A system identification approach for developing and parameterising an agroforestry system model under constrained availability of data
Highlights
► A priori evaluation of agroforestry(AF) system dynamics requires bio-physical models. ► Competitive interactions (water/light) are captured by the Yield-SAFE AF model. ► Modelling of European AF systems is hampered by limited availability of data. ► We follow a parameter optimization approach with constraints from literature/experts. ► We obtain an acceptable correspondence with validation data from an AF experiment.
Introduction
Silvoarable agroforestry (AF) comprises widely-spaced trees interspersed with arable crops. Recent findings indicate that modern silvoarable production systems are efficient in terms of resource use, that they can increase the level of carbon sequestration, reduce the level of nitrate leaching and create a more biologically-diverse habitat relative to sole arable or forestry-based systems ( Burgess, 1999, Graves et al., 2007, Graves et al., 2010, Palma et al., 2007a). Growing high quality trees in association with arable crops in European fields may improve the sustainability of farming systems, diversify farmers’ incomes, provide new products to the wood industry, and create novel landscapes of high value. One of the key questions, related to agroforestry in Europe, is under which conditions is agroforestry most profitable and environmentally advantageous?
For an economic evaluation of an AF system that can be affected by seasonal decisions, the development of a bio-physical model linked to an economic model is indispensable (Graves et al., 2007, Graves et al., 2011; see also Wise et al., 2007). To allow the analysis of a full tree rotation, say of 30–60 years, the bio-physical model should be of limited complexity. Hence, a simple daily time-step bio-physical model implementation, called Yield-SAFE, has been developed (Keesman et al., 2007, van der Werf et al., 2007).
Mathematical modelling has become a major tool to increase the understanding of the underlying crop/tree growth mechanisms under light, water and nutrient competition in AF systems, and to project (long-term) future yields of trees and crops for economic scenario analysis (Graves et al., 2007). In addition to this, mathematical models of AF systems have been used to assess the likely environmental effects of agroforestry at the landscape scale (Palma et al., 2007a, Palma et al., 2007b, Palma et al., 2007c). However, the mathematical model can only be applied successfully if, in terms of model structure and model parameter values, it is an appropriate description of the underlying system. Hence, there is a need for “identification” of the model from experimental data, where (system) “identification” is a general term to describe mathematical tools and algorithms that build dynamical models from measured data. In this paper, identification basically comprises: calibration, validation and model adaptation, which often results in an identification loop (see Norton, 1986, Ljung, 1999, Keesman, 2011).
Identification of European AF systems is hampered by limited availability of data. More specifically, information was limited to yield tables for trees, yield databases for crops, and two experimental AF sites with only 12 years of data. Hence, in short the problem is: given the prior knowledge on AF systems, and given limited data sets, how can we estimate unknown model parameters and how, in case of model deficiencies, can we adapt the model structure?
The objective of this paper is therefore to present a methodology for the identification of a process-based agroforestry model from limited experimental data. This paper articulates the system identification approach and, more specifically, the calibration, validation, and adaptation of the agroforestry model Yield-SAFE (van der Werf et al., 2007).
Section snippets
Summary of model
Yield-SAFE describes tree and crop growth in arable, forestry, and silvoarable systems according to light and water availability. The dynamic ‘core’ of the model comprises seven differential equations. These express the temporal dynamics of: (1) tree biomass; (2) tree leaf area; (3) number of shoots per tree; (4) crop biomass; (5) crop leaf area index; (6) heat sum, and (7) soil water content. The main outputs of the model are the growth dynamics and final yields of trees and crops. Daily
Model calibration
The general description of a finite-dimensional system, as for instance a silvoarable production system, is given bywhere t is the time variable, x is the state vector with initial states x0, u the control input vector, y the output vector and ϑ the parameter vector. Commonly, both vector functions f(.) and h(.) are found from prior system’s knowledge. These functions may, however, also be found after an approximation of an
Sensitivity analysis tree/crop
The O-A-T sensitivity analysis was performed for mono-cultures of crops and trees at two different test sites, one in the Atlantic (Vezenobres – France) and one in the Mediterranean (Dehesa - Spain) zone, respectively. The sensitivity analysis showed that for potential tree growth, that is neglecting the effects of water and management factors, and for both test sites the light use efficiency (eps_t), the light extinction coefficient (Kt_0), the maximum leaf area of a single tree shoot
Discussion and conclusions
This paper illustrates strengths as well as weaknesses in the application of a minimal modelling approach for studying production and resource use in agroforestry systems, particularly when making quantitative predictions for real systems. The strengths are (1) that a model can actually be constructed and parameterized with mechanistically plausible parameters, (2) that the model structure is transparent (van der Werf et al., 2007), and (3) that the quantitative results inspire sufficient
Acknowledgements
This research was carried out as part of the SAFE (Silvoarable Agroforestry for Europe) project funded by the EU under its Quality of Life programme, contract number QLF5-CT-2001-00560, and the support is gratefully acknowledged. We would also like to thank Klaas Metselaar for his early work on crop calibrations.
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