Forecast Uncertainty Research Articles

A novel interval estimation framework for wind power forecasting using multi-objective gradient descent optimization

Effective wind power forecasting enables reliable integration of renewable energy into the electric grid and enhances wind farm management and power system dispatch. To mitigate uncertainty in wind power forecasting, interval prediction is commonly used to provide information on confidence levels. The lower upper bound estimation (LUBE) method is a quality-driven solution that constructs prediction intervals (PIs) based on an ensemble loss function comprising two PI quality metrics without assuming any specific distribution function. However, the conventional LUBE method suffers from three major drawbacks: 1) it is incompatible with gradient descent (GD) due to its non-differentiable objective function; 2) its objective function is formulated based on qualitative assessment rather than on a statistical basis; and 3) the ensemble loss function cannot fully represent the PI quality information measured by two conflicting metrics, leading to potential performance loss. In this study, we propose a novel multi-objective gradient descent (MOGD)-based LUBE model to address these drawbacks. The loss function is derived based on the maximum likelihood estimation and is approximated by a sigmoid function to ensure its statistical basis and differentiable form. In the training process, MOGD is applied to search for the direction of GD subject to both PI metrics. The proposed model is compared with several benchmarks using four wind power datasets from different spatial locations. The numerical results indicate the superiority of the proposed MOGD-LUBE model over its counterparts in terms of the reliability and sharpness for efficient wind power forecasting.

Reservoir Risk Operation of 'Domestic-Production-Ecology' Water Supply Based on Runoff Forecast Uncertainty

Reservoir Risk Operation of 'Domestic-Production-Ecology' Water Supply Based on Runoff Forecast Uncertainty

Post-Shock Budgeting: A Methodological Framework

Traditional budgeting approaches have been criticised and called into question as not being able to adapt to management dynamics and context-specific planning needs. This is especially the case when major crises occur, with increased forecast uncertainty as a result. Adaptive techniques such as rolling and continuous budgeting have been developed to address such concerns, though trade-offs between the resulting optimisation of the planning, control and performance evaluation functions exist. A key, though not exclusive, effect of crises is the likely nonlinearity of effects of unit prices which will tend to revert to the mean, or in other words, rebound and gradually converge to pre-shock levels or to a steady state. Aiming to fill this research gap, this study presents a methodological framework, framed within a survival analysis paradigm, which can be used for post-shock budgeting. Following a description of the mathematical properties and steps required for application, the framework is illustrated using a stylised example of operational budget with results being compared between linear and nonlinear price rebound trajectories. The presented framework is a relatively simple and flexible solution to the issue of post-shock budgeting which can be readily developed and adapted, therefore lending itself to a widespread use.

Stratospheric impact on subseasonal forecast uncertainty in the Northern extratropics

Extreme states of the polar stratospheric circulation during winter tend to be followed by anomalies in the near-surface circulation for several weeks, especially over the North Atlantic/Eurasia (NAE) sector. Previous research has highlighted an associated robust increase in subseasonal to seasonal (S2S) forecast skill related to forecast ensemble mean anomalies. Here we explore the additional impact of polar stratospheric circulation extremes on ensemble spread, a key measure of forecast uncertainty and the associated predictability. We find that over the Norwegian Sea and around Scandinavia S2S ensemble spread in near-surface geopotential height is significantly reduced following weak polar vortex states (enhanced predictability), whereas it is increased following strong polar vortex states (reduced predictability), with anomaly magnitudes reaching as high as 20%. Notably, modulations of forecast uncertainty are found even over regions of near-zero ensemble mean anomaly. We find decreased forecast uncertainty to be linked to decreased synoptic-scale storm activity and vice versa for increased forecast uncertainty. Our results furthermore suggest that modulation of S2S forecast uncertainty by the stratosphere dominates over NAE, whereas over the North Pacific modulations due to El Niño/ La Niña are more important.

