Reliable Probabilistic Forecasts Research Articles

Statistical Postprocessing of Week-1 and Week-2 Precipitation Forecasts over Taiwan

Abstract 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.

Post-Processing Ensemble Precipitation Forecasts and Their Applications in Summer Streamflow Prediction over a Mountain River Basin

Ensemble precipitation forecasts (EPFs) can help to extend lead times and provide reliable probabilistic forecasts, which have been widely applied for streamflow predictions by driving hydrological models. Nonetheless, inherent biases and under-dispersion in EPFs require post-processing for accurate application. It is imperative to explore the skillful lead time of post-processed EPFs for summer streamflow predictions, particularly in mountainous regions. In this study, four popular EPFs, i.e., the CMA, ECMWF, JMA, and NCEP, were post-processed by two state of art methods, i.e., the Bayesian model averaging (BMA) and generator-based post-processing (GPP) methods. These refined forecasts were subsequently integrated with the Xin’anjiang (XAJ) model for summer streamflow prediction. The performances of precipitation forecasts and streamflow predictions were comprehensively evaluated before and after post-processing. The results reveal that raw EPFs frequently deviate from ensemble mean forecasts, particularly underestimating torrential rain. There are also clear underestimations of uncertainty in their probabilistic forecasts. Among the four EPFs, the ECMWF outperforms its peers, delivering skillful precipitation forecasts for 1–7 lead days and streamflow predictions for 1–4 lead days. The effectiveness of post-processing methods varies, yet both GPP and BMA address the under-dispersion of EPFs effectively. The GPP method, recommended as the superior method, can effectively improve both deterministic and probabilistic forecasting accuracy. Moreover, the ECMWF post-processed by GPP extends the effective lead time to seven days and reduces the underestimation of peak flows. The findings of this study underscore the potential benefits of adeptly post-processed EPFs, providing a reference for streamflow prediction over mountain river basins.

The Development of a Consensus Machine Learning Model for Hurricane Rapid Intensification Forecasts with Hurricane Weather Research and Forecasting (HWRF) Data

Abstract This study focused on developing a consensus machine learning (CML) model for tropical cyclone (TC) intensity-change forecasting, especially for rapid intensification (RI). This CML model was built upon selected classical machine learning models with the input data extracted from a high-resolution hurricane model, the Hurricane Weather Research and Forecasting (HWRF) system. The input data contained 21 or 34 RI-related predictors extracted from the 2018 version of HWRF (H218). This study found that TC inner-core predictors can be critical for improving RI predictions, especially the inner-core relative humidity. Moreover, this study emphasized the importance of performing resampling on an imbalanced input dataset. Edited nearest-neighbor and synthetic minority oversampling techniques improved the probability of detection (POD) by ∼10% for the RI class. This study also showed that the CML model has satisfactory performance on RI predictions compared to the operational models. CML reached 56% POD and 46% false alarm ratio (FAR), while the operational models had only 10%–30% POD but 50%–60% FAR. The CML performance on the non-RI classes was comparable to the operational models. The results indicated that, with proper and sufficient training data and RI-related predictors, CML has the potential to provide reliable probabilistic RI forecasts during a hurricane season.

Performance of a Convective-Scale Ensemble Prediction System on 2017 Warm-Season Afternoon Thunderstorms over Taiwan

