The use of weather forecasts to improve hay-making reliability

Agricultural Meteorology, 25 (1981) 27--34

27

Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

THE USE OF WEATHER FORECASTS TO IMPROVE HAY-MAKING RELIABILITY J.A. DYER and W. BAIER Agrometeorology Section, Land Resource Research Institute, Research Branch, Agriculture Canada, Ottawa, Ontario K1A 0C6 (Canada)

(Received December 8, 1980; accepted after revision May 12, 1981) ABSTRACT Dyer, J.A. and Baler, W., 1981. The use of weather forecasts to improve hay-making reliability. Agric. Meteorol., 25: 27--34. An index of weather forecast reliability was derived to assist farmers in making hay. The chances of field drying hay in four days or less were shown to be improved when the first one or more days after cutting were known to have no rain. The critical reliability levels which make two-, three- or four-day forecasts better criteria for scheduling hay cuts than one-day forecasts were demonstrated. This index could promote the optimum use of weather forecasts in scheduling hay cuts. However to apply the index, the actual reliability (chances of success) of forecasting sequences of rain-free days must be known. INTRODUCTION Field d r y i n g h a y is an a t t r a c t i v e o p t i o n in t o d a y ' s e n e r g y c o n s c i o u s f a r m i n g c o m m u n i t y , since it offers one of the s i m p l e s t w a y s o f e x p l o i t i n g solar energy. M e t h o d s o f harvesting which avoid field drying, such as haylage, are e x p e n s i v e in t e r m s of b o t h e q u i p m e n t and energy, so storing d r y h a y , either in bales or loose, is still a c o m m o n p r a c t i c e in m a n y areas o f Canada. T h e w e a t h e r risks a s s o c i a t e d with field d r y i n g a n d t h e ability to p r e d i c t w e a t h e r are a m a j o r c o n c e r n in m a k i n g g o o d d r y hay. In the earliest e f f o r t s to use w e a t h e r r e c o r d s to plan for h a y - m a k i n g , seq u e n c e s of days w i t h o u t rain were a n a l y s e d ( B o r g m a n and B r o o k e r , 1 9 6 1 ; M o o r e , 1971). H a y h o e and J a c k s o n ( 1 9 7 4 ) d e v e l o p e d an i n d e x f o r rating h a y d r y i n g d a y s on the bases of b o t h rain and 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 . A m o d i f i e d f o r m of this i n d e x was u s e d by D y e r a n d B r o w n ( 1 9 7 7 a ) to integrate b o t h d r y i n g a n d r e w e t t i n g c o n d i t i o n s f r o m the t i m e of c u t t i n g to the t i m e w h e n h a y is d r y e n o u g h to be c a r t e d a w a y and t o simulate the t i m e req u i r e d to dry. This m o d e l was used to do a historical analysis of h a y - m a k i n g w e a t h e r in O n t a r i o ( D y e r a n d B r o w n , 1 9 7 7 b ) . This a p p r o a c h entailed m a k i n g t h e a s s u m p t i o n t h a t the t i m e t a k e n to field-dry h a y was an i n d i c a t i o n of the q u a l i t y of hay. T h e m e t h o d of a p p l y i n g this m o d e l was described in detail b y D y e r and Selirio (1977). R e c e n t l y this m o d e l (called F H A Y D ) was applied to selected w e a t h e r records across C a n a d a (Dyer, 1 9 8 0 ) to p r o d u c e a n u m b e r of f r e q u e n c y d i s t r i b u t i o n s of d r y i n g periods, reflecting various possible field-drying t i m e s t h a t c o u l d result f r o m d i f f e r e n t m a n a g e m e n t practices, 0002-1571/81/0000--0000/$02.50

