Crop Yield Forecasting

meteorological statistical system.
2.1.4. 2.1.4. Models for for meteorology
The The basic basic statistical methods applied in in the the various meteorological institutions are are the the
following: key key meteorological factor factor model, model, yield yield decomposing model, model, climate suitability
model, model, vegetation index index model model or crop or crop growth simulation model. model.
I. Key Meteorological Factor Model:
I. Key The I. Key key Meteorological meteorological Factor Factor factor model Model: determines the relationship between crop yield and
The the The key key key meteorological factors model that model may determines critically the affect the relationship crop yields. The between common crop crop yield formula yield and and is the the
key based key meteorological on the simple factors factors multivariate that that may may regression critically affect set affect out crop in crop Equation yields. yields. The 2.5: The common formula is based is based
on on the the simple simple multivariate regression set set out out in in Equation 2.5: 2.5:
YY = YY aa = + aa bb + ! ×XX bb ! ×XX ! + ! bb + ! ×XX bb ! ×XX ! + ! bb + ! ×XX bb ! ×XX ! , ! , Equation 2.5 2.5
where Y stands for the yield of the specific crop; X 1 , X 2 , X 3 refer to the key meteorological
factors such as mean temperature, total rainfall and sun hours; a is constant and b 1 , b 2 , b 3 are
the coefficients of each weather factor.
where Y stands for the yield of the specific crop; X ! , X ! , X ! refer to the key meteorological
factors such as mean temperature, total rainfall 62 62 and sun hours; a is constant and b ! , b ! , b ! are
the coefficients of each weather factor.
II. Yield Decomposing Model
II. The Yield yield Decomposing decomposing Model model decomposes the yield (Y) into three parts: the potential yield
The (Y p ), yield the meteorological decomposing yield model (Y m
decomposes ) and the stochastic the yield yield (Y)(∆Y). into The three relevant parts: equation the potential is: yield
where (YY ! ), the Y meteorological stands for the yield (YY of ! ) the and specific the stochastic crop; X yield ! , X !
(∆YY). , X ! refer The relevant to the key equation meteorological is:
factors such as mean temperature, total rainfall and sun hours; a is constant and b
YY = YY ! + YY ! + ∆YY. Equation 2.6 ! , b ! , b ! are
the coefficients of each weather factor.
The potential yield yield (YY(Y ! ) p ) indicates the the optimal optimal crop crop yield yield under under normal normal weather weather conditions, conditions, which
II. Yield Decomposing Model
usually which usually follows follows an increasing an increasing trend due trend to due the to improved the improved productivity, productivity, breeding breeding and farming and
The yield decomposing model decomposes the yield (Y) into three parts: the potential yield
(YY technology. farming technology. Therefore, Therefore, YY ! is usually Y p is usually described described by a by a function of of time with a combination
of
! ), the meteorological yield (YY ! ) and the stochastic yield (∆YY). The relevant equation is:
historical of historical yields. yields. Various Various methods methods can be can adopted be adopted to estimate to estimate YY ! , such Y p , as such the as linear, the nonlinear,
piecewise, nonlinear, piecewise, linear
YY
running
= YY
linear ! + YY
averaging, !
running
+ ∆YY.
averaging, harmonic harmonic weighing weighing or exponential
Equation
or exponential smoothing
2.6
smoothing methods.
The methods. meteorological The meteorological yield (YY ! ) yield stands (Y m ) for stands the for effects the effects of weather of weather on yield, on yield, and is and usually is
The simulated potential by yield statistical (YY
usually simulated by ! ) indicates regression. the Typically, optimal crop the yield key meteorological under normal weather factor model conditions, (Equation which
statistical regression. Typically, the key meteorological factor model
2.5
usually above) follows is used; an other increasing statistical trend methods due to the include improved stepwise productivity, regression, breeding gradual and regression, farming
(Equation 2.5 above) is used; other statistical methods include stepwise regression, gradual
technology. integral regression Therefore, and the YY ! is multiple usually discriminant described by analysis. a function The stochastic of time with yield a (∆Y) combination refers to the of
stochastic
regression,
error
integral
and is
regression
often assumed
and the
to
multiple
be negligible
discriminant
in prediction
analysis.