Abstract A 16-member convective-scale ensemble prediction system (CEPS) developed at the Central Weather Bureau (CWB) of Taiwan is evaluated for probability forecasts of convective precipitation. To address the issues of limited predictability of convective systems, the CEPS provides short-range forecasts using initial conditions from a rapid-updated ensemble data assimilation system. This study aims to identify the behavior of the CEPS forecasts, especially the impact of different ensemble configurations and forecast lead times. Warm-season afternoon thunderstorms (ATs) from 30 June to 4 July 2017 are selected. Since ATs usually occur between 1300 and 2000 LST, this study compares deterministic and probabilistic quantitative precipitation forecasts (QPFs) launched at 0500, 0800, and 1100 LST. This study demonstrates that initial and boundary perturbations (IBP) are crucial to ensure good spread–skill consistency over the 18-h forecasts. On top of IBP, additional model perturbations have insignificant impacts on upper-air and precipitation forecasts. The deterministic QPFs launched at 1100 LST outperform those launched at 0500 and 0800 LST, likely because the most-recent data assimilation analyses enhance the practical predictability. However, it cannot improve the probabilistic QPFs launched at 1100 LST due to inadequate ensemble spreads resulting from limited error growth time. This study points out the importance of sufficient initial condition uncertainty on short-range probabilistic forecasts to exploit the benefits of rapid-update data assimilation analyses. Significance Statement This study aims to understand the behavior of convective-scale short-range probabilistic forecasts in Taiwan and the surrounding area. Taiwan is influenced by diverse weather systems, including typhoons, mei-yu fronts, and local thunderstorms. During the past decade, there has been promising improvement in predicting mesoscale weather systems (e.g., typhoons and mei-yu fronts). However, it is still challenging to provide timely and accurate forecasts for rapid-evolving high-impact convection. This study provides a reference for the designation of convective-scale ensemble prediction systems; in particular, those with a goal to provide short-range probabilistic forecasts. While the findings cannot be extrapolated to all ensemble prediction systems, this study demonstrates that initial and boundary perturbations are the most important factors, while the model perturbation has an insignificant effect. This study suggests that in-depth studies are required to improve the convective-scale initial condition accuracy and uncertainty to provide reliable probabilistic forecasts within short lead times.

Probabilistic forecasting of tropical cyclones intensity using machine learning model

This study proposes a machine learning approach to probabilistic forecasting of tropical cyclone (TC) intensity. The earth system is complex and nonlinear, leading to inherent uncertainty in TC forecasting at all times, and therefore a representation of this uncertainty should be provided. Previous studies construct this uncertainty through ensemble or statistical methods, neither of which can directly characterize this uncertainty and suffer from problems such as excessive computational effort. And for this reason, we propose to assess the forecast without this uncertainty through the forecast distribution. Meanwhile, none of the previous studies on TC intensity forecasting by artificial intelligence methods characterize the uncertainty, so this study is a new supplement to data-driven TC forecasting. During the 2010–2020 evaluation period, the model’s point forecast can outperform the current state-of-the-art operational statistic-dynamical model results, and can obtain forecast intervals to provide reliable probabilistic forecasts, which are critical for disaster warnings.

Probabilistic subseasonal precipitation forecasts using preceding atmospheric intraseasonal signals in a Bayesian perspective

Abstract. Accurate and reliable subseasonal precipitation forecasts are of great socioeconomic value for various aspects. The atmospheric intraseasonal oscillation (ISO), which is one of the leading sources of subseasonal predictability, can potentially be used as predictor for subseasonal precipitation forecasts. However, the relationship between atmospheric intraseasonal signals and subseasonal precipitation is of high uncertainty. In this study, we develop a spatiotemporal-projection-based Bayesian hierarchical model (STP-BHM) for subseasonal precipitation forecasts. The coupled covariance patterns between the preceding atmospheric intraseasonal signals and precipitation are extracted, and the corresponding projection coefficients are defined as predictors. A Bayesian hierarchical model (BHM) is then built to address the uncertainty in the relationship between atmospheric intraseasonal signals and precipitation. The STP-BHM model is applied to predict both the pentad mean precipitation amount and pentad mean precipitation anomalies for each hydroclimatic region over China during the boreal summer monsoon season. The model performance is evaluated through a leave-1-year-out cross-validation strategy. Our results suggest that the STP-BHM model can provide skillful and reliable probabilistic forecasts for both the pentad mean precipitation amount and pentad mean precipitation anomalies at leads of 20–25 d over most hydroclimatic regions in China. The results also indicate that the STP-BHM model outperforms the National Centers for Environmental Prediction (NCEP) subseasonal to seasonal (S2S) model when the lead time is beyond 5 d for pentad mean precipitation amount forecasts. The intraseasonal signals of 850 and 200 hPa zonal wind (U850 and U200) and 850 and 500 hPa geopotential height (H850 and H500) contribute more to the overall forecast skill of the pentad mean precipitation amount predictions. In comparison, the outgoing longwave radiation anomalies (OLRAs) contribute most to the forecast skill of the pentad mean precipitation anomaly predictions. Other sources of subseasonal predictability, such as soil moisture, snow cover, and stratosphere–troposphere interaction, will be included in the future to further improve the subseasonal precipitation forecast skill.

