WORKABLE TIMEAMDTHE WEATHER
J.H. Portiek
The estimation oftheprobability distributions oftheworkable time for
farmoperations raises several questions.Some ofthese questions are discussed,leaning on the literature on the subject and the estimation of
distributions ofworkable time for combineharvesting ofwheat inthe
Netherlands.
INTRODUCTION
The short and long term decisions on a farm strongly depend on the amount of
workable time thatwillbe available forthe individual operations.This time
isdetermined directly and indirectly (i.e.viathe crop and soil)by the
weather and just as difficult topredict.However,it ispossible to estimate
theprobability distributions ofworkable time on thebasis of observations
made inthepast.Given these distributions,the farmer is able to estimate
the risk related to his decision and thus tomake anoptimum choice.
The estimation ofthese probability distributions raises several questions,
which are answered differentlyby the various authors.What isworkable time?
How can or should itbemeasured ?Howmany observât.ionsareneeded tomake
accurate estimates ofthe distributions ?What is the relationship between
this distribution andtheweather,andhencetheperiod (oftheyear) and
the geographical location (forthe same operation) ?These and related
questions are discussedbelow.
WORKABLE TIME
There appeartobe almost asmany definitions ofworkable time inthe literature asthere are authors.The investigations by Roth,Anton andBeyse(1),
Lermer (2),Hesselbach (3),Reboul ('t),AlHamchari,Desbrosses andMamoun
(5), DeWiljes andZaat (6),andBischoff andKnecht (7)canbe defined as
follows.
Observationsononeormoreweathervariablesandontheworkabletimefor
agiven(typeof)operationinagivenperiodaremadeduringasmall
numberof(calender)yearsonarelativelylargenumberofsites(farms).
Theythushavetheobservations:
U v ij> ïij)»i=1>2 >
' n j> J=1'2'
m where
)•
y..=numberofworkabletimeunits(hours,days)atsitenoiinyearnoj
x.•=weather=avectorofweathervariables,suchasthenumberofdry
hours,therainfall,themeanradiationintensity,etc.intheperiod
underexaminationatsiteno.iinyearno.j.
Whatismeantby"theweather"x.•variesfromauthortoauthor.Thecontent
ofy..variesaswell.Roth,AntonandBeyse(1),andHesselbach (3)observe
thetimeduringwhichthejobisinterruptedbyrain,deworfrost,while
therestofthegivenperiodisdefinedasworkabletime.Reboul (U)and
AlHamchari,DesbrossesandMamoun (5)takethetimeduringwhichaccording
toworkrecordsoffarmersconsultedtheoperationhasbeenexecuted.Lermer
(2), DeWiljesandZaat(6), andBischoffandKnecht(?)takethetime
whichissaidtobeworkableinthejudgementofthefarmer(whetherthe
operationisexecutedornot).
Thebestfittingcurvey.•= t(x..)isdrawnthroughtheobservations
^(y..,x..), i=1,2,
,n.;j=1
,m](accordingtosome
curve-fittingprocedure).
Finally,theprobabilitydistributionofthetransformationy=t(x)is
estimatedonthebasisof:
(a)theassumptions:foralli= '. ,2
,n. ,andj=1,2,
m,
x. .hasthesamedistributionasx,andProb|"x«xj=Prob
[yv<t(x)l ,for -».$x<»,and
(b)theobservations ix..,i=1,2,
m,m+ 1
,M.
j
They,thus,changeoverfromtheobservations (y-->i= 1,2,
j=1,2
j= 1,2,
,m}totheobservations [y.. ,i=1,2,
,m,m + 1 ,
n.;
,n.;
M'J.Bydoingso,many (M)observationson
yarecreated.Nowtwoproblemsarise.
Thefirstconcernstheinterpretationofy,orthemodelwhereinyasan
estimatorisimbedded.Althoughtheauthorsarenotveryexplicitonthis
interpretationitwouldbedefinedbythefollowingfourpoints.
(1)The number ofworkable hoursW is atransformation ofthe weather
x :W =T(x).Theweather isnot known apriari and istherefore seen
as arandom variable.The events Be=xl and W =T ( X ) J
(2)The observations (onx)x..,i= 1,2,
— —iJ
are equivalent.
,n. andj= 1,2,
J
m
aremutually independent and identically distributed (so,the n.locations ofobservation are assumed to lie in ahomogeneous area.)
(3)The observationy..differs fromT(x..)with anerror e.•:
y.. =T(x..)+ e..,where e.- is (assumedtobe) normally
—
ij
—
ij
—
ij
p
—
^
J
d i s t r i b u t e d with an expectation Be- • = 0 and variance Var e• • = 6
for
a l l i and j .
(1») Given x = x , y = t ( x ) i s an estimate of W = T ( x ) , i . e . t h e c o e f f i c i e n t s
of t ( x ) are e s t i m a t e s of t h e c o e f f i c i e n t s of T ( x ) .
