Simple versus complex models 50 

When building a mathematical model to be representative of a system of interest, the first impulse is to include as many details as possible, in order to improve the description of the processes involved, and to obtain this way a better representation of the system. The tendency is therefore towards complex models. But while complex models have the advantage of relying on the best up-to-date knowledge of the considered system, the risk is to try to build a full-scale map of the World1_{. Complex models tend to be difficult to be implemented and imply} a considerable computational burden (e.g. Cayrol et al., 2000; Montaldo et al., 2005). Also, the high number of parameters included in the models, which has to be estimated, requires high amounts of field data, rarely available particularly in natural science investigations (e.g. Montaldo et al., 2003). Finally, the fact that these models are so detailed tends to give the impression that results are absolutely reliable, dozing off the user’s critical spirit.

Simple models, on the other hand, are usually quicker to build and easier to implement, interpret and update. Their relative transparency allows the user to adapt them to the particular characteristics of the considered system and parameters are fewer and of easier estimation. Undoubtedly, the risk is to simplify processes too much, so that instead of a simple model, a simplistic and completely unreliable model is implemented. To avoid this chance, it is essential that the most important processes of the system are identified and reproduced satisfactorily.

In this regard, Montaldo et al. (2005) analysed five variants of a vegetation dynamics model (VDM) included in a land surface model

1 _{"Del rigor en la ciencia", Jorge Luis Borges}

En aquel Imperio, el Arte de la Cartografía logró tal Perfección que el Mapa de una sola Provincia ocupaba toda una Ciudad, y el Mapa del Imperio, toda una Provincia. Con el tiempo, estos Mapas Desmesurados no satisficieron y los Colegios de Cartógrafos levantaron un Mapa del Imperio, que tenía el Tamaño del Imperio y coincidía puntualmente con él. Menos adictas al Estudio de la Cartografía, las Generaciones Siguientes entendieron que ese dilatado Mapa era Inútil y no sin Impiedad lo entregaron a las Inclemencias del Sol y los Inviernos. En los Desiertos del Oeste perduran despedazadas Ruinas del Mapa, habitadas por Animales y por Mendigos; en todo el País no hay otra reliquia de las Disciplinas Geográficas.

Implemented vegetation models 51

(LSM), starting with the most complex one and gradually reducing the VDM complexity and parameterization. The five variants are as follows: a) CVM, the complete VDM, which simulates three compartments of biomass (i.e. green aboveground, living root and standing dead). The number of parameters is 20, including 7 from the LSM;

b) SVM1, a simplified version of CVM (also with 20 parameters), which simulates the three biomass compartments but uses a simplified equation for photosynthesis computation;

c) SVM2, a simplified version of SVM1, which does not explicitly treat root biomass. The number of parameters is 15, of which 6 from LSM; d) SVM3, a simplified version of SVM2, which only simulates green biomass. It has 13 parameters, including 6 from the LSM;

e) SVM4, a simplified version of SVM3, in which both senescence and respiration biomass loss terms are comprised into a single term, linearly related to biomass. The total number of parameters is 10 (6 from the LSM).

The comparison between the results of the five model versions and field data revealed that the complete model and the simplified models from number 1 to number 3 performed well and similarly. The SVM4, on the other hand, failed to capture plant respiration dynamics and therefore appeared to have an oversimplified structure. The authors concluded that SVM3 is a good compromise reconciling a low number of parameters with a satisfactory simulation of LAI dynamics and land surface fluxes.

Commonly, vegetation and hydrological models are either physically based or conceptual. A physically based model, or deterministic model, is based on complex physical theory and requires a large amount of data and computational time (Jajarmizadeh et al., 2012). Conceptual models, instead, are composed by a number of conceptual elements which are simple representations of a reference system. When dealing with highly complex systems, like water-vegetation ones in semi-arid climates, the poor level of understanding and/or observation of the processes involved makes conceptual modelling powerful, while the frequently limited available information requires a parsimonious approach.

Keeping in mind these needs, HORAS (Quevedo & Francés, 2008; Quevedo, 2010), a conceptual parsimonious vegetation model, was developed by the Research Group of Hydrological and Environmental Modelling at Universitat Politècnica de València. Considering the not entirely satisfactory results obtained by HORAS, the model was at first modified (Pasquato, 2011) and subsequently abandoned in favour of a modelling approach that, despite the fact of being founded on a conceptual scheme, maintains a certain connection with physiological processes. Two approaches to dynamic vegetation modelling were finally compared, to evaluate their ability to simulate the evolution of carbon and water exchange processes in a semi-arid region.