Crop simulation modelling using a transputer-based parallel computer

Agricultural Systems 35 (1991) 321-337

;aj Crop Simulation Modelling Using a Transputer-based Parallel Computer P. K. T h o r n t o n , a* J. A. Blair-Fish ~ & S. M. D. W i l s o n b a Edinburgh School of Agriculture, b Edinburgh University Computing Service, West Mains Road, Edinburgh EH9 3JG, UK (Received 22 February 1990; accepted 16 August 1990) ABSTRACT The adaptation of a biological model of the growth and development of wheat is described that allows simulations to be carried out concurrently. The number of simulations that can be carried out side-by-side is limited only by the number of transputers available to the user. The use of this version of CERES- Wheat is illustrated with reference to afertiliser experiment, and the speed of execution is compared with other hardware systems. Uses to which a parallel computer could be put in crop simulation modelling are discussed, and further developments are outlined.

INTRODUCTION The increasing speed and power of computers allows applications to be run routinely that would have been inconceivable a few years ago. While m a n y agricultural applications of computers are served adequately by the comparatively cheap desk-top machines of today, there are some that would benefit from still faster machines. In the search for speed, hardware and software design are developing along two distinct lines. The first involves the construction o f single processor machines, currently capable of 1-10 Gflops (1 G f l o p = 10 9 floating point operations per second), and a more efficient computer code written to run sequentially. The second, usually a much cheaper m e t h o d of attaining comparable speeds, is provided by the use of parallel computer * To whom correspondence should be addressed at: IFDC, P.O. Box 2040, Muscle Shoals, Alabama 35662, USA. 321 Agricultural Systems 0308-521X/91/$03"50 © 1991 ElsevierSciencePublishers Ltd, England. Printed in Great Britain

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architecture and appropriately structured programs, making use of multiple processors that can run different pieces of computer code at the same time. Concurrency, or parallelism, has developed substantially over the last few years, largely as a result of the transputer. While the number of agricultural modelling applications that require the speeds provided by a sequential or parallel super computer is unlikely ever to be numerous, there are sufficient to make investigation worthwhile. This paper describes the first steps taken in using an existing simulation model of the growth and development of an important agricultural crop (CERESWheat, Godwin et al., 1989), and modifying it to run on the Edinburgh Concurrent Supercomputer (ECS). The ECS and the nature of parallelism are described briefly. The modifications necessary to CERES-Wheat are then presented, and its use is illustrated by describing and analysing a computer-based fertiliser experiment that was carried out concurrently. Some speed comparisons are made with CERES-Wheat run on more traditional sequential machines, both large and small. Finally, possible uses of parallel machines are outlined with respect to agricultural modelling applications.

THE E D I N B U R G H C O N C U R R E N T S U P E R C O M P U T E R The Edinburgh Concurrent Supercomputer is a Meiko Computing Surface, and at present includes some 300 T800 Transputers and 100 T414 Transputers. The present machine dates from 1987, and will eventually consist of 1024 T800s. The system is made up of a number of'domains', each with a variable number of Transputers, so that up to 20 users can use the

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Fig. 1. Schematic diagram of the Edinburgh Concurrent Supercomputer (from Wallace, 1990).

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computer at a time (Fig. 1). The size and number of domains is flexible and can be changed to suit users. The system is essentially similar to a network of workstations and file servers, run under MEIKOS, a UNIX-like operating system. The Transputer lies at the heart of the system; it can be thought of as selfcontained computer processor, containing its own on-board memory. The top-of-the-range T800 is a 32-bit processor. Its performance depends on many things, but for the 20 MHz T800, 10mips (million instructions per second) and 1 Mflop may be taken as typical (Wexler & Prior, 1989). Transputers are designed so that they can be connected directly one to another, and messages passed. Each can be connected to a maximum of four others. Transputers can be linked together in any way the user sees fit, and the way in which this is done will affect the efficiency of problem solution. In general, designing a configuration for a particular problem is important and may be difficult. The ECS is software-configurable, which means that the Transputers already available to the user can be configured just prior to loading the program. The native language of the Transputer is Occam 2; this is a high-level language that provides for highly-structured sequential programming as well as full control of concurrent processes. There are F O R T R A N and C compilers, and utilities that provide flexibility in enabling an existing computer code to be run on the machine. The range of research projects supported by the machine is extremely wide, ranging from computational physics and simulations of all kinds (ships, stellar systems, gas explosions and crystal growth, for example) to image processing and neural network models (Wexler & Prior, 1989).

