Hydrologic uncertainty processor for probabilistic river stage forecasting: precipitation-dependent model

The recent emergence of the National Digital Forecast Database as the flagship product of the National Weather Service has resulted in an increased demand for forecast guidance products on fine-mesh grids. Unfortunately, fine-grid forecasts with geographically regionalized statistical models are usually plagued by nonmeteorological discontinuities at regional boundaries. This study treats the problem in a regionalized Global Forecast System (GFS)-based model output statistics (MOS) application that produces 6-h probabilistic quantitative precipitation forecasts (PQPFs) on a 4-km grid up to 192 h in advance. The technique involves incorporating areal overlap in the geographical regionalization and weighting multiple PQPFs in region-overlap zones. The degree of overlap ranges from about 20 km along meteorologically significant regional boundaries to about 150 km at quasi-arbitrary boundaries. The forecast-weighting constants for a grid point in an overlap zone vary in direct proportion to the distances to the closest associated regional boundaries. The application of the region-overlap and forecast-weighting techniques resulted in retention of sharp PQPF gradients along meteorologically significant regional boundaries and prevention of artificial discontinuities at quasi-arbitrary boundaries. The eradication of the discontinuities in the forecast patterns was achieved without sacrificing forecast skill. While the regionalization was customized for producing high-spatial-resolution 6-h PQPFs over the contiguous United States with a specialized gridded MOS application, the region-overlap and forecast-weighting techniques may have general applicability. Also, the quality of the 6-h PQPFs was not strongly dependent on customization of the regionalization.

Hamill et al. described a multimodel ensemble precipitation postprocessing algorithm that is used operationally by the U.S. National Weather Service (NWS). This article describes further changes that produce improved, reliable, and skillful probabilistic quantitative precipitation forecasts (PQPFs) for single or multimodel prediction systems. For multimodel systems, final probabilities are produced through the linear combination of PQPFs from the constituent models. The new methodology is applied to each prediction system. Prior to adjustment of the forecasts, parametric cumulative distribution functions (CDFs) of model and analyzed climatologies are generated using the previous 60 days’ forecasts and analyses and supplemental locations. The CDFs, which can be stored with minimal disk space, are then used for quantile mapping to correct state-dependent bias for each member. In this stage, the ensemble is also enlarged using a stencil of forecast values from the 5 × 5 surrounding grid points. Different weights and dressing distributions are assigned to the sorted, quantile-mapped members, with generally larger weights for outlying members and broader dressing distributions for members with heavier precipitation. Probability distributions are generated from the weighted sum of the dressing distributions. The NWS Global Ensemble Forecast System (GEFS), the Canadian Meteorological Centre (CMC) global ensemble, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast data are postprocessed for April–June 2016. Single prediction system postprocessed forecasts are generally reliable and skillful. Multimodel PQPFs are roughly as skillful as the ECMWF system alone. Postprocessed guidance was generally more skillful than guidance using the Gamma distribution approach of Scheuerer and Hamill, with coefficients generated from data pooled across the United States.

This study investigates the probabilistic quantitative precipitation forecast (PQPF) performance of typhoons that affected Taiwan during 2011–16. In this period, a total of 19 typhoons with a land warning issued by the Central Weather Bureau (CWB) are analyzed. The PQPF is calculated using the ensemble precipitation forecast data from the Taiwan Cooperative Precipitation Ensemble Forecast Experiment (TAPEX), and the verification data, verification thresholds, and typhoon characteristics are obtained from the CWB. The overall PQPF performance of TAPEX has an acceptable reliability and discrimination ability, and the higher probability error is distributed at the mountainous area of Taiwan. The PQPF performance is significantly influenced by typhoon characteristics (e.g., typhoon tracks, sizes, and forward speeds). The PQPFs for westward-moving, large, or slow typhoons have higher reliability and discrimination ability, and lower-probability error than those for northward-moving, small, or fast typhoons, except for similar reliability between fast and slow typhoons. Because northward-moving or small typhoons have larger forecast track error, and their PQPF performance is sensitive to the accuracy of the forecast track, a higher probability error occurs than that for westward-moving or large typhoons. Furthermore, because there is no difference in track error between fast and slow typhoons, the larger track spread for slow typhoons increases the rainfall forecast spread and reduces the probability error. The orientation of Taiwan’s topography and the topographic effect also influence and increase the distribution and value of probability error for northward-moving, small, or fast typhoons. In summary, forecast track characteristics are influenced by typhoon characteristics and further affect the PQPF performance.