Conditional scenario-based energy management algorithm with uncertain correlated forecasts

This paper introduces the application of the novel approach known as Conditional Scenario-Based Model Predictive Control (CSB-MPC) into energy management in a low voltage distribution system (LVDS). The LVDS comprises renewable energy sources (RES) and an energy storage system, with correlated power generation and demand under uncertainty. This correlation is leveraged to derive a reduced set of conditional scenarios and their associated probabilities. This reduced set retains the essential characteristics of a larger set of equiprobable scenarios generated based on information about uncertainties in power generation and demand forecasts. Instead of computationally demanding methods using the larger set, a feasible Scenario-Based Mixed-Integer Linear Program (MILP) is solved by employing the reduced set. This optimisation minimises costs associated with energy consumption from the main grid and the potential waste of generated power. In the objective function, the scenarios are weighted by their probabilities to mitigate the impact of less likely forecasts, leading to efficient LVDS component utilisation and reduced operating costs. Simulation results comparing the performance of the LVDS with CSB-MPC against other MPC approaches, including classic scenario-based, chance-constrained, and deterministic methods, reveal that CSB-MPC consistently exhibits higher probabilities of operational constraint satisfaction, with differences of up to 10% or even 30%. Notably, CSB-MPC achieves these results with similar solution times to classic scenario-based MPC but with lower LVDS operating costs, between 6.62% to 11.31% less.

Impact of DNI Forecast Quality on Performance Prediction for a Commercial Scale Solar Tower

Concerning current efforts to improve operational efficiency and to lower overall costs of concentrating solar power (CSP) plants with prediction-based algorithms, this study investigates the quality and uncertainty of nowcasting data regarding the implications for process predictions. DNI (direct normal irradiation) maps from an all-sky imager-based nowcasting system are applied to a dynamic prediction model coupled with ray tracing. The results underline the need for high-resolution DNI maps in order to predict net yield and receiver outlet temperature realistically. Furthermore, based on a statistical uncertainty analysis, a correlation is developed, which allows for predicting the uncertainty of the net power prediction based on the corresponding DNI forecast uncertainty. However, the study reveals significant prediction errors and the demand for further improvement in the accuracy at which local shadings are forecasted.

Assessment of Storage Sizing for Solar Tower Plants Using Model-Predictive Control for Dispatch Planning

Abstract Solar tower with thermal energy storage (ST-TES) represents a promising technology for large-scale exploitation of solar irradiation for electricity generation. A ST-TES has the potential to extend electricity generation to more favorable conditions, such as high electricity prices. The size of TES, however, constrains the flexibility of dispatching, especially when there is significant uncertainty in forecasts of solar irradiation and electricity prices. This study explores the impact of TES size when the plant uses model-predictive control (MPC) for dispatch planning. The performance of MPC is benchmarked against one perfect knowledge (PK) and two day-ahead strategies. The optimal achievable profit for each TES size is determined using the PK strategy. An analysis is conducted to evaluate the relative profit losses for all the other simulated strategies compared to the PK strategy. A case study is conducted for a hypothetical 115 MWe ST-TES in South Australia. For January and August, 100 tests are performed for each dispatch policy, with the TES size varying from 6 to 14 h. The revenue evaluation is conducted with both fixed and wholesale spot prices. The analysis shows that MPC-aided dispatching enables the adoption of a smaller TES compared to day-ahead policies while maintaining the same expected profit. The resulting TES size reduction from 14 to 10 h translates into approximately up to $45.4 million in capital cost savings. The findings of this study can inform the ST-TES plant’s design procedures and facilitate negotiations for electricity sales contracts.

Continuous power imbalance assessment from multi-area economic dispatch models

To be able to efficiently maintain a continuous balance between supply and demand in power systems with high shares of variable renewable energy (VRE) sources, a variety of studies related to the topic are needed. A fundamental input parameter for such studies is an assessment of the power system’s physical needs for balancing power, in form of power imbalances. This article presents a new model for simulating physical power imbalances with a 1-minute time resolution based on multi-area economic dispatch simulations. Compared to existing models with the same purpose, the new model includes the combination of simulating power imbalances with 1-minute time resolution, simulating forecast uncertainty, simulating the continuous behaviour of all power system components and simulating the transmission for netting of power imbalances between balancing areas. By applying the model to a case study of the Nordic synchronous power system in year 2045, the impact of including these features in the model is highlighted. Case study results also show that the size and pattern of power imbalances much depends on the characteristics of a balancing area, in terms of electricity demand, available generation technologies and interconnections to other balancing areas.

