Bluecat: A Local Uncertainty Estimator for Deterministic Simulations and Predictions

We present a new method for simulating and predicting hydrologic variables with uncertainty assessment and provide example applications to river flows. The method is identified with the acronym “Bluecat” and is based on the use of a deterministic model which is subsequently converted to a stochastic formulation. The latter provides an adjustment on statistical basis of the deterministic prediction along with its confidence limits. The distinguishing features of the proposed approach are the ability to infer the probability distribution of the prediction without requiring strong hypotheses on the statistical characterization of the prediction error (e.g., normality, homoscedasticity), and its transparent and intuitive use of the observations. Bluecat makes use of a rigorous theory to estimate the probability distribution of the predictand conditioned by the deterministic model output, by inferring the conditional statistics of observations. Therefore Bluecat bridges the gaps between deterministic (possibly physically based, or deep learning-based) and stochastic models, as well as between rigorous theory and transparent use of data with an innovative and user oriented approach. We present two examples of application to the case studies of the Arno river at Subbiano and Sieve river at Fornacina. The results confirm the distinguishing features of the method along with its technical soundness. We provide an open software working in the R environment, along with help facilities and detailed instructions to reproduce the case studies presented here

Climate Extrapolations in Hydrology: The Expanded Bluecat Methodology

Bluecat is a recently proposed methodology to upgrade a deterministic model (D-model) into a stochastic one (S-model), based on the hypothesis that the information contained in a time series of observations and the concurrent predictions made by the D-model is sufficient to support this upgrade. The prominent characteristics of the methodology are its simplicity and transparency, which allow its easy use in practical applications, without sophisticated computational means. In this paper, we utilize the Bluecat methodology and expand it in order to be combined with climate model outputs, which often require extrapolation out of the range of values covered by observations. We apply the expanded methodology to the precipitation and temperature processes in a large area, namely the entire territory of Italy. The results showcase the appropriateness of the method for hydroclimatic studies, as regards the assessment of the performance of the climate projections, as well as their stochastic conversion with simultaneous bias correction and uncertainty quantification

KNN vs. Bluecat—Machine Learning vs. Classical Statistics

Uncertainty is inherent in the modelling of any physical processes. Regarding hydrological modelling, the uncertainty has multiple sources including the measurement errors of the stresses (the model inputs), the measurement errors of the hydrological process of interest (the observations against which the model is calibrated), the model limitations, etc. The typical techniques to assess this uncertainty (e.g., Monte Carlo simulation) are computationally expensive and require specific preparations for each individual application (e.g., selection of appropriate probability distribution). Recently, data-driven methods have been suggested that attempt to estimate the uncertainty of a model simulation based exclusively on the available data. In this study, two data-driven methods were employed, one based on machine learning techniques, and one based on statistical approaches. These methods were tested in two real-world case studies to obtain conclusions regarding their reliability. Furthermore, the flexibility of the machine learning method allowed assessing more complex sampling schemes for the data-driven estimation of the uncertainty. The anatomisation of the algorithmic background of the two methods revealed similarities between them, with the background of the statistical method being more theoretically robust. Nevertheless, the results from the case studies indicated that both methods perform equivalently well. For this reason, data-driven methods can become a valuable tool for practitioners

A rainfall disaggregation scheme for sub-hourly time scales: coupling a Bartlett-Lewis based model with adjusting procedures

Many hydrological applications, such as flood studies, require the use of long rainfall data at fine time scales varying from daily down to 1 min time step. However, in the real world there is limited availability of data at sub-hourly scales. To cope with this issue, stochastic disaggregation techniques are typically employed to produce possible, statistically consistent, rainfall events that aggregate up to the field data collected at coarser scales. A methodology for the stochastic disaggregation of rainfall at fine time scales was recently introduced, combining the Bartlett-Lewis process to generate rainfall events along with adjusting procedures to modify the lower-level variables (i.e., hourly) so as to be consistent with the higher-level one (i.e., daily). In the present paper, we extend the aforementioned scheme, initially designed and tested for the disaggregation of daily rainfall into hourly depths, for any sub-hourly time scale. In addition, we take advantage of the recent developments in Poisson-cluster processes incorporating in the methodology a Bartlett-Lewis model variant that introduces dependence between cell intensity and duration in order to capture the variability of rainfall at sub-hourly time scales. The disaggregation scheme is implemented in an R package, named HyetosMinute, to support disaggregation from daily down to 1-min time scale. The applicability of the methodology was assessed on a 5-min rainfall records collected in Bochum, Germany, comparing the performance of the above mentioned model variant against the original Bartlett-Lewis process (non-random with 5 parameters). The analysis shows that the disaggregation process reproduces adequately the most important statistical characteristics of rainfall at wide range of time scales, while the introduction of the model with dependent intensity-duration results in a better performance in terms of skewness, rainfall extremes and dry proportions

