Abstract
Abstract. In this paper we propose adaptive clustering as a new method for reducing the computational efforts of distributed modelling. It consists of identifying similar-acting model elements during runtime, clustering them, running the model for just a few representatives per cluster, and mapping their results to the remaining model elements in the cluster. Key requirements for the application of adaptive clustering are the existence of (i) many model elements with (ii) comparable structural and functional properties and (iii) only weak interaction (e.g. hill slopes, subcatchments, or surface grid elements in hydrological and land surface models). The clustering of model elements must not only consider their time-invariant structural and functional properties but also their current state and forcing, as all these aspects influence their current functioning. Joining model elements into clusters is therefore a continuous task during model execution rather than a one-time exercise that can be done beforehand. Adaptive clustering takes this into account by continuously checking the clustering and re-clustering when necessary. We explain the steps of adaptive clustering and provide a proof of concept at the example of a distributed, conceptual hydrological model fit to the Attert basin in Luxembourg. The clustering is done based on normalised and binned transformations of model element states and fluxes. Analysing a 5-year time series of these transformed states and fluxes revealed that many model elements act very similarly, and the degree of similarity varies strongly with time, indicating the potential for adaptive clustering to save computation time. Compared to a standard, full-resolution model run used as a virtual reality “truth”, adaptive clustering indeed reduced computation time by 75 %, while modelling quality, expressed as the Nash–Sutcliffe efficiency of subcatchment runoff, declined from 1 to 0.84. Based on this proof-of-concept application, we believe that adaptive clustering is a promising tool for reducing the computation time of distributed models. Being adaptive, it integrates and enhances existing methods of static grouping of model elements, such as lumping or grouped response units (GRUs). It is compatible with existing dynamical methods such as adaptive time stepping or adaptive gridding and, unlike the latter, does not require adjacency of the model elements to be joined. As a welcome side effect, adaptive clustering can be used for system analysis; in our case, analysing the space–time patterns of clustered model elements confirmed that the hydrological functioning of the Attert catchment is mainly controlled by the spatial patterns of geology and precipitation.
Highlights
Hydrological systems are often characterised by considerable spatial heterogeneity of relevant properties, such as topography or soils (Schulz et al, 2006), and considerable temporal variability due to time-changing boundary conditions, such as precipitation or radiation, and time-changing system properties, such as vegetation cover (Zehe and Sivapalan, 2009)
We first show the results from analysing the subcatchment similarity, as it is a precondition for adaptive clustering, and results from comparing models runs with adaptive clustering to benchmark cases
The entire catchment is in a very homogeneous state, and subcatchments group into only three clusters. This state of high similarity comes to a sudden end with the onset of precipitation (Fig. 4d), which increases the diversity of subcatchment runoff to 18 clusters and leads to the development of a spatial pattern that is mainly influenced by rainfall spatial distribution and only to a lesser degree by geology
Summary
Hydrological systems are often characterised by considerable spatial heterogeneity of relevant properties, such as topography or soils (Schulz et al, 2006), and considerable temporal variability due to time-changing boundary conditions, such as precipitation or radiation, and time-changing system properties, such as vegetation cover (Zehe and Sivapalan, 2009). There may be many noncontiguous south-facing forested hillslopes with shallow soils in a watershed, in an intermediate wetness state, which will act very on a particular sunny day In this context, we suggest a new adaptive method for the clustering of model elements, which is not limited to contiguous regions. We suggest a new adaptive method for the clustering of model elements, which is not limited to contiguous regions It is motivated by the suggestions of Melsen et al (2016) “to further investigate and substantially improve the representation of spatial and temporal variability in largedomain hydrological models” and contributes to solving the computational challenges of hydrological modelling, as formulated by Clark et al (2017).
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