NOT
FOR QUOTATION WITHOUT PERMISSlON O F THE AUTHORTHE
ROLEOF
AG-TIC MODEISIN
ClJliM"I' W A C T ANALYSIS
T.R. Carter N.T. Konijn
RG.
WattsNovember 1 9 8 4 WP-84-98
Working Rzpers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute or of its National Member Organizations.
INTERNATIONAL
INSTITUTE
FOR APPLIEDSYSTEMS
ANALYSIS 2361 Laxenburg, AustriaPREFACE
In 1983 IlASA initiated, with support from t h e U.N. Environment Programme, a two-year project on climatic impact analysis. I t is being implemented by a small in-house core group with a collaborative network of 72 scientists working on 11 case studies a r o u n d t h e world.
The overall goals of this project a r e first, to evaluate t h e impact of climatic change and variability on food grain a n d livestock production, a n d second, t o assess appropriate policy responses to reduce the impacts of climate on agriculture. Each of t h e 11 c a s e studies has a t e a m of 4 t o 6 scientists which includes crop-climate and economic modelers, and a high-ranking agricultural planner. Outputs from cli- m a t e models (or from instrumental climatic records) a r e used as inputs t o impact models t o predict actual or potential yield responses t o climatic changes. Compati- bility between t h e case studies is e n s u r e d by using t h e same types of climatic scenario a n d similar types of impact model. To t r a c e t h e "downstream" effects of yield changes, outputs from t h e impact rnodels a r e used as inputs t o economic models (e.g. farm simulations, regional input-output models). Finally, agricultural planners or ministers of agriculture a r e being asked t o evaluate t h e range of poli- cies available for impact mitigation.
The c a s e studies are being collected together i n t o a n integrated s e t of climate impact assessments, the integration being achieved by methodological studies which seek to describe how different modeling approaches relate t o each other.
This paper by Carter, Konijn a n d Watts provides a n overview of t h e use of agro- climatic models in climate i m p a c t analysis, a context against which t h e case study models can subsequently be evaluated.
We acknowledge t h e financial support of t h e United Nations Environment Pro- g r a m m e a n d t h e Austrian Government for this work.
Dr. Martin Parry Leader
Climate Impacts Project
1. Introduction
2. Climate a n d t h e Crop Production System 2.1. Crop Production a n d Climate
2.2. Constructing a Farm Calendar 2.2.1. Crop Requirements
2.2.2. Fulfilling t h e Requirements 2.3. Long-Term Effects of Crop Production 3. Modeling t h e Crop Production System
3.1. Climate-Based Vegetation Mapping 3.2. Classifying Agroclimatic Models
3.3. Evaluating t h e Utility of Agroclimatic Models 3.3.1. Objectives
3.3.2. Logistics
3.3.3. Assumptions a n d Sources of Error 3.3.4. Validation
3.4. Agroclimatic Models in Climate Impact Analysis 3.4.1. Model Relationships
3.4.2. Model Runs for F u t u r e Climate
4. Exploring Model Sensitivity t o Climate: Two Experiments
4.1. Experiment 1. The Temporal Resolution of Input Data a n d Its Effect on Yield
4.2. Experiment 2. Comparing Short-Term a n d Long-Term Sensitivity of Yield t o Climatic Change
5. Agroclimatic Model Checklist 5.1. Model Components 5.2. Model Operation 6. Conclusions
References
THE ROLE O F AGROCUMATIC MOD= IN
CLIMATE
IMPACT ANALYSIST.R Carter, N.T. Konijn and
R.G.
WattsI t
would be a very convenient thing if farmers throughout t h e world could enjoy perfect weather and t h e absence of plant diseases and pests, and could grow perfect crops in perfect soils. In t h e r e a l (and perhaps m o r e exciting a n d interest- ing) world t h e f a r m e r m u s t deal with imperfect soil a n d variable weather, with t h e presence of pests a n d diseases, and with fluctuating m a r k e t s a n d prices a s well.The next most convenient thing t o having a perfect world would be t o have a per- fectly predictable world. If a f a r m e r could predict perfectly all of t h e factors t h a t influence t h e growth of his crops a n d t h e health of his livestock, and if he could in addition predict how his crops a n d livestock a r e influenced by these factors, how m a r k e t s would influence his profits, etc., t h e n h e could decide which crops t o plant in any given year, or whether t o p l a n t anything a t all. He could also use h i s perfect knowledge t o decide whether a n d how t o assist in the natural order by, for example, irrigation or t h e application of fertilizers.
F a r m e r s have, of course, been trying for centuries t o predict t h e outcome of e a c h cropping season. Each y e a r m a n a n d n a t u r e perform a n experiment. Nature varies t h e rainfall, t e m p e r a t u r e , s u n l i g h t , a n d other weather p a r a m e t e r s while indi- vidual f a r m e r s vary t h e r a t e s of fertilizer application, planting dates, etc. The r e s u l t s of t h e s e experiments over m a n y years forms t h e collective experience of t h e farmers. The pooling of t h i s experience provides then1 with information about when t o plant, fertilize, irrigate a n d harvest crops, and even when t o anticipate cer- t a i n kinds of disease a n d p e s t epidemics. Scientists have recently begun t o s t r e a m - line this process through t h e u s e of m a t h e m a t i c a l models. Crop models provide a m e c h a n i s m f o r efficiently distilling a n d organizing past experience on t h e behavior of crops in such a way t h a t f u t u r e behavior can be predicted. The m a t h e m a t i c a l model is, of course, n o t t h e r e a l system. I t is a s e t of variables and m a t h e m a t i c a l relationships by which we can a t t e m p t t o represent t h e r e a l system. If t h e model is perfect, a n d if all t h e external c h a n g e s a r e anticipated. t h e n t h e model will behave exactly a s n a t u r e behaves. We could t h e n predict what n a t u r e will do a n d we could
understand why. We can never hope to do this perfectly, of course. Instead, our task as modelers is t o discover which variables a r e required t o describe the real world adequately, and how these variables a r e related to one another mathemati- cally. We will be mainly interested in t h e response of crops to changes in climate, and we will refer t o t h e models discussed below as a g r o c l z m a t i c m o d e l s . The pur- pose of this paper is to provide an overview of the role of agroclimatic models in cli- m a t e impact analysis. 1
We will approach this task in three stages. Krstly, we will describe which processes are important in determining crop production and how the farmer exploits and modifies these in order to obtain optimum yields. Secondly. we look a t t h e types of mathematical models t h a t a r e commonly used to simulate t h e crop production system. By concentrating on model attributes and disadvantages, we will discuss t h e i r performance in estimating crop responses to present-day condi- tions and assess their suitability for simulating the effects of future climatic change. As illustration, we present the results of specific experiments in which we explore t h e sensitivity of two models to climatic variations over a range of time periods. Finally, these features are summarized in a tabulated checklist which allows u s to cross-compare t h e capabilities of particular models.
