A system identification approach for developing and parameterising an agroforestry system model under constrained availability of data

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Abstract

This paper introduces a system identification approach to overcome the problem of insufficient data when developing and parameterising an agroforestry system model. Typically, for these complex systems the number of available data points from actual systems is less than the number of parameters in a (process-based) model. In this paper, we follow a constrained parameter optimization approach, in which the constraints are found from literature or are given by experts. Given the limited a priori systems knowledge and very limited data sets, after decomposition of the parameter estimation problem and after model adaptation, we were able to produce an acceptable correspondence with validation data from a real-world agroforestry experiment.

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 byx(t)t=f(t,x(t),u(t),w(t);ϑ),x(0)=x0y(t)=h(t,x(t),u(t);ϑ)+v(t),tRwhere 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.

References (74)

  • K.J. Keesman et al.

    Mathematical production ecology: analysis of a silvo-arable agro-forestry system

    Mathematical Biosciences

    (2007)
  • J. Palma et al.

    Modelling environmental benefits of silvoarable agroforestry in Europe

    Agriculture Ecosystems & Environment

    (2007)
  • J. Palma et al.

    Methodological approach for the assessment of environmental effects of agroforestry at the landscape scale

    Ecological Engineering

    (2007)
  • J. Palma et al.

    Integrating environmental and economic performance to assess modern silvoarable agroforestry in Europe

    Ecological Economics

    (2007)
  • P. Prusinkiewicz

    Modelling plant growth development

    Current Opinion in Plant Biology

    (2004)
  • Y. Reisner et al.

    Target regions for silvoarable agroforestry in Europe

    Ecological Engineering

    (2007)
  • A. Saltelli et al.

    How to avoid a perfunctory sensitivity analysis

    Environmental Modelling & Software

    (2010)
  • M. van Ittersum et al.

    Concepts in production ecology for analysis and quantification of agricultural input-output combinations

    Field Crops Research

    (1997)
  • W. van der Werf et al.

    Yield-SAFE: a parameter-sparse, process-based dynamic model for predicting resource capture, growth, and production in agroforestry systems

    Ecological Engineering

    (2007)
  • J.K. Vanclay et al.

    Evaluating forest growth models

    Ecological Modelling

    (1997)
  • R. Wise et al.

    Fertilizer effects on the sustainability and profitability of agroforestry in the presence of carbon payments

    Environmental Modelling and Software

    (2007)
  • J.H.M. Wösten et al.

    Development and use of a database of hydraulic properties of European soils

    Geoderma

    (1999)
  • T. Ziehn et al.

    GUI-HDMR - A software tool for global sensitivity analysis of complex models

    Environmental Modelling & Software

    (2009)
  • A.A.A. Abusam et al.

    Sensitivity analysis in oxidation ditch modelling: the effect of variations in stoichiometric, kinetic and operating parameters on the performance indices

    Journal of Chemical Technology and Biotechnology

    (2001)
  • P. Balandier et al.

    Growth of widely spaced trees. A case study from young agroforestry plantations in France

    Agroforestry Systems

    (1998)
  • B. Boulet-Gercourt

    Le merisier

    (1997)
  • P.J. Burgess

    Effects of agroforestry on farm biodiversity in the UK

    Scottish Forestry

    (1999)
  • P.J. Burgess et al.

    The Impact of Silvoarable Agroforestry with Poplar on Farm Profitability and Biological Diversity

    (2003)
  • Burgess, P., Graves, A., Metselaar, K., Stappers, R., Keesman, K., Palma, J., Mayus, M., van der Werf, W., 2004a....
  • P.J. Burgess et al.

    Poplar (Populus spp) growth and crop yields in a silvoarable experiment at three lowland sites in England

    Agroforestry Systems

    (2004)
  • Centre Régional de la Propriété Forestière
    (1997)
  • M.-H. Chen et al.

    Monte Carlo Methods in Bayesian Computation

    (2000)
  • J.M. Christie

    Provisional Yield Tables for Poplar in Britain

    (1994)
  • J.S. Clark et al.

    Tree growth inference and prediction from diameter censuses and ring widths

    Ecological Applications

    (2007)
  • F.d. Coligny et al.

    CAPSIS: computer-aided projection for strategies in silviculture: advantages of a shared forest-modelling platform

    Modelling Forest Systems

    (2003)
  • No 1698/2005 of 20 September 2005 on Support for Rural Development by the European Agricultural Fund for Rural Development

    (2005)
  • P.H. Cournede et al.

    Computing competition for light in the GREENLAB model of plant growth: a contribution to the study of the effects of density on resource acquisition and architectural development

    Annals of Botany

    (2008)
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