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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.

Floods are a natural hazard evolving in space and time according to meteorological and river basin dynamics, so that a single flood event can affect different regions over the event duration. This physical mechanism introduces spatio‐temporal relationships between flood records and losses at different locations over a given time window that should be taken into account for an effective assessment of the collective flood risk. However, since extreme floods are rare events, the limited number of historical records usually prevents a reliable frequency analysis. To overcome this limit, we move from the analysis of extreme events to the modeling of continuous stream flow records preserving spatio‐temporal correlation structures of the entire process, and making a more efficient use of the information provided by continuous flow records. The approach is based on the dynamic copula framework, which allows for splitting the modeling of spatio‐temporal properties by coupling suitable time series models accounting for temporal dynamics, and multivariate distributions describing spatial dependence. The model is applied to 490 stream flow sequences recorded across 10 of the largest river basins in central and eastern Europe (Danube, Rhine, Elbe, Oder, Waser, Meuse, Rhone, Seine, Loire, and Garonne). Using available proxy data to quantify local flood exposure and vulnerability, we show that the temporal dependence exerts a key role in reproducing interannual persistence, and thus magnitude and frequency of annual proxy flood losses aggregated at a basin‐wide scale, while copulas allow the preservation of the spatial dependence of losses at weekly and annual time scales.

Data in support of the Water Resources Research Journal Article, Pollock et al. (2018) "Quantifying and Mitigating Wind-Induced Undercatch in Rainfall Measurements"

Electricity systems are undergoing unprecedented change, with growing capacity for low-carbon generation, and an increasingly distributed approach to network control. Furthermore, the severity of climate related threats is projected to increase. To improve our understanding of the risks from these changes, this paper presents a novel modeling approach to assess the resilience of future electricity networks to climate hazards. The approach involves consideration of the: 1) evolution of electricity networks in response to changes in demand, supply, and infrastructure development policies; 2) implication that these policies have on network configuration and resilience; and 3) impacts of potential changes in climate hazard on network resilience. We demonstrate the research on the National Electricity Transmission System of Great Britain and assess the resilience of this system to changes in the intensity of wind storms under alternative energy futures. The analysis shows that infrastructure policies strongly shape the long-term spatial configuration of electricity networks and consequently this has profound impacts on their resilience. Though the system is resilient to wind storms under the current climate, our analysis shows that the system fails to meet electricity demand after an increase of only 5–10% in the intensity and frequency of wind storms, and a 50% increase could lead to the loss of 85% of peak winter demand. The approach is useful for identifying and communicating potential network risks to wider stakeholders and policy makers seeking to design a transition toward a low-carbon, yet resilient, future electricity systems.

[1] This study attempts to reconcile the conflicting results reported in the literature concerning the behavior of peak-over-threshold (POT) daily rainfall extremes and their distribution. By using two worldwide data sets, the impact of threshold selection and record length on the upper tail behavior of POT observations is investigated. The rainfall process is studied within the framework of generalized Pareto (GP) exceedances according to the classical extreme value theory (EVT), with particular attention paid to the study of the GP shape parameter, which controls the heaviness of the upper tail of the GP distribution. A twofold effect is recognized. First, as the threshold decreases, and nonextreme values are progressively incorporated in the POT samples, the variance of the GP shape parameter reduces and the mean converges to positive values denoting a tendency to heavy tail behavior. Simultaneously, the EVT asymptotic hypotheses are less and less realistic, and the GP asymptote tends to be replaced by the Weibull penultimate asymptote whose upper tail is exponential but apparently heavy. Second, for a fixed high threshold, the variance of the GP shape parameter reduces as the record length (number of years) increases, and the mean values tend to be positive, thus denoting again the prevalence of heavy tail behavior. In both cases, i.e., threshold selection and record length effect, the heaviness of the tail may be ascribed to mechanisms such as the blend of extreme and nonextreme values, and fluctuations of the parent distributions. It is shown how these results provide a link between previous studies and pave the way for more comprehensive analyses which merge empirical, theoretical, and operational points of view. This study also provides several ancillary results, such as a set of formulae to correct the bias of the GP shape parameter estimates due to short record lengths accounting for uncertainty, thus avoiding systematic underestimation of extremes which results from the analysis of short time series. Citation: Serinaldi, F., and C. G. Kilsby (2014), Rainfall extremes: Toward reconciliation after the battle of distributions, Water Resour. Res., 50, 336–352, doi:10.1002/2013WR014211.

