Multi-objective parameter conditioning of a three-source wheat canopy model
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.
Section snippets
Model description
The physical model of soil–vegetation–atmosphere transfer used in this study is a highly simplified canopy energy balance and photosynthesis process scheme. The canopy is deemed as homogeneous at the patch scale and parts of the soil moisture and thermal dynamics are omitted. The model is treated as three sources, namely sunlit and shaded groups of leaves, and the ground surface.
Experimental data
The data used in this study were observed in a winter wheat field at Shunyi County, Beijing, China, from 1 to 23 April 2001. The incoming global radiation, net radiation, soil heat fluxes and wind speed were recorded every 5 min with data loggers. Two soil heat flux plates were buried at 1 cm depth. Wind speeds at heights of 1, 2, 3.5 m were measured with three-cup anemometers. At the same heights, dry and wet bulb temperatures in ventilated shields were measured with platinum thermistors. The
Summary of parameters required
Incident solar radiation is partitioned into NIR and VIS components and the VIS is used to approximate PAR in the photosynthesis scheme. The parameter values in the radiation approach are presented in Table 1. These parameters result in predictions of observed absorbed radiation that are highly correlated with the measurements (R2=0.99) and have therefore been fixed in this study. While recognising that there is the potential for interaction between the radiation parameters and other parameters
The GLUE methodology and multi-criteria likelihood measure
Within GLUE, the predictions of each Monte-Carlo sample parameter set are evaluated based on one or more generalised likelihood measures (e.g. Beven and Binley, 1992, Beven and Freer, 2001). The runs with likelihood higher than a threshold are kept as ‘behavioural’, whereas those with likelihood lower than the threshold are rejected as ‘non-behavioural’ and discarded from further analysis. GLUE can be used to describe the posterior parameter space and uncertainty bounds of prediction. It should
Parameter space
It is expected that there will be differing sensitivities of the model outputs to each of the model parameters. For example, aerodynamic parameters will be expected to show sensitivity to the energy partitioning and transfer predictions, but less so to the photosynthetic response. Even for some commonly sensitive parameters, the ranges within the parameter space that yield the highest likelihoods evaluated for each predicted variable do not usually overlay each other exactly. A behavioural
Conclusion
In this study, a canopy model that distinguishes canopy sunlit/shaded leaves and soil surface components was used to estimate canopy photosynthesis, latent and sensible heat fluxes. Following the GLUE methodology, the parameter sensitivities and uncertainty bounds for estimation of CO2 and heat fluxes estimation were implemented with a multi-objective likelihood measure, in which six parameters were selected for the Monte-Carlo sampling and simulation. Two data sets acquired before and after an
Acknowledgements
XM was supported by a Royal Society of London Research Fellowship, China’s special fund for major state basic research (Project No. 2002CB412500), and an Innovation Knowledge project of CAS (CXIOG-C00-05-01). Thanks are due to Prof. Sun and his group for providing the data. The contribution of KB was support by the UK NERC Long Term Grant NER/L/S/2001/00658.
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