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The number of rainfall observations from personal weather stations (PWSs) has increased significantly over the past years; however, there are persistent questions about data quality. In this paper, we reflect on three quality control algorithms (PWSQC, PWS-pyQC, and GSDR-QC) designed for the quality control (QC) of rainfall data. Technical and operational guidelines are provided to help interested users in finding the most appropriate QC to apply for their use case. All three algorithms can be accessed within the OpenSense sandbox where users can run the code. The results show that all three algorithms improve PWS data quality when cross-referenced against a rain radar data product. The considered algorithms have different strengths and weaknesses depending on the PWS and official data availability, making it inadvisable to recommend one over another without carefully considering the specific setting. The authors highlight a need for further objective quantitative benchmarking of QC algorithms. This requires freely available test datasets representing a range of environments, gauge densities, and weather patterns.

Weather radar is a crucial tool for rainfall observation and forecasting, providing high-resolution estimates in both space and time. Despite this, radar rainfall estimates are subject to many error sources – including attenuation, ground clutter, beam blockage and drop-size distribution – with the true rainfall field unknown. A flexible stochastic model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard weather radar processing methods and imposing path-integrated attenuation effects, a stochastic drop-size-distribution field, and sampling and random errors. This can provide realistic weather radar images, of which we know the true rainfall field and the corrected “best-guess” rainfall field which would be obtained if they were observed in a real-world case. The structure of these errors is then investigated, with a focus on the frequency and behaviour of “rainfall shadows”. Half of the simulated weather radar images have at least 3 % of their significant rainfall rates shadowed, and 25 % have at least 45 km2 containing rainfall shadows, resulting in underestimation of the potential impacts of flooding. A model framework for investigating the behaviour of errors relating to the radar rainfall estimation process is demonstrated, with the flexible and efficient tool performing well in generating realistic weather radar images visually for a large range of event types.

In this paper, the question of how the interpolation of precipitation in space by using various spatial gauge densities affects the rainfall–runoff model discharge if all other input variables are kept constant is investigated. The main focus was on the peak flows. This was done by using a physically based model as the reference with a reconstructed spatially variable precipitation model and a conceptual model calibrated to match the reference model's output as closely as possible. Both models were run with distributed and lumped inputs. Results showed that all considered interpolation methods resulted in the underestimation of the total precipitation volume and that the underestimation was directly proportional to the precipitation amount. More importantly, the underestimation of peaks was very severe for low observation densities and disappeared only for very high-density precipitation observation networks. This result was confirmed by using observed precipitation with different observation densities. Model runoffs showed worse performance for their highest discharges. Using lumped inputs for the models showed deteriorating performance for peak flows as well, even when using simulated precipitation.

Information about precipitation extremes is of vital importance for many hydrological planning and design purposes. However, due to various sources of error, some of the observed extremes may be inaccurate or false. The purpose of this investigation is to present quality control of observed extremes using space–time statistical methods. To cope with the highly skewed rainfall distribution, a Box–Cox transformation with a suitable parameter was used. The value at the location of a potential outlier is estimated using the surrounding stations and the calculated spatial variogram and compared to the suspicious observation. If the difference exceeds the threshold of the test, the value is flagged as a possible outlier. The same procedure is repeated for different temporal aggregations in order to avoid singularities caused by convection. Detected outliers are subsequently compared to the corresponding radar and discharge observations, and finally, implausible extremes are removed. The procedure is demonstrated using observations of sub-daily and daily temporal resolution in Germany.

