Effects of Weather Variables on
144 JOURNAL OF THE A.S.S.B.T W e a t h e r d a t a have b e e n r e c o r d e d at the Station since 1902. T h e rela- tionship between yield a n d various climatic variables was s t u d i e d to see which variables constrain yields the most in this region. T h e i n d e p e n d e n t variables studied were:
(a) T i m e ( a d v a n c i n g years);
(b) M e a n daily t e m p e r a t u r e ( m o n t h l y a n d seasonal);
(c) T o t a l degree days (base 4 2 ° F or 6°C) from m e a n p l a n t i n g d a t e t o m e a n harvest d a t e ;
(d) M e a n daily h o u r s of b r i g h t sunshine from May 1 to August 3 1 ; (e) T o t a l p r e c i p i t a t i o n for May a n d J u n e ;
(f) T o t a l p r e c i p i t a t i o n 7 days before a n d 7 days after p l a n t i n g ; (g) P l a n t i n g d a t e ;
(h) N u m b e r of frost-free days;
(i) N u m b e r of days with t e m p e r a t u r e s above 2 8 ° F or - 2 . 2 ° C . Multiple regression analyses of sugar beet yields between these vari- ables were p e r f o r m e d . T h e forward selection p r o c e d u r e was used to insert t h e i n d e p e n d e n t variables one at a time into t h e regression e q u a t i o n . A 't- test' was p e r f o r m e d for t h e variable most recently e n t e r e d to i n d i c a t e w h e t h e r t h a t variable h a d a c c o u n t e d for a significant a m o u n t of the variation over t h a t removed by the previous variables in the regression.
To forecast yields several years in a d v a n c e , a d d i t i o n a l calculations be- tween yield a n d time were p e r f o r m e d . First, the time t r e n d was analyzed, using t h e linear a n d curvilinear regression m e t h o d s , with time as t h e inde- p e n d e n t variable. After the t r e n d factors were a c c o u n t e d for, a detailed time-series analysis was p e r f o r m e d , using the m e t h o d of Jenkins a n d W a t t s (5). T h e homogeneity of the v a r i a n c e with t i m e was tested, by d e c a d e s , using Bartlett's test (9). T h e n , the serial correlations a n d v a r i a n c e spec- t r u m were c o m p u t e d (5), to establish w h e t h e r t h e r e was any cycling in the yield d a t a . Finally, a c o m p l e t e statistical forecasting m o d e l was assembled t h a t gave the m e a n yields a n d the probabilities associated with a r a n g e of yields.
Results and Discussion
A s u m m a r y of some of t h e long-term (1902-1975) w e a t h e r d a t a for s o u t h e r n A l b e r t a a p p e a r s in T a b l e 1.
T h e m u l t i p l e stepwise regression analysis of t h e d a t a showed t h a t tem- p e r a t u r e a n d time were t h e only factors t h a t explained significant a m o u n t s of the variability in yield. T h e o t h e r climatic factors did not a c c o u n t for a significant a m o u n t of t h e residual variability. However, t h e n u m b e r of hours of b r i g h t sunshine a n d t e m p e r a t u r e was significantly c o r r e l a t e d (r = 0.48).
T h e regression of a n n u a l yields on a d v a n c i n g years (time) is shown in Figure 1. T h e regression coefficients a n d their levels of significance for t h e unfertilized a n d fertilized plots were 0.12 t o n / a c r e / y e a r (P < 0.01) a n d 0.10 t o n / a c r e / y e a r (P < 0.025), respectively. Because these t r e n d s were
Table 1.—Summary of weather data (1902-1975 mean) for Lethbridge, Alberta.
Mean
Precipitation temperature1 Sunshine2
Month (in.) (°F) (hr) January
February March April
July August October November December Total Mean
1The number of frost-free days and crop days (above 28°F) was 117 and 140.
267-year average.
significant, t h e regression line with t i m e was used as t h e basis for f u r t h e r analysis.
Bartlett's test (9) i n d i c a t e d no significant differences a m o n g t h e variances c o m p u t e d by d e c a d e s ; h e n c e , further c o m p u t a t i o n s based on a h o m o g e n e o u s v a r i a n c e were valid. Serial c o r r e l a t i o n a n d spectral analysis i n d i c a t e d t h a t t h e r e was some m i n o r cycling in t h e v a r i a n c e . However, n o n e of t h e cycles e x p l a i n e d e n o u g h of t h e v a r i a n c e to be useful for fore- casting. Deviations were n o t significantly skewed from t h e t r e n d line.