PARALLELISM The parallel approach to a computing problem differs in fundamental respects to the sequential approach. The idea of parallelism is as follows: if it takes 10 s to solve a problem on a single processor, then, by splitting the problem up in a suitable way, two processors could produce the solution in 5 s, each working on different parts of the program. In general, if the problem takes n seconds on one processor, then the ideal is represented by the case where rn processors take n/rn seconds. This 100% efficiency is never achieved, although some applications may come close. Efficiency tends to fall off as more processors are added, but there are classes of problem where this fall-off is not serious. There are essentially three approaches to making use of parallelism, termed event, geometric and algorithmic parallelism (Wesler & Prior, 1989).

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(i) Event parallelism This approach can be used when the overall problem consists of many independent but similar problems. A copy of the code for the complete algorithm can be loaded directly onto each Transputer. An ideal situation exists where the different data required for each sub-problem can be simply loaded onto each Transputer. This is directly applicable to only a few problems (although the one considered below falls in this category). The important thing in this case is that the individual processors do not have to share any data. It does not matter if solutions take different times. A master processor can send a batch of data to each of several worker processors. When any worker has completed its task, the result is returned to the master, and the master will send the worker a further batch of data. A worker that receives some 'easy' batches may process several while another worker is working on one 'difficult' batch. All the workers are kept busy, and the system runs efficiently. This is called 'task farming'.

(ii) Geometric parallelism There are also classes of problems that, unlike the case outlined above, involve inter-processor communication. This is termed geometric parallelism. Sometimes a problem can be divided up into 'clusters' whose behaviour depends only on their own internal workings and those of their immediate neighbours. An example of this type of problem is image processing, where the analysis of a particular picture element (pixel) is carried out with reference to neighbouring pixels, but independently of pixels elsewhere. This type of problem is not susceptible to task farming, and is c o m m o n in computational physics. Some problems require a combination of event and geometric parallelism for efficient use of concurrency: again, for instance, in image processing, where some areas of the image require much more intensive computation than others.

(iii) Algorithmic parallelism Sometimes whole algorithms can be divided up into stages that are then run on separate processors. In this case, every item of data is processed in turn by each processor involved. In other words, the algorithm is distributed, rather than the data of geometric parallelism. Efficiency is served if the various stages of the algorithm each take approximately the same time to complete. Most problems at present are approached using the notion of geometric parallelism; the development of parallel algorithms is in its infancy and is

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usually extremely difficut, not least because of the problems of attempting to conceptualise concurrent activities. Some applications are designed from the start with a particular type of parallelism in mind. For others, conversion of the computer code is required, and this may not be a trivial problem. An important set of utilities on the ECS help in this respect; these are 'harnesses' that provide support for particular parallel models. Unlike the normal method of sequential programming, where a user will often call library subroutines provided by the makers of the language compiler (such as a F O R T R A N function to calculate a square root), a harness is in effect a main program from which the user hangs his own subroutines to perform the tasks required. As will be seen below, harnesses considerably lighten the load of the Transputer user: for instance, CERES-Wheat has no internal, inherent concurrency, nor is it necessary for it to have such. The literature on Transputers, the ECS and parallelism in general is already substantial, and many more details than it is appropriate to include here can be found in Wexler and Prior (1989), Wexler and Wilson (1989), and Wallace (1990), for example.

CERES-WHEAT The model used in the present work was CERES-Wheat (Godwin et al., 1989). This is a detailed biological simulation model of the growth and development of the crop, and has been designed to be portable between radically different environments (Otter-Nficke et al., 1986). The model operates on a daily time step. Potential dry matter production is a function of photo-synthetically active radiation, and the dry matter produced on any day is partitioned between the plant organs that are growing at that time. Crop development is driven by the accumulation of daily thermal time or degree days, which is defined as the daily mean air temperature minus some base temperature below which it is assumed no development occurs. The inputs required to run the model are daily weather variables, crop and management information, and soil profile data. The weather and soil data combine to make the model site- and time-dependent. A number ofcultivarspecific coefficients are defined that are assumed to explain the variability exhibited between cultivars. In addition to water, weather and cultivar type, the results obtained from CERES-Wheat are sensitive to nitrogen movement in the soil and plant, and to management factors such as planting data and plant population. The most recent versions of the model contain routines for modelling phosphorus movement in the soil and plant, but not the version used here.