The predictability of precipitation is hindered by finer-scale processes not captured explicitly in global numerical models, such as convective interactions, cloud microphysics, and boundary layer dynamics. However, there is growing demand across various sectors for medium- (3–10-day) and extended-range (10–30-day) quantitative precipitation forecasts (QPFs) and probabilistic QPFs (PQPFs). This study uses a novel statistical postprocessing technique, APPM, that combines analog postprocessing (AP) with probability matching (PM) to produce week-1 and week-2 accumulated precipitation forecasts over Taiwan. AP searches for historical predictions that closely resemble the current forecast and create an AP ensemble using the observed high-resolution precipitation patterns corresponding to these forecast analogs. Frequency counting and PM are then separately applied to the AP ensemble to produce calibrated and downscaled PQPFs and bias-reduced QPFs, respectively. Evaluation over a 22-yr (1999–2020) period shows that raw ensemble forecasts from the GEFS of NOAA/NWS/Environmental Modeling Center, collected for the subseasonal experiment, are underdispersive with a wet bias. In contrast, the AP ensemble spread well represents forecast uncertainty, leading to substantially more reliable and skillful probabilistic forecasts. Furthermore, the AP-based PQPF demonstrates superior discrimination ability and yields notably greater economic benefits for a wider range of users, with the maximum economic value increasing by 30%–50% for the week-2 forecast. Compared to the raw ensemble mean forecast, the calibrated QPF exhibits lower mean absolute error and explains 3–8 times more variance in observations. Overall, the APPM technique significantly improves week-1 and week-2 QPFs and PQPFs over Taiwan. Significance Statement There are two significant challenges in improving precipitation forecasts beyond a few days in Taiwan. First, large-scale numerical models often struggle with accurately predicting precipitation locations, magnitudes, and providing sufficient detail. Second, probabilistic precipitation forecasts have been unreliable, failing to convey accurate uncertainty information to users. In response to these challenges, this study has developed a relatively simple yet effective technique that corrects the spatiotemporal distribution of predicted precipitation and downscales the forecasts from a 1° to 1-km spatial resolution. Our results demonstrate that this technique significantly alleviates these two issues, resulting in more accurate precipitation forecasts and more reliable probabilistic precipitation forecasts within a 2-week timeframe.

Highlights A web application, ShellCast, was created to issue near-term temporary shellfish harvest closures. ShellCast’s final version uses the probabilistic quantitative precipitation forecast on the backend. A pilot program was organized to evaluate end-user perspectives on the tool. ShellCast is most useful for growers managing farms in waters with low rainfall thresholds. ABSTRACT. Farmers and harvesters of molluscan shellfish (e.g., clams, oysters, mussels) in estuarine waters must adapt to periodic temporary harvest closures due to water quality concerns, which are issued without advance notice. Shellfish sanitation programs commonly use rainfall thresholds to assess water quality impairment risks (e.g., 2 inches of rain in 24 hours) and make decisions on temporary harvest closures. To help shellfish farmers and harvesters anticipate near-term closures, we created ShellCast, a forecast and notification system that alerts users when closure risk is moderate to very high today, tomorrow, or in two days. In this Research Brief, we summarize the development of the ShellCast web application for shellfish growing areas in North Carolina, USA, and changes made to accommodate its expansion to South Carolina and Florida. We also summarize findings from a pilot deployment program that was organized with end-users from North Carolina in which participants were asked to describe their experiences with, and perceptions of, ShellCast. ShellCast application development has iterated through the use of different rainfall forecast products and methods on the backend, with the U.S. National Weather Service’s Probabilistic Quantitative Precipitation Forecast driving the present-day version of ShellCast. From the pilot deployment program, we learned that text and email notifications were the most appreciated features of the ShellCast web application and that the forecasts are most useful for those who manage leases in waters with low rainfall thresholds where frequent closures are relatively more common. Findings from the development and evaluation of ShellCast could be used by others who are seeking to create decision-support tools for recreational fishers and food producers who are subject to weather-driven disruptions. Keywords: Clams, Decision-support tool, Fecal coliforms, Fecal indicator bacteria, Oysters, Water quality, Web application.

