Abstract. According to Dooge (1986) intermediate-scale catchments are systems of organized complexity, being too organized and yet too small to be characterized on a statistical/conceptual basis, but too large and too heterogeneous to be characterized in a deterministic manner. A key requirement for building structurally adequate models precisely for this intermediate scale is a better understanding of how different forms of spatial organization affect storage and release of water and energy. Here, we propose that a combination of the concept of hydrological response units (HRUs) and thermodynamics offers several helpful and partly novel perspectives for gaining this improved understanding. Our key idea is to define functional similarity based on similarity of the terrestrial controls of gradients and resistance terms controlling the land surface energy balance, rainfall runoff transformation, and groundwater storage and release. This might imply that functional similarity with respect to these specific forms of water release emerges at different scales, namely the small field scale, the hillslope, and the catchment scale. We thus propose three different types of "functional units" -specialized HRUs, so to speak -which behave similarly with respect to one specific form of water release and with a characteristic extent equal to one of those three scale levels. We furthermore discuss an experimental strategy based on exemplary learning and replicate experiments to identify and delineate these functional units, and as a promising strategy for characterizing the interplay and organization of water and energy fluxes across scales. We believe the thermodynamic perspective to be well suited to unmask equifinality as inherent in the equations governing water, momentum, and energy fluxes: this is because several combinations of gradients and resistance terms yield the same mass or energy flux and the terrestrial controls of gradients and resistance terms are largely independent. We propose that structurally adequate models at this scale should consequently disentangle driving gradients and resistance terms, because this optionally allows Published by Copernicus Publications on behalf of the European Geosciences Union. E. Zehe et al.: HESS Opinions: Thermodynamic reinterpretation of the HRU conceptequifinality to be partly reduced by including available observations, e.g., on driving gradients. Most importantly, the thermodynamic perspective yields an energy-centered perspective on rainfall-runoff transformation and evapotranspiration, including fundamental limits for energy fluxes associated with these processes. This might additionally reduce equifinality and opens up opportunities for testing thermodynamic optimality principles within independent predictions of rainfall-runoff or land surface energy exchange. This is pivotal to finding out whether or not spatial organization in catchments is in accordance with a fundamental organizing principle.

[1] We have investigated the potential of combining cross-hole georadar velocity and attenuation tomography as a method for characterizing heterogeneous alluvial aquifers. A multivariate statistical technique, known as k-means cluster analysis, is used to correlate and integrate information contained in velocity and attenuation tomograms. Cluster analysis allows us to identify objectively the major common trends in the tomographic data and thus to ''reduce'' the information to a limited number of characteristic parameter combinations. The application of this procedure to two synthetic data sets indicates that it is a powerful tool for converting the complex relationships between the tomographically derived velocity and attenuation structures into a lithologically and hydrologically meaningful zonation of the probed region. In addition, these synthetic examples allow us to evaluate the reliability of further petrophysical parameter estimates. We find that although absolute values of the tomographically inferred petrophysical parameters often differ significantly from the actual parameters, the clustering approach enables us to reliably identify the major trends in the petrophysical properties. Finally, we have applied the approach to a cross-hole georadar data set collected in a well-studied alluvial aquifer. A comparison of the clustered tomographic section with well-log data demonstrates that our approach delineates the hydrostratigraphic zonation.

Three-dimensional ground-penetrating radar ͑GPR͒ data are routinely acquired for diverse geologic, hydrogeologic, archeological, and civil engineering purposes. Interpretations of these data are invariably based on subjective analyses of reflection patterns. Such analyses are heavily dependent on interpreter expertise and experience. Using data acquired across gravel units overlying the Alpine Fault Zone in New Zealand, we demonstrate the utility of various geometric attributes in reducing the subjectivity of 3D GPR data analysis. We use a coherence-based technique to compute the coherency, azimuth, and dip attributes and a graylevel co-occurrence matrix ͑GLCM͒ method to compute the texture-based energy, entropy, homogeneity, and contrast attributes. A selection of the GPR attribute volumes allows us to highlight key aspects of the fault zone and observe important features not apparent in the standard images. This selection also provides information that improves our understanding of gravel deposition and tectonic structures at the study site.Anew depositional/structural model largely based on the results of our analysis of GPR attributes includes four distinct gravel units deposited in three phases and a well-defined fault trace. This fault trace coincides with a zone of stratal disruption and shearing bound on one side by upward-tilted to synclinally folded stratified gravels and on the other side by moderately dipping stratified alluvial-fan gravels that could have been affected by lateral fault drag. When used in tandem, the coherence-and texture-based attribute volumes can significantly improve the efficiency and quality of 3D GPR interpretation, especially for complex data collected across active fault zones.