by Irrigation and Nitrogen Fertilizer
1 M . K . N I C H O L S O N , T . K I B R E A B , R . K . D A M E L S O N ,a n d R . A . Y O U N G2
Received for publication September 10, 1973 I n t r o d u c t i o n
T h e i n f l u e n c e of i r r i g a t i o n a n d of soil n i t r o g e n fertility levels on t h e yield of r o o t s a n d s u c r o s e by s u g a r b e e t s has b e e n r e p o r t e d for various c o n d i t i o n s of c l i m a t e a n d soils (2, 5, 7, 9, 14, 16, 17)3. R e c o m - m e n d a t i o n s d e v e l o p e d for i r r i g a t i o n s c h e d u l i n g a n d n i t r o g e n fertiliza- tion practices h a v e usually b e e n b a s e d u p o n a goal o f m a x i m u m p r o d u c t i o n a n d n o t o f m a x i m u m profit t o t h e p r o d u c e r . Even so, t h e r e h a s b e e n c o n s i d e r a b l e variation i n t h e e x p e r i m e n t a l results a n d i n t h e c o n c l u s i o n s d r a w n f r o m t h e s t u d i e s . H a d d o c k (5) r e c o m m e n d e d t h a t i r r i g a t i o n s h o u l d begin w h e n t h e soil m o i s t u r e t e n s i o n ( m a t r i c suction) at t h e 12-inch d e p t h is a b o u t 0.5, 0.8, a n d 2.0 b a r s for s a n d y l o a m , l o a m , a n d clay loam soils, respectively- In g e n e r a l , t h e yield of r o o t s a n d s u c r o s e h a s b e e n s h o w n t o d e c r e a s e a s t h e m a t r i c s uc t i on allowed t o d e v e l o p b e t w e e n i r r i g a t i o n s increases. A n o v e r s u p p l y o f w a t e r a p p e a r s to be less h a r m f u l t h a n a deficiency, b u t excesses m a y also d e c r e a s e beet, yields (12). N u m e r o u s s t u d i e s h a v e s h o w n t h a t t h e c o n c e n t r a t i o n a n d p u r i t y of s u c r o s e in t h e r o o t d e c r e a s e as t h e soil n i t r o g e n available to t h e c r o p is raised a b o v e critical levels, p a r t i c u l a r l y d u r i n g t h e l a t t e r p a r t of t h e g r o w i n g season (2, 8, 13, 15, 16). T h e re- d u c t i o n in s u c r o s e c o n t e n t a n d p u r i t y often r e s u l t s in a m a x i m u m yield o f e x t r a c t a b l e s u g a r a t a l o w e r level o f n i t r o g e n t h a n t h a t r e q u i r e d for m a x i m u m r o o t yield (15).
T h e m a g n i t u d e o f yield variability d u e t o p l a n t p o p u l a t i o n d e n s i t y h a s n o t b e e n satisfactorily d e t e r m i n e d . Plant d e n s i t y may vary d u e t o s p a c i n g a t t h i n n i n g o r t o d e a t h o f p l a n t s s u b s e q u e n t t o t h i n n i n g . C o n - s i d e r a b l e c o n t r o v e r s y h a s o c c u r r e d c o n c e r n i n g t h e r e c o m m e n d e d r o w w i d t h a n d p l a n t s p a c i n g ( 3 , 1 0, 14). M o r a g h a n (9) has s h o w n t h a t water- u s e by t h e c r o p m a y be i n f l u e n c e d by p l a n t s p a c i n g . T h i s c o u l d influ- e n c e t h e results o b t a i n e d f r o m i r r i g a t i o n e x p e r i m e n t s .
'Contribution from the Departments of Economics and Agronomy, Colorado State University, Fort Collins. The study was conducted under a cooperative agreement with the Center for Agricul- tural and Economic Development, Iowa State University, with financial support from the U. S.
Bureau of Reclamation. Published with the approval of the Colorado State University Experiment Station as Scientific Series Paper No. 1894.
2Former graduate research assistant, Department of Economics; graduate student, Department of Agronomy; Professor of Agronomy; and Professor of Economics, respectively.
'Numbers in parentheses refer to literature cited.