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Under the auspices of the International Benchmark Sites Network for Agrotechnology Transfer (IBSNAT) project (Uehara, 1989), work is proceeding at various institutions in the US and elsewhere on the effects of pests and diseases, and plant competition, with respect to weeds and intercropping. Output from the model includes final yield and biomass partitioning between the various plant components at harvest. A variety of variables can be produced by the model at intervals through the growing season, including leaf area index, biomass, dates of attainment of various growth stages, and water and nitrogen content in the soil horizons. Probability distributions of yields can be generated in response to a management strategy over many simulated weather sequences. Such strategies might involve different fertiliser or irrigation application rates, or different planting dates and seedling densities. Running the crop model with simulated climate sequences, obtained using a statistical weather generator (Richardson, 1985, for example), allows the variability of yield over time to be investigated explicitly. Yields, or any other output of interest, can be assembled into cumulative probability functions. Such information allows an objective comparison to be made between varieties and management inputs on the basis of variability over time, by incorporating the cumulative probability functions directly into an economic analysis.

Adaptation of CERES-Wheat CERES-Wheat is not suited to algorithmic parallelism, since day-by-day simulation is, by its very nature, a sequential process (what happens on any day is largely a function of what happens on previous days). Rather than attempt to split the algorithm, the approach taken involved perhaps the most obvious feature of the model that could be treated in a parallel fashion, viz. replication of treatments using event parallelism and task farming. Currently, the four weather variables are the only stochastic input to the model. Control over simulated weather sequences is afforded through manipulation of the pseudo-random number generator seeds that are used by statistical weather sequence generators. For using the task farm harness, a program has to be split up into three parts: (1) A driving sub-program process that reads any input file, generates tasks, and then passes these on to the worker Transputers; (2) A worker sub-program that performs the task and generates results; (3) A collection sub-program that collects results and writes these to an output file.

Crop simulation modelling using transputers

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The driver and collector reside on one Transputer, called the master, and both have access to i n p u t - o u t p u t files (see Fig. 2). One 'copy' or image of each worker sub-program is put on each worker Transputer (in a typical ECS domain, there are eight Transputers: one master and seven workers). In such an arrangement (necessitated by the harness, not the computer), efficiency is served if input and output are confined to the driver and the collector subprograms. Thus, the worker sub-program has to be largely self-contained, apart from the data sent to it for each run by the driver. Many changes were made to the structure of CERES-Wheat, but the most important were the following: (1)

The numerous i n p u t - o u t p u t files (described in Godwin et al., 1989, and IBSNAT, 1988) were suppressed, along with all the interactive menus, and many of the variables were 'hard-wired' into the program. All associated read and write statements were excised. The variables that were sent to each worker, and thus went to define the replicate of the particular treatment being considered, are listed in Table 1. Similarly, the variables (results) that are sent back to the collector and written to the new output file are shown in Table 1 also. It is straight-forward to change the file-based input and output variables; thus if irrigation were to be investigated rather than nitrogen applications, or if different varieties were to be used the relevant changes could be made to the program quickly and easily.

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TABLE 1

File-based Input and Output Variables Used in the Edinburgh Concurrent Supercomputer Version of CERES-Wheat

(2)

Input

Seed for the random number (RN) generator Starting date of simulation Planting date Second seed for the RN generator Day number from which the second RN seed should be used No, of fertiliser applications (0-2) Fertiliser application 1: date Amount Depth of incorporation Type code (e.g. NH4NO 3 = 1) Fertiliser application 2: date Amount Depth of incorporation Type code

Output

Job number First RN seed Planting date Germination date Emergence date Terminal spikelet date End of vegetative stage date End of pre-anthesis ear growth date Beginning of grain fill date Physiological maturity date Anthesis date Final grain yield Kernel weight Grains per square metre Grains per ear Maximum leaf area index Total biomass Straw biomass Grain N content (%) Total N uptake Straw N uptake Grain N uptake

