Basil Acock

Modularity and genericness in plant and ecosystem models

Abstract In this paper, we present definitions of modularity and genericness that are based on sets of criteria and rules for model design and which encompass the goal of developing an efficient and flexible structure for plant and ecosystem models. Model structure should be based on modules that (1) relate directly to real world components or processes; (2) have input and output variables that are measurable values; and (3) communicate solely via these input and output variables. Such a model structure has the advantage that it can be incrementally improved by simply replacing one module with another that has the same input and output variables. The underlying mechanism in the replacement module can be different, which facilitates the incorporation of the latest experimental research results and allows modelers to readily test alternative hypotheses about mechanisms. Thus, modularity and genericness open models to contributions from many authors, facilitate the comparison of alternative hypotheses, and extend the life and utility of simulation models.

Predicting the response of plants to increasing carbon dioxide: A critique of plant growth models

Abstract It is widely recognized that increasing global carbon dioxide concentration in the atmosphere may alter the growth of plants. This has lead to speculation about the long-term impact of rising CO2 on agricultural productivity and on natural ecosystems, e.g. shifts in native species distributions and sequestering of carbon in forests. In this paper we critique some existing plant growth models with regard to their potential for predicting and evaluating possible scenarios of vegetation response to elevated CO2 levels. To facilitate this, we present various criteria for model evaluation, specify a minimum set of plant processes that should be considered for inclusion in a generic model capable of predicting plant response to CO2. survey numerous published plant growth models with respect to these criteria, and propose a scheme for identifying the various options available for modeling the response of vegetation to CO2.

An adequate model of photosynthesis—I Parameterization, validation and comparison of models

Abstract Many models of leaf photosynthesis have been proposed but there have been few attempts to compare them and determine their adequacy for various purposes. Three of the most popular models of leaf photosynthesis were compared quantitatively and qualitatively. The models were the rectangular hyperbola, Farquhars model, and Harleys interpretation of Farquhars model. The methodology for statistical assessment and comparison is described. The models were fitted to experimental data for tomato plants ( Lycopersicon esculentum Mill., cv. Rutgers Large Red) by an optimization procedure. The data set consisted of leaf light response curves measured at temperatures of 18, 25 and 32°C and CO 2 concentrations of 100, 350, 700 and 1000 vpm. The hyperbolic model of leaf photosynthesis proved to be adequate quantitatively, and it can be used in models of productivity for predictive calculations. It is not necessary to introduce a more complicated model with a greater number of parameters. The two interpretations of Farquhars model (his own and Harleys) were quantitatively and qualitatively adequate, and can be used for research purposes.

A model 2DLEAF of leaf gas exchange: development, validation, and ecological application

A two-dimensional model (2DLEAF) of leaf photosynthesis and transpiration has been developed that explicitly accounts for gas diffusion through the boundary layer and the intercellular space as well as for stomatal regulation. The model has been validated for tomato. It was used to study the effect of stomatal density on photosynthesis and transpiration rate. It has been demonstrated by varying stomatal density in the model that the stomatal density measured on tomato leaves provides the maximal photosynthesis rate for both 300 and 600 μl 1−1 [CO2]. The transpiration rate varied in direct proportion to stomatal density at all values of stomatal aperture, but transpiration efficiency (photosynthesis rate/transpiration rate) was higher at 600 μl 1−1 [CO2] with a normal stomatal density than at 300 μl 1−1 [CO2] with a stomatal density reduced 25%. Such calculations with 2DLEAF can be useful for analysis of contradicting data presented in publications on possible changes in stomatal density in a future high [CO2] atmosphere.

Indirect estimation of soil hydraulic properties to predict soybean yield using GLYCIM

GLYCIM, a mechanistic model of soybean (Glycine Max L.) growth and development, requires soil hydraulic parameters as input. These data are usually not readily available. The objective of this study alas to compare yields calculated with measured hydraulic properties to those calculated with hydraulic properties estimated from soil texture and bulk density. We reviewed estimation methods and chose two methods to estimate a soil moisture release function and two methods to obtain saturated hydraulic conductivity. Both methods use soil texture and bulk densit), as predictors. Soil water retention predicted bJ3 these methods correlated ,t,ell with measured soil water retention whereas the estimation of saturated hydraulic conductivity was poor. Soybean yields were simulated using GLYCIM with and without irrigation ,for seven locations in Mississippi. USA, using seven years of weather records. Simulated Isields lz’ere aJTected more by the method of estimating the moisture release curve than b>, the method of estimating saturated hJ,draulic conductivity. The average simulated yields from estimated properties tz‘ere higher than those from measured properties because estimated bllater retention provided more availuble water. Correlation betbtleen yields simulated using measured and estimated hydraulic properties was higher under non-irrigated conditions than ti,ith irrigation. Averaging I’ields over years lcith diflerent lveather conditions greatl_v improved the correlations. Published b?, Elserier Science Ltd

