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For users of hydrological models, the suitability of models can depend on how well their simulated outputs align with observed discharge. This study emphasizes the crucial role of factoring in discharge observation uncertainty when assessing the performance of hydrological models. We introduce an ad hoc approach, implemented through the eWaterCycle platform, to evaluate the significance of differences in model performance while considering the uncertainty associated with discharge observations. The analysis of the results encompasses 299 catchments from the Catchment Attributes and MEteorology for Large-sample Studies Great Britain (CAMELS-GB) large-sample catchment dataset, addressing three practical use cases for model users. These use cases involve assessing the impact of additional calibration on model performance using discharge observations, conducting conventional model comparisons, and examining how the variations in discharge simulations resulting from model structural differences compare with the uncertainties inherent in discharge observations. Based on the 5th to 95th percentile range of observed flow, our results highlight the substantial influence of discharge observation uncertainty on interpreting model performance differences. Specifically, when comparing model performance before and after additional calibration, we find that, in 98 out of 299 instances, the simulation differences fall within the bounds of discharge observation uncertainty. This underscores the inadequacy of neglecting discharge observation uncertainty during calibration and subsequent evaluation processes. Furthermore, in the model comparison use case, we identify numerous instances where observation uncertainty masks discernible differences in model performance, underscoring the necessity of accounting for this uncertainty in model selection procedures. While our assessment of model structural uncertainty generally indicates that structural differences often exceed observation uncertainty estimates, a few exceptions exist. The comparison of individual conceptual hydrological models suggests no clear trends between model complexity and subsequent model simulations falling within the uncertainty bounds of discharge observations. Based on these findings, we advocate integrating discharge observation uncertainty into the calibration process and the reporting of hydrological model performance, as has been done in this study. This integration ensures more accurate, robust, and insightful assessments of model performance, thereby improving the reliability and applicability of hydrological modelling outcomes for model users. [ABSTRACT FROM AUTHOR]

Terrestrial microwave links are increasingly being used to estimate path-averaged precipitation by determining the attenuation caused by rainfall along the link path, mostly with commercial microwave links from cellular telecommunication networks. However, the temporal resolution of these rainfall estimates and the method to derive them are often determined by the temporal sampling strategy that is employed by the mobile network operators. Currently, the links are most often sampled at a temporal resolution of 15 min with a recording of the minimum and maximum values, while more recently, a form of instantaneous sampling with possible intervals up to 1 s has also been set up. For rainfall research purposes, often high temporal resolutions in combination with averaged values are preferred. However, it is uncertain how these various temporal sampling strategies affect the estimated rainfall intensity. Here we aim to understand how temporal sampling strategies affect the measured rainfall intensities using microwave links. To do so, we use data from three collocated microwave links, two 38 GHz and one 26 GHz, sampled at 20 Hz and covering a 2.2 km path over the city of Wageningen, the Netherlands. We aggregate the microwave link power levels to multiple time intervals (1 s to 60 min) and use a mean, instantaneous, and minimum and maximum value to characterize the signal. Based on the aggregated data, we compute rainfall intensities and compare these with 20 Hz rainfall estimates, such that we isolate errors and uncertainties caused by the sampling strategies from instrumental effects, such as different biases between instruments and representativeness errors. In general, our results show that for all sampling strategies, an increase in sampling time interval reduces the performance of the rainfall estimates, which especially holds for the instantaneous sampling strategy. Even the mean sampling strategy, which generally performs best of all strategies, is sensitive to this reduction in temporal resolution and could lead to significant underestimations. This sensitivity of the mean sampling to the temporal resolution seems to be largely affected by the non-linear relation between attenuation and rainfall. The min–max sampling strategy is mostly prone to minor underestimations or large overestimations of the path-averaged rainfall intensities. Moreover, our results, including a comparison with theoretical events, show that the attenuation due to wet antennas not only affects the comparison between the rainfall estimates obtained with a microwave link and another reference instrument but also has a significant influence on the performance of the rainfall retrieval algorithm, especially for devices with relatively long duration of the wet-antenna attenuation combined with the longer sampling time intervals. Overall, this study demonstrates the effect a selected sampling strategy can have on rainfall intensity estimates using (commercial) microwave links. [ABSTRACT FROM AUTHOR]

Terrestrial microwave links are increasingly being used to estimate path-averaged precipitation by determining the attenuation caused by rainfall along the link path, mostly with commercial microwave links from cellular telecommunication networks. However, the temporal resolution of and method to derive these rainfall estimates is often determined by the temporal sampling strategy that is employed by the mobile network operators. Currently, the links are most often sampled at a temporal resolution of 15 minutes with a recording of the minimum and maximum values, while more recently also a form of instantaneous sampling with possible intervals up to 1 s has been set up. For rainfall research purposes, often high temporal resolutions in combination with averaged values are preferred. However, it is uncertain how these various temporal sampling strategies affect the estimated rainfall intensity. Here we aim to understand how temporal sampling strategies affect the measured rainfall intensities using microwave links. To do so, we use data from three collocated microwave links, two 38 GHz and one 26 GHz, sampled at 20 Hz and covering a 2.2 km path over the city of Wageningen, the Netherlands. We aggregate the microwave link power levels to multiple time intervals (1 s to 60 min) and use a mean, instantaneous, and minimum and maximum value to characterize the signal. Based on the aggregated data, we compute rainfall intensities and compare these with 20 Hz rainfall estimates, such that we isolate errors and uncertainties caused by the sampling strategies from instrumental effects, such as different biases between instruments and representativeness errors. In general, our results show that for all sampling strategies an increase in sampling time interval reduces the performance of the rainfall estimates, which especially holds for the instantaneous sampling strategy. Even the mean sampling strategy, which generally performs best of all strategies, is sensitive to this reduction in temporal resolution and could lead to significant underestimations. In this, the non-linear relation between attenuation and rainfall intensity seems to play an important role. The min-max sampling strategy is mostly prone to minor underestimations or large overestimations of the path-averaged rainfall intensities. Moreover, our results, including a comparison with theoretical events, show that the attenuation due to wet antennas not only affects the comparison between the rainfall estimates obtained with a microwave link and another reference instrument, but also has a significant influence on the rainfall retrieval algorithm. Overall, this study demonstrates the effect a selected sampling strategy can have on rainfall intensity estimates using (commercial) microwave links. [ABSTRACT FROM AUTHOR]