V O L . 18, No. 1, A P R I L 1974 35
T h e p u r p o s e o f this s t u d y was t o e x a m i n e t h e e c o n o m i c implica- tions o f i r r i g a t i o n a n d n i t r o g e n fertilizer levels i n s u g a r b e e t p r o d u c t i o n a t Walsh, C o l o r a d o i n t h e e x t r e m e s o u t h e a s t e r n c o r n e r o f t h e state.
T h e r e g i o n i s o n e o f very h i g h p o t e n t i a l e v a p o t r a n s p i r a t i o n , d u e p a r t i c u l a r l y to h o t w i n d s , a n d only a limited i r r i g a t e d a r e a h a s b e e n d e v e l o p e d f r o m g r o u n d w a t e r s u p p l i e s . T h r e e variables—available soil n i t r o g e n , w a t e r u s e b y t h e c r o p , a n d p l a n t s p a c i n g — w e r e a n a l y z e d in r e l a t i o n to r o o t yield, s u c r o s e p e r c e n t a g e , a n d net r e t u r n to be re- ceived by t h e p r o d u c e r . K n o w l e d g e of t h e s e r e l a t i o n s h i p s m a y be a useful tool i n p r o d u c t i o n p l a n n i n g . U s i n g m u l t i p l e r e g r e s s i o n t e c h - n i q u e s t h e r e l a t i o n s h i p o f n i t r o g e n , w a t e r , a n d p l a n t d e n s i t y t o root yield a n d s u c r o s e p e r c e n t a g e i s d e t e r m i n e d . T h e s e r e l a t i o n s h i p s a r e t h e n i n c o r p o r a t e d i n t o a n e q u a t i o n d e f i n i n g t h e r e t u r n r e c e i v e d b y t h e p r o d u c e r , a n d t h e i n p u t levels w h i c h m a x i m i z e profit a r e d e r i v e d . P r o d u c t i o n function analysis is a s t a n d a r d e c o n o m i c t e c h n i q u e for e x a m i n i n g i n p u t - o u t p u t r e l a t i o n s h i p s . T h e basic p r o c e d u r e can b e f o u n d in a n u m b e r of s o u r c e s , an e x c e l l e n t e x a m p l e of which is H e a d y a n d Dillon (6).
F i e l d Study
Field plots w e r e e s t a b l i s h e d on a d e e p clay l o a m soil at t h e C o l o - r a d o State University I r r i g a t i o n R e s e a r c h C e n t e r a t Walsh, C o l o r a d o d u r i n g 1970. Five levels of n i t r o g e n fertilization a n d five i r r i g a t i o n t r e a t m e n t s w e r e i n c l u d e d i n a n i n c o m p l e t e r a n d o m i z e d block d e s i g n , with 2 2 plots p e r block a n d two r e p l i c a t i o n s o f e a c h block. T r e a t m e n t levels a n d r e p l i c a t i o n s a r e given in T a b l e 1.
T a b l e 1 . — I r r i g a t i o n a n d n i t r o g e n f e r t i l i z e r t r e a t m e n t s . T r e a t m e n t
D e s i g n a t i o n I-0 I-100 I-400 II-50 II-200 III-0 III-100 III-400 IV-50 IV-2 00
V-0 V-100 V-400
I r r i g a t i o n M a x . S u c t i o n
B a r sa
0.65 0.65 0.65 1.00 1.00 3.00 3.00 3.00 6.00 6.00 9.00 9.00 9.00
T r e a t m e n t s No. o f I r r i g a t i o n s
7 7 7 5 5 4 4 4 4 4 3 3 3
I n c h e s A p p l i e db
21 21 21 15 15 12 12 12 12 12 9 9 9
N i t r o g e n F e r t i l i z e r l b s / a c r e N
0 100 4 0 0 50 2 0 0 0 100 4 0 0 50 2 0 0 0 100 4 0 0
T o t a l N u m b e r o f P l o t s
4 4 4 2 2 4 4 4 2 2 4 4 4
aSoil w a t e r suction at 12-inch d e p t h w h e n irrigation a p p l i e d .
bA c r e inches p e r a c r e a d d e d t o soil profile d u r i n g g r o w i n g season.