Many-Objective Hierarchical Pre-Release Flood Operation Rule Considering Forecast Uncertainty

Flood control operation of cascade reservoirs is an important technology to reduce flood disasters and increase economic benefits. Flood forecast information can help reservoir managers make better use of flood resources and reduce flood risks. In this paper, a hierarchical pre-release flood operation rule considering the flood forecast and its uncertainty information is proposed for real-time flood control. A many-objective optimization model considering the cascade reservoir’s power generation objective, flood control objective, and navigation objective is established. Then, a region search evolutionary algorithm is applied to optimize the many-objective optimization model in a real-world case study upstream of the Yangtze River basin. The optimization experimental results show that the region search evolutionary algorithm can balance convergence and diversity well, and the HV value is 40% higher than the MOEA/D algorithm. The simulation flood control results of cascade reservoirs upstream of the Yangtze River demonstrate that the optimized flood control rule can increase the average multi-year power generation of cascade reservoirs by a maximum of 27.72 × 108 kWh under the condition of flood control safety. The rules proposed in this paper utilize flood resources by identifying runoff forecast information, and pre-release to the flood limit level 145 m before the big flood occurs, so as to ensure the safety downstream and the dam’s own flood control and provide reliable decision support for reservoir managers.

An intelligent interval forecasting system based on fuzzy time series and error distribution characteristics for air quality index

Due to the emergency environment pollution problems, it is imperative to understand the air quality and take effective measures for environmental governance. As a representative measure, the air quality index (AQI) is a single conceptual index value simplified by the concentrations of several routinely monitored air pollutants according to the proportion of various components in the air. With the gradual enhancement of awareness of environmental protection, air quality index forecasting is a key point of environment management. However, most of the traditional forecasting methods ignore the fuzziness of original data itself and the uncertainty of forecasting results which causes the unsatisfactory results. Thus, an innovative forecasting system combining data preprocessing technique, kernel fuzzy c-means (KFCM) clustering algorithm and fuzzy time series is successfully developed for air quality index forecasting. Concretely, the fuzzy time series that handle the fuzzy set is used for the main forecasting process. Then the complete ensemble empirical mode decomposition and KFCM are respectively developed for data denoising and interval partition. Furthermore, the interval forecasting method based on error distribution is developed to measure the forecasting uncertainty. Finally, the experimental simulation and evaluation system verify the great performance of proposed forecasting system and the promising applicability in a practical environment early warning system.

Visualizing the Shelf Life of Population Forecasts: A Simple Approach to Communicating Forecast Uncertainty

It is widely appreciated that population forecasts are inherently uncertain. Researchers have responded by quantifying uncertainty using probabilistic forecasting methods. Yet despite several decades of development, probabilistic forecasts have gained little traction outside the academic sector. Therefore, this article suggests an alternative and simpler approach to estimating and communicating uncertainty which might be helpful for population forecast practitioners and users. Drawing on the naïve forecasts idea of Alho, it suggests creating “synthetic historical forecast errors” by running a regular deterministic projection model many times over recent decades. Then, borrowing from perishable food terminology, the “shelf life” of forecast variables, the number of years into the future the forecast is likely to remain “safe for consumption” (within a specified error tolerance), is estimated from the “historical” errors. The shelf lives are then applied to a current set of forecasts and presented in a simple manner in graphs and tables of forecasts using color-coding. The approach is illustrated through a case study of 2021-based population forecasts for Australia. It´s concluded that the approach offers a relatively straightforward way of estimating and communicating population forecast uncertainty.