Postprocessing of hydrometeorological ensemble forecasts based on multisource precipitation in Ganjiang River basin, China

Flood forecasting is a challenging task with major concerns that include forecast uncertainty and lead time. This paper aims to comprehensively address the data correction issue for hydrological models by developing an integrated postprocessing framework for hydrometeorological ensemble forecasts based on three types of ensemble precipitation forecasts (ECMWF, GEFS, and CFSv2). This framework mainly comprises the Ensemble Preprocessor (EPP) and the Bayesian model averaging (BMA) scheme: (1) the EPP eliminates various deviations from the ensemble precipitation forecasts, with the canonical event model extracting useful predictive information and extending the lead time by linking the forecasts seamlessly, and (2) the BMA scheme develops more skillful and reliable probabilistic hydrological forecasts from ensemble streamflow forecasts generated by three hydrological models (XAJ, VIC and DTVGM) driven by the postprocessed ensemble precipitation forecasts. The Ganjiang River Basin was selected as a case study to examine the capacity and efficiency of our developed framework. We found that the performance of the integrated postprocessing of hydrometeorological ensemble forecasts benefitted from a reasonable design of canonical events, especially when the observed precipitation was factored into the canonical events. Streamflow forecasts with increased lead times and accuracy were obtained by employing postprocessed precipitation forecasts instead of raw forecasts as the input for the hydrological models. We also found that the BMA scheme further improved the forecast effect by generating more skillful and reliable forecasts than a single hydrological model, which was verified by a series of statisticalindices and uncertainty analysis. Our results underscore the importance of considering both input and output for hydrological models in hydrological forecasting.

An efficient method to identify uncertainties of WRF-Solar variables in forecasting solar irradiance using a tangent linear sensitivity analysis

Uncertainty in predicting solar energy resources introduces major challenges in power system management and necessitates the development of reliable probabilistic solar forecasts. As the first part of the development of probabilistic forecasts based on the Weather Research and Forecasting model with solar extensions (WRF-Solar), this study presents a tangent linear approach to identify input variables responsible for the largest uncertainties in predicting surface solar irradiance and clouds. A tangent linear analysis is capable of efficiently investigating sensitivities of output variables with respect to various input variables of WRF-Solar because this approach avoids the computational burden of perturbing the initial conditions of individual input variables. We develop tangent linear models (TLMs) for six WRF-Solar physics packages that control the formation and dissipation of clouds and solar radiation, and we evaluate the validity of TLMs using a linearity test. The tangent linear sensitivity analysis is conducted under various scenarios based on satellite observations and model simulations to consider realistic input conditions. A simple method is used to quantify the impact of the uncertainty of input variables on the output variables from the TLMs. The results demonstrate that uncertainties in the output variables that are the focus of this study—including global horizontal irradiance, direct normal irradiance, cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes—are highly sensitive to uncertainties in 14 input variables. This study indicates that the tangent linear method can identify key variables of physics modules in WRF-Solar that can be stochastically perturbed to generate ensemble-based probabilistic forecasts.