36 JOURNAL OF THE A. S. S. B. T.
T h e s u g a r b e e t s w e r e p l a n t e d o n A p r i l 6 a n d t h i n n e d a n d side- d r e s s e d with a m m o n i u m n i t r a t e o n J u n e 5 a n d 6 . Each plot consisted of e i g h t 2 2 - i n c h rows 30 feet in l e n g t h , s u r r o u n d e d by a b o r d e r d i k e a n d s e p a r a t e d f r o m a d j a c e n t plots by alleys a p p r o x i m a t e l y seven feet w i d e . Electrical r e s i s t a n c e u n i t s ( B o u y o u c o s g y p s u m blocks) w e r e p l a c e d i n e a c h plot a t t h e 12-inch d e p t h . I r r i g a t i o n t r e a t m e n t s w e r e b a s e d u p o n t h e soil w a t e r suction a s m e a s u r e d b y t h e g y p s u m blocks.
W h e n t h e a v e r a g e suction for t h e plots in a given t r e a t m e n t r e a c h e d t h e d e s i r e d value (see T a b l e 1), t h o s e plots w e r e i r r i g a t e d by a p p l y i n g t h r e e i n c h e s o f w a t e r , m e t e r e d a c c u r a t e l y i n t o e a c h basin. A p p l i c a t i o n efficiency, t h e r e f o r e , a p p r o a c h e d 100 p e r c e n t . T h e n u m b e r o f i r r i g a - tions a n d t h e s e a s o n a l a p p l i c a t i o n r a t e s a r e given for e a c h i r r i g a t i o n t r e a t m e n t in T a b l e 1. S e a s o n a l c o n s u m p t i v e u s e of w a t e r was c a l c u l a t e d for e a c h i r r i g a t i o n t r e a t m e n t f r o m t h e a m o u n t o f w a t e r a d d e d b y irri- gation a n d p r e c i p i t a t i o n a n d t h e d i f f e r e n c e i n soil m o i s t u r e c o n t e n t a t t h e b e g i n n i n g a n d e n d o f t h e s e a s o n . O n J u l y 8 soil s a m p l e s w e r e t a k e n i n t h e alleys a t t h e c o r n e r s o f a d j a c e n t plots. T h e s a m p l e s w e r e o b t a i n e d in o n e - f o o t i n c r e m e n t s to a d e p t h of f o u r feet a n d w e r e a n a l y z e d for o r g a n i c m a t t e r a n d n i t r a t e n i t r o g e n c o n t e n t s . U s i n g con- version factors o f 3 0 p o u n d s p e r acre foot o f n i t r o g e n for e a c h p e r c e n t o r g a n i c m a t t e r a n d 3.6 p o u n d s p e r a c r e l o o t for each p p m o f N O3- K , t h e a m o u n t o f r e s i d u a l soil n i t r o g e n b e c o m i n g available t o t h e c r o p was e s t i m a t e d . T h i s was a d d e d t o t h e fertilizer a p p l i c a t i o n t o p r o v i d e t h e a m o u n t o f n i t r o g e n available t o t h e c r o p for e a c h p l o t ( 1 1). T h e a v e r a g e for all plots was a p p r o x i m a t e l y 107 p o u n d s per a c r e of r e s i d u a l soil n i t r o g e n . Petiole s a m p l e s w e r e collected f r o m r a n d o m p l a n t s i n each o f t h e f o u r c e n t e r r o w s o f e a c h plot o n S e p t e m b e r 2 . T h e s e w e r e a n a l y z e d for total n i t r o g e n c o n t e n t .
Climatological d a t a , s u m m a r i z e d i n T a b l e 2 , w e r e o b t a i n e d f r o m a n official w e a t h e r station a t t h e R e s e a r c h C e n t e r a n d f r o m a t h e r m o - g r a p h , used t o m e a s u r e soil t e m p e r a t u r e . Rainfall for t h e g r o w i n g season was 12.46 i n c h e s c o m p a r e d t o t h e l o n g - t e r m a v e r a g e p r e c i p i - tation in t h e a r e a of 1 1.77 i n c h e s for t h e m o n t h s of A p r i l - O c t o b e r . An u n u s u a l l y h i g h a m o u n t o f rainfall o c c u r r e d i n A u g u s t .