Multilayered Energy Management Framework for Extreme Fast Charging Stations Considering Demand Charges, Battery Degradation, and Forecast Uncertainties

To achieve a cost-effective and expeditious charging experience for extreme fast charging station (XFCS) owners and electric vehicle (EV) users, the optimal operation of XFCS is crucial. It is however challenging to simultaneously manage the profit from energy arbitrage, the cost of demand charges, and the degradation of a battery energy storage system (BESS) under uncertainties. This paper, therefore, proposes a multi-layered multi-time scale energy flow management framework for an XFCS by considering long- and short-term forecast uncertainties, monthly demand charges reduction, and BESS life degradation. In the proposed approach, an upper scheduling layer (USL) ensures the overall operation economy and yields optimal scheduling of the energy resources on a rolling horizon basis, thereby considering the long-term forecast errors. A lower dispatch layer (LDL) takes the short-term forecast errors into account during the real-time operation of the XFCS. Per the latest research, monthly demand charges can be as high as 90% of the total monthly bills for EV fast charging stations; to this end, this paper takes the first attempt at the reduction of demand charges cost by considering the trade-off between the energy cost and monthly demand charges. Contrasting literature, this work allocates an energy reserve in the BESS stored energy to deal with the impact of short-term forecast errors on the optimized real-time operation of the XFCS. Moreover, degradation modeling considers the trade-off between short-term benefits and long-term BESS life degradation. Lastly, case studies and a comparative analysis prove the efficacy of the proposed framework.

A Multi‐Model Ensemble of Baseline and Process‐Based Models Improves the Predictive Skill of Near‐Term Lake Forecasts

AbstractWater temperature forecasting in lakes and reservoirs is a valuable tool to manage crucial freshwater resources in a changing and more variable climate, but previous efforts have yet to identify an optimal modeling approach. Here, we demonstrate the first multi‐model ensemble (MME) reservoir water temperature forecast, a forecasting method that combines individual model strengths in a single forecasting framework. We developed two MMEs: a three‐model process‐based MME and a five‐model MME that includes process‐based and empirical models to forecast water temperature profiles at a temperate drinking water reservoir. We found that the five‐model MME improved forecast performance by 8%–30% relative to individual models and the process‐based MME, as quantified using an aggregated probabilistic skill score. This increase in performance was due to large improvements in forecast bias in the five‐model MME, despite increases in forecast uncertainty. High correlation among the process‐based models resulted in little improvement in forecast performance in the process‐based MME relative to the individual process‐based models. The utility of MMEs is highlighted by two results: (a) no individual model performed best at every depth and horizon (days in the future), and (b) MMEs avoided poor performances by rarely producing the worst forecast for any single forecasted period (<6% of the worst ranked forecasts over time). This work presents an example of how existing models can be combined to improve water temperature forecasting in lakes and reservoirs and discusses the value of utilizing MMEs, rather than individual models, in operational forecasts.

Don’t blame the government!? An assessment of debt forecast errors with a view to the EU Economic Governance Review

In view of the increased importance of debt developments in the EU governance framework, this paper investigates the accuracy and the main economic causes of forecast errors in (government) debt projections. We find a positive average debt forecast error for European Union member states, which increases with the projection horizon. Underestimation of debt growth is particularly relevant for countries with high government debt. The main drivers of the debt forecast errors seem to be partly outside direct government control: Wrongly projected overall GDP developments and stock flow adjustments - a factor which has not been considered in the literature so far. Moreover, the high uncertainty in debt forecasts is also inherent in the European Commission’s benchmark forecasts: only their now-cast remains unbiased.

