Hydrologic Uncertainty Processor Research Articles

Quantifying and reducing flood forecast uncertainty by the CHUP-BMA method

Abstract. The Bayesian model averaging (BMA), hydrological uncertainty processor (HUP), and HUP-BMA methods have been widely used to quantify flood forecast uncertainty. This study proposes the copula-based hydrological uncertainty processor BMA (CHUP-BMA) method by introducing a copula-based HUP in the framework of BMA to bypass the need for a normal quantile transformation of the HUP-BMA method. The proposed ensemble forecast scheme consists of eight members (two forecast precipitation inputs; two advanced long short-term memory, LSTM, models; and two objective functions used to calibrate parameters) and is applied to the interval basin between the Xiangjiaba and Three Gorges Reservoir (TGR) dam sites. The ensemble forecast performance of the HUP-BMA and CHUP-BMA methods is explored in the 6–168 h forecast horizons. The TGR inflow forecasting results show that the two methods can improve the forecast accuracy over the selected member with the best forecast accuracy and that the CHUP-BMA performs much better than the HUP-BMA. Compared with the HUP-BMA method, the forecast interval width and continuous ranked probability score metrics of the CHUP-BMA method are reduced by a maximum of 28.42 % and 17.86 % within all forecast horizons, respectively. The probability forecast of the CHUP-BMA method has better reliability and sharpness and is more suitable for flood ensemble forecasts, providing reliable risk information for flood control decision-making.

Exploration of dual-attention mechanism-based deep learning for multi-step-ahead flood probabilistic forecasting

In order to improve the flood forecasting accuracy and reflect the forecast uncertainty information in the Three Gorges Reservoir (TGR) interval-basin in China, this study integrates the feature and temporal dual-attention (DA) mechanism and recursive encoder-decoder (RED) structure into the long short-term memory (LSTM) neural network to develop a DA-LSTM-RED model. The feature attention acts on the input variables of the encoder, and the temporal attention mechanism acts on the hidden layer states extracted by the LSTM neural network during encoding process, prompting the proposed model to extract critical input information among different types and moments of input variables to improve the multi-step-ahead flood forecasting accuracy. Second, the copula-based Hydrological Uncertainty Processor (copula-HUP) is used to quantify the forecast uncertainty of the proposed model meanwhile creating multi-step-ahead flood probabilistic forecasts. Combining the long-term 6 h hydrologic data series of the Xiangjiaba-TGR interval-basin and the forecasted precipitation from the European Centre for Medium-Range Weather Forecasts (ECMWF), the effectiveness of the proposed model, the effect of forecast precipitation on multi-step-ahead flood forecasting, and the effect of different copula functions on the probabilistic forecast of copula-HUP are investigated, respectively. The results show that the DA-LSTM-RED model can effectively improve the forecasting accuracy for long forecast horizons (3-7d) compared to the LSTM-RED model, and the average absolute error metrics are reduced by 10%-17%. Meanwhile, the proposed model can identify input variables with a high correlation with the target output variables, which improves the interpretability of deep learning to a certain extent. The Student copula-HUP has the lowest RB and CRPS metrics than the Frank and Gaussian copula-HUP, which can better quantify the DA-LSTM-RED model's forecast uncertainty. Therefore, combining the proposed model with the Student copula-HUP can effectively reduce the forecasting uncertainty, enhance the forecasting reliability and accuracy for future horizons, and provide reliable risk information for the TGR flood control scheduling decision.