~ 1981 Elsevier Scientific Publishing Company

28 including cutting or carting away at different moisture levels and increasing the drying rate by raking the swath. These relative frequencies imply the certainty with which successful harvesting can be carried out. Short term synoptic weather forecasts are relied upon by many farmers for scheduling of cutting dates. The effect of weather forecasts on decisions to cut hay constitutes a shortcoming in the m e t h o d described by Dyer and Selirio (1977). Since every day was considered to be a possible cutting day, random cutting was implied. How serious this problem is depends partly on how the reliability of the forecasts and the confidence that farmers have in them, affect their decision to cut. This problem is not so serious for studying the relative changes in certainty due to different methods of harvest or different climates, as was done by Dyer (1980). To estimate the actual level of certainty of drying hay in a limited time period more realistically, the method of Dyer and Selirio (1977) should be modified to account for the influence of weather forecasts on decisions to cut. The first goal of this analysis was to show the increase in certainty of cutting and field drying hay within a specified period when the first one or more days of that period are dry. The second goal was to provide a measure of how reliable a weather forecast must be in order for a hay cut scheduled on the basis of it to have an increased chance of success. This entailed the development of an index of critical reliability levels for forecasts. METHOD The simulation model for hay drying developed by Dyer and Brown (1977a) was used to generate two types of frequency distributions, based on random cutting and scheduled cutting. In the latter, cuts were assumed only when the first rn days after cutting were known to have no rain. In both cases the distributions consisted of the fractions of cuts that took n days or less to dry. Dyer and Brown (1977b) pointed out that as a general rule, good quality hay must be in the field no longer than four days, so n is set to 4 in this discussion. Based on random cutting the certainty of drying within four days (Po) was computed by dividing the number of cuts taking four days or less to dry by the total number of possible starting days. For weekly estimates of Po the number of starting days is given by the years of weather records used in the simulation multiplied by 7. The certainty of drying in four days, for cuts scheduled using m dry-day sequences (Pro) was computed by dividing the number of cuts taking four days or less, when the first rn days were known to be dry, by the number of times that rn dry days occurred in sequence in the years studied, each week. Po is a special case of Prn and the range of Prn is from Po to 1.0. The relationship between Prn and Po satisfies the first goal of the analysis. To achieve the second goal a probability, rather than absolute certainty was assumed for the occurrence of dry days in sequence. The actual certainty of a hay-drying period (Crn) based on a synoptic weather forecast of

29 m dry days, was ~ Pro, and ~ Po depending on the reliability with which m dry days in sequence could be forecast. The possibility of forecasts being so p o o r that th ey would make scheduled cuts have lower chances of drying in f o ur days than r a n d o m cuts was ignored in this discussion. A reliability factor (F) of the confidence which can be put in a forecast of m dry days was introduced. F o r F m = 0, the forecast is held to be no more reliable than a statistical forecast, based on the average frequency of occurrence of m dry days in sequence. For F m = 1.0, the forecast is always reliable. Negative F m values are not considered. Cm approaches P m as F m approaches 1.0 and Cm approaches Po as Frn approaches 0. T her e f or e certainties of actually drying hay in 4 days or less based on m dry days forecasts can be expressed as C m = Po + ( P m -

Po)Fm

(1)

where C m = certainty of hay drying in four days given that the first rn days were forecast dry; P m = certainty of hay drying in four days given that the first rn days were known to be dry; Po = certainty of hay drying in four days based on r an d o m cutting; F m = reliability with which a sequence of m dry days can be forecast. if longer forecasts are to be of value in scheduling a cut of hay, then there must be some increase in certainty over cuts based on shorter forecasts. The m in imu m acceptable level of a longer dry sequence forecast, compared to a shorter forecast can be defined by assuming no change in Cm in eq. 1. If there are no differences in C m for different values of m then the term (Pro -- P o ) F m is constant with respect to m. Changes in P m can be shown by simulation with FHAYD. Comparing the case for m dry day sequences to the case for k dry day sequences, where k :/= rn, gives C m = Ck. By substituting k for m in eq. 1, the right hand side of the new equation can be compared to the right hand side of eq. 1 giving (Pm -- P o ) F m

= (Pk -- Po)F~

(2)

Since on the morning of a planned cutting day the cut can be rescheduled if rain threatens, the reliabilities of longer forecasts were compared to oneday forecasts. Thus by assigning k the value of 1 and rearranging eq. 2, threshold levels of F m can be expressed in terms of Pro, P, and Fj as follows: Fm=

F l (P, -- P o ) / ( P m -- Po)

(3)

for m = 1 to n and Cm = C , . Ratios of Pt - - P o to P m - - P o are given in Table I. These include different values of m averaged over the season, for each site and for the average of four sites. Care must be taken in interpreting F m . The actual rate at which forecasts must be correct (f) depends on the frequencies of occurrence of m dry-day sequences, which are n o t constant over the season or from site to site, since rainfall distributions change. To interpret F m , the frequencies of occurrence of m dry days in sequence at various sites and weeks of the year are needed. The actual fraction of forecasts t hat must be correct is

3O TABLE I Critical reliability levels for two, three and four dry days weather forecasts given that the reliability of a one dry day forecast is 1.0" m

2 3 4

(Pl -- Po)/(Pm -- Po)