Given the importance of snow on different land and atmospheric processes, accurate representation of seasonal snow evolution, including distribution and melt volume, is highly imperative to any water resources development trajectories. The limitation of reliable snowmelt estimation in mountainous regions is, however, further exacerbated by data scarcity. This study attempts to develop relatively simple extended degree-day snow models driven by freely available snow-cover images. This approach offers relative simplicity and a plausible alternative to data-intensive models, as well as in situ measurements, and has a wide range of applicability, allowing for immediate verification with point measurements. The methodology employs readily available MODIS composite images to calibrate the snowmelt models on spatial snow distribution in contrast to the traditional snow-water-equivalent-based calibration. The spatial distribution of snow-cover is simulated using different extended degree-day models with parameters calibrated against individual MODIS snow-cover images for cloud-free days or a set of images representing a period within the snow season. The study was carried out in Baden-Württemberg (Germany) and in Switzerland. The simulated snow-cover data show very good agreement with MODIS snow-cover distribution, and the calibrated parameters exhibit relative stability across the time domain. Furthermore, different thresholds that demarcate snow and no-snow pixels for both observed and simulated snow cover were analyzed to evaluate these thresholds' influence on the model performance and identified for the study regions. The melt data from these calibrated snow models were used as standalone inputs to a modified Hydrologiska Byråns Vattenbalansavdelning (HBV) without the snow component in all the study catchments to assess the performance of the melt outputs in comparison to a calibrated standard HBV model. The results show an overall increase in Nash–Sutcliffe efficiency (NSE) performance and a reduction in uncertainty in terms of model performance. This can be attributed to the reduction in the number of parameters available for calibration in the modified HBV and an added reliability of the snow accumulation and melt processes inherent in the MODIS calibrated snow model output. This paper highlights that the calibration using readily available images used in this method allows for a flexible regional calibration of snow-cover distribution in mountainous areas with reasonably accurate precipitation and temperature data and globally available inputs. Likewise, the study concludes that simpler specific alterations to processes contributing to snowmelt can contribute to reliably identify the snow distribution and bring about improvements in hydrological simulations, owing to better representation of the snow processes in snow-dominated regimes.

Statistical tools are crucial for a variety of hydrological applications, whether to model processes and enhance understanding and knowledge or to design infrastructure systems. Given the rapid evolution of statistical methods and the need for a solid theoretical foundation for their correct application, a multidisciplinary community STAtistics in HYdrology Working Group (STAHY-WG) aggregated under the International Association of Hydrological Sciences (IAHS) umbrella to contribute to this research field. Now, more than 15 years since its inception, this paper summarizes the main achievements of this productive community collaboration in four (of many) branches of statistical hydrology: extreme value analysis, multivariate analysis, time series analysis, and regionalization. The aim is to provide an overview of recent developments, offer practical suggestions (e.g. software packages), and outline future challenges to support scientists and practitioners in their endeavours within the realm of statistical hydrology studies. [ABSTRACT FROM AUTHOR]

The number of rainfall observations from personal weather stations (PWSs) has increased significantly over the past years; however, there are persistent questions about data quality. In this paper, we reflect on three quality control algorithms (PWSQC, PWS-pyQC, and GSDR-QC) designed for the quality control (QC) of rainfall data. Technical and operational guidelines are provided to help interested users in finding the most appropriate QC to apply for their use case. All three algorithms can be accessed within the OpenSense sandbox where users can run the code. The results show that all three algorithms improve PWS data quality when cross-referenced against a rain radar data product. The considered algorithms have different strengths and weaknesses depending on the PWS and official data availability, making it inadvisable to recommend one over another without carefully considering the specific setting. The authors highlight a need for further objective quantitative benchmarking of QC algorithms. This requires freely available test datasets representing a range of environments, gauge densities, and weather patterns. [ABSTRACT FROM AUTHOR]

Weather radar is a crucial tool for rainfall observation and forecasting, providing high-resolution estimates in both space and time. Despite this, radar rainfall estimates are subject to many error sources – including attenuation, ground clutter, beam blockage and drop-size distribution – with the true rainfall field unknown. A flexible stochastic model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard weather radar processing methods and imposing path-integrated attenuation effects, a stochastic drop-size-distribution field, and sampling and random errors. This can provide realistic weather radar images, of which we know the true rainfall field and the corrected "best-guess" rainfall field which would be obtained if they were observed in a real-world case. The structure of these errors is then investigated, with a focus on the frequency and behaviour of "rainfall shadows". Half of the simulated weather radar images have at least 3 % of their significant rainfall rates shadowed, and 25 % have at least 45 km2 containing rainfall shadows, resulting in underestimation of the potential impacts of flooding. A model framework for investigating the behaviour of errors relating to the radar rainfall estimation process is demonstrated, with the flexible and efficient tool performing well in generating realistic weather radar images visually for a large range of event types. [ABSTRACT FROM AUTHOR]