HUP‐BMA: An Integration of Hydrologic Uncertainty Processor and Bayesian Model Averaging for Streamflow Forecasting

AbstractUncertainty quantification and providing probabilistic streamflow forecasts are of particular interest for water resource management. The hydrologic uncertainty processor (HUP) is a well‐known Bayesian approach used to quantify hydrologic uncertainty based on observations and deterministic forecasts. This uncertainty quantification is model‐specific; however, utilizing information from multiple hydrologic models should be advantageous and should lead to better probabilistic forecasts. Using seven, structurally different, conceptual models, this study first aims at evaluating the effects of implementing different hydrologic models on HUP performance. Second, using the concepts of the Bayesian Model Averaging (BMA) approach, a multimodel HUP‐based Bayesian postprocessor (HUP‐BMA) is proposed where the combination of posterior distributions derived from HUP with different hydrologic models are used to better quantify the hydrologic uncertainty. All postprocessing approaches are applied for medium‐range daily streamflow forecasting (1–14 days ahead) in two watersheds located in Ontario, Canada. The results indicate that the HUP forecasts for short lead‐times are negligibly affected by implementing different hydrologic models, while with increasing lead‐time and flow magnitude, they significantly depend on the quality of the deterministic forecast. Moreover, the superiority of the proposed HUP‐BMA method over HUP is demonstrated based on various verification metrics in both watersheds. Additionally, HUP‐BMA outperformed the original BMA in quantifying hydrologic uncertainty for short lead‐times. However, by increasing lead‐time, considering the effects of initially observed flow on HUP‐BMA formulation may not be beneficial. So, its modified version unconditioned on initial observations is preferred.

Consideration of streamflow forecast uncertainty in the development of short-term hydropower station optimal operation schemes: A novel approach based on mean-variance theory

The uncertainty of streamflow forecast will cause the ineffectiveness on the short-term hydropower station optimal operation (SHSOO) and lead to the risk of producing less hydropower than planned. Traditionally, stochastic optimal theory represented by the stochastic dynamic programming model (SDPM) is commonly used for SHSOO, which is focus on the uncertainty during a single lead time and lack of an overall consideration of multiple independent lead times of differing length. Thus, this paper proposes a short-term hydropower station optimal operation model based on mean-variance theory (MV-SHSOOM) for reducing operational risk. The proposed multi-step model considers the forecasting uncertainty of different lead times as an integral component to guide a station’s optimal operation. Specifically, the forecast uncertainty was integrated by the joint probability distribution of forecast error using a multivariate hydrologic uncertainty processor (HUP) at first. Then, possible observed streamflow sequences were obtained using the joint probability distribution of forecast error and taken as input to the short-term optimal operation model of the hydropower station. Finally, the mean-variance theory was applied to construct the optimal operation model for balancing the power generation and operational risk. The proposed model was applied to the Jinxi hydropower station, China, to determine its performance. The results show that: 1) the dependent structure among the forecast errors at different lead times is significant in terms of Spearman correlation, and the joint probability distribution of forecast error can be effectively described by a multivariate HUP; 2) the proposed MV-SHSOOM is superior to the traditional deterministic dynamic programming model (DDPM) and SDPM, and can more effectively reduce operational risk while increasing power generation.

On the Operational Flood Forecasting Practices Using Low-Quality Data Input of a Distributed Hydrological Model

Low-quality input data (such as sparse rainfall gauges, low spatial resolution soil type and land use maps) have limited the application of physically-based distributed hydrological models in operational practices in many data-sparse regions. It is necessary to quantify the uncertainty in the deterministic forecast results of distributed models. In this paper, the TOPographic Kinematic Approximation and Integration (TOPKAPI) distributed model was used for deterministic forecasts with low-quality input data, and then the Hydrologic Uncertainty Processor (HUP) was used to provide the probabilistic forecast results for operational practices. Results showed that the deterministic forecasts by TOPKAPI performed poorly in some flood seasons, such as the years 1997, 2001 and 2008, despite which the overall accuracy of the whole study period 1996–2008 could be acceptable and generally reproduced the hydrological behaviors of the catchment (Lushi basin, China). The HUP model can not only provide probabilistic forecasts (e.g., 90% predictive uncertainty bounds), but also provides deterministic forecasts in terms of 50% percentiles. The 50% percentiles obviously improved the forecast accuracy of selected flood events at the leading time of one hour. Besides, the HUP performance decayed with the leading time increasing (6, 12 h). This work revealed that deterministic model outputs had large uncertainties in flood forecasts, and the HUP model may provide an alternative for operational flood forecasting practices in those areas with low-quality data.