Deep Learning for Postprocessing Global Probabilistic Forecasts on Subseasonal Time Scales

Abstract Subseasonal weather forecasts are becoming increasingly important for a range of socioeconomic activities. However, the predictive ability of physical weather models is very limited on these time scales. We propose four postprocessing methods based on convolutional neural networks to improve subseasonal forecasts by correcting systematic errors of numerical weather prediction models. Our postprocessing models operate directly on spatial input fields and are therefore able to retain spatial relationships and to generate spatially homogeneous predictions. They produce global probabilistic tercile forecasts for biweekly aggregates of temperature and precipitation for weeks 3–4 and 5–6. In a case study based on a public forecasting challenge organized by the World Meteorological Organization, our postprocessing models outperform the bias-corrected forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF), and achieve improvements over climatological forecasts for all considered variables and lead times. We compare several model architectures and training modes and demonstrate that all approaches lead to skillful and well-calibrated probabilistic forecasts. The good calibration of the postprocessed forecasts emphasizes that our postprocessing models reliably quantify the forecast uncertainty based on deterministic input information in the form of ECMWF ensemble mean forecast fields only.

Making Ecosystem Modeling Operational–A Novel Distributed Execution Framework to Systematically Explore Ecological Responses to Divergent Climate Trajectories

AbstractMarine Ecosystem Models (MEMs) are increasingly driven by Earth System Models (ESMs) to better understand marine ecosystem dynamics, and to analyze the effects of alternative management efforts for marine ecosystems under potential scenarios of climate change. However, policy and commercial activities typically occur on seasonal‐to‐decadal time scales, a time span widely used in the global climate modeling community but where the skill level assessments of MEMs are in their infancy. This is mostly due to technical hurdles that prevent the global MEM community from performing large ensemble simulations with which to undergo systematic skill assessments. Here, we developed a novel distributed execution framework constructed of low‐tech and freely available technologies to enable the systematic execution and analysis of linked ESM/MEM prediction ensembles. We apply this framework on the seasonal‐to‐decadal time scale, and assess how retrospective forecast uncertainty in an ensemble of initialized decadal ESM predictions affects a mechanistic and spatiotemporal explicit global trophodynamic MEM. Our results indicate that ESM internal variability has a relatively low impact on the MEM variability in comparison to the broad assumptions related to reconstructed fisheries. We also observe that the results are also sensitive to the ESM specificities. Our case study warrants further systematic explorations to disentangle the impacts of climate change, fisheries scenarios, MEM internal ecological hypotheses, and ESM variability. Most importantly, our case study demonstrates that a simple and free distributed execution framework has the potential to empower any modeling group with the fundamental capabilities to operationalize marine ecosystem modeling.

Reliable precipitation nowcasting using probabilistic diffusion models

Abstract Precipitation nowcasting is a crucial element in current weather service systems. Data-driven methods have proven highly advantageous, due to their flexibility in utilizing detailed initial hydrometeor observations, and their capability to approximate meteorological dynamics effectively given sufficient training data. However, current data-driven methods often encounter severe approximation/optimization errors, rendering their predictions and associated uncertainty estimates unreliable. Here a probabilistic diffusion model-based precipitation nowcasting methodology is introduced, overcoming the notorious blurriness and mode collapse issues in existing practices. Diffusion models learn a sequential of neural networks to reverse a pre-defined diffusion process that generates the probability distribution of future precipitation fields. The precipitation nowcasting based on diffusion model results in a 3.7% improvement in continuous ranked probability score compared to state-of-the-art generative adversarial model-based method. Critically, diffusion model significantly enhance the reliability of forecast uncertainty estimates, evidenced in a 68% gain of spread-skill ratio skill. As a result, diffusion model provides more reliable probabilistic precipitation nowcasting, showing the potential to better support weather-related decision makings.