The comparison of models in geosciences involves refining a single model or comparing various model structures. However, such model comparison studies are potentially invalid without considering the uncertainty estimates of observations in evaluating relative model performance. The temporal sampling of the observation and simulation time series is an additional source of uncertainty as a few observation and simulation pairs, in the form of outliers, might have a disproportionate effect on the model skill score. In this study we highlight the importance of including observation uncertainty and temporal sampling uncertainty when comparing or evaluating hydrological models. In hydrology, large-sample hydrology datasets contain a collection of catchments with hydro-meteorological time series, catchment boundaries and catchment attributes that provide an excellent test-bed for model evaluation and comparison studies. this study, two model experiments that cover different purposes for model evaluation are set up using 396 catchments from the CAMELS-GB dataset. The first experiment, intra-model, mimics a model refinement case by evaluating the streamflow estimates of the distributed wflow_sbm hydrological model with and without additional calibration. The second experiment, inter-model, is a model comparison based on the streamflow estimates of the distributed PCR-GLOBWB and wflow_sbm hydrological models. The temporal sampling uncertainty, the result of outliers in observation and simulation pairs, is found to be substantial throughout the case study area. High temporal sampling uncertainty indicates that the model skill scores used to evaluate model performance are heavily influenced by only a few data points in the time series. This is the case for half of the simulations 210) of the first intra-model experiment and 53 catchment simulations of the second inter-model experiment as indicated by larger sampling uncertainty than the difference in the KGE-NP model skill score. These cases highlight the importance of reporting and determining the cause of temporal sampling uncertainty before drawing conclusions on large-sample hydrology based model performance. The streamflow observation uncertainty analysis shows similar results. One third of the catchments simulations (123) of the intra-model experiment contains smaller streamflow simulation differences between models than streamflow observation uncertainties, compared to only 4 catchment simulations of the inter-model experiment due to larger differences between streamflow simulations. These catchments simulations should be excluded before drawing conclusions based on large-samples of catchments. The results of this study demonstrate that it is crucial for benchmark efforts based on large-samples of catchments to include streamflow observation uncertainty and temporal sampling uncertainty to obtain more robust results. [ABSTRACT FROM AUTHOR]

Distributed hydrological modelling moves into the realm of hyper-resolution modelling. This results in a plethora of scaling-related challenges that remain unsolved. To the user, in light of model result interpretation, finer-resolution output might imply an increase in understanding of the complex interplay of heterogeneity within the hydrological system. Here we investigate spatial scaling in the form of varying spatial resolution by evaluating the streamflow estimates of the distributed wflow_sbm hydrological model based on 454 basins from the large-sample CAMELS data set. Model instances are derived at three spatial resolutions, namely 3 km, 1 km, and 200 m. The results show that a finer spatial resolution does not necessarily lead to better streamflow estimates at the basin outlet. Statistical testing of the objective function distributions (Kling–Gupta efficiency (KGE) score) of the three model instances resulted in only a statistical difference between the 3 km and 200 m streamflow estimates. However, an assessment of sampling uncertainty shows high uncertainties surrounding the KGE score throughout the domain. This makes the conclusion based on the statistical testing inconclusive. The results do indicate strong locality in the differences between model instances expressed by differences in KGE scores of on average 0.22 with values larger than 0.5. The results of this study open up research paths that can investigate the changes in flux and state partitioning due to spatial scaling. This will help to further understand the challenges that need to be resolved for hyper-resolution hydrological modelling. [ABSTRACT FROM AUTHOR]

Distributed hydrological modelling moves into the realm of hyper-resolution modelling. This results in a plethora of scaling related challenges that remain unsolved. In light of model result interpretation, finer resolution output might implicate to the user an increase in understanding of the complex interplay of heterogeneity within the hydrological system. Here we investigate spatial scaling in the realm of hyper-resolution by evaluating the streamflow estimates of the distributed wflow_sbm hydrological model based on 454 basins from the large-sample CAMELS data set. Model instances were derived at 3 spatial resolutions, namely 3 km, 1 km, and 200 m. The results show that a finer spatial resolution does not necessarily lead to better streamflow estimates at the basin outlet. Statistical testing of the objective function distributions (KGE score) of the 3 model instances show only a statistical difference between the 3 km and 200 m streamflow estimates. However, results indicate strong locality in scaling behaviour between model instances expressed by differences in KGE scores of on average 0.22. This demonstrates the presence of scaling behavior throughout the domain and indicates where locality in results is strong. The results of this study open up research paths that can investigate the changes in flux and state partitioning due to spatial scaling. This will help further understand the challenges that need to be resolved for hyper resolution hydrological modelling. [ABSTRACT FROM AUTHOR]