It was d e c i d e d from t h e p r e c e d i n g analyses to base forecasts on a p r o - jection of the regression line a n d to assign probabilities to a r a n g e of yields
YEARS
Figure 1.—Regression of sugar beet yields in a 10-year irrigated crop rotation, with and without fertilizer, on advancing years.
144 JOURNAL OF THE A . S . S . B . T . W e a t h e r d a t a have been r e c o r d e d at t h e Station since 1902. T h e rela- tionship between yield a n d various climatic variables was studied to see which variables constrain yields the most in this region. T h e i n d e p e n d e n t variables studied were:
(a) T i m e ( a d v a n c i n g years);
(b) M e a n daily t e m p e r a t u r e ( m o n t h l y a n d seasonal);
(c) T o t a l degree days (base 4 2 ° F or 6°C) from m e a n p l a n t i n g d a t e to m e a n harvest d a t e ;
(d) M e a n daily h o u r s of b r i g h t sunshine from May 1 to A u g u s t 3 1 ; (e) T o t a l p r e c i p i t a t i o n for May a n d J u n e ;
(f) T o t a l p r e c i p i t a t i o n 7 days before a n d 7 days after p l a n t i n g ; (g) P l a n t i n g d a t e ;
(h) N u m b e r of frost-free days;
(i) N u m b e r of days with t e m p e r a t u r e s above 2 8 ° F or - 2 . 2 ° C . Multiple regression analyses of sugar beet yields between these vari- ables were p e r f o r m e d . T h e forward selection p r o c e d u r e was used to insert the i n d e p e n d e n t variables one at a time into the regression e q u a t i o n . A 't- test' was p e r f o r m e d for the variable most recently e n t e r e d to i n d i c a t e w h e t h e r t h a t variable h a d a c c o u n t e d for a significant a m o u n t of the variation over t h a t removed by the previous variables in the regression.
To forecast yields several years in advance, a d d i t i o n a l calculations be- tween yield a n d time were p e r f o r m e d . First, the time t r e n d was analyzed, using t h e linear a n d curvilinear regression m e t h o d s , with t i m e as the inde- p e n d e n t variable. After t h e t r e n d factors were a c c o u n t e d for, a detailed time-series analysis was p e r f o r m e d , using the m e t h o d of J e n k i n s a n d W a t t s (5). T h e h o m o g e n e i t y of the v a r i a n c e with t i m e was tested, by d e c a d e s , using Bartlett's test (9). T h e n , the serial correlations a n d v a r i a n c e spec- t r u m were c o m p u t e d (5), to establish w h e t h e r t h e r e was any cycling in t h e yield d a t a . Finally, a c o m p l e t e statistical forecasting m o d e l was assembled t h a t gave the m e a n yields a n d t h e probabilities associated with a r a n g e of yields.
Results and Discussion
A s u m m a r y of some of the long-term (1902-1975) w e a t h e r d a t a for s o u t h e r n A l b e r t a a p p e a r s in T a b l e 1.
T h e m u l t i p l e stepwise regression analysis of the d a t a showed t h a t tem- p e r a t u r e a n d time were the only factors t h a t e x p l a i n e d significant a m o u n t s of the variability in yield. T h e o t h e r climatic factors did not a c c o u n t for a significant a m o u n t of t h e residual variability. However, t h e n u m b e r of hours of b r i g h t sunshine a n d t e m p e r a t u r e was significantly c o r r e l a t e d (r = 0.48).
T h e regression of a n n u a l yields on a d v a n c i n g years (time) is shown in Figure 1. T h e regression coefficients a n d their levels of significance for the unfertilized a n d fertilized plots were 0.12 t o n / a c r e / y e a r (P < 0.01) a n d 0.10 t o n / a c r e / y e a r (P < 0.025), respectively. Because these trends were
V O L . 19, N o . 2 , O C T O B E R 1976
T a b l e 1.—Summary of weather data (1902-1975 mean) for Lethbridge, Alberta.
Mean
Precipitation temperature1 Sunshine2
Month (in.) (°F) (hr) J a n u a r y
February March April May J u n e July August September October November December Total
Mean 40.9
1T h e n u m b e r of frost-free days a n d crop days (above 28°F) was 117 a n d 140.
267-year average.
significant, the regression line with time was used as the basis for further analysis.
Bartlett's test (9) indicated no significant differences a m o n g t h e variances c o m p u t e d by decades; hence, further c o m p u t a t i o n s based on a homogeneous variance were valid. Serial correlation a n d spectral analysis indicated t h a t there was some m i n o r cycling in the variance. However, none of the cycles explained e n o u g h of the variance to be useful for fore- casting. Deviations were not significantly skewed from the trend line.