A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space

Hydrological forecasting plays an important role in basin flood control systems, and the uncertainty of hydrological forecasting is helpful to reveal basin hydrological characteristics and provide support to decision makers in formulating water resources management schemes. The hydrologic uncertainty processor (HUP) has been widely employed in hydrological uncertainty prediction. However, in the HUP normal quantile transform (NQT) space, the posteriori distribution is derived from the Bayesian theory. This increases the difficulty of the theory and calculations. In this paper, a new method is proposed to deduce the posterior residual equation, and the HUP-Gaussian mixture model (HUP-GMM) is adopted to simplify the calculations. By maintaining the original hypothesis, since the posterior residual is known to follow a normal distribution, the posterior linear correlation equation can be directly assumed without prior and likelihood inferences. In particular, the complex Bayesian inference is replaced with simple linear equations. By converting the linear equation into the original space, we obtain a new method consisting of the HUP linear GMM (HUP-LG). In the study area, the parameters of the HUP-LG and HUP-GMM in the NQT space are calculated, and corresponding expressions of the probability density in the original space are obtained. The results reveal that the HUP-LG simplifies the calculation process in the NQT space, and attains the same performance as that of the HUP-GMM.

A crash-testing framework for predictive uncertainty assessment when forecasting high flows in an extrapolation context

Abstract. An increasing number of flood forecasting services assess and communicate the uncertainty associated with their forecasts. While obtaining reliable forecasts is a key issue, it is a challenging task, especially when forecasting high flows in an extrapolation context, i.e. when the event magnitude is larger than what was observed before. In this study, we present a crash-testing framework that evaluates the quality of hydrological forecasts in an extrapolation context. The experiment set-up is based on (i) a large set of catchments in France, (ii) the GRP rainfall–runoff model designed for flood forecasting and used by the French operational services and (iii) an empirical hydrologic uncertainty processor designed to estimate conditional predictive uncertainty from the hydrological model residuals. The variants of the uncertainty processor used in this study differ in the data transformation they use (log, Box–Cox and log–sinh) to account for heteroscedasticity and the evolution of the other properties of the predictive distribution with the discharge magnitude. Different data subsets were selected based on a preliminary event selection. Various aspects of the probabilistic performance of the variants of the hydrologic uncertainty processor, reliability, sharpness and overall quality were evaluated. Overall, the results highlight the challenge of uncertainty quantification when forecasting high flows. They show a significant drop in reliability when forecasting high flows in an extrapolation context and considerable variability among catchments and across lead times. The increase in statistical treatment complexity did not result in significant improvement, which suggests that a parsimonious and easily understandable data transformation such as the log transformation or the Box–Cox transformation can be a reasonable choice for flood forecasting.

Multicriteria assessment framework of flood events simulated with vertically mixed runoff model in semiarid catchments in the middle Yellow River

Abstract. Flood forecasting in semiarid regions is always poor, and a single-criterion assessment provides limited information for decision making. Here, we propose a multicriteria assessment framework called flood classification–reliability assessment (FCRA) that combines the absolute relative error, flow classification and uncertainty interval estimated by the hydrologic uncertainty processor (HUP) to assess the most striking feature of an event-based flood: the peak flow. A total of 100 flood events in four catchments of the middle reaches of the Yellow River are modeled with hydrological models over the period of 1983–2009. The vertically mixed runoff model (VMM) is compared with one physically based model, the MIKE SHE model (originating from the Système Hydrologique Européen program), and two conceptual models, the Xinanjiang model (XAJ) and the Shanbei model (SBM). Our results show that the VMM has a better flood estimation performance than the other models, and the FCRA framework can provide reasonable flood classification and reliability assessment information, which may help decision makers improve their diagnostic abilities in the early flood warning process.