The quantification of the consequences of climate change (CC) on the hydrology of the West Africa region was performed using a validated Hydrologiska Byrans Vattenbalansavdelning hydrological model and regional climate models which was driven by different general circulation models (GCMs) from the Coordinated Regional Downscaling Experiment (CORDEX) and the Regional Climate Division of the Institute of Meteorology and Climate Research at Karlsruhe Institute of Technology (IMK-IFU). The quantile mapping and linear-scaling bias adjustment methods were used to correct the inherent errors in the climate simulations. Flow duration curves (FDCs) and generic annual discharge cycles were used in determining the impacts of the change on hydrology (river flow) in the Black Volta catchment within the subregion. It was found out that, in the first segment of the FDCs representing high flows, there was a slight increase in the future flow characterizing a higher watershed water yield from high rainfall events in the future. The 10–40% exceedance probabilities of flow representing wet conditions; 40–60% relating to mid-range flows; 60–90% representing dry period conditions; and low flows (90–100%) all show a decrease in the future flows for four out of the five GCM driving models. Most worrying is the reduction in flows for the 90–100% exceedance probabilities in the future relating to the sustainability of streamflow in the long term. It was concluded that CC could negatively impact and decrease the hydrology of the subregion in the future with most of the rivers in the catchment running dry in most months of the annual discharge cycle. HIGHLIGHTS The study demonstrates the effectiveness of using simple and less data demanding tools in quantifying the hydrological consequences of climate change in the subregion.; We were able to bias correct the climate simulations using measured (observed) rainfall and temperature data as the ‘correct’ data.; We used two different correction methods in this study and their accompanying effects on the hydrology of the region.;

The accuracy of spatial precipitation estimates with relatively high spatiotemporal resolution is of vital importance in various fields of research and practice. Yet the intricate variability and intermittent nature of precipitation make it very difficult to obtain accurate spatial precipitation estimates. Radars and rain gauges are two complementary sources of precipitation information: the former are inaccurate in general but are valid indicators of the spatial pattern of the rainfall field; the latter are relatively accurate but lack spatial coverage. Several radar–gauge merging techniques that can provide spatial precipitation estimates have been proposed in the scientific literature. Conditional simulation has great potential to be used in spatial precipitation estimation. Unlike commonly used interpolation methods, conditional simulation yields a range of possible estimates due to its Monte Carlo framework. However, one obstacle that hampers the application of conditional simulation in spatial precipitation estimation is the need to obtain the marginal distribution function of the rainfall field with sufficient accuracy. In this work, we propose a method to obtain the marginal distribution function from radar and rain gauge data. A conditional simulation method, random mixing (RM), is used to simulate rainfall fields. The radar and rain gauge data used in the application of the proposed method are derived from a stack of synthetic rainfall fields. Due to the full control over the stochastic process, the accuracy of the estimates is verified comprehensively. The results from the proposed approach are compared with those from three well-known radar–gauge merging techniques: ordinary Kriging, Kriging with external drift, and conditional merging, and the sensitivity of the approach to two factors – the number of rain gauges and the random error in the radar estimates – is analysed in the same experimental context.

The number of personal weather stations (PWSs) with data available through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation using a novel approach based on indicator correlations and rank statistics. Due to unknown errors and biases of the observations, rainfall amounts from the PWS network are not considered directly. Instead, it is assumed that the temporal order of the ranking of these data is correct. The crucial step is to find the stations which fulfil this condition. This is done in two steps – first, by selecting the locations using the time series of indicators of high precipitation amounts. Then, the remaining stations are then checked for whether they fit into the spatial pattern of the other stations. Thus, it is assumed that the quantiles of the empirical distribution functions are accurate. These quantiles are then transformed to precipitation amounts by a quantile mapping using the distribution functions which were interpolated from the information from the German National Weather Service (Deutscher Wetterdienst – DWD) data only. The suggested procedure was tested for the state of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amount of 1, 3, 6, 12 and 24 h. For each of these temporal aggregations, nearly 200 intense events were evaluated, and the improvement of the interpolation was quantified. The results show that the filtering of observations from PWSs is necessary as the interpolation error after the filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest temporal aggregations.

