Agricultural and Forest Meteorology 101 2000 151–166
A parsimonious, multiple-regression model of wheat yield response to environment
S. Landau
a,∗
, R.A.C. Mitchell
b
, V. Barnett
c
, J.J. Colls
d
, J. Craigon
d
, R.W. Payne
e
a
Department of Biostatistics and Computing, Institute of Psychiatry King’s College, London SE5 8AF, UK
b
Biochemistry and Physiology Department, IACR-Rothamsted, Harpenden, Hertfordshire AL5 2JQ, UK
c
Department of Mathematics, University of Nottingham, Nottingham NG7 2RD, UK
d
Environmental Science Division, University of Nottingham, Sutton Bonington, Loughborough, Leicestershire LE12 5RD, UK
e
Statistics Department, IACR-Rothamsted, Harpenden, Hertfordshire AL5 2JQ, UK Received 8 February 1999; received in revised form 20 November 1999; accepted 23 November 1999
Abstract
A database of nearly 2000 yield observations from winter wheat crops grown in UK trials between 1976 and 1993 was used to develop a new model of effects of weather on wheat yield. The intention was to build a model which was parsimonious
i.e., has the minimum number of parameters and maximum predictive power, but in which every parameter reflected a known climate effect on the UK crop-environment system to allow mechanistic interpretation. To this end, the model divided
the effects of weather into phases which were predicted by a phenology model. A maximum set of possible weather effects in different phenological phases on yield was defined from prior knowledge. Two-thirds of the database was used to select
which effects were necessary to include in the model and to estimate parameter values. The final model was tested against the independent data in the remaining third of the data set 246 aggregated yield observations and showed predictive power
r=0.41, which was improved when comparing against mean annual yields r=0.77. The final model allowed the relative importance of the 17 explanatory variables, and the weather effects they represent defined before fitting, to be assessed. The
most important weather effects were found to be: 1 negative effects of rainfall on agronomy before and during anthesis, during grain-filling and in the spring 2 winter frost damage 3 a positive effect of the temperature-driven duration of grain-filling
and 4 a positive effect of radiation around anthesis, probably due to increased photosynthesis. The model developed here cannot be applied outside the UK, but the same approach could be employed for applications elsewhere, using appropriate
yield, weather and management data. ©2000 Elsevier Science B.V. All rights reserved.
Keywords: Winter wheat; Grain yields; Weather; Prediction; Parsimony
1. Introduction
A variety of mathematical models relating en- vironmental and management factors to crop yield
have been proposed throughout this century. Most of
∗
Corresponding author. Tel.: +44-0171-919-3313; fax: +44-0171-919-3304.
E-mail address: spakssliop.kcl.ac.uk S. Landau.
these models can be broadly classified as empirical regression-type models, derived from large amounts
of yield data, or deterministic crop simulation mod- els, based on experiments on crops and incorporating
knowledge of processes. Early investigations into the effects of climate on crops used regression-type mod-
els. Work on wheat yields in the UK was dominated by analyses of the relationship between climate variables
and crop yields from a long-term experiment the
0168-192300 – see front matter ©2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 9 9 0 0 1 6 6 - 5
152 S. Landau et al. Agricultural and Forest Meteorology 101 2000 151–166
Broadbalk wheat experiment at Rothamsted Fisher, 1924; Tippett, 1926; Alumnus, 1932; Cochran, 1935;
Buck, 1961; Thorne et al., 1988 and Chmielewski and Potts, 1995, amongst others. With these single-site
models, workers were able to find correlations be- tween observed and predicted yields in the range
0.45–0.6, thus explaining 20–35 of the variability in grain yields. Further wheatclimate investigations in
the UK include the early work of Lawes and Gilbert 1880; Hooker 1907 and Barnard 1936 and the
relatively recent work of Spence 1989.
Regression models have been criticised, since un- derlying mechanisms which transform climatic input
into yield are not explicitly described and the hierar- chical structure of the underlying physiological pro-
cesses is not taken into account Katz, 1977; Monteith, 1981; France and Thornley, 1984; Touré et al., 1994.
For example, monthly climatic effects predicted by a regression model are not easily interpreted from a
physiological background because the model can only be an approximation of the underlying processes, and
may fail to include some of them. Because of their empirical nature, regression models are restricted
to the range of climate data from which they are developed.
Advances in scientific understanding of the plant’s growth processes led to the formulation of determin-
istic growth models. They attempt to simulate the growth processes throughout the year by modelling
relevant plant processes. The Global Climate and Terrestrial Ecosystems GCTE group recognises that
there are at least 14 wheat models which attempt to account for physiological processes that gov-
ern wheat growth and development GCTE, 1992. Wheat simulation models applicable to UK climatic
conditions include AFRCWHEAT2 Porter, 1993, CERES-wheat Ritchie and Otter, 1985 and SIRIUS
Jamieson et al., 1998. Such models are widely ap- plied in decision support and studies of the impact of
climate change on wheat production.
Crop simulation models assume that the dynamic mechanistic process formulations can be represented
accurately, and that the model parameters can be correctly determined. However, of necessity, most of
the important processes within simulation models are described by empirical functions, since no models
exist for the enormously complex and poorly un- derstood mechanisms underlying phenology, canopy
development and senescence, partitioning etc. Thus, simulation models also cannot be used outside the re-
gion they were developed for with confidence. Young et al. 1996 argued that “a data-based mechanistic
modelling” philosophy is the way forward. This sug- gests a model category — a mechanistic and statistical
model — between the extreme modelling approaches outlined earlier which assume that either nothing or
everything is known about the crop-climate system. The means to achieve this is the derivation of the
most parsimonious model based on knowledge of the system; i.e. one that uses the minimum number of
parameters without losing predictive power.
In the present study, we employ a large yield data set from agricultural experiments on winter wheat
in the UK to develop a new model for predicting well-managed wheat grain yields from climatic in-
put. The objective of this work was to develop, as an example of the new methodology described ear-
lier, a parsimonious, empirically-based model which takes into account mechanisms of wheat growth and
development. In order to establish how well such a hybrid-model behaves in the multi-site, multi-year
UK environment, we also perform an extensive inde- pendent test of the suggested model.
2. Data sources and methods