Assessing Hydrologic Uncertainty Processor Performance for Flood Forecasting in a Semiurban Watershed

AbstractA key challenge in enhancing flood forecast relies in the difficulty of reducing predictive uncertainty. The precipitation-dependent hydrologic uncertainty processor (HUP) is a flexible mod...

Probabilistic Flood Forecasting Using Hydrologic Uncertainty Processor with Ensemble Weather Forecasts

Recent advances in the field of flood forecasting have shown increased interests in probabilistic forecasting as it provides not only the point forecast but also the assessment of associated uncertainty. Here, an investigation of a hydrologic uncertainty processor (HUP) as a postprocessor of ensemble forecasts to generate probabilistic flood forecasts is presented. The main purpose is to quantify dominant uncertainties and enhance flood forecast reliability. HUP is based on Bayes’s theorem and designed to capture hydrologic uncertainty. Ensemble forecasts are forced by ensemble weather forecasts from the Global Ensemble Prediction System (GEPS) that are inherently uncertain, and the input uncertainty propagates through the model chain and integrates with hydrologic uncertainty in HUP. The bias of GEPS was removed using multivariate bias correction, and several scenarios were developed by different combinations of GEPS with HUP. The performance of different forecast horizons for these scenarios was compared using multifaceted evaluation metrics. Results show that HUP is able to improve the performance for both short- and medium-range forecasts; the improvement is significant for short lead times and becomes less obvious with increasing lead time. Overall, the performances for short-range forecasts when using HUP are promising, and the most satisfactory result for the short range is obtained by applying bias correction to each ensemble member plus applying the HUP postprocessor.

Hydrological Uncertainty Processor (HUP) with Estimation of the Marginal Distribution by a Gaussian Mixture Model

Uncertainty assessments of hydrological prediction results can reflect additional hydrological information and reveal important hydrological characteristics of river basins, which is of great significance to disaster prevention and reduction. The hydrological uncertainty processor (HUP), which is a key part of the Bayesian forecasting system (BFS), has derived a variety of methods for hydrological uncertainty forecasting. The HUP allows for any form of marginal distributions of hydrological data and does not require a unified estimation structure for the marginal distribution function. The Gaussian mixture model (GMM) is a probability distribution estimation model that can approximate any probability distribution with arbitrary precision. In this paper, the GMM was used to estimate the marginal distribution of observed and modelled data, and this method is called HUP-GMM. The uncertainty of river discharge at the Yichang hydrological station on the main stem of the Yangtze River in China is predicted by the HUP-GMM. The Weibull and Gamma distributions, which are commonly used hydrological probability distributions, are compared to analyse the performance of the GMM. In June, when the measured flow h3 is 13,850 m3/s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 1.63E-04, 1.05E-04 and 9.50E-05 and the posterior probabilities are 2.57E-04, 1.61E-04 and 1.38E-04, respectively. In September, when the measured flow h3 is 35,400 m3/s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 5.98E-05, 2.21E-05 and 2.18E-05 and the posterior probabilities are 1.64E-04, 9.15E-05 and 8.43E-05, respectively. The results show that the performance of the uncertainty estimation of the prior and posterior probability distributions in the HUP-GMM has been improved.