T h e plots w e r e h a r v e s t e d o n O c t o b e r 2 3 a n d 2 4 . A n a r e a f o u r rows w i d e a n d 2 2 feet l o n g i n t h e c e n t e r o f t h e plots was u s e d i n o r d e r
Table 2.—Summary of climatological data.
Month April Mav J u n e July Aug.
Sept.
Oct.
A i r Temp.
Maximum 65.3 82.0 86.5 91.4 92.1 83.1 64.0
M (°F) i m m u m
33.8 50.2 55.0 64.4 66.4 50.4 55.0
Soil Temp.
Maximum
83.3 87.6 81.9 76.5
at 4 in. (°F) Mi immum
67.3 68.2 64.9 61.5
Rainfall (inches) 1.12 0.19 0.30 2.77 5.11 2.47 0.50
Open Pan Evaporation (inches)
9.76 14.04 16.17 13.66 14.35 10.25 5.17
V O L . 18, No. 1, A P R I L 1974 37
to avoid border effects. The beets harvested from each plot were counted and percent stand was calculated as the number of beets per 100 feet of row. A sample of beets from each plot was obtained at random for tare, sucrose percentage, and apparent sucrose purity determinations. T h e average yield and quality for Baca County, Colo- rado in 1970 was 13.5 tons per acre with 13.7 percent sucrose and 86.0 percent purity.
Table 3.—Average yield and quality of sugarbeets at harvest and petiole nitrogen content on September 2.
T r e a t m e n t I-0 I-100 I-400 Ave.
II-50 II-200
Ave.
III-0 III-100 III-400 Ave.
IV-50 I V - 2 0 0
Ave.
V-0 V-100 V-400 Ave.
R o o t Y i e l d T o n s / A c r e
18.6 19.5 21.8 20.0 19.0 17.4 18.2 13.9 17.2 14.1 15.1 16.9 15.3 16.1 13.2 14.4
1.45
14.0
S u c r o s e
% 16.8 15.6 12.7 15.1 15.9 14.2 15.0 14.2 15.3 12.0 13.8 16.9 12.0 14.5 15.1 14.0 10.4 13.2
Purity
% 9 6 . 4 9 4 . 9 91.6 9 4 . 3 96.5 92.5 94.5 9 6 . 0 9 4 . 4 88.2 9 2 . 8 97.9 9 0 . 3 94.1 9 5 . 8 9 3 . 4 8 7 . 3 92.2
E x t r a c t a b l e S u g a r T o n s / A c r e
2.92 2.90 2.52 2.78 2.91 2.25 2.58 1.82 2.49 1.49 1.94 2.83 1.66 2.24 2.00 1.87 1.32 1.73
Petiole N
% 1.20 1.43 2.67 1.77 1.29 2.06 1.68 1.18 1.65 2.55 1.79 1.13 1.96 1.55 1.12 1.34 2.51 1.66
T h e total water use by the crop, as determined from irrigation applications, rainfall, and soil water contents at the beginning and end of the season, varied almost directly with the amount of water made available by irrigation (Table 4). Comsumptive use by the crop grown under irrigation treatment I was probably very near the potential for the climatic conditions of the season since the soil moisture stress was maintained at very low levels all season. Transpiration was restricted in the other treatments due to limited availability of soil water during varying periods prior to each irrigation. Nitrogen fertilizer levels within irrigation treatment did not influence seasonal water use. This is as expected since evapotranspiration is essentially controlled by soil water and climatic conditions whenever the crop provides full ground cover. Water use efficiency for the various treatments, expressed in terms of sucrose production per unit of water, is given in Table 4.
The values are calculated for both total water use by the crop and for
irrigation water applied.
38 JOURNAL OF THE A. S. S. B. T.
Table 4.—Seasonal consumptive use and water efficiency.