Heavy-rainfall events are common in southern France and frequently result in devastating flash floods. Thus, an appropriate anticipation of future rainfall is required: for early flood warning, at least 12–24 h in advance; for alerting operational services, at least 2–3 days ahead. Precipitation forecasts are generally provided by numerical weather prediction models (NWP), and their associated uncertainty is generally estimated through an ensemble approach. Precipitation forecasts also have to be adapted to hydrological scales. This study describes an alternative approach to commonly used limited-area models. Probabilistic quantitative precipitation forecasts (PQPFs) are provided through an analog sorting technique, which directly links synoptic-scale NWP output to catchment-scale rainfall probability distributions. One issue concerns the latest developments in implementing a daily version of this technique into operational conditions. It is shown that the obtained PQPFs depend on the meteorological forecasts used for selecting analogous days and that the method has to be reoptimized when changing the source of synoptic forecasts, because of the NWP output uncertainties. Second, an evaluation of the PQPFs demonstrates that the analog technique performs well for early warning of heavy-rainfall events and provides useful information as potential input to a hydrological ensemble prediction system. It is shown that the obtained daily rainfall distributions can be unreliable. A statistical correction of the observed bias is proposed as a function of the no-rain frequency values, leading to a significant improvement in PQPF sharpness.

U.S. National Weather Service (NWS) River Forecast Centers (RFCs) have produced monthly to seasonal hydrologic forecast ensemble outlooks for many years using historical precipitation and temperature as the forcing data for the ensembles within the Advanced Hydrologic Prediction System (AHPS). This has worked well for many water resources applications relying on long lead-time ensembles of greater than thirty days. In the eastern United States, there is considerable interest in shorter lead-time ensembles, particularly in the period of one to seven days that convey hydrologic forecast uncertainty resulting directly from the uncertainties in precipitation and temperature forecasts, with a focus on flood forecasting. This paper demonstrates the use of numerical weather prediction (NWP) model ensembles as the forcing for hydrologic models within the NWS hydrologic forecasting system, the Deltares Flood Early Warning System (FEWS) based Community Hydrologic Prediction System (CHPS), utilizing Ensemble Streamflow Prediction (ESP) system techniques. This approach makes it possible to produce probabilistic hydrologic forecasts that incorporate the skill and uncertainty of atmospheric models. Significant issues exist with directly using the meteorological ensembles, including biases and spatial resolution of the available data, but the approach allows for the generation of valuable information for end-user decision makers, covering a time frame for which there is little current probabilistic hydrologic guidance available. This paper presents a description of a joint project among four NWS RFCs to incorporate ensemble forecasts from a variety of meteorological model ensembles. These include the National Oceanic and Atmospheric Administration (NOAA) NWS National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System (GEFS), North American Ensemble Forecast System (NAEFS), and Short Range Ensemble Forecast System (SREF). Verification results are presented for operational NAEFS and SREF based MMEFS real-time probabilistic hydrologic forecasts covering multi-year period. Improvements to the MMEFS are also recommended.