Designing an object-oriented structure for crop models

Abstract Object-oriented design (OOD) and programming (OOP) offer many advantages for developing modular crop models. The model structure is well-defined, reuse of code is facilitated through inheritance, and data can be hidden (encapsulated) inside objects that correspond to physical components of the real system, e.g. roots, stems, leaves, or soil layers. However, OOD is best suited to describing the relationship between freely interacting objects, and it has so far been used almost exclusively for modeling simple, discrete and sequential actions. Plant models are not like the automatic teller machine software that is often used in examples of OOD. Plant organs, i.e. objects on the plant, do not wait passively for input from other organs, but they all grow in response to their environment and interact with each other simultaneously and continuously. Also, our ignorance of the processes controlling plant growth forces us to use devices like the limiting factor model to handle these interactions. Many plant models therefore calculate potential growth, limitations imposed by various factors, and then actual growth. In short, there are procedural elements in plant models that do not easily fit an OOD. However, some OOP languages like C + + allow mixed designs to be implemented, so we have developed a mixed, but mostly object-oriented structure that (1) contains the components familiar in extant procedural designs; (2) can be used for modeling at several levels of complexity; and (3) can be used to model any plant. The mixed procedural/object-oriented design has been implemented in C + + as a shell using dummy algorithms, and its operation verified. The problems and advantages are discussed.

Use of the beta distribution for parameterizing variability of soil properties at the regional level for crop yield estimation

Abstract In order to use mechanistic crop models for regional estimates of crop yield it is often necessary to include soil parameters which may not be readily available from published sources or which may be at the wrong level of resolution. A method is proposed for aggregating the values of individual soils to the level of the soil association. This method involves creating frequency distributions based on the recorded properties of the individual soils within the association, and then approximating this distribution by the use of a beta-function. In multiple simulation runs, this method allows the inclusion of the soil variability found in the soil association while modeling crop response over the area of the association.

A two-dimensional model of leaf gas exchange with special reference to leaf anatomy

This model of leaf gas exchange includes (1) two-dimensional C02, 02 and water vapour diffusion in inter- cellular space schematized according to leaf anatomy, (2) CO2 assimilation by mesophyll cells as described by Farquhars model of photosynthesis and (3) stomatal movements as a regulating factor. Parameters describing the leaf cross-section and gas diffusion properties replace the empirical parameters of earlier models. The model was tested for soybean and performed well in representing light, CO2 concentration ((CO21), and temperature response curves as well as the dependence of transpiration on temperature and water vapour deficit. The model allows the calculation of the steady state distribution of CO2 and water vapour concentrations in the intercellular space and the boundary layer. The direct calculation of diffusion in leaves showed that stomatal aperture effectively regulates the transpi- ration rate but usually has a much smaller effect on the rate of assimilation.

Convective-diffusive model of two-dimensional root growth and proliferation

Simulations of crop productivity and environmental quality depend strongly on the root activity model used. Flexible, generic root system models are needed that can easily be coupled to various process-based soil models and can easily be modified to test various hypotheses about how roots respond to their environment. In this paper, we develop a convective-diffusive model of root growth and proliferation, and use it to test some of these hypotheses with data on the growth of roots on potted chrysanthemum cuttings. The proliferation of roots is viewed as a result of a diffusion-like gradient-driven propagation in all directions and convection-like propagation downwards caused by geotropism. The finite element method was used to solve the boundary problem for the convective-diffusive equation. To test hypotheses, we wrote modules in a way that caused a test parameter to be zero, should the hypothesis be rejected. These modules were added or removed to test each hypothesis in turn and in various combinations. The model explained 92% of the variation in the experimental data of Chen and Lieth (1993) on root growth of potted chrysanthemum cuttings. For this dataset the following hypotheses were accepted: (1) root diffusivity (colonization of new soil) did not depend on root density, (2) there was no geotropic trend in root development, (3) potential root growth increased linearly with root density, (4) there were (at least) two classes of roots with different rates of growth and proliferation, and (5) potential root growth rate decreased with distance from the plant stem base.

Error analysis of soil temperature simulations using measured and estimated hourly weather data with 2DSOIL

Many crop simulation models use 1-h time steps for atmospheric, soil and plant processes but often meteorological data are only available as daily summaries. The objective of this study was to investigate how errors in estimation of hourly values of solar radiation and air temperature affect errors in simulation of soil temperature using the model 2DSOIL. 2DSOIL is a two-dimensional finite element model that simulates water flow, chemical, water and solute uptake by plant roots, chemical equilibria processes, and gas and heat transport in soil. The standard deviations of the differences between hourly estimated air temperatures were about 2 � Ca nd 85 Wm � 2 for solar radiation. The mean difference in simulated and measured soil temperatures using measured hourly weather data for all depths at both sites was less than 1 � C and standard deviations were about 1–3 � C indicating low bias. The range of errors was highest in the surface soils when the soil was wetted after rainfall. Relative to simulated soil temperatures using measured hourly data, simulated soil temperatures using estimated data were, on average over all depths, 2 � C lower and standard deviations ranged from 2 to 3 � C. The errors were similar over all depths. Use of estimated hourly air temperature and radiation generally resulted in underpredictions of soil temperature by 2–3 � C and increased error. Also maximum daily soil temperatures were underestimated. Published by Elsevier Science Ltd.