T r e a t m e n t I-0 I-100 I-400 II-50 II-200 III-0 III-100 III-400 I V - 5 0 IV-200
V-0 V-100 V-400
C o n s u m p t i v e U s e ( i n c h e s )
34.3 34.8 35.2 30.8 31.0 27.3 27.5 27.6 27.6 27.8 24.5 23.8 25.4
W a t e r U s e P o u n d s S u c r o s e p e r
A c r e I n c h ( C . U . ) 170 167 143 189 145 133 181 108 205 119 163 157 104
E f f i c i e n c y
P o u n d s S u c r o s e p e r A c r e I n c h ( i r r i g a t i o n )
2 7 8 2 7 6 2 4 0 3 8 8 3 0 0 3 0 3 4 1 5 2 4 8 472 277 4 4 4 4 1 6 2 9 3
Production Function Analysis Root yield
A production function for sugar beet yield was fitted through multiple regression techniques. The equation which exhibited the best fit was the following:
[1] y = 30790.92765 - 822.84063 S + 13.19953 N + 1810.44025 W + 1.60913 S
2- .10324 N
2- 41.68863 W
2+ .34872 SN + 13.70151 SW + .46103 NW
R
2= .5222 F = 4.1286
Where:
Y = estimated yield of sugar beets, measured in pounds per acre N = amount of available nitrogen (total of applied and residual),
measured in pounds per acre
W = consumptive use of water, measured in inches per acre S = percentage stand, using one beet per foot = 1 00 percent
stand as the basis
T h e model explains about 52 percent of the observed variation in
yield and the F-statistic is significant at the .0012 level. In the linear
formulation of the model, only the coefficient for water was signifi-
cantly different from zero at the five percent probability level. T h e full
quadratic form, as in equation [1], was chosen because it exhibits
diminishing returns to the independent variables and has a higher
proportion of explained variance. However, in the full quadratic
form, none of the regression coefficients is significantly different from
zero at the five percent level.
V O L . 18, No. 1, A P R I L 1974 3 9
Alternative formulations were tested, in which applied nitrogen and applied irrigation water were the independent variables, but they were less satisfactory than equation [1] in terms of the above measures of statistical reliability. Data representing the variables in equation [1]
were also fit to linear and logarithmic equations, but these approaches were also less satisfactory.
Equation [1] was used to predict yields of sugar beets at various levels of available nitrogen and water consumption, given 100 percent stand. The results are displayed in Table 5. T h e equation could also be evaluated at any other plant density within the range of the obser- vations.
Table 5.—Predicted yield of sugar beets in pounds per acre, at 100 beets per 100 feet and varying levels of nitrogen and water.
Total Water Consumption
(in.) 21 2 3 25 27 29 31 33 35 37 39 41 4 3
5 0 15,648 18,387 20,792 2 2 , 8 6 4 24,602 2 6 , 0 0 6 2 7 , 0 7 8 2 7 , 8 1 5 28,219 2 8 , 2 9 0 2 8 , 0 2 7 2 7 , 4 3 0
1 0 0 17,762 20,546 2 2 , 9 9 8 25,1 16 2 6 , 9 0 0 28,350 29,467 3 0 , 2 5 2 30,702 30,818 30,602 30,051
Available
1 5 0 19,359 22,190 24,687 26,851 2 8 , 6 8 1 3 0 , 1 7 8 31,342 32,171 3 2 , 6 6 8 32,830 32,660 3 2 , 1 5 6
Nitrogen (lb./A.) 2 0 0 2 0 , 4 4 0 2 3 , 3 1 7 2 5 , 8 6 0 2 8 , 0 7 0 2 9 , 9 4 7 3 1 , 4 9 0 32,699 3 3 , 5 7 5 3 4 , 1 1 8 3 4 , 3 2 6 34,202 33,744
2 5 0 21,004 2 3 , 9 2 8 2 6 , 5 1 7 2 8 , 7 7 3 3 0 , 6 9 6 3 2 , 2 8 5 3 3 , 5 4 0 3 4 , 4 6 2 35,051 35,306 3 5 , 2 2 8 3 4 , 8 1 6
3 0 0 21,053 24,022 26,658 28,960 30,929 32,564 33,866 34,834 35,468 35,770 35,737 35,371
3 5 0 20,585 23,601 26,282 28,631 30,646 32,327 33,675 34,689 35,370 35,717 35,731 35,411
4 0 0 19,601 22,664 25,391 27,785 2 9 , 8 4 6 31,592 3 2 , 9 6 7 3 4 , 0 2 8 34,755 3 5 , 1 4 8 3 5 , 2 0 8 3 4 , 9 3 4
T h e number of beets per 100 feet of row was not an experimental variable in the study. However, considerable variation in stand did occur in the experiment, and thus a variable representing stand was included in the statistical analysis. The values estimated for the coef- ficients of the stand variables (S and S
2) in equation [1] imply that with- in the range of the experimental observations, yield exhibits slightly increasing returns to percentage stand. That is, if water and nitrogen are held constant, an increase in stand by a given percentage is pre- dicted to increase yield by an even greater proportion. A wider range of observations on the stand variable would no doubt encounter a range of diminishing returns.
