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Keywords:

  • Distributed modelling;
  • Heterogeneity;
  • Spatial scale;
  • Spatial variability;
  • Continuum assumption;
  • Spectral gap;
  • Separation of scales;
  • Characteristic velocity

Abstract

Since the paper of Wood et al. (1988), the idea of a representative elementary area (REA) has captured the imagination of catchment modellers. It promises a spatial scale over which the process representations can remain simple and at which distributed catchment behaviour can be represented without the apparently undefinable complexity of local heterogeneity. This paper further investigates the REA concept and reassesses its utility for distributed parameter rainfall-runoff modelling. The analysis follows Wood et al. (1988) in using the same topography and the same method of generating parameter values. However, a dynamic model of catchment response is used, allowing the effects of flow routing to be investigated. Also, a ‘nested catchments approach’ is adopted which better enables the detection of a minimum in variability between large- and small-scale processes. This is a prerequisite of the existence of an REA.

Results indicate that, for an impervious catchment and spatially invariant precipitation, the size of the REA depends on storm duration. A ‘characteristic velocity’ is defined as the ratio of a characteristic length scale (the size of the REA) to a characteristic time-scale (storm duration). This ‘characteristic velocity’ appears to remain relatively constant for different storm durations. Spatially variable precipitation is shown to dominate when compared with the effects of infiltration and flow routing. In this instance, the size of the REA is strongly controlled by the correlation length of precipitation. For large correlation lengths of precipitation, a separation of scales in runoff is evident due to small-scale soil and topographic variability and large-scale precipitation patterns. In general, both the existence and the size of an REA will be specific to a particular catchment and a particular application. However, it is suggested that a separation of scales (and therefore the existence of an REA), while being an advantage, is not a prerequisite for obtaining simple representations of local heterogeneity.