Indeed, t h e number of workable time u n i t s i s not only a function of t h e
weather (and t h e crop and s o i l ) , but a l s o of a set of w o r k a b i l i t y c r i t e r i a
( t e c h n i c a l , economical, e t c . ) of t h e farmer. The workable time forms p a r t
of t h e management decision p r o c e s s , and depends on t h e d e c i s i o n c r i t e r i a
and c o n s t r a i n t s . In o t h e r words: every fanner has h i s own d e f i n i t i o n of
workable t i m e , and hence h i s own p r o b a b i l i t y d i s t r i b u t i o n of workable t i m e .
This view c l e a r l y disagrees with (a) t h e i n t e r p r e t a t i o n of z- • as an e r r o r
of observation or judgement, and (b) t h e assumption t h a t t h e p r o b a b i l i t y
d i s t r i b u t i o n of y . • does not depend on i . Another d i f f i c u l t y i s t h e accuracy
with which t h e p r o b a b i l i t y d i s t r i b u t i o n of W = T(x) i s e s t i m a t e d . This
accuracy i s a function of both t h e number of o b s e r v a t i o n s on x and t h e
(in)accuracy of t h e c o e f f i c i e n t s of t ( x ) (which, in t u r n , i s a function of
the number of p a i r e d observations on x and y, and variance of y ) . In most
c a s e s , however, t h e l a t t e r source of u n c e r t a i n t y i s not taken i n t o account.
Very important, of c o u r s e , i s t h e choice of t h e general form and t h e f a c t o r s
of T ( x ) , which i s f a i r l y a r b i t r a r y in t h i s approach.
In t h e most recent l i t e r a t u r e , we see a d i f f e r e n t approach. A f u r t h e r anal y s i s i s made of t h e workable time function, i . e . T ( x ) . This approach (see
Smith ( 8 ) , Kish and P r i v e t t e ( 9 ) , Baier ( 1 0 ) , Hassan and Broughton ( 1 1 ) ,
E l l i o t , Lembke and Hunt ( 1 2 ) , Ayres ( 1 3 ) , and P o r t i e k (ll*))can be summarized
as follows :
(1) The r e l e v a n t s t a t e s . ( t ) - at time t = 1,
1
K, in year no. j =
, m - of a given s o i l - c r o p - w e a t h e r system i s estimated by s . ( t ) =
f ( x . ( t ) ) , where x . ( t ) = weather at time t in year no j .
(2) The r e s e a r c h e r chooses some w o r k a b i l i t y c r i t e r i a . These c r i t e r i a divide
the p o s s i b l e values of s . ( t ) i n t o a s e t of workable s t a t e s and a set
of unworkable s t a t e s .
(3) The time i n t e r v a l ( t - p At, t + (1-p) A t ) , 0 < p < 1, At > 0, i s s a i d
t o be workable i f (and only i f ) s . ( t ) belongs t o the s e t of workable
states.
The values of p and At are chosen by t h e r e s e a r c h e r ; t h e most common
values of p are 0, g and 1 ; t h e most common value of At i s 1 (day or hour)
(1*) The number of workable hours (days) in a given p e r i o d in year no j , £ • , i s
found by counting t h e number of workable i n t e r v a l s in t h a t p e r i o d .
(5) The p r o b a b i l i t y d i s t r i b u t i o n of y , t h e number of workable hours (days)
in a y e a r , i s estimated on the b a s i s of the observations {f.,
j = 1 ,. . . ,m}
The advantages of t h i s approach l i e in t h e fact t h a t t h e w o r k a b i l i t y c r i t e r i a
are s t a t e d e x p l i c i t l y . Objective observations can be made on t h e s o i l - c r o p weather system and t h e influence of d i v e r s e w o r k a b i l i t y c r i t e r i a on t h e p r o b a b i l i t y d i s t r i b u t i o n of workable time can be examined e a s i l y .
Of course, the problems concerning the i n t e r p r e t a t i o n and accuracy of e s t i mation are s h i f t e d t o t h e formulation of s . ( t ) = f ( x . ( t ) ) .
To find s - ( t ) , some r e s e a r c h e r s take a small sample, ^ _ ( s . ( t ) , x . ( t ) ) , t =
—
J
—J
—J
1, 2 ,
K; j = 1 , 2 ,
, • ] , and then apply a c u r v e - f i t t i n g p r o c e dure.
Others make a f u r t h e r a n a l y s i s of s . ( t ) where, at the most elementary l e v e l of
a n a l y s i s , t h e c o e f f i c i e n t s a r e estimated by a c u r v e - f i t t i n g procedure, e s t a b l i s h e d by d i r e c t observation or deduced from the laws of n a t u r e .
In most c a s e s , t h e empirical b a s i s of t h e models i s very small. Apparently
(and for obvious reasons) t h e r e s e a r c h e r ' s a t t e n t i o n was devoted p r i m a r i l y t o
t h e b u i l d i n g and subsequent use of t h e model. For the future however, t h e
primary t a s k seems t o be t h e g a t h e r i n g of empirical d a t a .