Fredericton

Normandin

Harrow

Lacombe

All sites

0.501 0.302 0.257

0.463 0.280 0.268

0.468 0.261 0.218

0.503 0.330 0.310

0.484 0.293 0.263

* Based on weather records used by Dyer (1980). fm=

Rm + (1--Rm)Fm

(4)

w h e r e R m = average f r e q u e n c y of o c c u r r e n c e for m d r y d a y s in sequence. T h e a d v a n t a g e o f using F m instead o f fro, was t h a t F m d o e s n o t v a r y as a f u n c t i o n o f R m a n d d o e s n o t change f r o m site to site. RESULTS In Figs. l a to l d , P m was p l o t t e d w e e k l y t h r o u g h o u t the s u m m e r f o r values o f m o f 0 - - 4 , at f o u r sites. A l t h o u g h a n u m b e r o f d i f f e r e n t m a n a g e m e n t p r a c t i c e s c o u l d have been a s s u m e d (Dyer, 1980), o n l y the s i m p l e s t c o n d i t i o n s f o r field d r y i n g were used here. T h e initial m o i s t u r e was a s s u m e d to be 80% wb, t h e final m o i s t u r e was 25% a n d n o aids to increase the d r y i n g r a t e were used. E a c h i n c r e m e n t in P m w i t h m c o n s t i t u t e s a significant increase in the c h a n c e s of d r y i n g during m o s t weeks, at all stations. Occasionally at higher values o f m, P m is less t h a n Pro-, f o r t w o reasons. First, as m b e c o m e s greater, t h e r e are f e w e r cases o f m d r y d a y s in sequence. T h u s , estim a t e s o f P m are based on smaller s a m p l e s and s h o w m o r e r a n d o m fluctuation. S e c o n d , for c o o l e r climatic c o n d i t i o n s , such as at N o r m a n d i n , or in S e p t e m b e r at o t h e r stations, d r y spells m a y o f t e n also be c o o l spells. In these cases h a y s w a t h s m a y n o t always d r y s u f f i c i e n t l y in f o u r days. In spite o f f l u c t u a t i o n s in Po, averaging o f t h e P ~ - - P o : P m - - P o r a t i o o v e r the season, as in T a b l e I, was justified. T a b l e I s h o w s t h a t this ratio was similar at e a c h o f t h e f o u r sites. T h e averages for all f o u r sites (Table I) were used in eq. 3 to g e n e r a t e a set o f curves o f critical F m values, s h o w n in Fig. 2, based o n selected F l values o f 1.0, 0.95, 0.9, 0.8, 0.67 a n d 0.5. T h e validity o f t h e F m curves in Fig. 2 was illustrated by showing t h a t Cm was c o n s t a n t with m a t d i f f e r e n t sites, t h r o u g h o u t the s u m m e r . Cm was calc u l a t e d f r o m eq. 1 at e a c h site o v e r the s u m m e r , f o r values o f m o f 1--4. T h e d i s t r i b u t i o n s f o r H a r r o w were p l o t t e d in Fig. 3. E a c h F m was c a l c u l a t e d f r o m eq. 3 f o r a o n e d a y f o r e c a s t reliability f a c t o r (F~) o f 0.95. T h e averages a n d s t a n d a r d d e v i a t i o n s o f Cm ~ C1 at all f o u r sites are given in T a b l e II. Using eq. 3 to d e f i n e F m resulted in d i s t r i b u t i o n s of Cm which s h o w

z

3~0

6I

JUNE

I 13

IFR E D/RICTON E

20

~~7

1.

I

5

. 18 . 25 .

JULY

.11

1~

.

.8

. 15 . 22 . 29 . AUGUST

5.

1

. 12

. 19 .

IR

19

SEPTEMBER

--3

.

.

.

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]

2

.

. 30 .

'!i

6

lO-

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JUNE

13

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20

1

27

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4

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18 JULY

11

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25

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1

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8

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AUGUST

1~

I

I 22

I

j9

[

0

2 1

m

[ 12

I

, ~9

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II

SEPTEMBER

;

I

Fig. 1. Chances of drying hay in 4 days or less w h e n the first m (0--4) days were dry, at (a) Fredericton, (b) Normandin, (c) Harrow and (d) Lacombe.

lo

oa

32 10-

8

Fm ,1

2

2

3

4

Fig. 2. Critical reliability levels for m rain-free day forecasts relative to the reliability level o f a o n e rain-free day forecast.

1°1 [

HARROW

Cm

i -

-

m

:

-

3

.....

r 3{}

r 5

l

I

r ~3

JUNE

2~)

r 21

T 4

, II

JULY

T 18

r 25

: 8

T ;b

AUGUST

:2

r 29

T 12

]g

SEPTEMBER

Fig. 3. Certainty o f drying hay in 4 days or less w h e n the first m days were forecast rainfree at critical levels o f reliability.