CERES-Wheat was compiled with the Richardson (1985) weather generator (WGEN) and associated user-written subroutines, to enable independent weather sequences for each season to be simulated prior to the running o f CERES-Wheat. The simulated weather variables were then stored internally in the program, and not as a file on disk (see Fig. 3). Note that, unlike a sequential program, a

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task farm program has three separate 'main' programs at the highest level in the subroutine hierarchy. The amount of code necessary for the driver, worker and collector is small, amounting to approximately 25 lines for each. The controller subroutines that are necessary are not lengthy, either. In all, however, the rest of the program, including WGEN and CERES-Wheat, amounted to some 3800 lines of FORTRAN.

A N ILLUSTRATION: A FERTILISER EXPERIMENT To illustrate the use of the program, a fertiliser experiment was devised (Table 2). The soil used was a clay loam, and the Richardson generator was used to simulate weather at Pittsworth, Queensland (Godwin, 1988). Mean rainfall at Pittsworth is 698 mm, and 68% of this falls between October and March. The average maximum temperature in January is 30"4°C, and in July, 18.6°C. Wheat growing is thus a winter occupation. The variety used was Heron. The input file for the master Transputer was assembled, one record for each treatment. This file was then expanded using a F O R T R A N program that assigned seeds for the random number generator to 50 replicates of each treatment, to result in an input file of 2000 records, each record being equivalent to one task (a full treatment description and a unique random number seed, to ensure different weather sequences for each replicate, see Table 1). The entire experiment ran in some 771 s, using a domain with eight Transputers (one master and seven workers). Timings for CERES-Wheat on

P. K. Thornton, J. A. Blair-Fish, S. M. D. Wilson

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TABLE 2 Experimental Design for an Illustrative Simulation Experiment

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Number of treatments = 4 × 3 × 3 + 4 = 40. Number of replicates = 50. Number of season simulations = 40 × 50 = 2000.

other hardware systems are shown in Table 3. Note that with a larger domain, the advantage of the Meiko Computing Surface over the VAX 8500 would be considerably enhanced; theoretically, an array of 700 T800 Transputers could perform a 2000-season experiment in some 8 s. Note also, that the timings in Table 3 can be taken as elapsed times, except for the two VAX machines, which are multi-user single processor systems. The output file was downloaded to a microcomputer for analysis. Results Results are shown in Figs 4 and 5, where the effect of planting date on yieldis plotted for various nitrogen strategies, and the effect of N application is TABLE 3 Timings of Various Versions of CERES-Wheat on Various Hardware Configurations

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plotted for various planting dates. Standard statistical tests are of no use in such a situation, since significant differences, however small, can always be obtained if enough replicates are run. For this reason, results are presented in terms of the mean and the 25th and 75th percentile of the cumulative probability function of the relevant yield distribution. This presentation conveys something of the variability of each treatment and the skewness of the resultant distribution. Perhaps the most difficult problem facing any analysis of these data is that the intrinsic error of CERES-Wheat, in terms of accuracy of yield simulation, is unknown. It may well be that some of the effects in Figs 4 and 5 can be ascribed to the model rather than to real life. Similarly, it is essentially unknown if CERES-Wheat accurately simulates yield distributions in response to weather patterns. It is known that the Richardson generator seriously underestimates yearly rainfall variances (Godwin, 1988; Thornton, unpublished), but the performance of a crop model is harder to assess since the data necessary to validate it are not routinely collected from field trials (in contrast to a weather station, for instance).

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It is thus difficult to draw any firm conclusions from this (admittedly hypothetical) experiment. The suggestion exists that N is largely wasted if the crop is planted early; there is little response to late N application, or to split N applications. If planting later, then some yield response to N is obtained, but this may not be economic, depending on the relationship between the cost of N and the price of wheat. Early planting tends to result in lower yield variances and lower mean yields; a mean-variance diagram is plotted in Fig. 6 for all 40 treatments, together with the EV-efficient frontier. To give an idea of the shape of these yield distributions, the 6 EV-efficient treatments are shown in Fig. 7 as cumulative probability function plots. Of the 40 treatments, 11 belong to the second-order stochastic dominant set, using the algorithm of Anderson et al. (1977). As with all simulation experimentation, problems are encountered in attempting to analyse the results; in the present study, such problems are

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exacerbated by the ability to produce large quantities of output in a very short time. It would appear that before a great deal of use is made of multireplicate, multi-treatment simulation experiments, some characterisation of the error involved in modelling the mean and the distribution of response is desirable. Without it, it remains unknown what effects are an artifice of the model and which ones can confidently be expected to be mirrored in any field trials that are undertaken, perhaps as a result of the modelling work.