2. CLTMATE
AND
THECROP
PRODUCTION !WETEMStrictly speaking, any treatment of the crop production system should embrace t h e full range of conditions t h a t a r e important in t h e cultivation and hus- bandry of crops. However, since no single model has yet been developed t h a t incor- porates all features of the system, we will restrict our &scussion only to those com- ponents t h a t we believe a r e pertinent in assessing t h e impacts of climatic change.
In this section, we have developed a scheme t h a t is designed t o reflect t h e real- ity of crop production a t t h e plant or field level, while offering the possibility t o match t h a t reality with t h e conditions simulated by agroclimatic models. First, we describe crop production in terms of t h e influences of natural conditions on processes t h a t determine productivity. Second, we itemize t h e more important requirements necessary for the development of a healthy crop and consider how t h e farmer a t t e m p t s t o modify the physical environment in order to fulfill these requirements. The importance of t h e timing of an thropogenic activities with respect to natural events is illustrated by combining t h e m in the form of a farm calendar. Thirdly, t h e effects of crop production and t h e influence of technology on long-term crop productivity a r e discussed.
2.1. Crop Production and Climate
To be able t o show the effects of climatic changes on t h e physical processes determining crop growth, a model should respond to a t least one of the variables t h a t help to describe t h e climate. No m a t t e r where crop production takes place the following conditions determine t h e final production level: the radiative and tem- perature regime, t h e soil water available for plant growth, t h e availability of plant n u t r i e n t s and the interference of pests and diseases. When any of these is n o t con- sidered in a model, i t often means t h a t under the actual local physical environment t h a t particular variable does not induce annual responses sufficiently large to affect crop yields. Such an omission may become significant when longer-term climatic changes a r e considered.
'we shall focus primarily on egricultural crop models although much of our discussion is equally applica- ble to other plant models (such as the forest g o d model reported by Kauppi and Posch, 1985).
The more important processes a r e illustrated in Figure 1 and have been grouped according t o their parent research discipline. The implication is t h a t for a model incorporating all these aspects in any detail, teamwork is essential.
METEOROLOGY & CLIMATOLOGY
Transpiration
PHYSIOLOGY
Evaporation
Immobilization Mineralization
Water transport Nutrient transport
Capillary rise
T
DrainageI 1 Leaching
Figure 1. Physical processes in plant production.
2.2. Constructing a Farm Calendar
Some agroclimatic models r e l a t e only climatic factors t o crop yield, b u t we will take a broader view, here, recognizing t h a t other variables including farm manage- m e n t activities, do not only contribute t o t h e level of t h e crop yield, but can be decisive in whether one obtains a yield a t all. For example, excessive rainfall may cause a delay in planting time, or even make planting impossible, with obvious consequences for plant production. Of course, a f a r m e r usually aims a t achieving a n optimal result, within t h e frame of his knowledge a n d his available options, and t h e weather often plays an important role in influencing his decisions.
The development of a crop and its sensitivity t o the physical environment is strongly plant-type dependent. A farmer's activities a r e also plant-type dependent although many a r e common t o all crops. Here, we will present an example. for a specific crop, of what can be called a farm calendar. Similar calendars exist for o t h e r crops, and these a r e described elsewhere in t h e literature (e.g. FAO, 1978;
Duckharn, 1963). The models we a r e interested in can be compared with t h e appropriate calendar t o see whether certain important variables a r e included. In a l a t e r section we will offer a means t o carry out this matching by way of a checklist.
Spring wheat is taken as our example. The crop has many characteristics in common with other cereals; but i t differs from winter varieties in being day-neutral (i.e. its development is not influenced by day-length) and in not requiring a cold (vernalization) period before heading.
2.2.1. &op Requirements
The development of t h e crop is indicated in Figure 2. Various development stages a r e recognized which a r e related to t h e crop's special requirements. The fol- lowing a r e distinguished: respectively, t h e requirements for radiation, water, n u t r i e n t s , weed control, pest control, soil conservation and temperature. These a r e represented over time as horizontal bars; t h e denser t h e lines i n t h e bar t h e more important a r e t h e requirements.
Solar radiation stimulates a crop t o convert absorbed carbon dioxide t o car- bohydrates (i.e. plant material) through t h e process of photosynthesis. During t h e early development of a crop, in particular, its rate of growth is strongly influenced by t h e amount of radiation i t intercepts.
Water s t r e s s in plants is one of t h e m o s t common factors limiting crop produc- tion.
I t
is not just t h e annual rainfall t h a t determines whether t h e r e is enough water available for plant growth, b u t t h e timing and distribution of rainfall, evapo- transpiration and soil characteristics play a role as well, both before and during t h e growing season.Of t h e nutrients, only t h e t h r e e main 'macronutrients' a r e dist'inguished, and t h e i r relative importance is staggered over t h e period of crop growth. Potassium tends to be more important a t t h e beginning of t h e vegetative period, nitrogen fol- lowing tillering, and phosphorous during heading.
The climate may play a decisive role in pest control, and activities of m o s t of t h e lower organisms like fungi a r e triggered by humidity and temperature. As for weed control. weather conditions can affect both t h e competitiveness between weed c u l t u r e s and with t h e crops. .
Soil erosion is a problem in many agricultural areas. For example, during t h e period after plowing but before t h e crop has fully developed, rain can a c t directly on t h e soil surface, causing a large amount of soil loss. Rainfall of high intensity, surface runoff, or wind, together with an easily erodible soil can lead to several tens of m e t r i c t o n s of soil loss per hectare.
Each plant type has its typical optimum temperature range although this may vary from growth stage t o growth stage. Temperatures below zero degrees Celsius do not permit growth and extremely high temperatures may also be damaging to t h e crop. Plants have adapted t o daily fluctuations in temperature: given a suffi- c i e n t supply of carbon dioxide, t h e higher temperatures during daylight promote a maximum photosynthesis rate, while lower nighttime temperatures reduce the losses of photosynthates by slowing down t h e process of maintenance respiration.
For spring wheat the optimum t e m p e r a t u r e range lies between 15 and 25°C and the minimum temperature for both growth and germination is about 4°C. At ripening, t h e period preceding harvest, a i r t e m p e r a t u r e s above 18°C together with calm dry weather a r e optimum, leading to t h e minimum harvest losses.