(Wang
The
and
stochastic
He 2009).
yield
historical yields. Various methods can be adopted to estimate YY ! , such as the linear, nonlinear,
(∆Y) refers to the stochastic error and is often assumed to be negligible in prediction (Wang
piecewise, linear running averaging, harmonic weighing or exponential smoothing methods.
The III. and Climate meteorological
He 2009). Suitability yield Model (YY ! ) stands for the effects of weather on yield, and is usually
simulated Meteorological by statistical conditions regression. have a direct Typically, impact the key on crop meteorological growth and factor will model ultimately (Equation affect 2.5 the
above) crop yield. is used; In climate other suitability statistical model, methods temperature, include stepwise rainfall and regression, sunshine hours gradual are regression, considered
integral climate
III. Climate regression factors
Suitability
that and are the Model
critical multiple in discriminant measuring the analysis. impact The of stochastic the climate yield on (∆Y) crop refers growth to the at
stochastic
various periods. By integrating three climate factors, a synthetic Climate Suitability Index (CSI)
Meteorological error and conditions is often have assumed a direct to be impact negligible on crop in prediction growth (Wang and will and ultimately He 2009). affect
can be developed to estimate crop yield, by means of the following procedures (Liu et al. 2008;
Wei the et crop al. 2009; yield. Yi In et climate al. 2010). suitability model, temperature, rainfall and sunshine hours are
III. Climate Suitability Model
considered climate factors that are critical in measuring the impact of the climate on crop
Meteorological First, the impact conditions of each climate have a factor direct is impact described on crop by one growth suitability and will function ultimately based affect on fuzzy the
growth at various periods. By integrating three climate factors, a synthetic Climate Suitability
crop set theory: yield. In climate suitability model, temperature, rainfall and sunshine hours are considered
climate Index (CSI) factors can that be developed are critical
TT tt ! = ! !!! !" × to ! in !!
estimate !! measuring
! !
crop the yield, impact by means of the of the climate following on crop procedures growth at
! ! !! !" × ! !! !! !; Equation 2.7
various (Liu et periods. al. 2008; By Wei integrating et al. 2009; three Yi et ! climate al. 2010). factors, a synthetic Climate Suitability Index (CSI)
can be developed to estimate crop yield, by means of the following procedures (Liu et al. 2008;
BB = ! !!!!
Wei !"
First,
et
the
al. 2009;
impact
Yi
of
et
each
al. 2010). , Equation 2.8
! !" !! !"
climate factor is described by one suitability function based on fuzzy
First, set theory:
impact of each climate factor is described by one suitability function based on fuzzy
where T tt ! refers to the average temperature suitability for dekad i (ten days); tt ! stands for
set theory:
the average temperature for dekad i; and tt !" , tt !! and tt !" respectively indicate the lowest,
highest and optimal TT tt ! temperature = ! !!! !" × ! !! !! ! !
in dekad ; i.
Equation 2.7
! ! !! !" × ! !! !! !
!
BB = ! !!!! !"
,
RR rr = rr !/rr !! rr !" < rr !!
Equation 2.8
! !" !! !" , Equation 2.9
rr !! /rr ! rr !" ≥ rr !!
where T tt ! refers to the average temperature suitability for dekad i (ten days); tt ! stands for
where RR rr ! refers to the average rainfall suitability for dekad i; rr ! stands for the average rainfall
the average temperature for dekad i; and tt !" , tt !! and tt !" respectively indicate the lowest,
highest
for dekad
and
i;
optimal
and rr !" indicates
temperature
crop
in
water
dekad
demand
i.
(mm) for dekad i.
Crop Yield Forecasting: Methodological and Institutional Aspects 69
SS ss ! ee![(! !!! !! )/!] ! ss ! < ss !
RR rr , Equation 2.10
! = rr !/rr !! rr !" < rr !!
1 ss ! ≥ ss , Equation 2.9
rr !! /rr ! rr !" ≥ rr !! !