A Physically Based Stochastic Boundary Layer Perturbation Scheme. Part II: Perturbation Growth within a Superensemble Framework

AbstractConvection-permitting forecasts have improved the forecasts of flooding from intense rainfall. However, probabilistic forecasts, generally based upon ensemble methods, are essential to quantify forecast uncertainty. This leads to a need to understand how different aspects of the model system affect forecast behavior. We compare the uncertainty due to initial and boundary condition (IBC) perturbations and boundary layer turbulence using a superensemble (SE) created to determine the influence of 12 IBC perturbations versus 12 stochastic boundary layer (SBL) perturbations constructed using a physically based SBL scheme. We consider two mesoscale extreme precipitation events. For each, we run a 144-member SE. The SEs are analyzed to consider the growth of differences between the simulations, and the spatial structure and scales of those differences. The SBL perturbations rapidly spin up, typically within 12 h of precipitation commencing. The SBL perturbations eventually produce spread that is not statistically different from the spread produced by the IBC perturbations, though in one case there is initially increased spread from the IBC perturbations. Spatially, the growth from IBC occurs on larger scales than that produced by the SBL perturbations (typically by an order of magnitude). However, analysis across multiple scales shows that the SBL scheme produces a random relocation of precipitation up to the scale at which the ensemble members agree with each other. This implies that statistical postprocessing can be used instead of running larger ensembles. Use of these statistical postprocessing techniques could lead to more reliable probabilistic forecasts of convective events and their associated hazards.

Probabilistic Geomagnetic Storm Forecasting via Deep Learning

AbstractGeomagnetic storms, which are governed by the plasma magnetohydrodynamics of the solar‐interplanetary‐magnetosphere system, entail a formidable challenge for physical forward modeling. Yet, the abundance of high‐quality observational data has been amenable to the application of data‐hungry neural networks to geomagnetic storm forecasting. Almost all applications of neural networks to storm forecasting have utilized solar wind observations from the Earth‐Sun first Lagrangian point (L1) or closer and generated deterministic output without uncertainty estimates. Furthermore, forecasting work has focused on indices that are also sensitive to induced internal magnetic fields, complicating the forecasting problem with another layer of non‐linearity. We address these points, presenting neural networks trained on observations from both the solar disk and the L1 point. Our architecture generates reliable probabilistic forecasts over Est, the external component of the disturbance storm time index, showing that neural networks can gauge confidence in their output.

Using Artificial Neural Networks for Generating Probabilistic Subseasonal Precipitation Forecasts over California

AbstractForecast skill of numerical weather prediction (NWP) models for precipitation accumulations over California is rather limited at subseasonal time scales, and the low signal-to-noise ratio makes it challenging to extract information that provides reliable probabilistic forecasts. A statistical postprocessing framework is proposed that uses an artificial neural network (ANN) to establish relationships between NWP ensemble forecast and gridded observed 7-day precipitation accumulations, and to model the increase or decrease of the probabilities for different precipitation categories relative to their climatological frequencies. Adding predictors with geographic information and location-specific normalization of forecast information permits the use of a single ANN for the entire forecast domain and thus reduces the risk of overfitting. In addition, a convolutional neural network (CNN) framework is proposed that extends the basic ANN and takes images of large-scale predictors as inputs that inform local increase or decrease of precipitation probabilities relative to climatology. Both methods are demonstrated with ECMWF ensemble reforecasts over California for lead times up to 4 weeks. They compare favorably with a state-of-the-art postprocessing technique developed for medium-range ensemble precipitation forecasts, and their forecast skill relative to climatology is positive everywhere within the domain. The magnitude of skill, however, is low for week-3 and week-4, and suggests that additional sources of predictability need to be explored.