It was decided from the preceding analyses to base forecasts on a pro- jection of the regression line a n d to assign probabilities to a r a n g e of yields
Figure 1.—Regression of sugar beet yields in a 10-year irrigated crop rotation, with and without fertilizer, on advancing years.
Y E A R S
1 4 6 JOURNAL OF THE A.S.S.B.T.
An a t t e m p t to p r e d i c t the m e a n daily t e m p e r a t u r e for a g r o w i n g sea- son from the m e a n daily t e m p e r a t u r e s of previous m o n t h s ( O c t o b e r - D e - c e m b e r , O c t o b e r - M a r c h , a n d O c t o b e r - M a y ) proved unsuccessful because there was n o d e p e n d e n c e . T h e earliest t h a t a n i m p r o v e d forecast u s i n g t e m p e r a t u r e d a t a from previous m o n t h s c a n be m a d e is after t h e c r o p is p l a n t e d . T h e yield e q u a t i o n s a n d s t a n d a r d deviations t h a t were c a l c u l a t e d by m o n t h s after the c r o p was p l a n t e d a r e shown in T a b l e 3.
I n c o r p o r a t i o n o f May o r May plus J u n e t e m p e r a t u r e d a t a i n t o t h e p r e d i c t i o n e q u a t i o n after t h e c r o p was p l a n t e d resulted in a significant r e d u c t i o n in t h e m a g n i t u d e of t h e s t a n d a r d deviation of t h e forecast. Ad- d i t i o n o f July, August, a n d S e p t e m b e r t e m p e r a t u r e s d i d n o t i m p r o v e t h e yield forecasts significantly, w h i c h suggests t h a t t h e t e m p e r a t u r e s d u r i n g these m o n t h s in this a r e a a r e n e a r o p t i m a l for s u g a r beets. A l t h o u g h it was n o t statistically significant, t h e regression coefficient for t h e J u l y t e m p e r a - t u r e variable was negative. T h i s suggests t h a t p e r h a p s t h e m e a n J u l y t e m - p e r a t u r e m i g h t be slightly high for o p t i m a l p r o d u c t i o n .
T h e significant a n d positive regression coefficient of 0.1 t o n / a c r e / y e a r p r o b a b l y resulted from i m p r o v e d soil fertility (3), use of b e t t e r a d a p t e d varieties, a n d i m p r o v e d m a n a g e m e n t t h a t o c c u r r e d with t i m e .
based o n t h e n o r m a l d i s t r i b u t i o n . T h e e q u a t i o n used for forecasting yields was:
where Y = yield in tons p e r acre t h a t corresponds to a specific year; a = intercept; b = slope; year = c a l e n d a r year; a = s t a n d a r d deviation of t h e regression line; a n d e = a s t a n d a r d i z e d v a r i a t e with a m e a n of 0 a n d a s t a n d a r d deviation of 1.
T h e e q u a t i o n was used to p r e d i c t t h e yield for 1975 at various p r o b - ability levels, a n d these a r e shown in T a b l e 2.
T h e best forecast yields for 1975, using this e q u a t i o n , were 19.67 a n d 21.84 t o n s / a c r e for t h e unfertilized a n d fertilized plots in this r o t a t i o n . T h e a c t u a l yields were 19.26 a n d 22.30 t o n s / a c r e , respectively, from t h e two plots. T h e above predictions were c a l c u l a t e d w i t h o u t a d j u s t m e n t for any of the w e a t h e r p a r a m e t e r s . T h e c a l c u l a t e d regression coefficients on t e m p e r a t u r e after t h e time t r e n d was removed for t h e unfertilized a n d fer- tilized plots were 0.72 (P < 0.025) a n d 1.02 (P < 0.005) t o n / a c r e / ° F .
Table 2.—The probability that a given yield would not be equaled or exceeded in 1975.
Prob- Yield (tons/acre) ability
level (96) Unfertilized Fertilized Expression
148 JOURNAL OF THE A.S.S.B.T.
T h e s e results agree with those of others (2, 5, 6, 9), w h o found t h a t t e m p e r a t u r e was the most i m p o r t a n t climatic factor affecting s u g a r beet yields. Swift a n d C l e l a n d (9) used m e a n t e m p e r a t u r e s of several m o n t h s t h a t p r e c e d e d the p l a n t i n g d a t e in their forecast of yields. However, we found no discernible d e p e n d e n c e of growing season t e m p e r a t u r e s on tem- p e r a t u r e s of m o n t h s t h a t p r e c e d e d the m o n t h of p l a n t i n g . After t h e c r o p was p l a n t e d , i n c o r p o r a t i o n of May or May plus J u n e t e m p e r a t u r e s i n t o t h e prediction e q u a t i o n r e d u c e d the size of t h e s t a n d a r d deviation of the fore- cast. T h e s t a n d a r d deviation would p r o b a b l y be further r e d u c e d if an average yield for several sites is to be p r e d i c t e d (6).
