Multi-objective parameter conditioning of a three-source wheat canopy model

Abstract

A three-source canopy model, which distinguishes the energy budgets for sunlit and shaded leaves and the underlying soil surface, is applied within the generalised likelihood uncertainty estimation (GLUE) methodology for a site near Beijing, China. Parameter sensitivities and uncertainty bounds for CO₂ and heat fluxes were analysed based on a multi-objective evaluation of Monte-Carlo realisations of model parameters. Two data sets acquired before and after an irrigation event in a wheat field were used to constrain the model. The results show that some of the six parameters varied are strongly conditioned by the observed fluxes, especially by the observations of CO₂ flux above the canopy, but the scatter plots and cumulative distributions of parameter spaces are quite different between the two data sets. The predicted canopy photosynthesis rate demonstrates wider 95% uncertainty bounds than the latent and sensible heat fluxes. Comparison of model performances between two-source and three-source models shows that the parameter sensitivities are different and that the three-source model gives more constrained uncertainty bounds. Finally, a ‘best’ parameter set is used to estimate the energy budgets at the three sources. It is shown that the net radiation on shaded leaves is about 20% of the sunlit leaves, whereas the ratio is 50% for latent heat flux around noon. Hence, the shaded leaves are predicted as acting as sinks of sensible heat, reducing the predicted temperature differences between the two groups of leaves.

Introduction

Energy and mass exchanges at the land–atmosphere interface has a considerable effect on climate, ecology and hydrological cycling. Soil–vegetation–atmosphere transfer (SVAT) models have been developed and refined to represent these exchange processes, which are driven by multiple input variables and are capable of predicting the evolution of some observable variables (e.g. surface temperature, and soil moisture) and fluxes (e.g. latent heat, sensible heat, CO₂ and runoff) at the scale of a vegetation “patch”.

In SVAT models, two kinds of approach have been used to scale up from leaf to canopy. One is the multilayer model (e.g. Nagai, 2002), the second is the ‘big leaf’ model in which the properties of the whole canopy are mapped onto the ‘big leaf’ before calculating canopy fluxes. Among the ‘big leaf’ models, there are three kinds of treatments. The first is the Penman–Monteith model that takes the canopy and the soil beneath as one layer. The second is the two-source model that treats the canopy and soil surface as two different sources of heat and mass fluxes (Shuttleworth and Wallace, 1985). The third is the sunlit/shaded model that treats the sunlit and shaded leaves, as well as the soil surface as three different sources (De Pury and Farquhar, 1997, Wang and Leuning, 1998, Zhan and Kustas, 2001, Mo and Liu, 2001).

The application of the sunlit/shaded canopy model is based on the following understanding of the canopy processes. Because leaves respond non-linearly to irradiance and the radiation load on sunlit and shaded leaves in the canopy is significantly different, shading can have an important effect on the leaf photosynthetic rate. In addition, photosynthesis and the partitioning of the available energy are also non-linearly related to leaf temperature and the temperature difference from leaf to air. It is reported that sunlit leaves may be several degrees warmer than shaded leaves under sunny and dry conditions, so ignoring the distinction between sunlit and shaded leaves will markedly bias the estimates of photosynthesis and energy fluxes from the canopy (Spitters, 1986, Myneni and Ganapol, 1992).

Generally, complete SVAT models, even greatly simplified, still have a large number of parameters to describe vegetation characteristics, soil hydraulic and physical properties that must be specified. Among these parameters, some are measurable at patch and larger scales, such as albedo and fraction of vegetation cover; however, some are scale dependent and not easily measured at the relevant scale, such as soil hydraulic conductivity and leaf stomatal conductance (Bastidas et al., 1999). Consequently, there are scale issues when calibrating the model parameters. The scaled up parameters are derived indirectly by calibration with canopy or larger scale measurements, such as heat and CO₂ fluxes above canopy, and measured “surface” temperature. Effective canopy scale parameters may be different from values calculated from direct measurements at the leaf scale.

The wide range of physical processes involved in a SVAT model increases the degrees of freedom in physical and physiological parameter specification. It is reported that even simple manual adjustment of a few parameters can result in significant improvement in the model performance (Lettenmaier et al., 1996). With the very limited available observations for constraining the parameter space, it is unavoidable that many different parameter sets, from physically feasible ranges, will provide an acceptable fit to the observed data. This has been called the equifinality problem (Beven and Binley, 1992, Franks and Beven, 1997, Beven, 2002). It is the interaction between the parameters, not just the role of a single parameter, which determines whether the model performance will be considered as behavioural. As a consequence, it is not possible to identify a unique optimum parameter set for a specific objective function.

Different behavioural models, although satisfying the same performance criteria, will produce different spatial and/or temporal patterns of model predictions. This allows uncertainty in model predictions to be assessed. This problem will increase as more physical processes and parameters are introduced into the model structure if no additional independent data are available for evaluating the performance of the feasible models. The generalised likelihood uncertainty estimation (GLUE) methodology has been developed to address the equifinality problem and to estimate the predictive uncertainty bounds associated with the behavioural simulations (Beven and Freer, 2001). Some primary applications have been done on SVAT model calibration and uncertainty analysis (Franks and Beven, 1997, Franks and Beven, 1999, Franks et al., 1997, Schulz and Beven, 2003). It has been suggested in more traditional approaches to model calibration that one way of reducing the potential for equifinality of parameter sets is to increase the information content of the evaluation data by applying different, independently observed variables with multi-criteria or multi-objective methods (Yapo et al., 1998, Kuczera and Mroczkowski, 1998, Gupta et al., 1999, Bastidas et al., 1999).

In this paper, we first describe a three-source approach to canopy energy balance and photosynthesis, in which the available energy is partitioned between sunlit and shaded leaf groups and the ground surface. Summing the fluxes from the three components then gives the total surface flux exchanges between the canopy and the atmosphere. Here, we represent the heat flux expressions in a similar form to the Penman–Monteith equation. Then, the parameter space and prediction uncertainty of heat and CO₂ fluxes are analysed with the GLUE methodology. Thirdly, the differences in the predicted energy budget, photosynthesis, and leaf temperatures between sunlit and shaded leaves are examined.