Probabilistic forecasting based on ensemble forecasts and EMOS method for TGR inflow

Probabilistic inflow forecasts can quantify the uncertainty involved in the forecasting process and provide useful risk information for reservoir management. This study proposed a probabilistic inflow forecasting scheme for the Three Gorges Reservoir (TGR) at 1–3 d lead times. The post-processing method Ensemble Model Output Statistics (EMOS) is used to derive probabilistic inflow forecasts from ensemble inflow forecasts. Considering the inherent skew feature of the inflow series, lognormal and gamma distributions are used as EMOS predictive distributions in addition to conventional normal distribution. Results show that TGR’s ensemble inflow forecasts at 1–3 d lead times perform well with high model efficiency and small mean absolute error. Underestimation of forecasting uncertainty is observed for the raw ensemble inflow forecasts with biased probability integral transform (PIT) histograms. The three EMOS probabilistic forecasts outperform the raw ensemble forecasts in terms of both deterministic and probabilistic performance at 1–3 d lead times. The EMOS results are more reliable with much flatter PIT histograms, coverage rates approximate to the nominal coverage 89.47% and satisfactory sharpness. Results also show that EMOS with gamma distribution is superior to normal and lognormal distributions. This research can provide reliable probabilistic inflow forecasts without much variation of TGR’s operational inflow forecasting procedure.

Hydrological post-processing of streamflow forecasts issued from multimodel ensemble prediction systems

Hydrological simulations and forecasts are subject to various sources of uncertainties. Thiboult et al. (2016) constructed a 50,000-member great ensemble that ultimately accounts for meteorological forcing uncertainty, initial condition uncertainty, and structural uncertainty. This large 50,000-member ensemble can also be separated into sub-components to untangle the three main sources of uncertainties mentioned above. However, in Thiboult et al. (2016) model outputs were simply pooled together, considering equiprobable members. This paper studies the use of Bayesian model averaging (BMA) to post-process multimodel hydrological forecasts. BMA assigns multiple sets of weights on different models and may then generate more skillful and reliable probabilistic forecasts. BMA weights explicitly quantify the level of confidence one can have regarding each candidate hydrological model and lead to a predictive probabilistic density function (PDF) containing information about uncertainty. The BMA scheme improves the overall quality of forecasts mainly by maintaining the ensemble dispersion with the lead time. It also has the ability to improve the reliability and skill of multimodel systems that only include two sources of uncertainties that the 50,000-member great ensemble using all forecasting tools (i.e., multimodel, EnKF, and meteorological ensemble forcing) could predict jointly. Furthermore, Thiboult et al. (2016) showed that the meteorological forecasts they used were somehow biased and unreliable on some catchments. The BMA scheme is capable to improve the accuracy and reliability of the hydrological forecasts in that case as well.

Constrained Quantile Regression Splines for Ensemble Postprocessing

Abstract Statistical postprocessing of ensemble forecasts is widely applied to make reliable probabilistic weather forecasts. Motivated by the fact that nature imposes few restrictions on the shape of forecast distributions, a flexible quantile regression method based on constrained spline functions (CQRS) is proposed and tested on ECMWF Ensemble Prediction System (ENS) wind speed forecasting data at 125 stations in Norway. First, it is demonstrated that constraining quantile functions to be monotone and bounded is preferable. Second, combining an ensemble quantile with the ensemble mean proved to be a good covariate for the respective quantile. Third, CQRS only needs to be applied to about 10 equidistant quantiles, while those between can be obtained by interpolation. A comparison of CQRS versus a mixture model of truncated and lognormal distributions showed slight overall improvements in quantile score (less than 1%), reliability, and to some extent also sharpness. For strong wind speed forecasts the quantile score was improved by up to 4.5% depending on lead time.

Statistical Postprocessing of Water Level Forecasts Using Bayesian Model Averaging With Doubly Truncated Normal Components

AbstractAccurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state‐of‐the‐art hydrological ensemble prediction models are usually driven with meteorological ensemble forecasts. Hence, biases and dispersion errors of the meteorological forecasts cascade down to the hydrological predictions and add to the errors of the hydrological models. The systematic parts of these errors can be reduced by applying statistical postprocessing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical postprocessing methods should be tailored to the particular forecast variable at hand. Former studies have shown that it can make sense to treat hydrological quantities as bounded variables. In this paper, a doubly truncated Bayesian model averaging (BMA) method, which allows for flexible postprocessing of possibly multimodel ensemble forecasts of water level, is introduced. A case study based on water levels for a gauge of river Rhine reveals a good predictive skill of doubly truncated BMA compared both to the raw ensemble and the reference ensemble model output statistics approach. Using rolling training periods, BMA considerably outerperforms ensemble model output statistics. However, this gap shrinks drastically when using analog‐based training periods.