CROP REQUIREMENTS ANTHROPOGENIC ROLE OF ACTIVITIES CLIMATE
M I N G HARVEST r u m
+ +
mopll- mil
Figure 2. Farm calendar for spring wheat.
Extreme events t h a t sometimes occur may not simply reduce yields, b u t can cause total losses. The occurrence of frost during t h e flowering period illustrates such an event. Lodging because of high rainfall accompanied by wind during grain formation can also lead to heavy losses. P l a n t breeders have come t o t h e aid of farmers in this respect, introducing b e t t e r adapted varieties like, for example, t h e s h o r t straw varieties t h a t have reduced lodging in cereals.
2.2.2. F W f i l l i n g the hbtpirernents
For most of t h e crop requirements t h e farmer h a s tools to reduce any adverse effects of t h e environment. Thus, t h e requirements indicated in Figure 2 a r e accompanied by a bar t h a t shows how farmers can a c t , given t h a t they have t h e m e a n s and t h e sufficient know-how.
For example, t h e soil may not be capable of meeting t h e n u t r i e n t require- ments, therefore, applied fertilizers may increase production, provided they a r e applied a t t h e right t i m e and in t h e c o r r e c t way. How far those applied n u t r i e n t s become available to t h e plant, however, is also a function of t h e weather. And although t h e farmer can t o a certain degree counteract t h e negative effects of t h e weather, losses in n u t r i e n t s may still occur due to leaching, fixation or volatiliza- tion.
Through suitable conservation measures, soil erosion losses can be reduced to practically nothing. The planting of wind barriers, for example, a t appropriate dis- t a n c e s and perpendicular t o t h e dominant wind direction will often reduce losses considerably.
Ironically, many of t h e areas where shortage of water is a constraint on growth a r e also areas with a favorable radiative and t e m p e r a t u r e regime. However, if no o t h e r factor is limiting, irrigation c a n transform those areas into t h e most produc- tive regions in t h e world.
2.3. hng-Term Effects of Crop Production
Throughout a crop's growth, t h e resources upon which it depends a r e them- selves undergoing a continuous process of change. Moreover, these changes a r e n o t always measurable. For example, t h e soil texture is not likely t o change signifi- cantly within a man's generation, due t o t h e robustness of t h e soil minerals. In contrast, t h e organic m a t t e r c o n t e n t a n d composition may change considerably even within a growing season. Although anthropogenic activities play an important role in controlling t h e r a t e s of some of these changes, t h e effect of t h e climate should not be underestimated. For example, t h e decay of organic m a t t e r is greatly influenced by fluctuating moisture and t e m p e r a t u r e conditions, suggesting t h a t any future changes in these conditions might induce rapid responses in decay r a t e s .
When we extend t h e time horizon beyond t h e short-term, i t is important t o recognize also t h e effects on crop production of various cropping practices, such as rotations, multiple cropping, consecutive cropping, etc. On a particular t r a c t of land, over a series of years, any n u m b e r of crops may have been grown, e a c h uniquely affecting t h e long-term s t a t u s of t h e soil. Furthermore, a change in t h e crop mix, due perhaps t o a changing climate, might a l t e r significantly t h e r a t e s of processes such as soil degradation and erosion, maybe feedng-back t o t h e crop sys- t e m and accentuating t h e impact.
Finally, the rapid increases in crop yields reported from m a n y parts of t h e world over the last two decades give testimony to some enormous advances in farm management practices and technology. Clearly, for as long as improvements in crop productivity a r e feasible, man will strive towards their a t t a i n m e n t , through plant breeding and genetic engineering, development of new machinery and fertil- izers and evolution of improved conservation techniques. These technological trends will continue to exert an important and, very likely, dominant role in future crop production.
3. MODELING THE
CROP
PRODUCIlON SYSEMWe can view a mathematical model as a s e t of input variables t h a t affect a s e t of output variables through a number of mathematical relationships. In an agro- climatic model, the output variable of primary interest usually involves some measure of crop productivity (e.g. yield, biomass potential, land suitability, etc.).
Input variables include climatic variables such as temperature, precipitation, windspeed, solar r a h a t i o n and t h e like. Other environmental variables t h a t might affect yield have already been referred to as natural input variables. These were distinguished from another group, labeled anthropogenic input variables which a r e associated with direct intervention by man and include, for example, irrigation and the application of fertilizers and pesticides (Figure 2).
The principal purposes of t h e modeling procedure a r e t o understand t h e sys- t e m and to develop predictive capability. Ultimately, we would like t o be able to predict the consequences of changes in both natural and anthropogenic input vari- ables. The former would tell us how natural changes will affect crop productivity.
The l a t t e r would suggest to u s how we might a c t to optimize productivity by alter- ing anthropogenic inputs.
Before attempting t o assess t h e characteristic features of different model .types, l e t us consider first one of t h e simplest methods of relating plant growth to
climate: t h e climate-based vegetation map.
3.1. Climate-Based Vegetation Mapping
Several schemes have been proposed which classify natural vegetation zones according t o mean climate (particularly measures of temperature a n d moisture conditions) and there a r e many examples of global maps which illustrate regional vegetation patterns based on observed mean climate (e.g. Koppen, 1936; Holdridge, 1947). This approach can be regarded a s correlative modeling in t h e very loosest sense, where a number of discrete vegetation classes a r e 'correlated' with climate on t h e basis of a sample of observations from around t h e world. The i n t e r e s t in such a procedure for climate impact analysis lies in o u r ability t o introduce a climatic change by adjusting t h e values of mean climate for a region. According to the changed climatic conditions we can then 'predict' (i.e. re-map) t h e new vegeta- tion pattern and can assess t h e impacts in terms of geographical shifts over space.
Examples of the mapping of vegetation shifts include experiments using Holdridge Life Zones under a 2 x C02 climate (Emanuel et al., 1985), and for Kippen Vegeta- tion Zones under t h e climatic conditions simulated for the peak of t h e last ice age, 18000 years ago (Hansen et d . , 1984). Clearly, this type of analysis can be applied only t o broad scale vegetation changes which, given t h e high temporal inertia of ecological systems would be measured over t h e long-term. F u r t h e r since it is strictly a climate classification other factors such as soil properties, fire risk and species competition need to be overlaid on the basic classification in order to gain a realistic assessment of t h e impact of climatic change.
Vegetation maps provide a useful first approximation of t h e biological response t o changes in climate a t a continental o r global scale. Experiments of t h e kind dis- cussed offer a framework within which t o focus our studies of crop response using agroclimatic models.