Rainfall-runoff modeling is highly uncertain for a number of different reasons. Hydrological processes are quite complex, and their simplifications in the models lead to inaccuracies. Model parameters themselves are uncertain—physical parameters because of their observations and conceptual parameters due to their limited identifiability. Furthermore, the main model input—precipitation is uncertain due to the limited number of available observations and the high spatio-temporal variability. The quantification of model output uncertainty is essential for their use. Most approaches used for the quantification of uncertainty in rainfall-runoff modeling assign the uncertainty to the model parameters. In this contribution, the role of precipitation uncertainty is investigated. Instead of a standard sensitivity analysis of the model output with respect to the input variations, it is investigated to what extent realistic precipitation fields could improve model performance. Realistic precipitation fields are defined as gridded realizations of precipitation which reproduce the observed values at the observation locations, with values which reproduce the distribution of the observed values and with spatial variability the same as the spatial variability of the observations. The above conditions apply to each observation time step. Through an inverse modeling approach based on Random Mixing precipitation fields fulfilling the above conditions and reproducing the discharge output better than using traditional interpolated observations can be obtained. These realizations show how much rainfall runoff models may profit from better precipitation input and how much remains for the parameter and model concept uncertainty. The methodology is applied using two hydrological models with a contrasting basis, SHETRAN and HBV, for three different mesoscale sub-catchments of the Neckar basin in Germany. Results show that up to 50% of the model error can be attributed to precipitation uncertainty. Further, inverting precipitation using hydrological models can improve model performance even in neighboring catchments which are not considered explicitly.

The accuracy of quantitative precipitation estimation (QPE) over a given region and period is of vital importance across multiple domains and disciplines. However, due to the intricate temporospatial variability and the intermittent nature of precipitation, it is challenging to obtain QPE with adequate accuracy. This paper aims to simulate rainfall fields while honoring both the local constraints imposed by the point-wise rain gauge observations and the global constraints imposed by the field measurements obtained from weather radar. The conditional simulation method employed in this study is modified phase annealing (PA), which is practically an evolution from the traditional simulated annealing (SA). Yet unlike SA, which implements perturbations in the spatial field, PA implements perturbations in Fourier space, making it superior to SA in many respects. PA is developed in two ways. First, taking advantage of the global characteristic of PA, the method is only used to deal with global constraints, and the local ones are handed over to residual kriging. Second, except for the system temperature, the number of perturbed phases is also annealed during the simulation process, making the influence of the perturbation more global at initial phases and decreasing the global impact of the perturbation gradually as the number of perturbed phases decreases. The proposed method is used to simulate the rainfall field for a 30 min event using different scenarios: with and without integrating the uncertainty of the radar-indicated rainfall pattern and with different objective functions.

The flow duration curve (FDC) of streamflow at a specific site has a key role in the knowledge on the distribution and characteristics of streamflow at that site. The FDC gives information on the water regime, providing information to optimally manage the water resources of the river. In spite of its importance, because of the lack of streamflow gauging stations, the FDC construction can be a not straightforward task. In partially gauged basins, FDCs are usually built using regionalization among the other methods. In this paper we show that the FDC is not a characteristic of the basin only, but of both the basin and the weather. Different weather conditions lead to different FDCs for the same catchment. The differences can often be significant. Similarly, the FDC built at a site for a specific period cannot be used to retrieve the FDC at a different site for the same time window. In this paper, we propose a new methodology to estimate FDCs at partially gauged basins (i.e., target sites) using precipitation data gauged at another basin (i.e., donor site). The main idea is that it is possible to retrieve the FDC of a target period of time using the data gauged during a given donor time period for which data are available at both target and donor sites. To test the methodology, several donor and target time periods are analyzed and results are shown for different sites in the USA. The comparison between estimated and actually observed FDCs shows the reasonability of the approach, especially for intermediate percentiles.