Uncertainty analysis of hydrological multi-model ensembles based on CBP-BMA method

Abstract Quantification of the inherent uncertainty in hydrologic forecasting is essential for flood control and water resources management. The existing approaches, such as Bayesian model averaging (BMA), hydrologic uncertainty processor (HUP), copula-BMA (CBMA), aim at developing reliable probabilistic forecasts to characterize the uncertainty induced by model structures. In the probability forecast framework, these approaches either assume the probability density function (PDF) to follow a certain distribution, or are unable to reduce bias effectively for complex hydrological forecasts. To overcome these limitations, a copula Bayesian processor associated with BMA (CBP-BMA) method is proposed with ensemble lumped hydrological models. Comparing with the BMA and CBMA methods, the CBP-BMA method relaxes any assumption on the distribution of conditional PDFs. Several evaluation criteria, such as containing ratio, average bandwidth and average deviation amplitude of probabilistic application, are utilized to evaluate the model performance. The case study results demonstrate that the CBP-BMA method can improve hydrological forecasting precision with higher cover ratios more than 90%, which are increased by 4.4% and 3.2%, 2.2% and 1.7% over those of BMA and CBMA during the calibration and validation periods, respectively. The proposed CBP-BMA method provides an alternative approach for uncertainty estimation of hydrological multi-model forecasts.

Hydrological uncertainty processor based on a copula function

ABSTRACTQuantifying the uncertainty in hydrological forecasting is valuable for water resources management and decision-making processes. The hydrological uncertainty processor (HUP) can quantify hydrological uncertainty and produce probabilistic forecasts under the hypothesis that there is no input uncertainty. This study proposes a HUP based on a copula function, in which the prior density and likelihood function are explicitly expressed, and the posterior density and distribution obtained using Monte Carlo sampling. The copula-based HUP was applied to the Three Gorges Reservoir, and compared with the meta-Gaussian HUP. The Nash-Sutcliffe efficiency and relative error were used as evaluation criteria for deterministic forecasts, while predictive QQ plot, reliability, resolution and continuous rank probability score (CRPS) were used for probabilistic forecasts. The results show that the proposed copula-based HUP is comparable to the meta-Gaussian HUP in terms of the posterior median forecasts, and that its probabilistic forecasts have slightly higher reliability and lower resolution compared to the meta-Gaussian HUP. Based on the CRPS, both HUPs were found superior to deterministic forecasts, highlighting the effectiveness of probabilistic forecasts, with the copula-based HUP marginally better than the meta-Gaussian HUP.

Performance assessment of hydrologic uncertainty processor through integration of the principal components analysis

Abstract Uncertainty analysis is important and should be always considered when using models for flood forecasting. In this paper, the ‘Principal Components Analysis-Hydrologic Uncertainty Processor’ (PCA-HUP) was developed for probabilistic flood forecasting (PFF) and further evaluated in the middle Yellow River, China. Due to the severe sediment erosion, small and medium floods drain in the main channel (normal floods) while large floods would spill over the bank and drain in river floodplains (overbank floods). Thus, the practical routing methods were used to provide the deterministic flood forecasting (DFF) input for PCA-HUP. PCA-HUP quantifies the forecast uncertainty and provides PFF results. The comparison of performance between the DFF and PFF outputs indicated that PFF could also provide a good accuracy of deterministic hydrograph. In order to explore the performance decay of DFF and PFF with lead time increasing, the lead times n = 1, 6 and 10 hours were chosen for comparison. Results suggested that, with the increasing lead time, the performances of both DFF and PFF decayed accordingly. As a consequence, this study proved the practicability of PCA-HUP in the operational forecasting for both normal and overbank floods in the middle reach of Yellow River.

A data-driven SVR model for long-term runoff prediction and uncertainty analysis based on the Bayesian framework