3.2. Classitping Agroclimatic Models
There a r e a number of excellent reviews of agroclimatic modeling in t h e litera- t u r e (e.g. Baier, 1982; Sakamoto, 1981; Robertson, 1983) and all a t t e m p t some kind of model classification. In general, models fall into two broad classes: empirical- statistical models and simulation models.
h p i r i c a l - s t a i i s t i c a l models a r e developed by taking a sample of annual crop yield data from a certain area together with a sample of weather data for the same area and time period, and relating t h e m through statistical techniques such as multiple regression analysis. This procedure is sometimes labeled a black-box approach since it does not easily lead t o a causal explanation of t h e relationships between climate and crop yield. This description should not imply, however, t h a t these models a r e developed blindly or indiscriminately. The most effective empirical-statistical models a r e usually the product of very careful and well- informed selection of suitable explanatory variables, based on a n intimate knowledge of basic crop physiology.
Sbnulation models generally t r e a t t h e dynamics of plant o r crop growth over t h e growing season through a s e t of mathematical expressions tying together the interrelationships of plant, soil and climate processes. Some of these relationships a r e well-enough understood to be regarded a s accepted laws of physics, chemistry and biology a n d a r e often r e f e r r e d t o as deterministic functions (Lyons, 1982).
Other processes which a r e e i t h e r poorly understood or of secondary i n t e r e s t t o the modeler a r e frequently represented by empirical functions.
Thus. no simulation model can be described a s truly deterministic since all incorporate a t least some empirical (black-box) elements. However, they differ from empirical crop models in their development and operation. In t h e l a t t e r models, t h e output data (such as yield) must be sampled a n d related to the input data in order to construct t h e statistical model which is t o be used a s a predictive tool (Figure 3a). In t h e simulation approach, t h e plant growth processes are prespecified, and output d a t a a r e generated i n t e d l y by t h e model, a s illustrated in Figure 3b.
3.3. Evaluating
the Utility
of Agroclimatic ModelsWe c a n evaluate a model according t o t h e following general criteria: objectives, logistics, assumptions and sources of error, and validation.
3.3.1. Objectives
In general, models a r e constructed in order to satisfy certain objectives.
These a r e bound to condition what levels of detail and explanation a r e required in developing the model. As a simplification, empirical statistical models a r e built for t h e sole purpose of yleld pre&ction; simulation models offer a m e a n s t o analyze as well as to estimate yield. These differences in modeling objectives should become more apparent in the following discussion.
REGRESSION MODEL DATA INPUTS
(variables YIELDS
MODEL
I
1
-
, (sample ofa t ,
41
c,-
CONSTRUCTIONyears t = 1, n) Y l . y2, Y,)
ACTUAL
1 r YIELD ywl
b) Simulation INDEPENDENT
DATA INPUTS
LAWS &
..---. . + ,
,,,-EXPERIMENTS &THEORIES OBSERVATIONS
MODEL CONSTRUCTION
2
EXPLANATORY ESTIMATED
INPUT VARIABLES
a w l
bHl YIELD
=,,+I
INTERACTIVE MODEL
Figure 3. The construction, operation and validation of a) an empirical/statistical (black-box) model and b) an interactive simulation model (schematic).
3.3.2. Logistics
I t is probably t r u e t o say t h a t a model is only as good as t h e data s e t upon which it is based. Adequate data a r e required first, for constructing t h e model algo- rithms, second, for running t h e model (i.e. as inputs) and third, as independent objective measures against which t o validate model outputs. In considering t h e effects of climatic change one important concern is for a model t o be capable of responding t o those a n n u a l fluctuations over several decades t h a t a r e characteris- tic features of most regional climates.
In general, with fewer and simpler model variables one can e q e c t a longer time series of data and a more straightforward and rapid calculation process. Most empirical-statistical models are constructed t o meet this objective, both for t h e purpose of simplicity and t o avoid t h e statistical problem of inflated correlation coefficients due t o a high n u m b e r of explanatory variables (Sakamoto, 1981). Con- tinuing this line of reasoning, i t is no surprise that some of t h e most effective sta- tistical models have been developed in areas where crop growth and yield a r e governed by a s i n g l e major weather factor (e.g. temperature and hay yields in Ice- land, Bergthorsson. 1985).
For an empirical t r e a t m e n t of a more complex system, data bases may become prohibitively large, and in t h i s situation t h e explanatory, simulation approach might be a viable substitute since some of t h e variables can be generated internally by t h e model. However, d a t a requirements a r e normally greater for simulation models anyway, given t h e short time-steps frequently employed. Moreover, s u c h line scale data a r e seldom available over long time periods imposing a formidable restriction on t h e applicability of many simulation models for t h e analysis of climatic fluctuations on a decadal basis.
An additional logistical advantage of most empirical models lies in their predic- tion of yields for quite large regions. Thus, climatic data a r e often regional aver- ages derived from a number of sites, any one of which need not necessarily provide a continuous record. Conversely, simulation models tend t o be site-specific, requir- ing a single, unbroken r u n of d a t a for all variables.
3.3.3. Assumptions a n d S o u r c e s of ~ O T
In a perfect model, all variables contributing t o t h e growth of a crop would be represented exactly and connected with an unbroken logic. However, because c u r r e n t understanding of plant processes is so imperfect, modelers m u s t adopt a pragmatic approach, selecting only those variables thought t o have a significant influence on crop growth, and where t h e interrelationships between these variables cannot be represented, even a s empirical functions, assumptions m u s t be intro- duced which a r e based on t h e modelers' experience and judgement. The effective- ness of a model, for whatever purpose i t is designed, invariably rests on t h e n a t u r e a n d validity of its assumptions. Although each model has its own unique s e t of assumptions, some a r e common to most models.
Many of t h e weaknesses of empirical models, in particular, can be a t t r i b u t e d t o t h e i r statistical assumptions. In t h e classical linear regression analysis, i t is assumed that variables a r e independent. Unfortunately, few of t h e climatic vari- ables t h a t impact on crop yield a r e n o t related t o each other and f u r t h e r , many a r e also related t o themselves over t i m e (i.e. autocorrelated). These problems of mul- f i c o U i n e a r i t y usually result in regression coefficients with large, unstable vari- ances. In addition, t h e relationships between crop yields and climatic variables a r e rarely linear. Where they a r e modeled as such, this can also lead t o inflated vari- ance, and the resulting coefficients may be unstable t o t h e extent t h a t t h e i r sign can change with t h e addition of new observations (Biswas, 1980).