Sucrose percentage
It is equally important in this study to be able to predict the effects
on sucrose percentage when each of the inputs is varied, since con-
tract payment formulas are based on sucrose percentage as well as on
beet tonnage and the net return which the sugar processor receives on
the market. T h e grower cannot directly control the price of the refined
40 JOURNAL OF THE A. S. S. B. T.
s u g a r , b u t h e can influence t h e first two variables, a n d t h r o u g h t h e m his r e t u r n s a n d profits a r e affected.
I n o r d e r t o b e able t o p r e d i c t s u g a r p e r c e n t a g e , t h e e x p e r i m e n t a l results w e r e s u b j e c t e d t o r e g r e s s i o n analysis a n d e q u a t i o n [2] d e r i v e d :
[2] %S = 7 . 7 5 4 3 4 + . 0 0 0 0 7 S + . 0 0 3 1 8 N + . 2 7 6 1 W - . 0 0 0 0 8 S2 - . 0 0 0 0 2 N2 - . 0 0 6 2 5 W2 - . 0 0 0 0 2 SN + . 0 0 1 7 8 SW + . 0 0 0 0 3 NW
R2 - . 6 6 3 6 F = 6.36
W h e r e :
% S = p r e d i c t e d p e r c e n t a g e s u c r o s e , a n d t h e o t h e r symbols a r e a s p r e v i o u s l y d e f i n e d
I n t h e l i n e a r f o r m u l a t i o n , coefficients for w a t e r a n d n i t r o g e n w e r e significantly d i f f e r e n t f r o m z e r o at t h e five p e r c e n t level of p r o b a b i l i t y a n d for s t a n d a t t h e t e n p e r c e n t level.
E q u a t i o n [2] was u s e d to g e n e r a t e t h e values s h o w n in T a b l e 6.
S u g a r p e r c e n t consistently d e c r e a s e s with i n c r e a s e s in available n i t r o - g e n , a n d d e c r e a s e s m o r e rapidly a t very h i g h levels, i n g e n e r a l , s u g a r c o n t e n t i n c r e a s e s as total w a t e r u s e i n c r e a s e s , e x c e p t at very h i g h levels.
A b u n d a n t w a t e r t e n d s t o offset t h e n e g a t i v e effects o f h i g h levels o f n i t r o g e n . T w o factors which w e r e n o t c o n s i d e r e d i n this e x p e r i m e n t , t e m p e r a t u r e a n d light ( a n d t h e i r i n t e r a c t i o n ) , p r o b a b l y play a s i m p o r - t a n t a p a r t , o r m o r e so, t h a n d o n i t r o g e n a n d w a t e r a s influences o n s u g a r p e r c e n t a g e .
F o r t h e p u r p o s e of this study, p u r i t y p e r c e n t a g e was i g n o r e d in t h e P r o d u c t i o n F u n c t i o n , since n o n e o f t h e s a m p l e s f r o m t h e test fell below 80 p e r c e n t p u r i t y , t h e p o i n t at which a p e n a l t y is i m p o s e d by t h e s u g a r c o m p a n y . Purity was u s e d t o calculate e x t r a c t a b l e s u c r o s e , h o w e v e r .
Table 6.—Expected sugar percentages, at 100 beets per 100 feet and varying levels of nitrogen and water.