To study the impact of training sample heterogeneity on the performance of Bayesian model averaging (BMA), two BMA experiments were performed on probabilistic quantitative precipitation forecasts (PQPFs) in the northern China region in July and August of 2010 generated from an 11-member short-range ensemble forecasting system. One experiment, as in many conventional BMA studies, used an overall training sample that consisted of all available cases in the training period, while the second experiment used stratified sampling BMA by first dividing all available training cases into subsamples according to their ensemble spread, and then performing BMA on each subsample. The results showed that ensemble spread is a good criterion to divide ensemble precipitation cases into subsamples, and that the subsamples have different statistical properties. Pooling the subsamples together forms a heterogeneous overall sample. Conventional BMA is incapable of interpreting heterogeneous samples, and produces unreliable PQPF. It underestimates the forecast probability at high-threshold PQPF and local rainfall maxima in BMA percentile forecasts. BMA with stratified sampling according to ensemble spread overcomes the problem reasonably well, producing sharper predictive probability density functions and BMA percentile forecasts, and more reliable PQPF than the conventional BMA approach. The continuous ranked probability scores, Brier skill scores, and reliability diagrams of the two BMA experiments were examined for all available forecast days, along with a logistic regression experiment. Stratified sampling BMA outperformed the raw ensemble and conventional BMA in all verifications, and also showed better skill than logistic regression in low-threshold forecasts.

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A feed-forward neural network is configured to calibrate the bias of a high-resolution probabilistic quantitative precipitation forecast (PQPF) produced by a 12-km version of the NCEP Regional Spectral Model (RSM) ensemble forecast system. Twice-daily forecasts during the 2002–2003 cool season (1 November–31 March, inclusive) are run over four U.S. Geological Survey (USGS) hydrologic unit regions of the southwest United States. Calibration is performed via a cross-validation procedure, where four months are used for training and the excluded month is used for testing. The PQPFs before and after the calibration over a hydrological unit region are evaluated by comparing the joint probability distribution of forecasts and observations. Verification is performed on the 4-km stage IV grid, which is used as “truth.” The calibration procedure improves the Brier score (BrS), conditional bias (reliability) and forecast skill, such as the Brier skill score (BrSS) and the ranked probability skill score (RPSS), relative to the sample frequency for all geographic regions and most precipitation thresholds. However, the procedure degrades the resolution of the PQPFs by systematically producing more forecasts with low nonzero forecast probabilities that drive the forecast distribution closer to the climatology of the training sample. The problem of degrading the resolution is most severe over the Colorado River basin and the Great Basin for relatively high precipitation thresholds where the sample of observed events is relatively small.

Addendum to Bayesian ensemble forecast of river stages and ensemble size requirements

Probabilistic quantitative precipitation forecasts (PQPFS) for discrete amount classes can be formulated as the product of precipitation probabilities (as issued in PoP forecasts) and the climatological probabilities of precipitation in specified categories conditional on the occurrence of measurable precipitation. Such forecasts, derived from historical subjective PoP forecasts, are investigated here for the 12–24 hour projection using two types of conditional climatologies. The first involves simply the conditional probabilities of precipitation in selected amount classes given that at least 0.254 mm (0.01″) occurred. The second conditional climatology involves three distributions for the same events, conditional both on the occurrence of measurable precipitation and on the magnitude of the PoP forecast. In this later case, separate conditional distributions are tabulated for occasions when “low” (0%–20%), “moderate” (30%–50%), and “high” (60%–100%) subjective PoP forecast were issued. Comparison of the conditional climatological distributions shows clearly that forecast periods for which “high” PoPs were issued are characterized by distributions having higher probabilities of larger amounts and lower probabilities of smaller amounts, as compared to both distributions conditioned on other PoP categories and distributions not conditioned on the PoP forecasts. The reverse is true of distributions conditioned on “low” PoP values. These are seen to be general properties of PoP forecasts issued for the conterminous United states. Forecast results are presented for Brownsville, Houston, and San Antonio, Texas, and for the period February 1981 to June 1982. This choice allows comparison of the present results with those of a subjective PQPF experiment conducted at these stations during this period. Surprisingly, the present forecasts show skill comparable to or somewhat better than that exhibited by the subjective PQPFs in the Texas experiment and the corresponding model output statistics (MOS) PQPFS. Use of climatological precipitation amount distributions conditioned on the magnitude of the subjective PoP forecasts improves overall skill worn only modestly, but (importantly) in a way that allows more frequent use of higher probabilities for the larger precipitation amount categories.

