This chapter reviews the general procedures and methodologies used for validating growth and yield models. More specifically, it addresses: (i) the optimism principle and model validation; (ii) model validation procedures, problems and potential areas of needed research; (iii) data considerations and data-splitting schemes in model validation; and (iv) operational thresholds for accepting or rejecting a model. The roles of visual or graphical validation, dynamic validation, as well as statistical and biological validations are discussed in more detail. The emphasis in this chapter is placed on the understanding of the validation process rather than the validation of a specific model. The limitations and the pitfalls of model validation procedures, as well as some of the frequent misuses of these procedures are discussed. Several technical and practical recommendations concerning the validation of growth and yield model are made.

The spatial pattern of precipitation is known to be highly dependent on meteorological conditions and relief. However, the relationships between precipitation and topography in mountainous areas are not very well known, partly because of the complex topography in these regions, and partly because of the sparsity of information available to study such relationships in high elevation areas. The purpose of the investigation was to find a method of mapping extreme rainfall in the mountainous region of Scotland, which was easy to use and to understand, and which gave satisfactory results both in terms of statistical performance and consistency with meteorological mechanisms.Among the interpolation methods described in the literature, ordinary kriging and modified residual kriging have been found attractive by reason of their simplicity and ease of use. Both methods have been applied to map an index of extreme rainfall, the median of the annual maximum daily rainfall (RMED), in the mountainous region of Scotland. Rainfall records from a network of 1003 raingauges are used, covering Scotland with uneven density. A 4-parameter regression equation developed in a previous study, relating a transformed variable of RMED to topographical variables, is used in the modified residual kriging method. Comparing the relative performances of ordinary kriging and modified residual kriging shows that the use of topographical information helps to compensate for the lack of local data from which any interpolation method, such as ordinary kriging, might suffer, thus improving the final mapping.

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The spatial pattern of precipitation is known to be highly dependent on meteorological conditions and relief. But the relationships between precipitation and topography in mountainous areas are not very well known, partly because of the complex topography in these regions, and partly because of the sparsity of information available to study such relationships in high elevation areas. Moreover, studies are usually focused on mean annual precipitation, and so the patterns of extreme precipitation at short time steps, like daily, remain difficult to model. Daily annual maximum precipitation for 1003 gauges in Scotland, the most mountainous region of the United Kingdom, are studied to investigate the relationships between the median of the daily rainfall annual maximum, RMED, and the topography. A set of 14 topographical variables, some of them defined with respect to one of eight cardinal directions, are calculated from a 1×1 km digital terrain model (DTM). A particular effort has been made to improve the definition of some of the topographical variables suggested in the literature, either to provide a better physical definition or to better reflect the spatial variability of the topography. Single and multiple regression analyses have been made in some parts of the Highlands, leading to a 4‐parameter model. This model is a mixture of geographical parameters (distance from the sea in opposing directions) and of topographical parameters (obstruction against the prevailing winds, and roughness between the main moisture source and the gauge). Special care has been taken to define a model whose physical sense is consistent with the meteorological conditions and whose parameters are not too interdependent. © 1998 Royal Meteorological Society

Abstract. The Focused Rainfall Growth Extension (FORGEX) method produces rainfall growth curves focused on a subject site. Focusing allows the incorporation of rainfall extremes observed regionally while respecting local variations in growth rates. The starting point for the analysis is an extensive set of annual maximum rainfalls, with values at each gauged site standardized by the median. Following the philosophy of the earlier FORGE method, a strongly empirical approach is adopted. The rainfall growth curve is represented by linear segments on a Gumbel scale, and is fitted by a least-squares criterion. The selection of data points is intricate and includes both the traditional pooling of regional extremes and the incorporation of network maximum events. The latter comprise the largest events from successive hierarchical networks of gauges, focused on the site for which estimates are requires. Their treatment takes account of interdependence using the Dales and Reed model of spatial dependence in rainfall extremes.