Accurate and reliable long-term forecasting plays an important role in water resources management and utilization. In this paper, a hybrid model called SVR-HUP is presented to predict long-term runoff and quantify the prediction uncertainty. The model is created based on three steps. First, appropriate predictors are selected according to the correlations between meteorological factors and runoff. Second, a support vector regression (SVR) model is structured and optimized based on the LibSVM toolbox and a genetic algorithm. Finally, using forecasted and observed runoff, a hydrologic uncertainty processor (HUP) based on a Bayesian framework is used to estimate the posterior probability distribution of the simulated values, and the associated uncertainty of prediction was quantitatively analyzed. Six precision evaluation indexes, including the correlation coefficient (CC), relative root mean square error (RRMSE), relative error (RE), mean absolute percentage error (MAPE), Nash-Sutcliffe efficiency (NSE), and qualification rate (QR), are used to measure the prediction accuracy. As a case study, the proposed approach is applied in the Han River basin, South Central China. Three types of SVR models are established to forecast the monthly, flood season and annual runoff volumes. The results indicate that SVR yields satisfactory accuracy and reliability at all three scales. In addition, the results suggest that the HUP cannot only quantify the uncertainty of prediction based on a confidence interval but also provide a more accurate single value prediction than the initial SVR forecasting result. Thus, the SVR-HUP model provides an alternative method for long-term runoff forecasting.

Risk Analysis of Reservoir Flood Routing Calculation Based on Inflow Forecast Uncertainty

Possible risks in reservoir flood control and regulation cannot be objectively assessed by deterministic flood forecasts, resulting in the probability of reservoir failure. We demonstrated a risk analysis of reservoir flood routing calculation accounting for inflow forecast uncertainty in a sub-basin of Huaihe River, China. The Xinanjiang model was used to provide deterministic flood forecasts, and was combined with the Hydrologic Uncertainty Processor (HUP) to quantify reservoir inflow uncertainty in the probability density function (PDF) form. Furthermore, the PDFs of reservoir water level (RWL) and the risk rate of RWL exceeding a defined safety control level could be obtained. Results suggested that the median forecast (50th percentiles) of HUP showed better agreement with observed inflows than the Xinanjiang model did in terms of the performance measures of flood process, peak, and volume. In addition, most observations (77.2%) were bracketed by the uncertainty band of 90% confidence interval, with some small exceptions of high flows. Results proved that this framework of risk analysis could provide not only the deterministic forecasts of inflow and RWL, but also the fundamental uncertainty information (e.g., 90% confidence band) for the reservoir flood routing calculation.

Comparative Study of Three Updating Procedures for Real-Time Flood Forecasting

Accurate real-time flood forecasting is essential for flood control and warning system, reservoir operation and other relevant water resources management activities. The objective of this study is to investigate and compare the capability of three updating procedures, namely autoregressive (AR) model, recursive least-squares (RLS) model and hydrologic uncertainty processor (HUP) in the real-time flood forecasting. The Baiyunshan reservoir basin located in southern China was selected as a case study. These three procedures were employed to update outputs of the established Xinanjiang flood forecasting model. The Nash-Sutcliffe efficiency (NSE) and Relative Error (RE) are used as model evaluation criteria. It is found that all of these three updating procedures significantly improve the accuracy of Xinanjiang model when operating in real-time forecasting mode. Comparison results also indicated that the HUP performed better than the AR and RLS models, while RLS model was slightly superior to AR model. In addition, the HUP implemented in the probabilistic form can quantify the uncertainty of the actual discharge to be forecasted and provide a posterior distribution as well as interval estimation, which offer more useful information than two other deterministic updating procedures. Thus, the HUP updating procedure is more promising and recommended for real-time flood forecasting in practice.

