.88
1.88
1.14
0.76
0.76
1.14
1.14
1 .14
1.14
1.07
0.94
0.23
0.51
0.69
0.74
0.74
0.45
0.30
0.30
0.45
0.45
0.45
0.45
0.42
0.37
0.09
0.20
0.27
7/10
7/17
7/24
7/29
8/10
8/13
3.66
4.29
4.42
6.20
1.63
0.97
1.44
1.69
1.74
2.44
0.64
0.38
80
Table 2 2. I r r ig a tio n data fo r quadrant 2
Year 1979
date
depth
(cm) (in )
6/04
6/12
6/15
6/19
6/28
7/18
7/19
7/21
7/24
7/29
8/03
8/09
8/13
8/20
8/22
8/24
0.58
2.92
2.18
2.82
2.77
1.47
1.52
1.50
2.87
2.90
2.54
0.74
0.74
0.74
0.71
1.45
0.23 .
0.86
0.86
1.11
1.09
0.58
0.60
0.59
1.13
1.14
1.00
0.29
0.29
0.29
0.28
0.57
1981
1980
date
depth
(cm) (in )
d ate
depth
(cm) (in )
7/10
7/12
7/17
7/22
7/23
7/25
7/26
7/28
7/30
7/31
8/05
8/08
8/10
1.88
1.88
1.14
0.76
0.76
1.14
1.14
1.14
1.14
1.07
0.94
0.23
0.51
7/11
7/18
7/25
8/01
8/10
8/13
3.66
4.29
4.42
6.20
1.63
0.97
0.74
0.74
0.45
0.30
0.30
0.45
0.45
0.45
0.45
0.42
0.37
0.09
0.20
1.44
1.69
1.74
2.44
0.64
0.38
Table 22. Irr ig a tio n data fo r quadrant 3
Year 1979
date
depth
(cm) (in )
6/04
6/12
6/16
6/26
7/18
7/21
7/25
7/30
8/05
8/09
8/13
8/20
8/22
8/25
0.58
2.18
2.59
2.59
1.47
1.50
2.87
2.90
2.90
0.74
0.74
0.74
0.71
1.55
0.23
0.86
1.02
1.02
0.58
0.59
1.13
1.14
1.14
0.29
0.29
0.29
0.28
0.61
1981
1980
date
depth
(cm) (in )
d ate
depth
(cm) (in )
7/11
7/13
7/17
7/22
7/24
7/27
7/29
7/30
7/31
8/06
8/08
8/10
1.88
1.88
1.14
0.76
1.14
1.14
1,14
1.14
1.07
0.94
0.23
0.51
0.74
0.74
0.45
0.30
0.45
0.45
0.45
0.45
0.42
0.37
0.09
0.20
7/13
7/19
7/27
8/03
8/11
3.66
4.29
4.42
6.20
1.63
1.44
1.69
1.74
2.44
0.64
81
Table 23. I r r ig a tio n data fo r quadrant 4
Year 1979
depth
date
(cm) (in )
6/04
6/13
6/18
6/2?
7/19
7/20
7/22
7/25
7/30
8/06
8/09
8/13
8/20
8/22
8/23
0.58
2.24
2.84
2.74
1.52
1.45
2.90
2.87
2.90
2.92
0.74
0.74
0.74
0.71
1.57
0.23
0.88
1.12
1.08
0.60
0.57
1.14
1.13
1.14
1.15
0.29
0.29
0.29
0.28
0.62
1980
1981
d ate
depth
(cm) (in )
d ate
depth
(cm) (in )
7/11
7/13
7/18
7/23
7/24
7/25
7727
7/29
7/30
7/31
8/04
8/06
8/09
8/11
1.88 0.74
1.88 0.74
1.14 0.45
0.76 0.30
1.14 0.45
1.14 0.45
1.14 0.45
1.14 0.45
1.14 0.45
1.07 0.42
0.94 0.37
0.97 0.38
0.51 0.20
0.69 0.27
7/14
7/21
7/28
8/04
8/12
3.66
4.29
4.42
6.20
1.63
1.44
1.69
1.74
2.44
0.64
82
APPENDIX B
D escription o f Program M odifications
83
Before the SPAW and Plantgro models could be used on an AT&T 6300
microcomputer, i t was necessary to modify the programs.
Both models
w ere m o d ified to be more co m p atab le w ith th e in p u t re q u ire m e n ts o f
microcomputers and to conform w ith the syntax o f M icrosoft0 FORTRAN 77.
The models were modified to allow the use of sev eral s e ts o f data fo r
c o n se c u tiv e program ru n s.
T h is was a cco m p lish ed th ro u g h th e use o f
counter statem ents which opened and closed sep erate input and output
f i l e s depending on th e v a lu e o f th e s e c o u n te rs .
The m odels w ere
ad ap ted so t h a t up to e ig h t c o n s e c u tiv e s e t s o f d a ta could be
sim ulated.
Syntax m o difications were a lso necessary since the programs were
w ritte n in FORTRAN IV and a FORTRAN 77 com piler was used.
These syntax
m o d ifications included; specifying th a t c e rta in v a ria b le s rep resen tin g
c h arac ters other than numbers were c h a ra c te rs, form at statem ents used
as d a ta by th e SPAW model were s p e c if ie d as and re a d as c h a r a c te r
s tr in g s ra th e r than ch aracter arra y s and comment, statem en ts appearing
w ith in data and common statem ent continuation lin e s were moved outside
o f the data and common statem ents.
Program l is ti n g s fo r the SPAW and Plantgro models can be found in
th e u s e r 's m anuals f o r th e r e s p e c tiv e program s.
These l i s t i n g a re .
m ainfram e com puter, FORTRAN BZ v e rs io n s o f th e m odels.
lis tin g s
Com plete
and a d d itio n a l d o cu m en tatio n f o r th e FORTRAN 77,
IBM
compatable microcomputer versions of the programs can be obtained from:
The Dept, of Ag. Engineering
409 Cobleigh H all
Bozeman, MT 59717
* M icrosoft i s a trademark
MONTANA STATE UNIVERSITY LIBRARIES
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Modeling v a ria tio n s in
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