Total Water Available Nitrogen
Consumption (lb./A.) (in.) 50 100 150 200 250 300 350
21 23 25 27 2 9 31 33 35 37 39 41
13.8 14.1 14.4 14.7 14.9 15.1 15.2 15.2 15.3 15.2 15.1
13.7 14.1 14.4 14.7 14.9 15.0 15.1 15.2 15.2 15.2 15.1
13.6 13.9 14.2 14.5 14.7 14.9 1 5.0 15.1 15.1 15.0 15.0
13.3 13.7 14.0 14.3 14.5 14.6 14.8 14.8 14.8 14.8 14.7
12.9 13.3 13.6 13.9 14.1 14.3 14.4 14.5 14.5 14.5 14.4
12.5 12.8 13.2 13.4 13.7 13.8 14.0 14.1 14.1 14.1 14.0
J 1.9 12.3 12.6 12.9 12.9 13.3 13.4 1 3.5 13.5 13.5 13.4
V O L . 18, No. 1, APRIL 1974 4 1
Payment to grower
T h e total price received by the grower is based on both percentage sugar content of the beets and the processor's "average net return" on sugar. The processor's average net return on sugar is determined by deducting from the price for which the processor sells refined sugar certain specified operating expenses. T h e schedule specifying pay- ments per ton for varying levels of sugar content and average net return is typically provided in the company's grower contract.
T h e actual net returns in the study area were $ .0853/lb. in 1969,
$ .0922/lb. in 1970 and $ .0984/lb. in 1971. Hence, we used $ .10 per lb. in subsequent calculations.
Using the guidelines found in the contract (1), a simple formula for price per ton of sugar beets was calculated by a regression fit to the contract table.
Net Receipts to Grower
T h e information from the above sections provides the basis for determining net receipts per acre to the grower under alternative water and nitrogen applications. T h e total payment per acre of sugar beets is a direct function of three variables: the yield of sugar beets per acre, the average sugar percentage, and the average net return (ANR) on sugar to the processor. Both the yield of sugar beets and the sugar percentage are in turn dependent on the amounts of water and nitro- gen and the plant population used in beet production.
Gross return per ton estimates for alternative nitrogen and irriga- tion applications were generated using the price formula, percent of sucrose values drawn from equation [2], and assuming ANR = $ .10.
Each figure thus generated was then applied to the appropriate sugar beet yield derived from equation [1].
To determine net receipts per acre to the grower, costs of applied water and nitrogen were subtracted from gross returns. Up to this point, water and nitrogen were expressed on a total available basis.
However, in order to compute input costs, only the amount of irriga- tion water and fertilizer actually applied must be considered. To adjust total available nitrogen levels to nitrogen applied, 100 pounds (approx- imately the average residual nitrogen level of the soil) was subtracted.
Thus, if the optimum amount of available nitrogen were 150 pounds
per acre, the approximate amount necessary for the producer to apply
would be 50 pounds per acre. In the case of irrigation water, adjust-
ments must be made for effective rainfall, soil moisture depletion, and
on-farm delivery losses. T h e long-term average rainfall in the area
during the growing season has been 1 1.77 inches and the average soil
moisture depletion measured in this particular experiment was 2.60
inches. It is further assumed that in commercial production one-third
42 JOURNAL OF THE A. S. S. B. T.
of the water diverted or pumped is lost during irrigation (i.e., farm irrigation efficiency is 67 percent).
A sample net return array is shown in Table 7. The figures in the table would vary as plant density, average net return on sugar, and the prices of water and nitrogen vary. Under the assumptions defined for Table 7, where variable water costs are $ .50 per acre inch and nitrogen costs $ .08 per lb., maximum net return over variable nitrogen and water costs would occur where approximately 100 pounds of nitrogen fertilizer and 37 inches of irrigation water are used. Note, however, that a fairly wide range of water and nitrogen inputs can lead to profits which closely approximate that of the optimum levels. Thus, any com- binations of water diversion ranging from 28 to 40 inches and nitrogen ranging from 50 to 150 lbs. per acre delivered returns that were not strikingly less than the optimum.
Table 7.—Net return in dollars per acre over variable input costa. Irrigation
Water Diverted (in./A.)
10.5 13.5 16.5 19.5 22.5 25.5 28.5 31.5 34.5 37.5 40.5
0
$ 122.81 146.01 166.53 185.27 200.59 212.07 221.04 227.48 229.59 229.03 224.11
Nitrogen 50
$ 129.26 151.68 172.65 191.79 207.46 220.90 230.39 237.13 239.60 237.59 234.74
Fertilizer (lb./A.)