A probabilistic approach to the concept of Probable Maximum Precipitation

The concept of Probable Maximum Precipitation (PMP) is based on the assumptions that (a) there exists an upper physical limit of the precipitation depth over a given area at a particular geographical location at a certain time of year, and (b) that this limit can be estimated based on deterministic considerations. The most representative and widespread estimation method of PMP is the so-called moisture maximization method. This method maximizes observed storms assuming that the atmospheric moisture would hypothetically rise up to a high value that is regarded as an upper limit and is estimated from historical records of dew points. In this paper, it is argued that fundamental aspects of the method may be flawed or inconsistent. Furthermore, historical time series of dew points and "constructed" time series of maximized precipitation depths (according to the moisture maximization method) are analyzed. The analyses do not provide any evidence of an upper bound either in atmospheric moisture or maximized precipitation depth. Therefore, it is argued that a probabilistic approach is more consistent to the natural behaviour and provides better grounds for estimating extreme precipitation values for design purposes

A parametric rule for planning and management of multiple-reservoir systems

Abstract. A parametric rule for multireservoir system operation is formulated and tested. It is a generalization of the well-known space rule to simultaneously account for various system operating goals in addition to the standard goal of avoiding unnecessary spills, including: avoidance of leakage losses, avoidance of conveyance problems, the impact of the reservoir system topology, and assurance of satisfying secondary uses. Theoretical values of the rule’s parameters for each one of these isolated goals are derived. In practice, parameters are evaluated to optimize one or more objective functions selected by the user. The rule is embedded in a simulation model so that optimization requires repeated simulations of the system operation with specific values of the parameters each time. The rule is tested on the case of the multi-reservoir water supply system of the city of Athens, Greece, which is driven by all of the operating goals listed above. Two problems at the system design level are tackled. First, the total release from the system is maximized for a selected level of failure probability. Second, the annual operating cost is minimized for given levels of water demand and failure probability. A detailed simulation model is used in the case study. Sensitivity analysis to the rule’s parameters revealed a subset of insensitive parameters that allowed for rule simplification. Finally, the rule is validated through comparison with a number of heuristic rules also applied to the test case. 2 1

A large sample analysis of European rivers on seasonal river flow correlation and its physical drivers

The geophysical and hydrological processes governing river flow formation exhibit persistence at several timescales, which may manifest itself with the presence of positive seasonal correlation of streamflow at several different time lags. We investigate here how persistence propagates along subsequent seasons and affects low and high flows. We define the high-flow season (HFS) and the low-flow season (LFS) as the 3-month and the 1-month periods which usually exhibit the higher and lower river flows, respectively. A dataset of 224 rivers from six European countries spanning more than 50 years of daily flow data is exploited. We compute the lagged seasonal correlation between selected river flow signatures, in HFS and LFS, and the average river flow in the antecedent months. Signatures are peak and average river flow for HFS and LFS, respectively. We investigate the links between seasonal streamflow correlation and various physiographic catchment characteristics and hydro-climatic properties. We find persistence to be more intense for LFS signatures than HFS. To exploit the seasonal correlation in the frequency estimation of high and low flows, we fit a bi-variate meta-Gaussian probability distribution to the selected flow signatures and average flow in the antecedent months in order to condition the distribution of high and low flows in the HFS and LFS, respectively, upon river flow observations in the previous months. The benefit of the suggested methodology is demonstrated by updating the frequency distribution of high and low flows one season in advance in a real-world case. Our findings suggest that there is a traceable physical basis for river memory which, in turn, can be statistically assimilated into high- and low-flow frequency estimation to reduce uncertainty and improve predictions for technical purposes

Climate and human forcing of Alpine river flow

River flow in Alpine environments is likely to be highly sensitive to climate change because of the effects of warming upon snow and ice, and hence the intra-annual distribution of river runoff. It is also likely to be influenced strongly by human impacts both upon hydrology (e.g. flow abstraction) and river regulation. This paper compares the river flow and sediment flux of two Alpine drainage basins over the last 5 to 7 decades, one that is largely unimpacted by human activities, one strongly impacted by flow abstraction for hydroelectricity. The analysis shows that both river flow and sediment transport capacity are strongly dependent upon the effects of temperature and precipitation availability upon snow accumulation. As the latter tends to increase annual maximum flows, and given the non-linear form of most sediment transport laws, current warming trends may lead to increased sedimentation in Alpine rivers. However, extension to a system impacted upon by flow abstraction reveals the dominant effect that human activity can have upon river sedimentation but also how human response to sediment management has co-evolved with climate forcing to make disentangling the two very difficult