One potential solution for reducing collinearity is t o combine intercorrelated variables into an a g r o c l i m a t i c indez. Surrogate variables such as these have been used to represent soil moisture information or heliothermic conditions and can be related directly t o yields (e.g. Williams. 1985).
A third, simplifying assumption, which pervades most models but may have a g r e a t e r influence in t h e empirical-statistical type, concerns t h e i n t e r p o l d i o n and e z t r a p o l d i o n of values. Since most models a r e developed and 'tuned' using func- tions pertaining t o a n observed range of present-day conditions, i t is likely t h a t interpolation will be t h e dominant procedure employed in model r u n s conducted
under 'normal' conditions. However, altering the climate may introduce values outside t h e modeled range. Thus prediction becomes speculation a s we must extra- polate t h e functional relationships in order t o estimate response. This unsatisfac- tory procedure merely re-emphasizes the need t o develop models over t h e p a t e s t possible range of observed con$itions.
A fourth assumption, which affects both model types but in different ways, involves the inclusion of m a n a g e m e n f practices m d technology as explanatory vari- ables (see Section 2.3.). In simulation models these a r e e i t h e r included as explicit input variables, or specified as constants. In the l a t t e r case, this assumption may r e s t r i c t t h e model's effectiveness in estimating long-term effects of technological change.
Empirical-statistical models often t r e a t technological change a s a time t r e n d based on yield statistics over a relatively long period of time. This procedure has two disadvantages. F ~ r s t , it relies upon t h e subjective separation of technological trends from those t h a t can be attributed t o the environment (including climate).
Secondly, as in the case of simulation models, a future scenario requires some assumptions about t h e extrapolation of t h e technology trend.
Finally, sporadic c l i m a t i c e v e n t s such a s hail storms, floods, late or early frosts can often have devastating effects on crops. While simulation models generally make allowance for these episodic events through the use of critical tolerance lev- els, empirical-statistical models often do not, and this can have implications in the analysis of longer-term climatic change (see Section 3.4.1.).
We have given s h o r t descriptions h e r e of some of the more important model assumptions and sources of error. More complete discussions of these and others can be foundin t h e reviews by Sakamoto, 1981; Baier. 1981. 1982; Biswas, 1980 and Katz, 1979.
9.3.4. Vdidation
The ultimate t e s t of a n y model is t o assess how closely i t s estimates of real world conditions correspond t o actual measured observations. The whole credibil- ity of a model's forecast of crop response r e s t s on the rigorous testing of its sensi- tivity and verification of i t s outputs against independent observations.
A sensitivity analysis can tell us a lot about the inherent stability of a model, i t s effective range of operation and its potential applicability to climatic change experiments. In essence. a sensitivity analysis seeks t o evaluate a model's responses to incremental changes i n magnitude of each input variable (both singly a n d in combination). These adjustments should be distributed such t h a t t h e extreme values lie well outside the observed natural range. A similar procedure is employed for those mechanisms, including feedback processes, t h a t a r e generated internally. In this way, we c a n gain insights into:
a ) t h e physical realism of t h e modeled relationships over a wide range of condi- tions;
b) t h e relative importance of t h e various types of external forcing;
c ) t h e relative influence of each modeled variable in determining model outputs;
an d
d) some of the model's limitations, including information concerning (i) t h e con- ditions under which the model breaks down, and (ii) which of its coefficients are potentially unstable, under what circumstances a n d with what effect (e.g.
see Katz, 1979).
In order to appraise its performance, it is necessary to validate a model's esti- m a t e s against observed data. This procedure has a number of a t t e n d a n t difficul- ties, not least t h e problem of securing adequate data for its implementation. The types of data required for validation depend t o a large extent on t h e nature of the model's predictions.
As a minimum requirement, t h e outputs from an empirical-statistical model should be verified against a t least ten years of independent crop yield data, reflect- ing a variety of conditions. Ideally, these should be different bodies of data from those used t o construct t h e model, and for t h e same time period, in order t o test t h e model's common applicability. However, because of t h e area-specific n a t u r e of most statistical models (due in part t o their general neglect of variables such as soils, drainage and m a n a g e m e n t t h a t are often highly heterogeneous over space) t h i s form of cross-validation is rare. Model results a r e usually compared with observations from t h e s a m e a r e a but for a different time period (Figure 3a).
For simulation models, t h e problems are slightly different. Firstly, t h e data requirements a r e usually very m u c h greater than for statistical models. A proper validation procedure should include not only a comparison of modeled outputs with r e a l conditions, but also t h e verification of each and every internally derived value (Flgure 3b). In some instances, however, it may be either impractical or even technically impossible t o m e a s u r e a particular variable.
Secondly, t o r e s t a t e t h e need for internal validation, let us consider some pos- sible validation outcomes. For example, a perfect correspondence of observed with predicted outputs such as yield can, when taken in isolation, mask an internal caco- phony of errors. Conversely, where t h e internal validation is apparently good, t h e output estimates may be discordant. This condition might be explained by t h e cumulative effect of small, seemingly inconsequential structural errors, or by the omission of important explanatory variables from t h e model, or indeed by a combi- nation of t h e two effects.
Finally, in validating any type of model, care should be taken t o ensure t h a t t h e independent observations being used a r e totally compatible with t h e model esti- mates. Efficient scrutiny of t h e data may uncover unforeseen peculiarities to which a model may or may n o t be sensitive (such as t h e introduction of irrigation t o an area, t h e replacement of a crop hybrid, or a change in t h e total area under t h e crop).
3.4. Agmclimatic Models
in
Climate Lnopact AnatygisIn t h e late 1960s and early 1970s, when modelers First began t o address t h e problem of examining crop responses t o possible future climatic change, m a n y con- ducted their experiments using models t h a t were not always appropriate for t h e task. Most models had been constructed either a s predictive tools for estimating year-to-year yields, or as r e s e a r c h tools t o investigate detailed cropenvironment interrelationships during a typical growing season. Now, over a decade later, i't has become increasingly clear t h a t by extendmg t h e time horizon of study beyond the immediate short-term (for which many models are tuned) we r u n into a whole s e t of fresh problems. These can be grouped into two categories: (i) problems relating to t h e validity of model relationships and (ii) difficulties concerning which methods t o adopt in simulating climatic change.
3.4.1. Model Relationships
All facets of t h e n a t u r a l environment a r e undergoing a continuous process of change. Over s h o r t time periods, in situatiorls where r a t e s of change a r e relatively slow, their effects may be imperceptible. Thus, for t h e purposes of modeling short- t e r m crop response t h e y c a n often be parameterized as constants. However, in a
consideration of longer-term climatic changes, over periods ranging from decades t o centuries, these processes may exert an influential and possibly dominant role in crop growth. I t is therefore important t o incorporate these effects in models, a t least on an annual updated basis. Examples include changes in soil properties (see Section 2.3.) and the natural adaptation of certain plant species t o stressful weather.