USES OF P A R A L L E L C O M P U T E R S F O R CROP M O D E L L I N G Speed is only one benefit of using a model on a supercomputer, and by itself it is probably of limited value, compared with the benefits of parallelism p e r se. Of the crop modelling applications that may in the future make extensive use of supercomputing facilities, three are discussed below.

(i) Crop management optimisation One application that suggests itself is the use of the model in an optimisation role. There are many decisions that have to be taken when considering how to grow a crop. Some need be taken once only each season (what variety should be grown?); once the crop is growing, other questions will need to be asked continuously (does the crop need spraying for disease? Does it need irrigating?). Crop management can thus be thought of as a sequence of decision points that build up into a decision tree (Thornton & McGregor, 1988). A crop model could be used in real time to help the grower identify the most appropriate (in terms of the objectives of the grower) management regime, based on particular soil and climate conditions. The basis for handling management decision trees is already built into the version of CERES-Wheat described above. Before the crop is planted each season, there is a particular probability distribution for yield associated with any particular variety, soil and climate. This distribution is essentially unchanging from year to year, and it can be derived through simulations with the crop model where the entire season's weather is generated stochastically, as in the example above. As time progresses and the crop starts to develop in the field, more and more weather becomes known or fixed: crop development depends on climate, among other things, and the performance of the crop at any time during the season is related to the weather up to that point. The distribution of crop yield, if simulated using historical weather data up to this point and generated weather thereafter, may look very different to the pre-season yield distribution: the season may have been unusually dry, so that the probability

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(ii) Modelling of multiple crop enterprises and whole farms There are a number of problem areas that involve a study at the level of the whole farm, taking into account all the enterprises with which the farmer is concerned and the competition for resources. Some benefits are likely to be

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P. K. Thornton, J. A. Blair-Fish, S. M. D. Wilson

gained from using a Transputer-based computer for such problems, although the most efficient way of handling crops growing in the ground at the same time may not necessarily be to assign one worker to each 'field'.

(iii) Model linkages with geographic information systems An important future area of research lies in the construction of decision support systems at a regional or national scale (Dent & Thornton, 1989). One way in which this can be done is through the development of a spatial land-use database for a region, based upon a geographic information system (GIS); this consists of a graphics base, a set of map-orientated computer programs, and a data base that contains the data, or attributes, that belong to a particular map, such as soil, weather and regional information. Crop simulation models can then be linked to the GIS, to produce estimates of regional production, for example. It is an application particularly suited to the ECS, since crop performance in any agroecological zone in a region is unaffected by performance elsewhere, and thus can be carried out using the task farm concept outlined above. For regions where the number of agroecological zones is large, the concurrent estimation of crop production and its variability is an obvious but interesting possible application of a Transputer-based computer.

CONCLUDING REMARKS The problems involved in mounting sequentially-designed computer programs onto a multi-processor computer system are by no means insurmountable. It is pertinent to consider whether the benefits outweigh the costs of doing so, especially with respect to agriculture, where the number of applications of supercomputing is likely to remain strictly limited for the foreseeable future. There would appear, however, to be sufficient to make the development of parallel programs worthwhile, particularly in the areas of management optimisation and modelling using GIS. The substantial increases in speed highlight the problems of inherent model error and how this can be measured; in addition, it is likely that some methodological developments are required to enable large-scale, multireplicate simulation experiments to be analysed in a meaningful fashion. Further work will concentrate on the three application areas noted above. It would also be beneficial to investigate ways of mounting CERES-Wheat and similar models with the minimum of structural alterations. CERESWheat is undergoing continual revision and improvement, and incorporating updates to the ECS version is a major task at present.

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ACKNOWLEDGEMENTS IBSNAT is a program of the United States Agency for International Development (US AID), implemented by the University of Hawaii under Cooperative Agreement No. AID/DAN-4054-A-00-7081-00.

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