A hydrologic uncertainty processor (HUP) that the prior density and likelihood function are explicitly expressed is introduced based on a copula function. The results show that the copula-based HUP is comparable to the meta-Gaussian HUP regarding the posterior median forecasts. Besides, the probabilistic forecasts produced by the copula-based HUP have slightly higher reliability and lower resolution, as compared to those of the meta-Gaussian HUP. A Copula Bayesian processor associated with the Bayesian model averaging (CBP-BMA) method is used with ensemble lumped hydrological models. Compared with the BMA and Copula-BMA methods, the CBP-BMA method relaxes any assumption on the distribution of conditional PDFs. The case study results demonstrate that the CBP-BMA method can improve hydrological forecasting precision with higher coverage ratios. The copula-based HUP and CBP-BMA methods provide alternative approaches to uncertainty analysis of hydrological forecasts.

Conventional statistical postprocessing techniques offer limited ability to improve the skills of probabilistic guidance for heavy precipitation. This paper introduces two artificial neural network (ANN)-based, geographically aware, and computationally efficient postprocessing schemes, namely, the ANN-multiclass (ANN-Mclass) and the ANN–censored, shifted gamma distribution (ANN-CSGD). Both schemes are implemented to postprocess Global Ensemble Forecast System (GEFS) forecasts to produce probabilistic quantitative precipitation forecasts (PQPFs) over the contiguous United States (CONUS) using a short (60 days), rolling training window. The performances of these schemes are assessed through a set of hindcast experiments, wherein postprocessed 24-h PQPFs from the two ANN schemes were compared against those produced using the benchmark quantile mapping algorithm for lead times ranging from 1 to 8 days. Outcomes of the hindcast experiments show that ANN schemes overall outperform the benchmark as well as the raw forecast over the CONUS in predicting probability of precipitation over a range of thresholds. The relative performance varies among geographic regions, with the two ANN schemes broadly improving upon quantile mapping over the central, south, and southeast, and slightly underperforming along the Pacific coast where skills of raw forecasts are the highest. Between the two schemes, the hybrid ANN-CSGD outperforms at higher rainfall thresholds (i.e., >50 mm day−1), though the outperformance comes at a slight expense of sharpness and spatial specificity. Collectively, these results confirm the ability of the ANN algorithms to produce skillful PQPFs with a limited training window and point to the prowess of the hybrid scheme for calibrating PQPFs for rare-to-extreme rainfall events.

This paper briefly discusses the nature, the causes and the role of predictive uncertainty in flood forecasting and proposes a novel approach to its estimation. Following the definition of predictive uncertainty, its importance in the decision process is highlighted in relation to the different sources of errors (model, parameter, observations, boundary conditions) that affect flood forecasting. Moreover, the paper briefly analyses the importance of using a full predictive uncertainty, obtained by marginalising the parameter uncertainty, instead of the predictive uncertainty conditional to a single parameter set. Finally, a new Model Conditional Processor (MCP) for the assessment of predictive uncertainty is then proposed as an alternative to the Hydrologic Uncertainty Processor (HUP) introduced by Krzysztofowicz as well as to the Bayesian Model Averaging (BMA) approach due to Raftery et al. The new MCP approach, which aims at assessing, and possibly reducing, predictive uncertainty, allows combination of the observations with one or several models’ forecasts in a multi‐Normal space, by transforming observations and model forecasts in a multivariate Normal space by means of the Normal Quantile Transform. The results of the new approach are shown for the case of the River Po in Italy, and compared with the results obtainable both with the HUP and the BMA.