As a result of readjusting model parameters many of the functional relation- ships, adequate in describing short-term processes, may become invalid and require re-evaluation (Wigley, 1984). Moreover, a change in climate may alter t h e importance of critical threshold values for crop growth (e.g. a climate warming might reduce markedly the risk of cold damage to a cereal crop but may increase t h e probability of h e a t stress; and see Rosenberg, 1982). Further, if a crop i s espe- cially vulnerable t o the effects of episodic events then i t is of critical importance t h a t such events should be modeled effectively, for any change in their frequency m a y have dramatic consequences.
F~nally, attendant on, and possible contributing to climatic change could be factors s u c h as atmospheric, soil and water pollution. However, for modelers t o simulate the d r e c t crop responses to such complex problems a s increased atmos- pheric carbon dioxide concentrations, or acid precipitation, is placing a r a t h e r large onus on their skills if we consider the prevailing uncertainties existing within these fields. Nevertheless, t h e r e have been several recent attempts, aIbeit not within a formal model framework, to quantify t h e direct effects of carbon dioxide on crop yield (e.g. Rosenberg, 1981; Waggoner, 1983).
3.4.2. Mode 1 Runs f o r A r t u r e C l i m a t e
A first consideration for modelers wishing to simulate t h e effects of future climatic change is how best to quantify t h a t change. There exist predictions of change simulated by a suite of global climate models of varying type and complex- ity, predictions based on using past climatic anomalies as analogs of future con&- tions, and prechctions generated stochastically and/or synthetically. The temporal and spatial resolution of these p r e d c t i o n s varies widely, and i t is this consideration which is a major determining factor in t h e selection of an appropriate scenario as an input to a particular model.
One method of improving t h e 'compatibility of scales' where t h e resolution of t h e predicted climate variables is too coarse for input into an agroclimatic model, is to generate a synthetic s e t of finer-scale d a t a Methods exist for generating daily temperatures from monthly m e a n s (e.g. Brooks, 1943), for adjusting weekly precipi- tation by allocating fixed proportions of t h e weekly total to particular days (e-g.
Stewart, forthcoming), and for stochastic simulation of daily weather data (e.g.
Richardson, 1901; Mearns e t d,, 1984). Alternatively, instead of improving t h e reso- lution of the input data, another more common compromise is t o run t h e impact model a t a coarser resolution. The possible errors involved i n this procedure a r e discussed more fully in Section 4.
A final consideration when running a climate impact scenario concerns how models handle a climatic change. This can be approached on two levels. First, a model's simulation of year-to-year crop response may be s t a t i c or dynamic.
Briefly, a scenario using a static model usually involves t h e input of one s e t of changed climatic means (averaged over several decades) with t h e output assumed t o represent mean response over t h e s a m e period. The procedure is suspect, how- ever, for in reality i t is very r a r e for a period-averaged climate to resemble any one of the constituent years of weather within t h a t period (particularly in the case of precipitation). Moreover, the crop yield estimated for a 'mean climate' year can be quite different from crop yield estimates calculated for each year and averaged
over t h e whole period (see, for example, Table 1, Section 4.1.). 2
Thus, a more satisfactory s c e n a r i o i s one which t r e a t s climate a s a variable, dynamic entity, a n d models year-to-year fluctuations both for t h e p r e s e n t day a n d f u t u r e climatic'regimes. Of course, a static-type model can be used for this pur- pose by repeating individual r u n s for varied inputs. However, i t is more efficient (and elegant) if a model c a n collect t h e separate s e t s of input data together a n d c o n d u c t multiple r u n s in a single operation. Year-to-year variability about a f u t u r e climatic m e a n can be simulated by generating synthetic data, and some of t h e m o r e sophisticated models have t h i s capability built-in. Under conditions of 'stable' climate, model r u n s of t h i s kind should normally be conducted over a period of several decades in order t o s i m u l a t e equilibrium conditions.
The second level of approach t o climatic change considers whether we should model change a s step-like or t r a n s i e n t . If we a c c e p t t h a t long-term climatic change is likely t o involve a gradual process of change, then we should appreciate t h e dangers of t r e a t i n g change a s a n a b r u p t perturbation, for n o t only is s u c h a climatic change r a t h e r unrealistic, b u t t h e model responds t o t h e change a s if i t were p a r t of t h e year-to-year variability. Thus, longer-term processes such a s soil a d j u s t m e n t s a r e n o t allowed t i m e t o r e a c t (unless changed equilibrium conditions a r e simulated). Unfortunately, all too m a n y model experiments have been con- d u c t e d using t h i s 'sudden shock' approach a n d t h e modeiing of t r a n s i e n t changes (whether linear, exponential or cyclic) h a s been largely neglected. Reasons for this m a y include t h e r e q u i r e m e n t for large i n p u t data s e t s and considerations of com- p u t e r time.
4. EXPLOmG MODEL
SEN- TO
CLIMATE:TWO EXP-
Our eventual major i n t e r e s t , a s modelers, will be in predicting t h e effect of climatic change on f u t u r e c r o p yield. In o r d e r t o do this, we will need t o know t h e f u t u r e distribution of t h e various climatic variables over both space arid time.
Clearly, t h e prediction of daily w e a t h e r events over an e n t i r e season will n o t be feasible in t h e n e a r f u t u r e , if, indeed, i t is e v e r possible (Lorenz, 1968). Predicting seasonal, or even monthly averages s m o o t h e d over large a r e a s , however, s e e m s a goal t h a t m i g h t be achieved i n t h e n o t t o o d i s t a n t f u t u r e . I t will be very nice if t h i s kind of t i m e and space averaged i n p u t d a t a can be used in agroclirnatic models with s o m e a s s u r a n c e t h a t reasonably a c c u r a t e c r o p yields will be predicted.
