Process-based hydrological models seek to represent the dominant hydrological processes in a catchment. However, due to unavoidable incompleteness of knowledge, the construction of “fidelius” process-based models depends largely on expert judgment. We present a systematic approach that treats models as hierarchical assemblages of hypotheses (conservation principles, system architecture, process parameterization equations, and parameter specification), which enables investigating how the hierarchy of model development decisions impacts model fidelity. Each model development step provides information that progressively changes our uncertainty (increases, decreases, or alters) regarding the input-state-output behavior of the system. Following the principle of maximum entropy, we introduce the concept of “minimally restrictive process parameterization equations—MR-PPEs,” which enables us to enhance the flexibility with which system processes can be represented, and to thereby investigate the important role that the system architectural hypothesis (discretization of the system into subsystem elements) plays in determining model behavior. We illustrate and explore these concepts with synthetic and real-data studies, using models constructed from simple generic buckets as building blocks, thereby paving the way for more-detailed investigations using sophisticated process-based hydrological models. We also discuss how proposed MR-PPEs can bridge the gap between current process-based modeling and machine learning. Finally, we suggest the need for model calibration to evolve from a search over “parameter spaces” to a search over “function spaces.”.

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.