Because rainfall was not significantly r e l a t e d with yield, irrigation as p r a c t i c e d in this r o t a t i o n a p p a r e n t l y provided a d e q u a t e m o i s t u r e for sugar beets. Yields were also unaffected by t h e a m o u n t of p r e c i p i t a t i o n t h a t oc- c u r r e d i m m e d i a t e l y before a n d after p l a n t i n g . T h i s m a y b e e x p l a i n e d i n p a r t by the fact t h a t fall irrigation was usually p r a c t i c e d , the soil has a relatively fine texture, a n d the r a t e of seeding was usually sufficiently high to ensure a good s t a n d .
T h e average p l a n t i n g d a t e of s u g a r beets on this r o t a t i o n was A p r i l 29 11 days, a n d yields were n o t significantly affected by this v a r i a b l e . An- derson et al. (1) r e p o r t e d t h a t sugar beet yields at L e t h b r i d g e were n o t sig- nificantly affected when t h e c r o p was p l a n t e d between April 20 a n d May 10.
S u m m a r y
An e q u a t i o n for p r e d i c t i n g sugar beet yields based on regression analysis of 50 years of yield d a t a from one site in s o u t h e r n A l b e r t a is p r e - sented. U n d e r irrigation, t e m p e r a t u r e was f o u n d to be t h e only climatic variable t h a t significantly affected s u g a r beet yields. T e m p e r a t u r e s d u r i n g a growing season were not d e p e n d e n t on those of previous m o n t h s . Incor- p o r a t i o n o f May a n d J u n e t e m p e r a t u r e s o f t h e c u r r e n t year i n t o t h e e q u a - tion r e d u c e d the size of t h e s t a n d a r d deviation of t h e forecast. T h e precision of t h e p r e d i c t i o n would p r o b a b l y be further i m p r o v e d if d a t a from a d d i t i o n a l sites were i n c o r p o r a t e d .
Literature Cited
(1) ANDERSON, D. T . , S. DUBETZ, and G. C. RUSSELL. 1958. Studies on trans- planting sugar beets in southern Alberta. Proc. Am. Soc. Sugar Beet Technol. 10: 150-155.
(2) BRUMMER, V. 1961. On the relations between sugar beet yields and certain climatic factors in Finland. A statistical study and some cultivation tech- nique applications [in Finnish]. Suom. Maataloust. Seur. Julk. 98: 1-180.
(3) DUBETZ, S. 1954. The fertility balance in a ten-year sugar beet rotation after forty-two years of cropping. Proc. Am. Soc. Sugar Beet Technol. 8: 81- 85.
(4) HILL, K. W. 1951. Effects of forty years of cropping under irrigation. Sci.
Agr. 31: 349-357.
(5) JENKINS, G. M. and D. G. W A T T S . 1968. Spectral analysis and its applica- tion. Holden-Day, San Francisco, Calif. 525 pp.
(6) KELCHEVSKAYA, L. S. 1965. Complex estimate of the heat and moisture suf- ficiency of the vegetative period of sugar beets. Treatises Cent. Forecast- ing Inst. 1965(140): 97-104. (Transl. from Russian.)
(7) KRUMBIEGEL, DIETMAR. 1972. The effect of meteorological conditions on the level and stability of crop yields [German, English summary]. Arch.
Acker-Pflanzenbau Bodenkd. 16: 771-777.
(8) SCOTT, R. K., S. D. ENGLISH, D. W. W O O D , and M. H. UNSWORTH. 1973.
The yield of sugar beet in relation to weather and length of growing sea- son. J. Agric. Sci. 81: 339-347.
(9) STEEL, R. G. D. and J. H. T O R R I E . 1960. Principles and procedures of sta- tistics. McGraw-Hill Book Company, Inc., Toronto. 481 pp.
(10) SWIFT, EDWARD L. and FRANK A. CLELAND. 1946. The effect of climate on sugar beet yields in western Montana. Proc. Am, Soc. Sugar Beet Technol. 4: 135-140.