The n a t u r e of t h i s problem brings o u t very nicely t h e idea t h a t t h e effects of t i m e a n d space resolution a r e n o t e n t i r e l y independent. Rainfall, for example, t e n d s t o be a highly localized phenomenon in both t i m e and space. Averaging rain- fall over e i t h e r t i m e or space hides t h e variability of t h e t r u e signal, and t h i s varia- bility m i g h t be a very i m p o r t a n t f a c t o r in c r o p growth and yield. On t h e o t h e r h a n d , r e a l rainfall d a t a a r e seldom available on less t h a n a daily averaged basis, a n d t h e n only a t specific sites. The rainfall in a given cropping region m i g h t vary appreciably over both space a n d time. If we average over space, does i t make sense n o t t o average over t i m e ? I t is also p e r h a p s worth pointing o u t t h a t empirical- statistical models generally a t t e m p t t o c o r r e l a t e c r o p yield with monthly, season- ally, or even annually averaged t e m p e r a t u r e , precipitation and t h e like. Can t h i s ever be expected to be a reasonable approach? In what detail m u s t we know a n d specify t h e i n p u t variables in a n agroclimatic model in order t o have a reasonably good chance of predicting t h e effects of t h e s e variables on crop yield? Must we use daily or even hourly d a t a , or c a n we use monthly or seasonal or a n n u a l averages?
'1t ahould be noted, however, that this effect m e y not be so important for models operating with a time- step exceeding one month.
The yield of a particular crop depends upon many climatic variables, such a s rainfall, t e m p e r a t u r e , sunlight, and t h e i r seasonal variations. In addition t o cli- m a t e directly, yield depends upon a variety of chemical a n d physical properties of t h e soil; for example, i t s permeability, a c i h t y , and available nutrients. These pro- perties c a n change in response, for example, t o precipitation changes, with t i m e c o n s t a n t s of m a n y years. These long t e r m changes m i g h t affect yield. In fact t h e sensitivity of yield t o long t e r m climatic change might be very different from t h e sensitivity t o year t o year variations.
In t h e light of t h e above, i t might be useful t o use agroclimatic models t o explore both ends of t h e t i m e scale. We p r e s e n t h e r e t h e results of two s e t s of n u m e r i c a l experiments through which we explore t h e effect of temporal resolution of t h e ' i n p u t precipitation on yield, a n d t h e difference between short-term a n d long-term sensitivity of yield t o climatic change.
4.1. Ekperiment 1. The Temporal Resolution of Input Data a n d Its Elfect on Yleld The first s e t of experiments was performed with a crop production model described by Konijn (1984). The model was chosen strictly on t h e basis of i t s availa- bility a n d on i t s suitability for performing t h e experiments described below. The model e s t i m a t e s c r o p yields based on characteristics t h a t describe t h e physical e n v i r o n m e n t (including t h e climate). The data for t h e s e experiments were taken from t h e Stavropol region of t h e
USSR
Only one soil type was considered and t h e growth of t h e chosen crop, oats, was assumed not t o be limited by diseases, pests, o r s h o r t a g e of n u t r i e n t s .The model was f i r s t r u n for each of t h e 12 years, 1971-1982, using t e n day aver- aged rainfall d a t a for e a c h year. Next, t h e t e n day rainfall data in each year were averaged by t h r e e s t o obtain thirty day averages. The model was t h e n r u n with t h e s a m e t i m e s t e p a s before, but using t h i r t y day averaged rainfall a s input data. An ensemble average of t h e t e n day rainfall d a t a was also c r e a t e d by averaging e a c h t e n day period over t h e e n t i r e twelve y e a r d a t a set. A similar ensemble average s e t was c r e a t e d from t h e t h i r t y day averages. The model was r u n with these ensemble averaged precipitation data.
The r e s u l t s a r e s u m m a r i z e d in Table 1. The yield computed using the t e n day a n d t h i r t y day rainfall i n p u t d a t a differ by less t h a n 3% in half t h e cases. In n o case do t h e y differ by m o r e t h a n 10%. In most, b u t n o t all, cases t h e use of t h i r t y day averaged d a t a (smoothing t h e data) r e s u l t s in higher yields. The yield resulting from t h e use of t h e ensemble average precipitation d a t a (again, smoothing) i s higher t h a n t h e average yield over t h e twelve y e a r period. This is especially t r u e of t h e t e n d a y data.
We have chosen t h r e e years for closer examination. The precipitation d a t a for t h e s e y e a r s (1971, 1975, and 1982) a r e shown in Figure 4. The solid lines a r e t e n day averaged a n d t h e dashed lines t h i r t y day averaged precipitation. The beginning a n d end of t h e growing season a r e marked by arrows on t h e horizontal (time) axis.
Table 2 shows, for t h e s a m e t h r e e years, t h e total dry weight assimilation broken down into four plant components: leaf, root, s t e m , and grain.
1982 was a relatively wet year during t h e growing season, a n d t h e grain yield was high. Smoothing t h e precipitation data (using t h e t h i r t y day average) r e s u l t e d i n a 5.1X h i g h e r predicted yield. The variability of t h e t e n day rainfall d a t a is m u c h h i g h e r t h a n t h a t of t h e t h i r t y day data. When very high rainfall occurs during a ten day period, t h e runoff c a n be considerable. This water i s effectively lost from t h e system. During 1982 t h e variability was especially high during t h e early a n d middle p a r t s of t h e growing season. This i s reflected in t h e fact t h a t t h e leaf dry weight.
which develops mainly during t h i s period, i s n e a r l y 10% higher for t h e t h i r t y day
Table 1. Comparison of grain yields of oats estimated using precipitation data averaged over 10 day and 30 day time-steps. Data refer t o t h e period 1971-82 a t Stavropol,
U.S.S.R.
averaged data t h a n for t h e ten day averaged data.
YEAR 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 12 Y r Avg Yield
Ensemble Average Rainfall Data
For the 1975 case, averaging over thirty days instead of t e n days results in a lower predicted grain yield. Leaf, root, and stem dry weights a r e all slightly higher, however, (see Table 2). The reason for this is the following: Although t h e t e n day averaged precipitation is. of course, less smooth than t h e thirty day average values, t h e r e a r e only two ten day periods during which precipitation exceeds 40 mm.
Thus, t h e smoothing of precipitation input, and t h e resulting decrease of runoff, should not greatly increase t h e efficiency with which t h e plants can use t h e mois- t u r e . On the other hand, during t h e last two ten day periods of t h e growing season.
the particular way i n which the averaging was done resulted in t h e fact t h a t a very dry t e n day period outside the growing season was used to compute t h e last thirty day averaged data. The precipitation during t h e last twenty days of t h e growing season was t h u s underestimated in t h e t h i r t y day averaged case.
The very low precipitation during t h e 1971 growing season resulted in t h e smallest grain yield of any of t h e twelve years studied. Variability of precipitation was also low. In no t e n day period &d t h e precipitation exceed 30 rnm, and in only t h r e e cases was it less than 10 mm. H e n c e , values obtained from model r u n s using ten and thirty day precipitation averages differed by less than 1%.