WORKABLE HOURS FOR COMBINE-HARVESTING OFWHEAT IN THE NETHERLANDS
Concepts and data
An hour is saidtobeworkable for combine-harvesting if:
- the amount ofrain inthat hour« 0.1 mm.
- themoisture attached totheplants dueto rain inthat hour< 0.5 kg/ha.
- themoisture attached totheplants dueto condensation^ 0.5 kg/ha.
- thekernelmoisture content < q= 17,19,21,23,25, 21%.
Themoisture state ofthe crop (wheat,combine ripe)is calculated using a
model described byVan Elderen and VanHoven (15),with the inputvariables:
rain,cloudiness,vapour pressure,temperature,radiation,andwind velocity
l
^
1)
( a t hour t ) . The weather data are taken from De B i l t For every hour in t h e p e r i o d between J u l y 16th and September 30th, in t h e
period 1957 - 1968, t h e r a i n d a t a and t h e c a l c u l a t e d moisture s t a t e s are
compared with the w o r k a b i l i t y c r i t e r i a . The numbers of workable hours in
periods of 1, 2 , 3, h and 5 half-months, in t h e 2k hours day and p a r t s
of
t hII
e day,16.
are-then
e s t a b l i s h e d . The half-months a r e :
July
31. July
Aug I
Aug II
Sept I
Sept II
1. - 15. August
16. - 31. August
1. - 15-
September
16. - 30. September
The numbers of workable hours i n d i f f e r e n t years at the same place
and in
t h e same period of t h e year are assumed t o be mutualLy independent and
i d e n t i c a l l y d i s t r i b u t e d . The f i r s t p a r t of t h i s assumption (mutual idependence) has been t e s t e d on t h e observations and not r e j e c t e d a t t h e 5$-level
of s i g n i f i c a n c e . ( S e r i e s t e s t on o b s e r v a t i o n s , De Jonge ( 1 6 ) ) . The second
p a r t ( i d e n t i c a l d i s t r i b u t i o n ) could not be t e s t e d , but seems t o be a c c e p t a b l e ,
since these numbers of workable hours are generated by t h e same c r i t e r i a ,
the same crop and ( p r a c t i c a l l y ) t h e same climate system.
F i g s . 1 - 5 show t h e cumulative frequency d i s t r i b u t i o n s of t h e workable hours
in J u l y I I , Aug I , Aug I I , Sept I , and Sept I I , r e s p e c t i v e l y for combine h a r v e s t i n g a t maximum k e r n e l moisture contents of 17, 19, 2 1 , 2 3 , 25 and 21%.
The small numbers are year numbers: 1 = 1957, e t c .
1) Meteorological s t a t i o n i n t h e centre of The Netherlands.
R~-,
m
a
2°
S3—-J
«•*-•• a l
Q S
eS—»«
!»
J
\\Y
V. ^
SE--»' 1 \ \ r
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\ \ " »-3 =
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r*~s
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v
o
=
aèl
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a
=' ~
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se I
^ ^"""•s^S
10
=
-
\
='
oo
«0
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ci
(0
* •
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a
^""""•»ji
<P
7^
— œ
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o
ai
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co
oo
C
M
i-
o
2°
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SzqsrzzzzTz
•a
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O -g
co E
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= £ CM
T-
o
a)
oo
r» co m
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<-
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m
en
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2°
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os
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in
a
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to m
co
CM
t-
o
Fig.5Cumulative frequency distributions of
the
numbers ofworkable hours forcombine harvestingatmaximum kernelmoisture contents
of 17,19,21,23,25and277»inSept II(all
hours).DeBilt,years 1= 1957,
,
12= 1968.
CUIT l u l a t i v e
17
19
*
freel u e n c y
12
11
10 -
10
9—
10. -
*m
V"^
6
J
y
8
5J
87
7
117
"•
*f
5
h
/8
V
I
»5
7J
9
»
h
2
0
I5
iY
\\J
11J
2 /
*&,
YS
iJ
y
•' ' ^ />n
2
1
0
m
~7w /*
*J
/
H'
3
2
7;
4 /
9 /
61
/
5 h
4
9V*
J6
Q
6
y^lO
10
2123 2527
3
3
\£*
C)
40
80
120
160
200
240
N u iTiber of w o r k a ble h o u r s
T a b l e 1. Means and s t a n d a r d d e v i a t i o n s ( s . d . ) o f t h e numbers of w o r k a b l e
h o u r s f o r c o m b i n e - h a r v e s t i n g a t maximum k e r n e l m o i s t u r e c o n t e n t s
of I T , 1 9 , 2 1 , 2 3 , 25 and 2f%t i n t h e h a l f - m o n t h s J u l y I I , Aug I ,
Aug I I , S e p t I and S e p t I I . De B i l t , 195T - 1968.
Maximum k e r n e l moi s t u r e c o n t e n t {7
July II
Aug
I
Aug I I
Sept I
Sept I I
21
23
25
w.b.)
27
17
19
mean
1*9.3
93.3
128.7
156.1
172.7
182.9
s.d.
