Although the theoretical aspects of rainfall monitoring through microwave links are quite well established, only few practical applications have evaluated this technique in an operational setting. Microwave links are of particular interest in urban areas, where high frequency measurements are needed due to the fast hydrological response of the system, and link networks are usually already in-place. This study presents the first results of an on-going experiment in Luxembourg-City, which includes two dual-frequency links and several rain gauges at intermediate locations along the links. The experimental set-up allows comparing rain rate estimates based on the individual frequencies as well as estimates based on the difference between the two frequencies. We compared several models for expressing the relationship between attenuation and rain rate, including different baseline estimation methods such as the traditional constant-baseline model and a one-parameter model based on a first order low-pass filter. The models were evaluated using a Bayesian approach and subjected to posterior scrutiny based on several diagnostics. In contrast to previous research, our results indicated that estimates based on the attenuation difference appeared poorer than the estimates based on individual frequencies. The one-parameter baseline estimation method provided consistently better results than the traditional constant-baseline method, which justifies the increased model complexity. Uncertainty of model predictions was relatively large for low intensity rainfall, which highlights one of the limitations of this technique. Models were validated in different periods and on different links, in some cases demonstrating large bias. Model parameters were generally well-identifiable, though uncertainty in the rainfall predictions appeared under-estimated in some cases.

This paper introduces a flexible framework for conceptual hydrological modeling, with two related objectives: (1) generalize and systematize the currently fragmented field of conceptual models and (2) provide a robust platform for understanding and modeling hydrological systems. In contrast to currently dominant "fixed" model applications, the flexible framework proposed here allows the hydrologist to hypothesize, build, and test different model structures using combinations of generic components. This is particularly useful for conceptual modeling at the catchment scale, where limitations in process understanding and data availability remain major research and operational challenges. The formulation of the model architecture and individual components to represent distinct aspects of catchment-scale function, such as storage, release, and transmission of water, is discussed. Several numerical strategies for implementing the model equations within a computationally robust framework are also presented. In the companion paper, the potential of the flexible framework is examined with respect to supporting more systematic and stringent hypothesis testing, for characterizing catchment diversity, and, more generally, for aiding progress toward more unified hydrological theory at the catchment scale.