[1] The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value Xp, volume V, duration D, and average intensity I. These variables play a fundamental role in hydrologic engineering as they are used, for instance, to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes. Given their inherent variability and the empirical evidence of the presence of a significant degree of association, such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions. The advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so-called dependence structure or copula. However, the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link , and I. In this study, we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern Europe, three 5 min rainfall series from central Italy, 80 daily streamflow series from the continental United States, and two sets of 200 simulated universal multifractal time series. Our results show that all the pairwise dependence structures between , and I exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques. Therefore, the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations. We also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs, meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of , and I. Finally, our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist. Confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results.

This report provides a summary of the 2009 UK Climate Projections (UKCP09), consolidating for the general reader the scientific reports describing the methodology and some key projections of future climate change for the UK over the 21st century. The UKCP09 Projections provide a basis for studies of impacts and vulnerability and decisions on adaptation to climate change in the UK over the 21st century. Projections are given of changes to climate, and of changes in the marine and coastal environment; recent trends in observed climate are also discussed. Each will be treated separately in this summary., Previously curated at: http://cedadocs.ceda.ac.uk/1321/ Main files in this record: breifing_report_full.pdf Item originally deposited with Centre for Environmental Data Analysis (CEDA) document repository by Miss Kate Winfield. Transferred to CEDA document repository community on Zenodo on 2022-11-24

In this report the UK Climate Projections (UKCP09) Weather Generator (WG) is introduced. This report covers the needs and principles and how it can be used to assess changes in extremes at spatial and temporal scales finer than the UKCP09 probability distribution functions (PDFs) can provide. Further, an illustration in the way the WG is perturbed to account for future climate change works and some illustrative maps of changes in extremes across the UK are also provided, Previously curated at: http://cedadocs.ceda.ac.uk/1335/ Main files in this record: weather_generator_full_report.pdf Item originally deposited with Centre for Environmental Data Analysis (CEDA) document repository by Miss Kate Winfield. Transferred to CEDA document repository community on Zenodo on 2022-11-24

Exploiting the duality between time series and networks, directed horizontal visibility graphs (DHVGs) are used to perform an unprecedented analysis of the dynamics of stream flow fluctuations with focus on time irreversibility and long range dependence. The analysis relies on a large quality-controlled data set consisting of 699 daily time series recorded in the continental United States (CONUS) that are not affected by human activity and primarily reflects meteorological conditions. DHVGs allow a clear visualization and quantification of time irreversibility of flow dynamics, which can be interpreted as a signature of nonlinearity, and long range dependence resulting from the interaction of atmospheric, surface and underground processes acting at multiple spatio-temporal scales. Irreversibility is explored by mapping the time series into ingoing, outgoing, and undirected graphs and comparing the corresponding degree distributions. Using surrogate data preserving up to the second order linear temporal dependence properties of the observed series, DHVGs highlight the additional complexity introduced by nonlinearity into flow fluctuation dynamics. We show that the degree distributions do not decay exponentially as expected, but tend to follow a subexponential behavior, even though sampling uncertainty does not allow a clear distinction between apparent or true power law decay. These results confirm that the complexity of stream flow dynamics goes beyond a linear representation involving for instance the combination of linear processes with short and long range dependence, and requires modeling strategies accounting for temporal asymmetry and nonlinearity.

SummaryLarge scale rainfall models are needed for collective risk estimation in flood insurance, infrastructure networks and water resource management applications. There is a lack of models which can provide simulations over large river basins (potentially multi-national) at appropriate spatial resolution (e.g., 5–25km) that preserve both the local properties of rainfall (i.e., marginal distributions and temporal correlation) and the spatial structure of the field (i.e., the spatial dependence structure). In this study we describe a methodology which merges meta-Gaussian random fields and generalized additive models to simulate realistic rainfall fields at daily time scale over large areas. Unlike other techniques previously proposed in the literature, the suggested approach does not split the rainfall occurrence and intensity processes and resorts to a unique discrete–continuous distribution to reproduce the local properties of rainfall. This choice allows the use of a unique meta-Gaussian spatio-temporal random field substrate that is devised to reproduce the spatial properties and the short term temporal characteristics of the observed precipitation. The model is calibrated and tested on a 25km gridded daily rainfall data set covering the 817000km2 of the Danube basin. Standard and ad hoc diagnostics highlight the overall good performance over the whole range of rainfall values at multiple scales of spatio-temporal aggregation with particular attention to extreme values. Moreover, the modular structure of the model allows for refinements, adaptation to different areas and the introduction of exogenous forcing variables, thus making it a valuable tool for classical hydrologic analyses as well as for new challenges of network and reinsurance risk assessment over extensive areas.