56.6
69.1
65.7
6O.5
52.7
1+8.6
mean
3 0 .k
7^.7
109.6
1 3U, 3
151.5
165.5
s.d.
33.0
37.3
37.8
37.3
36.3
35.0
mean
26.6
73.6
106.9
131.5
11*6.6
159.8
s.d.
29.3
57.2
67.0
71.0
68.9
65.2
mean
38-8
•61.8
83-5
101-8
118-2
132-8
s.d.
73.1
85.1
86.9
83.9
77.7
71.5
mean
13.9
33.5
58.5
89.3
108.3
122.1+
s.d.
36.5
62.8
66.1
62.7
63.9
65.1
Table 2. Mean numbers of workable hours for combine-harvesting at maximum
k e r n e l moisture contents of 17, 19, 2 1 , 2 3 , 25 and 27%in a h a l f
-month in four 6-hour p a r t s of the day, in percentages of t h e
mean number of workable hours in a l l hours of t h e day. De B i l t ,
1957 _
1968.
hour s of
Half-month
July II
Aug I
Aug II
Sept I
Sept II
4
10
the day
Maximum kernel moisture content (#w.b.)
17
19
21
23
11
25
27
12
13
12
25
0-
6
12
12
6-
12
23
21
23
25
21*
12-
18
32
36
18-
2k
33
35
32
30
35
28
35
28
28
0-
2k
100
100
100
100
100
100
10
10
10
25
26
26
35
0-
6
13
12
10
6-
12
18
19
22
12-
18
35
37
37
37
36
37
18-
21*
3k
32
31
28
28
27
0-
2k
100
100
100
100
100
100
0-
6
16
13
12
12
12
12
6-
12
16
16
21
22
22
22
12-
18
31+
39
38
38
39
1+0
18-
2k
31*
~2
29
28
27
26
0-
2k
100
100
100
100
100
100
0-
6
15
15
15
13
12
12
6-
12
25
23
23
22
23
23
12-
18
33
36
37
1*0
1*0
1*1
18-
2k
27
26
25
25
25
21*
0-
2k
100
100
100
100
100
100
0-
6
25
18
16
11*
12
16
17
19
20
12-
18
27
36
19
38
15
18
15
6-
ko
1+1
1*2
18-
2k
32
29
27
27
25
2k
0-
2k
100
100
100
100
100
100
These frequency d i s t r i b u t i o n s Tary with the maximum k e r n e l moisture c o n t e n t ,
both with respect t o t h e i r l o c a t i o n and shape. ( F i g s . 1 - 5 ) .
Table 1 gives t h e a r i t h m e t i c means and the standard d e v i a t i o n s . The mean
i n c r e a s e s with i n c r e a s i n g maximum k e r n e l moisture c o n t e n t , while the standard
deviation v a r i e s only s l i g h t l y .
In t h e course of t h e season (from J u l y I I t o Sept I I ) , the number of workable
hours for combine-harvesting in a half-month appears t o d e c r e a s e .
Table 2 gives the mean percentage d i v i s i o n of t h e number of workable hours
in a half-month i n t o four 6-hour p a r t s of t h e day, i . e . 100.y. ,z,
where z=.Ï, y . , and y. = 1/12 I
y . . , i = 1,
- i=1 ii'
ii
. •'-ij
15(16) 6
15(16)12
y-• = £
£ x., ;y„.=
l
l x., y,. =
Xl
J
k=1 m=1 " J k m - 2 j k=1 m=î- J k m ; " 3 j
, 4 , where:
E
15(16) 18
I
x., ;
k=1
m=13 " j k m
15(16) 21*
x
z x.,
k=1 m=19 " J k m
y,•=
"^
x., =numbers ofworkable hours in ahalf-month inyearno j , in
-Jkm
hournom ofdayno k.
Only little over 50% ofthenumber ofworkable hours are daytime hours
(0600 - 1800hours). Thispercentage of daytime hours increaseswith
maximumkernelmoisture content.
Estimating probabilities: accuracy andnumber of observations
Theobserved cumulative relative frequencies (Figs. 1 - 5 ) areconsidered as
estimates ofthe cumulative probabilities ofthe number ofworkablehours.
What isthe accuracy ofthese estimates ?
Take as ameasure of accuracy the 95%confidence intervals ofthe estimated
cumulative probabilities. (See Fraser (17)).
Let y, ,,y
,
,y/ >be the realisations - ranked inorder ofmagni-
tude -ofthe number ofworkable hoursy. The 93% confidence interval for
p. =Prob[Y<y .1 ,i= 1,
,12,is constructed as follows.
Consider thetest with nullhypothesis (H
p_ ,alternative hypo-
0
thcesis (H ) :p. ^p ,and teststatistic i=the numherof realisations
that are smaller or equal toy,.*.Under H ,this teststatistic ihas a
0'
12.
p and n
binomial d i s t r i b u t i o n with parameters p.
H i s r e j e c t e d i f Prob T i < i ; H J
i 0.025 or Prob \ i > i ; H I ^ 0 . 0 2 5 The upperbound, b„ , of t h e 95% confidence i n t e r v a l for p . i s t h e smallest
«i ;
< 0.025.