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.

An Iterative Work Flow for History Matching by Use of Design of Experiment, Response-Surface Methodology, and Markov Chain Monte Carlo Algorithm Applied to Tight Oil Reservoirs

Summary Although a large amount of wells has been extensively drilled to develop unconventional reservoirs, uncertainty associated with reservoir and fracture properties can significantly affect the evaluation of an individual well's performance with simulations. From the history-matching point of view, this uncertainty causes nonuniqueness of solutions that should be obtained with a robust probabilistic method without overly exhausting simulation resources. Because of the challenge in this work, a proxy-based history-matching approach can deliver unique advantages of reducing the computational requirement and providing probabilistic interpretation. The work flow presented in this paper is designed to exploit full ranges of proxy-modeling benefits from prioritizing significant reservoir properties, estimating the variation of model responses, and searching multiple history-matching solutions for reliable probabilistic forecasts. A screening process is introduced at the initial stage of the work flow with design of experiment (DOE) and response-surface methodology (RSM), so the dimensions of proxy models can be reduced. In addition, the proxy models progress through the work flow by iterations that aim to improve their accuracy. This iterative work flow efficiently uses simulation resources by use of all the completed runs to provide more information about the model responses for the subsequent iterations. While the work flow is being iterated, multiple proxy models are explored for history-matching solutions by a Markov chain Monte Carlo (MCMC) algorithm. Then, history-matching solutions are used to evaluate the probability distribution of the long-term estimated ultimate recovery (EUR). Finally, an application of the work flow to a horizontal well in the Middle Bakken is presented in this paper.

Probabilistic day-ahead forecasting of household electricity demand

Forecasting electricity demand at the local level of a building up to a feeder is increasingly necessary in several applications in the smart-grids context. Actors like aggregators and retailers, and tools like home energy management systems, require such forecasts as input. In this paper, a probabilistic day-ahead forecasting model is proposed to predict hourly electrical demand from individual households. This stochastic model uses smart-meter data and temperature predictions to make quantile forecasts. Performance is evaluated using data from a real-life smart grid demonstration site developed in Evora, Portugal as part of the European project SENSIBLE. The proposed model consistently outperforms a persistence model and provides reliable probabilistic forecasts.

Stochastic Parameterization: Toward a New View of Weather and Climate Models

Abstract The last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics, and turbulence is reviewed; its relevance for the climate problem is demonstrated; and future research directions are outlined.

Multi-Model Grand Ensemble Hydrologic Forecasting in the Fu River Basin Using Bayesian Model Averaging

Statistical post-processing for multi-model grand ensemble (GE) hydrologic predictions is necessary, in order to achieve more accurate and reliable probabilistic forecasts. This paper presents a case study which applies Bayesian model averaging (BMA) to statistically post-process raw GE runoff forecasts in the Fu River basin in China, at lead times ranging from 6 to 120 h. The raw forecasts were generated by running the Xinanjiang hydrologic model with ensemble forecasts (164 forecast members), using seven different “THORPEX Interactive Grand Global Ensemble” (TIGGE) weather centres as forcing inputs. Some measures, such as data transformation and high-dimensional optimization, were included in the experiment after considering the practical water regime and data conditions. The results indicate that the BMA post-processing method is capable of improving the performance of raw GE runoff forecasts, yielding more calibrated and sharp predictive probability density functions (PDFs), over a range of lead times from 24 to 120 h. The analysis of percentile forecasts in two different flood events illustrates the great potential and prospects of BMA GE probabilistic river discharge forecasts, for taking precautions against severe flooding events.