Ensemble Bayesian forecasting system Part I: Theory and algorithms

Summary The ensemble Bayesian forecasting system (EBFS), whose theory was published in 2001, is developed for the purpose of quantifying the total uncertainty about a discrete-time, continuous-state, non-stationary stochastic process such as a time series of stages, discharges, or volumes at a river gauge. The EBFS is built of three components: an input ensemble forecaster (IEF), which simulates the uncertainty associated with random inputs; a deterministic hydrologic model (of any complexity), which simulates physical processes within a river basin; and a hydrologic uncertainty processor (HUP), which simulates the hydrologic uncertainty (an aggregate of all uncertainties except input). It works as a Monte Carlo simulator: an ensemble of time series of inputs (e.g., precipitation amounts) generated by the IEF is transformed deterministically through a hydrologic model into an ensemble of time series of outputs, which is next transformed stochastically by the HUP into an ensemble of time series of predictands (e.g., river stages). Previous research indicated that in order to attain an acceptable sampling error, the ensemble size must be on the order of hundreds (for probabilistic river stage forecasts and probabilistic flood forecasts) or even thousands (for probabilistic stage transition forecasts). The computing time needed to run the hydrologic model this many times renders the straightforward simulations operationally infeasible. This motivates the development of the ensemble Bayesian forecasting system with randomization (EBFSR), which takes full advantage of the analytic meta-Gaussian HUP and generates multiple ensemble members after each run of the hydrologic model; this auxiliary randomization reduces the required size of the meteorological input ensemble and makes it operationally feasible to generate a Bayesian ensemble forecast of large size. Such a forecast quantifies the total uncertainty, is well calibrated against the prior (climatic) distribution of predictand, possesses a Bayesian coherence property, constitutes a random sample of the predictand, and has an acceptable sampling error—which makes it suitable for rational decision making under uncertainty.

Performance assessment of a Bayesian Forecasting System (BFS) for real-time flood forecasting

Summary The paper evaluates, for a number of flood events, the performance of a Bayesian Forecasting System (BFS), with the aim of evaluating total uncertainty in real-time flood forecasting. The predictive uncertainty of future streamflow is estimated through the Bayesian integration of two separate processors. The former evaluates the propagation of input uncertainty on simulated river discharge, the latter computes the hydrological uncertainty of actual river discharge associated with all other possible sources of error. A stochastic model and a distributed rainfall–runoff model were assumed, respectively, for rainfall and hydrological response simulations. A case study was carried out for a small basin in the Calabria region (southern Italy). The performance assessment of the BFS was performed with adequate verification tools suited for probabilistic forecasts of continuous variables such as streamflow. Graphical tools and scalar metrics were used to evaluate several attributes of the forecast quality of the entire time-varying predictive distributions: calibration, sharpness, accuracy, and continuous ranked probability score (CRPS). Besides the overall system, which incorporates both sources of uncertainty, other hypotheses resulting from the BFS properties were examined, corresponding to (i) a perfect hydrological model; (ii) a non-informative rainfall forecast for predicting streamflow; and (iii) a perfect input forecast. The results emphasize the importance of using different diagnostic approaches to perform comprehensive analyses of predictive distributions, to arrive at a multifaceted view of the attributes of the prediction. For the case study, the selected criteria revealed the interaction of the different sources of error, in particular the crucial role of the hydrological uncertainty processor when compensating, at the cost of wider forecast intervals, for the unreliable and biased predictive distribution resulting from the Precipitation Uncertainty Processor.

From HUP to MCP: Analogies and extended performances

► This work compares two known Predictive Uncertainty (PU) approaches, HUP and MCP. ► Both processors imply same joint distribution of predictand-model-latest observation. ► Both processors provide same correct results if lag-1 Markov is not assumed in HUP. ► Lag-1 Markov assumption in HUP leads to under-predict uncertainty estimates. ► MCP correct estimator of PU and extendable to multi site, multi temporal applications. This paper discusses the analogies and the performances of two uncertainty post-processors, the Hydrologic Uncertainty Processor (HUP) introduced by Krzysztofowicz (1999) and the Model Conditional Processor (MCP), which was proposed by Todini (2008) for the assessment of predictive uncertainty, as an alternative to HUP. The paper shows analytically and through a numerical example that the two uncertainty processors are strongly related and explains why MPC results into improved performances with respect to the HUP, when used with the same level of information. The simplicity of its derivation, the extended capabilities of MCP at tackling multi-predictand, multi-site, multi-model, multi-time problems together with the possible use of Truncated Normal Distributions in order to overcome heteroscedasticity in the residuals make MCP more easily applicable than HUP to describe predictive uncertainty in real time flood forecasting applications.