H0]
The lower bound, b , i s t h e l a r g e s t p for which Prob [ i > i ; H J < 0.025
Thus, we find:
(b < p. « b ) .
S0.31*
^ p1
« P2
0
0
«0.UU
0.02
<c P
0.09
< pU 5;0.66
« p5 « 0.73
^ p6 « 0.79
« p7 «O.85
« p8 < 0.91
^ P ^ 0.95
9
^ P ^ 0.98
10
« P11 «1
^ P10 <1
0.15
0.21
0.27
0.3U
0.1(2
O.52
O.67
O.78
« O.58
3
12
This accuracy leaves much t o be d e s i r e d .
Moreover, t h e s e i n t e r v a l
show t h a t a t e s t based on t h e 12 observarions i s
not very powerful. (Power defined as t h e p r o b a b i l i t y of r e j e c t i n g H in
favour of H , when H i s f a l s e ) . This means t h a t only l a r g e differences
between t h e n u l l - and t h e a l t e r n a t i v e hypothesis can be shown.
In order t o estimate with g r e a t e r accuracy and t e s t with more power, more
observations are needed. The minimum number of observations required for
g r e a t e r accuracy and power i s given by:
T
1-a • ' P W
P n -P
12
+
T
1-
• /p/1-p/
2
, (16)
where: n=number ofobservations required
1-a=probability ofnot rejectingH
1
T
n , when H- istrue.
=probability of rejecting H ,when H_ is false.
,T
= (1-a)and (1-ß)percentage points ofthe standard
i-ts
1i-a'
normal distribution
values of p = Prob Ty < y] s p e c i f i e d in H and H
•1
0.05 and 0 . 1 0 , and s e v e r a l values of
The values of n for p = 0 . 5 , a
p are as follows:
0.05
0.10
0.45
1536
0.1*0
3T6
655
161
- p \.a=ß=
0.35
163
69
0.30
88
0.25
53
37
22
0.20
31*
11*
Differences between the half-months
There are two reasons for studying more c l o s e l y the differences between t h e
observations of workable hours i - d i f f e r e n t half-months. In the case of
non-systematic d i f f e r e n c e s , t h e observations may be considered t o have t h e
same d i s t r i b u t i o n and (1) we have more than one observation per y e a r , and
(2) the user needs t o apply only one d i s t r i b u t i o n .
Table 1 and F i g s . 1 - 5 suggest t h e hypothesis t h a t the p r o b a b i l i t y d i s t r i bution of the number of workable hours changes s y s t e m a t i c a l l y in the course
of t h e period J u l y I I - Sept I I . To t e s t t h i s h y p o t h e s i s , T e r p s t r a ' s t e s t
i s applied (16).
The t e s t :
Given: k random samples : i y. . , j=1,
, n. ] , i=1,
, k.
N u l l h y p o t h e s i s , H : the samples are from the same population
Alternative
, H : t h e samples are not from t h e same population and show
a decreasing ( i n c r e a s i n g ) t r e n d in the order 1, 2 , . . . , k.
13
T e s t s t a t i s t i c : form p a i r s of the samples: ( 1 , 2 ) , ( 1 , 3)
, (1
t)
(2> 3 ' >
» ( 2 > k )>
> (k-1 , k ) . Assign t o the observations of p a i r
( i , in), i = 1,
, k - 1 ; m > i , ranks from 1 to (n. + n ) . Where n =
1
m
i
number of observations in sample i ) .
The t e s t s t a t i s t i c i s t h e n :
n.(n.+n +1) - 2S.
W= E — i — i — S
Ü L .
n.1nm
Km
where S^m =the sum ofthe ranks assigned to sample iinthepair (i,m).
The casen , = n 2 =
=n
v=n yields:
nk(k-l) (2n+l)- U.E. S. .
X
<J - ^ J
2
2n
with expectation EW= 0 and variance
W=
-
2
aw
=
nMk+1-2i)2 •
i=i
z
% l i
—r
2
3n
W
The random v a r i a b l e T =-Si s N(0,1) d i s t r i b u t e d .
Applications of T e r p s t r a ' s t e s t :
(a) Observations: the number of workable hours for combine-harvesting at a
maximum k e r n e l moisture content of 23% in the k=5 half-months, J u l y I I
- Sept I I , in t h e n=12 y e a r s , 1957 - 1968, at De B i l t .
R e s u l t s : W= -3.1527, (J 2 = 1.13U2, and T = - 2 . 9 6 0 3 .
W
SinceProb [ T «-2.9603]= 0.00154,H is rejected.
(b)Observations: as (a),except Sept II,sok=U.
Results:W =-0.1736,C 2 = O.569U,andT = -0.2308.
Since Prob [ T «:-0.2308)= 0.U090,H Q isnot rejected.
Now, it is interesting to examine two related (and relevant)weather variables.
(c)Observations:themean daily rainfall (mmday )inJuly II,Aug I,Aug
II,Sept I andSept II inthe 12years 1957- 1968at deBilt (Table3 ) .