Climate Change’s Impacts on Drought in Upper Zab Basin, Iraq: A Case Study

Iraq has a semiarid and desert climate. Also, it is predicted to be more susceptible to global warming effects. In the present study, daily climatic data from the past and projected future of the Upper Zab Basin, located in northern Iraq and considered an example of arid and semiarid climate conditions, were simulated using LARS-WG 6.0, i.e., a stochastic weather generator. The model also estimated daily rainfall and temperature. Using the RCP4.5 and RCP8.5 main emission scenarios, the future climate throughout the current century was estimated utilizing the MIROC5, CanESM2, HadGEM2-ES, ESM1-M, and CSIRO-Mk3.6.0 general circulation models (GCMs). This estimation was performed considering the significant uncertainty of future climate estimates. The model, constructed using thirty years' worth of historical data, was validated using climate data from the Upper Zab Basin in northern Iraq (1990–2021). According to the data, the average monthly maximum temperature will decline by 2.15–6.20 °C under RCP4.5 and 1.81–6.10 °C under RCP8.5 by the end of the twenty-first era for the corresponding upstream and downstream sub-basins. Precipitation projections from all GCMs showed varying patterns. Given that some models, like CanESM2, expected a rise in precipitation, while others, like MIROC5, forecasted a future with no change in precipitation or a falling trend, which illustrates the significant level of uncertainty in precipitation forecast when only one model was utilized. Also, the downstream sub-basin suffered the most during the 1999–2000 and 2007–2008 droughts, with average RDIst values of -1.97 and -1.64, respectively. However, the upstream sub-basin had moderate to severe droughts in 1999–2000 and 2007–2008, with average RDIst values of -0.81 and -1.84, respectively. The water available in the research location will be significantly impacted by variations in rainfall and temperature.

Forecasting Raw Material Demand for Battery Breaker Production Process

This study aims to identify the most effective forecasting method for predicting raw material demand in the tin smelting industry, addressing the challenge of uncertainty in material arrival and inaccurate demand forecasting. Three methods, namely moving averages with n = 3 and n = 5, and exponential smoothing, were evaluated using historical data. Results indicate that exponential smoothing with α = 0.2 outperformed the other methods, yielding the smallest error rate with a Mean Absolute Percentage Error (MAPE) of 23%, Mean Absolute Deviation (MAD) of 411, and Mean Squared Error (MSE) of 293303. The implication of these findings underscores the importance of employing appropriate forecasting techniques to optimize inventory management and mitigate shortages in critical industries reliant on volatile raw material supplies. Highlights : Accurate demand forecasting is crucial for companies engaged in smelting to prevent shortages and inventory increases. Three methods were used to determine the most appropriate forecasting method for raw material demand based on historical data: moving average with n = 3 and n = 5, and exponential smoothing with α = 0.2. The Exponential Smoothing Method with α = 0.2 had the smallest error rate, with a MAPE value of 23%, MAD of 411, and MSE of 293303, and can be used to optimize demand forecasting for the next period. Keywords: demand forecasting, smelting, raw materials, historical data, moving average, exponential smoothing.

Probabilistic Forecast of Ecological Drought in Rivers Based on Numerical Weather Forecast from S2S Dataset

Ecological droughts in rivers, as a new type of drought, have been greatly discussed in the past decade. Although various studies have been conducted to identify and evaluate ecological droughts in rivers from different indices, a forecast model for this type of drought is still lacking. In this paper, a numerical weather forecast, a hydrological model, and a generalized Bayesian model are employed to establish a new general framework for the probabilistic forecasting of ecological droughts in rivers, and the Daitou section in China is selected as the study area to examine the performance of the new framework. The results show that the hydrological model can accurately simulate the monthly streamflow with a Nash–Sutcliffe efficiency of 0.91 in the validation period, which means that the model can be used to reconstruct the natural streamflow from the impact of an upstream reservoir. Based on a comparison of ecological drought events from the observed and model-simulated streamflow series, the events from the observed series have a larger deficit volume and a longer duration of ecological droughts after 2014, indicating that human activities may lead to a more severe situation of ecological droughts. Furthermore, due to the uncertainty of precipitation forecasts, a probabilistic precipitation forecast is employed for probabilistic ecological drought forecasting. Compared to the deterministic forecast, the probabilistic ecological drought forecast has better performance, with a Brier score decrease of 0.35 to 0.18 and can provide more information about the risk of ecological droughts. In general, the new probabilistic framework developed in this study can serve as a basis for the development of early-warning systems and countermeasures for ecological droughts.