Applied 100
$ 129.63 153.37 174.47 194.04 209.99 222.04 233.46 238.81 241.55 241.68 237.33
150
$ 124.95 148.51 169.48 188.87 204.97 218.84 228.65 236.06 239.07 239.52 235.48
aReturn is net of nitrogen and water costs only. Assumptions: 100 beets per 100 feet, $ .10 average net return on sugar, $ .50 per acre-inch of water, 67 percent irrigation efficiency, $ .08 per pound of nitrogen.
Summary, Conclusions, and Limitations
Production functions for sugar beet root yield and sucrose
percentage using total available nitrogen, consumptive use of water,
and plant density as independent variables were derived from a field
experiment conducted at Walsh, Colorado, during 1970. Coefficients
of multiple correlation were .52 and .66, respectively. Yields and
sucrose percentage were predicted for various nitrogen and water
levels, using a given stand level of one beet per foot of row. A formula
to relate the processor's average net return and sugar percentage of
beets to the grower's price per ton was devised. Combining this for-
mula with the predicted yields and sugar percentages produced an
array of expected gross returns associated with varying levels of
nitrogen and water. Input costs of water and fertilizer were subtracted
V O L . 18, No. 1, APRIL 1974 4 3 t o d e t e r m i n e t h e m a x i m u m n e t r e t u r n a n d o p t i m a l i n p u t levels. N e t r e t u r n o v e r variable cost was h i g h e s t a t 3 7 i n c h e s o f w a t e r d i v e r t e d ( a s s u m i n g 6 7 p e r c e n t a p p l i c a t i o n efficiency) a n d 100 p o u n d s o f n i t r o g e n a p p l i e d p e r a c r e .
T o t a l available n i t r o g e n levels t e n d e d t o b e h i g h i n this e x p e r i - m e n t as a r e s u l t of a m o d e r a t e l y h i g h level of r e s i d u a l soil n i t r o g e n ( a v e r a g e 107 p o u n d s p e r a c r e ) . T h u s , little r e s p o n s e t o a p p l i e d n i t r o - g e n was e v i d e n t i n r o o t yields, a n d a p p l i e d n i t r o g e n fertilizer signifi- c a n t l y d e c r e a s e d s u g a r p e r c e n t a g e . N i t r o g e n h a d relatively little i n f l u e n c e o n n e t r e t u r n s b e c a u s e o f t h e relatively low cost o f fertilizer.
O p t i m u m w a t e r c o n s u m p t i o n i s e x t r a p o l a t e d b e y o n d t h e b o u n d s o f t h e e x p e r i m e n t a l d a t a , a n d s h o u l d b e h a n d l e d with c a u t i o n . Also, t h e e s t i m a t e d cost p e r a c r e - i n c h o f w a t e r , $ .50, reflects only v a r i a b l e p u m p i n g a n d a p p l i c a t i o n costs. I t d o e s n o t t a k e i n t o a c c o u n t t h e value of w a t e r as a n o n r e n e w a b l e r e s o u r c e (i.e., t h e fact t h a t it m a y be w o r t h m o r e left i n t h e a q u i f e r for p o t e n t i a l f u t u r e use), n o r d o e s i t a c c o u n t for t h e o p p o r t u n i t y cost o f w a t e r for o t h e r c r o p s o r p u r p o s e s .
P l a n t d e n s i t y was n o t originally a v a r i a b l e in t h e e x p e r i m e n t , b u t was i n c l u d e d b e c a u s e a g r e a t d e a l o f v a r i a t i o n was e v i d e n t . T h e r a n g e o f s p a c i n g s e n c o u n t e r e d i n t h e e x p e r i m e n t s h o w e d i n c r e a s i n g r e t u r n s t o p l a n t d e n s i t y ; this w o u l d n o t b e e x p e c t e d t o h o l d a s p l a n t s b e c a m e very c r o w d e d .
T h e s e c o n c l u s i o n s a r e a p p l i c a b l e t o t h e soil, climate, m o i s t u r e , a n d fertility c o n d i t i o n s e x p e r i e n c e d i n this p a r t i c u l a r e x p e r i m e n t , a n d can b e a p p l i e d t o o t h e r s i t u a t i o n s only with d u e c a u t i o n . Doll (4) h a s p r o v i d e d a p e r t i n e n t d i s c u s s i o n o f t h e applicability o f e c o n o m i c c o n c l u s i o n s d r a w n f r o m a single y e a r ' s e x p e r i m e n t .
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