Results:W = -0.9062,O 2 = 1.13^2,and T=-O.8509.
Since P r o b T ï <$-0.8509J= 0.1977,H Q isnot rejected.
14
(e)Observations: as (d),except Sept II.
Results:W = -3.9722,<S^=O.5691»,andT = -5.2807.
Since Pro"b[T« -5.2807] ï 10~ ,H is rejected.
(f)Observations:as (d),except Sept I andSept II.
R e s u l t s : W = -1 .6320, 0"^ = 0.2292, and T = -3.*t092.
Since Prob [ T « -3.>+092] = 0.000337, H i s r e j e c t e d .
We may conclude t h a t the number of workable hours for combine-harvesting per
half-month tends t o decrease s y s t e m a t i c a l l y , in t h e course of the cereal h a r vesting p e r i o d , i . e . September i s l i k e l y t o have fewer r a t h e r than more
workable hours than August.
In t h i s h a r v e s t i n g p e r i o d , the "wetting c o n d i t i o n s " ( r a i n ) are nearly the
same, but t h e "drying c o n d i t i o n s " ( r a d i a t i o n ) get worse.
R e l a t o i n s h i p between the number of workable hours and the weather
There i s , of course, a r e l a t i o n s h i p between the number of workable hours and
one or s e v e r a l of the f a c t o r s " r a i n " , r a d i a t i o n " , and "wind v e l o c i t y " . But
t o what extent and i s t h e r e a ( p r a c t i c a l l y acceptable and usable) simple
formula for the estimation of the workable time from weather data ?
Given are 12 observations of:
y = number of workable hours for combine-harvesting in a given period
x = rainfall (mmwater) inthe same period
x = accumulated hourly measurements ofradiation,cal cm
.
.
x-j=accumulated hourly measurements ofthewind velocity,cm sec
-2
-1
Table 5gives Spearman'srankcorrelation coefficients (16) forthe relationshipbetween the number ofworkable hours (y)and rain (x..),radiation (x„)
andwind velocity (x.,)respectively.
Table 5shows that the number ofworkable hours isto a significant degree
governed by the factors rain and radiation,and notby the factorwind
velocity. Some results of acurve fitting analysis aregiven inTable 6. The
analysis is carried out onthe observations (12years,De Bilt)of:
15
Table 3. Mean daily rainfall atDe Bilt inJuly II,
Year
July II
1957
4.33
58
4.20
59
2.28
1.1+7
60
1.23
1*.23
61
1.43
62
Aug I
,Sept II.(mmday )
Aug I I
Sept I
Sept I I
5.12
5.27
6.25
7.20
2.88
2.1*6
1.57
It. 78
0.20
0.01
0.20
5.26
1.33
0.79
2.03
3.11*
3.01
1.1*5
2.79
2.69
1.91*
2.13
1.lt7
63
0.45
lt.52
7.29
2.88
2.55
61*
1.81+
1.87
3.32
3.17
1.26
O.85
65
4.85
1.96
5.91
1*.01
66
10.50
3.27
1.56
3.23
0.01
67
1 .02
5.37
1.81*
2.52
2.33
68
1.1*3
1*.82
2.65
2.32
6.25
mean
3.03
3.35
3.1*1
2.70
2.1*3
Sept I
Sept I I
6.05
Table 1*. Mean ofhourly measurements of radiation atDe Bilt in
_2
July II,
,Sept II. (cal cm )
Year
July I I
Aug I
Aug I I
1957
15.32
12.69
11 .41
9.1+1
58
15.79
12.66
13.93
11 .69
7.78
59
20.61*
13.16
17.14
15.58
9.86
60
13.98
13.16
10.17
10.63
8.53
61
15.15
13.58
11.63
9.54
8.74
62
16.71
13.98
15.27
12.91
8.90
63
19.98
12.06
9.82
11.31
6.49
61*
17.58
14.02
14.32
11.39
10.45
65
11*.06
17.72
13.13
9.98
9.05
66
14.53
14.29
14.05
10.53
8.02
67
19.16
13.66
13.68
9.19
7.92
68
16.51
mean
16.62
16
I
12.07
13.72
10.53
6.61
13.59
13.19
11.06
8.20
y = number of workable hours for combine-harvesting at a maximum kernel
moisture content of 23% in a given period,
x and x = r a i n and r a d i a t i o n , as defined above, in t h e same p e r i o d .
The values â, b" and c are the l e a s t square estimates of the model c o e f f i c i e n t s a, b and c , r e s p e c t i v e l y . Transformations are In y = In a + b In x , for
y = ax , In y = In a + bx for y = ae , and In y + In a + b In x + c In x
be
for y = a.x:x0. When A i s the l e a s t square estimate of In a, then â = e .