33 T A B L E II Averages a n d s t a n d a r d d e v i a t i o n s (sd) o f changes in c e r t a i n t y m ) 1, at e a c h t e s t site C2 -- C1

Fredericton Normandin Harrow Lacombe

(Cm, e x p r e s s e d

C3 -- CI

as %), for

C4 -- Cl (× 100)

Av.

sd

Av.

sd

Av.

sd

--0.28 0.59 0.22 0.28

1.72 1.51 1.50 2.66

--0.51 0.22 0.56 0.32

2.18 2.21 1.85 3.57

0.01 0.81 1.59 0.15

2.66 3.58 2.30 4.10

almost no change with respect to m at Harrow. Although not shown, plots of Cm at the other three test sites had as much over-lapping among the Cm distributions as did Fig. 3. It can be seen in Table II t h a t differences between Cm and C l are very small and that these differences are similar at all four sites. These small random differences are related to fluctuating differences in the increments in Pm in Figs. l a to l d . DISCUSSION

The value of knowing t h a t the first one or more days after cutting will be dry can be easily seen in Figs. l a to ld. However, there are critical levels of reliability with which the additional dry days must be forecast, in order to make them an improved basis for scheduling cuts of hay. To significantly improve certainty over P1, the reliability of forecasts for more than one dry day, as measured by the index defined here (Fro), must be above the curves shown in Fig. 2. Frequency distributions of the type shown in Fig. 3 lie between Po and PI because each Fm value was a function of F1. If a forecast of two dry days is known, and is more reliable than shown in Fig. 2, then the reliability of a three day (F 3 ) or four day (F4) forecast should be compared to the known value of F2 rather than to F~. To estimate F4 given the value of F2 substitute F 2 and P2 for F 1 and P~ in eq. 3. CONCLUSIONS

Reliable weather forecasts can increase the certainty of harvesting a hay crop before it is damaged by rain. In the long term, this means more good quality feed being produced from a given area of land. For two-, three- or four-day forecasts of dry weather to be of more value than cutting randomly, or on the basis of the appearance of the sky on the cutting day, there are critical levels of reliability which these forecasts must have. Also, this analysis depended on synoptic weather forecasts being more reliable than statistical expectations (fm ~ Rm) so that Fm ~ O. Because the actual reliability levels are not known, it was impossible to make a specific recommendation

34 a b o u t the best length of forecast for hay making here. Both farmers and forecasters should be aware of what the critical reliability levels are. Also, farmers should be informed of the confidence that the forecasters have in any given forecast. Long-term planning decisions associated with hay involve the type of harvesting machinery and storage facilities invested in by the farmer. The extra expense of systems that require less field drying can be justified by the reduction in weather risks. If scheduling cutting days according to weather forecasts can reduce weather risks as much as these systems do, then reliable weather forecasts could represent significant savings to many farmers. A factor which must be considered by hay growers is that as the scheduling of cutting becomes dependent on longer forecasts, the number of cutting days which can be expected each year decreases. For example, cuts based on the first three days being dry are possible less often than cuts based on the first two days being dry, because the average frequency of occurrence is less for three dry day sequences than for two (Dyer, 1980). Machinery and labour must be enough to ensure that both cutting and harvesting can be completed in fewer days. The techniques described here could be used to study the role of weather forecasts in other hay-making methods that involve periods of field drying. The use of simulation to study weather risk for different practices has been demonstrated (Dyer, 1980) and the influence of weather forecasts has been shown through simulation here. Equation 3 provides a straightforward way of calculating the critical values of Fm which produce the threshold distributions of Cm.

REFERENCES Borgman, E. and Brooker, D.B., 1961. The weather and hay-making. University of Missouri, Agric. Expt. Stn., B777, 8 pp. Dyer, J.A., 1980. Hay harvesting weather at selected sites across Canada. Tech. Bull. 91, Agrometeorol. Sect., Res. Branch, Agric. Can., Ottawa, 66 pp. Dyer, J.A. and Brown, D.M., 1977a. A climatic simulator for field-drying hay. Agric. Meteorol., 18: 37--48. Dyer, J.A. and Brown, D.M., 1977b. Hay-making risk levels in Ontario. Tech. Memo. 77-1. Dept. of Land Resource Sci., University of Guelph, 24 pp. (separately bound

appendix, 16 pp.). Dyer, J.A. and Selirio, I.S., 1977..A new method of analysis for hay-drying weather. Can.

Agric. Eng., 19: 71--74. Hayhoe, N.H. and Jackson, L.P:, 1974. Weather effects on hay-drying rates. Can. J. Plant

Sci., 54: 479--484. Moore, C.E., 1971. Production and handling of forages. Ontario Min. Agric. Food, Publ. No. 369, 20 pp.