Study region: Iran Study focus: Gridded precipitation products are of great interest for hydrological applications. The inhomogeneous geography and uneven spatial distribution of rain gauges in Iran make it difficult to estimate valuable interpolated precipitation with daily or monthly resolutions. Therefore, we evaluated the performance of two empirical and four geostatistical interpolation methods. New hydrological insights for the region: Atmospheric circulation pattern (CP) classification was used to understand precipitation behavior and to improve interpolation. Based on 500 hPa geopotential fields, six CPs were identified, in order to explain large scale precipitation behavior. Variograms were normed and clustered to reduce the computational effort of the geostatistical methods.Leave-one-out cross-validation shows that the geostatistical methods outperform the empirical ones, and the differences among the geostatistical methods are small.The difference among all the methodologies decreased substantially for spatial aggregation to coarser resolutions. In contrast, temporal aggregation reduced the difference to a much lower extent.A large dataset consisting of 1561 locations with daily observations was used for this study. Comparison with the GPCC daily dataset shows that the data used for interpolation has a larger influence than the choice of the interpolation method.

Study region: The study region is Germany and two sub-regions in Germany, i.e. the state of Rhineland-Palatinate and the city of Reutlingen.Study focus: Opportunistic rainfall sensors, namely personal weather stations and commercial microwave links, together with rain gauge data from the German Weather Service, were used in different combinations to derive rainfall maps with a geostatistical interpolation framework for Germany. This kriging type framework considered the uncertainty of opportunistic sensors and the line structure of commercial microwave links. The resulting rainfall maps were compared to two gauge-adjusted radar products and evaluated to three reference gauge datasets in the respective study regions on both daily and hourly basis.New Hydrological Insights for the Region: The interpolated rainfall products from opportunistic sensors provided good agreement to the reference rain gauges. The dataset combinations including information from the opportunistic sensors performed best. The addition of rain gauges from the German Weather Service did not consistently lead to an improvement of the interpolated rainfall maps. On the country-wide, daily scale the interpolated rainfall maps performed well, but the gauge-adjusted radar products were closer to the reference. For the regional and local scale in Rhineland-Palatinate and Reutlingen with an hourly resolution, the interpolated rainfall maps outperformed the interpolated product from DWD rain gauges and showed a similar agreement to the reference as the radar products.

Stochastically generated streamflow time series are widely used in water resource planning and management. Such series represent sets of plausible yet unobserved streamflow realizations which should reproduce the main characteristics of observed data. These characteristics include the distribution of daily streamflow values and their temporal correlation as expressed by short- and long-range dependence. Existing streamflow generation approaches have mainly focused on the time domain, even though simulation in the frequency domain provides good properties. These properties comprise the simulation of both short- and long-range dependence as well as extension to multiple sites. Simulation in the frequency domain is based on the randomization of the phases of the Fourier transformation. We here combine phase randomization simulation with a flexible, four-parameter kappa distribution, which allows for the extrapolation to as yet unobserved low and high flows. The simulation approach consists of seven steps: (1) fitting the theoretical kappa distribution, (2) normalization and deseasonalization of the marginal distribution, (3) Fourier transformation, (4) random phase generation, (5) inverse Fourier transformation, (6) back transformation, and (7) simulation. The simulation approach is applicable to both individual and multiple sites. It was applied to and validated on a set of four catchments in Switzerland. Our results show that the stochastic streamflow generator based on phase randomization produces realistic streamflow time series with respect to distributional properties and temporal correlation. However, cross-correlation among sites was in some cases found to be underestimated. The approach can be recommended as a flexible tool for various applications such as the dimensioning of reservoirs or the assessment of drought persistence. Highlights. Stochastic simulation of streamflow time series for individual and multiple sites by combining phase randomization and the kappa distribution. Simulated time series reproduce temporal correlation, seasonal distributions, and extremes of observed time series. Simulation procedure suitable for use in water resource planning and management.