A
Very i n s t r u c t i v e a d d i t i o n a l information i s given in F i g s . 6 and 7, shoving the
r e l a t i o n s between y , the number of workable hours for combine-harvesting at
a maximum k e r n e l moisture content of 23%, and t h e r a i n f a l l (x..)
and r a d i a t i o n
(x ) , in t h e period July 16th - September 30th. Spearman's rank c o r r e l a t i o n
c o e f f i c i e n t s are -0.65 (Fig. 6) and +0.65 (Fig. 7 ) , i n d i c a t i n g t h a t t h e b e s t
f i t t i n g curve g r e a t l y depends on t h e presence of the two extreme p o i n t s .
Without t h e s e extremes, as i s the case in most periods of one, two or t h r e e
half-months, the r e l a t i o n s h i p i s very poor. (The r a n k c o r r e l a t i o n c o e f f i c i e n t s
are not s e n s i t i v e t o l e v e l differences in t h e o b s e r v a t i o n s ) .
Apparently, the number of workable hours in a period i s not a simple function
of some simple r e p r e s e n t a t i v e s of the weather in t h a t p e r i o d . The addition
of o t h e r f a c t o r s does not give much b e t t e r r e s u l t s . Presumebly, the most
important " f a c t o r " in addition t o r a i n (x ) and r a d i a t i o n (x ) i s the d i s t r i bution of these weather factors over time.
17
Table 5.
Spearman's c o e f f i c i e n t s ofrank c o r r e l a t i o n between numbers of
workable hours for combine-harvesting at maximum kernel moisture
contents of 17, 19, 2 1 , 2 3 , 25 and 27% and (1) the r a i n f a l l , mm,
-2
(2) t h e r a d i a t i o n , c a l cm , and (3) the wind v e l o c i t y , cm sec ,
-1
in half-month p e r i o d s .
Observations from De B i l t in t h e years 1957 - 1968.
Maximumkerne 1moisture
19
17
JulyII
AugI
AugII
SeptI
SeptII
rain
25
-.76**
-.76**
-.81***
85**
.79**
-.1*8
.78**
76**
-.50* .88**
63**
81***
wind
-.1*1*
1*1
.79**
-.1*8
27
-.50
1*1
30
.06
06
-.23
-.30
.21*
radiation
-.10
11*
.10
.29
.30
19
wind
-.28
09
.10
•05
.10
33
rain
-.51*
66**
-.76**
-.76**
-.77**
radiation
.79**
-.11
83**
wind
.91**
-.18
-.03
-.03
rain
-.50*
-.55*
rain
-
16
-
03
-.62**
.88**
.1*3
.1*8
.1*5
87**
1*6
69**
-.81**
-.76**
-.81**
81**
73**
60**
.71**
.1*8
.1*8
1*8
-.21*
-.23
23
wind
."•9
1*1
rain
-.33
.53
.00
5% l e v e l
88**
.90**
.85**
63**
66**
s i g n i f i c a n t at ~\0% l e v e l
7U**
-.63**
.76**
** s i g n i f i c a n t at
.89**
-
.76**
radiation
wind
18
23
radiation
radiation
*
content {%w .b.)
21
-.27
-
53*
Numberof
workable hours
1400
1300
1200
1100
1000
900
800
^v *
700
^v_
600
•
500
N^\? •
•
400
r2=0,76
•
—
300
200
r2=0,64Ss
100
0
100
200
300
400
500
xi Rain,mm
Fig. 6 Relation between t h e number of workable hours
for combine-harvesting at a maximum k e r n e l
moisture content of 23% (y) and the r a i n f a l l
(x ),mm. in the period J u l y 16th September 30th.
Observations De B i l t 195T-1968
19
Number of
workable hours
1400
1300
1200
•
r2 = 0,77
1100
1000
900
800
700
•
600
<
500
•
•
jé
•
•
•
400
r»
300
200
100
J\ _
0
200
220
240
260
280
300
(xioo)
x 2 Radiation ,cal-cm 2
F i g . 7 Relation between t h e number of workable hours
for combine-harvesting at a maximum k e r n e l
moisture content of 23$ (y) and t h e r a d i a t i o n
(x ), c a l cm , i n t h e period J u l y 16th September 30th.
Observation De B i l t 195T- 1968.
20
T a b l e 6 . R e s u l t s o f a c u r v e f i t t i n g a n a l y s i s . (De B i l t , 1957 - 1968)
y = number o f w o r k a b l e h o u r s f o r c o m b i n e - h a r v e s t i n g i n t h e g i v e n
period.
r a i n , xp = radiation (see t e x t ) .
-1
â , "6 and c a r e t h e l e a s t s q u a r e e s t i m a t e s o f t h e model c o e f f i c i e n t s
a, b , c.
2
r = c o e f f i c i e n t of determination.