Instead of continuing our experiments by running the model for longer and longer t i m e periods, we have plotted grain yield (computed using ten day averaged precipitation) against seasonally and annually averaged precipitation for each of the twelve years (Figure 5). There is a quite good correlation between yield and seasonally averaged precipitation, but only a very weak one for t h e case of annually averaged precipitation. The annually averaged precipitation in 1971 and 1982 were almost identical, but in 1971 t h e rain fell mostly outside t h e growing season, whereas in 1982 i t was distributed through t h e growing season with the larger
% Difference 1.0 2.1 3.3 0.7 -2.7 9.5 7.3 -4.0 0.7 7.4 -2.9 5.1 Grain Yield (&/ha)
10 Day 1458 2797 3201 2956 2623 3420 4750 4711 2257 3099 2865 4240 3 165 3449
30 Day 1472 2855 3307 2978 2552 3745 5099 4523 2273 3328 278 1 4455 3281 3434
Figure 4. 10 day (solid lines) and 30 day (dashed) averaged precipitation (mm) at Stavropol for the years 1971, 1975 and 1982.
Table 2. Dry m a t t e r production of oats (kg/ha) divided into four basic plant corn- ponents. Estimates a r e for three years (1971, 1975 a n d 1982) and for 10 day and 30 day precipitation averages.
portion falling i n t h e last half, when the grain was forming. I t seems clear from Flg- u r e 5 t h a t (as would be intuitively expected) the year to year change in annual pre- cipitation is not a very good measure of predicted crop yield. On t h e o t h e r hand, t h e correlation with precipitation during the cropping season is surprisingly good.
We a r e , of course, fully aware t h a t we have tested the response of a model of n a t u r e a n d not nature itself. If one finds t h a t ten day, monthly, or seasonal rainfall d a t a can be used with nearly equal accuracy in an agroclimatic model, it cannot automatically be concluded t h a t t h e same is t r u e in nature. Nevertheless, the results give us cause for hope t h a t this very convenient s t a t e of affairs might be t r u e . Obviously, i t would be very interesting t o repeat these experiments with a model t h a t could incorporate daily o r even hourly rainfall data.
4.2. Ehpriment 2. Comparing Short-Term and b n g - T e r m Sensitivity of Yield to Climatic Change
YEAR (Avg Period)
197 1 (10 day)
197 1 (30 day)
1975 (10 day)
1975 (30 day)
1982 (10 day)
1982 (30 day)
In order t o explore t h i s question we use the results of some experiments previ- ously reported by Watts (1983). The experiments were performed using t h e VNIISI model, an environmental model t h a t contains both crop growth and soil corn- ponents (Pitovranov et al., 1984). The crop model uses only annually averaged cli- m a t e data, but t h e soil model h a s the advantage of allowing soil characteristics t o evolve over very long time periods. It is therefore unique in t h a t it can be used t o explore t h e relative values of long- and short-term changes of yield in response t o climatic change. The sensitivity of the model to temperature and precipitation changes was examined in t h e following way. First t h e soil and geography in the model were fixed to represent approximately t h e Great Plains of t h e United States (plains, loamy sand). Nitrogen fertilizer application was fixed a t 50 kg/ha and phos- phorus a t 10 kg/ha (similar to c u r r e n t fertilizer use on wheat in Kansas). The model allows for local t e m p e r a t u r e to be changed as an input. Long-term average precipitation values can also be specified, but the model itself imposes a stochastic
PRECIPITATION (mm) DRY MA'ITER PRODUCTlON
(kg/ha)
ANNUAL
511.0
778.0
498.0
GROWING SEASON
136.8
30 1.0
314.0 LEAF
1029
1055 1366
1421 1889
2079
STEM
995
1005 1367
1392 1865
1943 ROOT
351
355 499
509 687
705
GRAIN 1458
1472 2623
2552 4240
4455
Growing =son precipitation
O
Annual precipitation0 I I I 1
1 I I I
0 200 400 600 800 loo0
Precipitation (mm)
Figure 5. Plots of modeled oats yield against seasonally and annually averaged pre- cipitation. Yields were computed using 10 day averaged precipitation.
variation of precipitation about the average value. A temperature and precipitation value was chosen and the model r u n until a statistical steady state was reached.
Average yield and the variations of precipitation and yield about the average were recorded. The experiment was then repeated for another s e t of average tempera- t u r e and precipitation data.
The results are shown in Figure 6. (Many runs for various soil types, fertilizer application rates, and geographic regions were made, and the results were d l quali- tatively similar t o those shown.) The solid lines show the steady s t a t e variations of yield with (average) precipitation for various temperatures. The slopes of these lines represent the long-term sensitivities of yield t o precipitation changes a t vari- ous temperatures. The dashed lines represent variations of yield caused by t h e year t o year variation of precipitation. The two a r e clearly not the same. In fact, for the cases of T
=
9TC, and T=
7°C with P=
670 mm/yr, the signs of t h e sensitivi- ties a r e different.Some interesting inferences can be drawn from this numerical experiment.
Short- and long-term sensitivities of agroclimatic models (and, by inference, real systems) can be very different. Many models, in particular, empirical-statistical models, measure only short-term sensitivities. In analyzing and attempting t o predict crop yield change due t o long-term climatic change both a r e important.
Annual precipitation (mm)
Figure 6. Long- and short-term sensitivities for wheat yields (nitrogen fertilizer, 50 kg/ha; phosphorus fertilizer, 10 kg/ha).
Long-term changes in climate, in t e m p e r a t u r e and precipitation, say, quite obvi- ously might affect average crop yields. It appears from t h e present results t h a t t h e sensitivity to short-term climatic variations, i.e., t h e short-term sensitivities, also change when long-term climatic change occurs. Variability of interannual tem- perature a n d precipitation is also expected t o change in response t o long-term climatic change. If a given climate change caused both these variabilities and t h e associated short-term sensitivities t o decrease, t h e variability of crop yields might decrease substantially, and t h i s could be very important for regions of marginal agriculture (Parry. 1976). On t h e o t h e r hand, increases in both variabilities and short-term sensitivities could prove disastrous to marginal agriculture, even if long-term average yields increased.
5. AGROCLIMATIC
MODEL
CHECKLISTThe preceding discussion has addressed a n u m b e r of questions concerning agroclimatic models and t h e i r applicability in climate impact analysis. Table 3 is an attempt t o fit together some of these points in t h e form of a model checklist.
This allows u s t o make o u r own assessment of a particular model on t h e basis of its component p a r t s a n d its operation.
5.1. Model Components
Three classes of model components are depicted:
a) h t a inputs