Period
Model
Coefficients
â
J u l y 16th - Sept 30th
J u l y 16th - Aug 3 1 t h
Sept 15th
Aug 1 5 t h - - S e p t 3 0 t h
r2
y=a+bx ( F i g 6)
1037.61
bx
y = a e -1
1135.65
b
( F i g . 6 ) 12761.56
=a
y ïi
y = a + b x 2 ( F i g 7) - 1 3 2 1 . 1 7
bx„
y=ae - 2
36.78
-1.85
0.61*
-2.8767x1Ö3
0.72
-O.58
O.76
y=a+bx +ex
b c
ï-aïlÏ2
-0.7806
y=a+bx 1
b~
- 592.20
O.083I
0.77
-1*
1.1895x10
2 . 7 9 5 6 x 1 Ö 3 -0.35^*9
0.73
5 95x1Ô 2
0.822
1*081
O.825
1
65>+.20
-1.5170
O.69
-0.5069
0.70
ïl
5098.98
y=a+bx2
-1*83.13
y=a+bx 1
668.73
-2.0736
0.73
y=ax1
5201.76
-O.5615
O.56
y=a+bx2
-757.25
y=a+bx 1
b
y=ax1
600.28
- 2 . 1 1 31*
2307-21*
-O.U563
0.59
y=a+bx2
-91*0.11*
0.1053
0.81*
ï
Aug 1 t h -
c
13
=a
5.5*+xl5 2
8.0707X1Ô 2
O.6O
0.61*
0.62
21
Conclusions
The amount ofworkable time is a function ofboth thepossibility andthe
utility of cultivating the crop andthe soilwithin afarm. Thus,every farmer
has his own definition ofworkable time,sothat the researcher has to consider several definitions ofworkabletime.
The location and shape oftheprobability distribution ofworkable time depend
onthe exact definition ofworkabletime.
Under theclimaticconditions oftheNetherlands,the variance ofthe number of
workable hours is very large.A sufficiently accurate estimation oftheprobability distribution ofworkable time needs,therefore,many observations: over
many years and inmanyplaces.
Theprobability distribution ofworkable time depends ontheweather,andhence
ontheperiod oftheyear (andthe geographical location).
Not only the amounts ofrain,radiation,wind velocity,etc. determine the
number ofworkable hours in agivenperiod,but alsothe distribution ofthese
amounts overtime.
22
References.
(1) H.A. Roth,A.Anton und 0.Beyse.
Agrotechnische Zeitspannen und verfügbare Zeiten für die Feldarbeit.
VEB Deutscher LandwirtschaftsVerlag.
(2) J . Lermer.
Arbeitszeitspannen und verfügbare A r b e i t s t a g e u n t e r dem E i n f l u s s von
Klimaund Bodenart im niederbayerischen Raum.
Bayerisches Landwirtschaftliches Jahrbuch, 38. J a h r g . , Heft 2/1961.
(3)
J . Hesselbach.
Zur Ermittlung a r b e i t s w i r t s c h a f t l i c h e r Daten hochmechanisierter E r n t e verfahren.
KTL-Berichte über Landtechnik 122 (19-68).
(U) C. Reboul.
Heures d i s p o n i b l e s pour l e moissonnage-battage des c é r é a l e s t a r d i v e s
en fonction des conditions de stockage.
B u l l e t i n des CE.T.A. - Mai 1966. Etude F.N.CE.T.A. - No. 1.129.
(5) M.C. Al Hamchari, B. Desbrosses, M. Mamoun
Pluviométrie et j o u r s d i s p o n i b l e s pour l e s travaux de champs.
INRA - P a r i s , 1975(6)
H.G. de Wiljes and J.C.A. Zaat.
The Influence of climate upon t h e number of weather-working hours in
combine-harvesting in the Netherlands.
Arch. Met.Geoph. B i o k l . , Ber. B, 16, 105 - II1* (1968) .
(T) Th. Bischofund G.Knecht.
ZurErmittlung von verfügbaren Feldarbeitstagen.
Berichte über LandwirtschaftU8(1970-2 ) .
(8) C.V. Smith
Weather and the grain harvest
Ann. Technol. a g r i c , 1973,22(3).
23
(9) A.J.Kish and C.V. Privette.
Number of fieldworking days a v a i l a b l e for t i l l a g e in South Carolina.
ASAE-paper No. 7U-I019.
(10) W.Baier.
Estimation of fieldworkdays inCanada from the versatile soilmoisture
budget.
Can.Agr.Engng.Vol. 15,No. 2,December 1973.
(11)
A.E. Hassan and R.S. Broughton.
Soilmoisture criteria for tractability.
Can.Agr.Engng.Vol. 17,No.2,December 1975.
(12) R.L.Elliot,W.D. Lembke andD.R. Hunt.
A simulationmodel forpredicting available days for soiltillage.
ASAE - 75-1501.
(13) G.E.Ayres.
A simulationmodel forpredicting days suitable for corn harvesting.
ASAE - 75-1502.
(1U) J.H. Portiek.
Werkbare uren voor de graanoogst.
IMAG,publ. 3h.
(15) E.vanElderen andS.P.J.H, vanHoven.
Moisture content ofwheat intheharvesting period.
J. Agric.Engng.Res.,(1973) 18,71 -93.
(16) H. de Jonge.
Inleiding tot demedische statistiek,I enII.
Leiden,1958.
(17) D.A.S. Fraser.
Statistics,an Introduction.
Wiley &Sons,1958.
24