Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

A Novel Hybrid Ensemble Learning Approach for Enhancing Accuracy and Sustainability in Wind Power Forecasting

Accurate wind power forecasting is critical for system integration and stability as renewable energy reliance grows.Traditional approaches frequently struggle with complex data and non-linear connections. This article presentsa novel approach for hybrid ensemble learning that is based on rigorous requirements engineering concepts.The approach finds significant parameters influencing forecasting accuracy by evaluating real-time Modern-EraRetrospective Analysis for Research and Applications (MERRA2) data from several European Wind farms usingin-depth stakeholder research and requirements elicitation. Ensemble learning is used to develop a robust model,while a temporal convolutional network handles time-series complexities and data gaps. The ensemble-temporalneural network is enhanced by providing different input parameters including training layers, hidden and dropoutlayers along with activation and loss functions. The proposed framework is further analyzed by comparing stateof-the-art forecasting models in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE),respectively. The energy efficiency performance indicators showed that the proposed model demonstrates errorreduction percentages of approximately 16.67%, 28.57%, and 81.92% for MAE, and 38.46%, 17.65%, and 90.78%for RMSE for MERRAWind farms 1, 2, and 3, respectively, compared to other existingmethods. These quantitativeresults show the effectiveness of our proposed model with MAE values ranging from 0.0010 to 0.0156 and RMSEvalues ranging from 0.0014 to 0.0174. This work highlights the effectiveness of requirements engineering in windpower forecasting, leading to enhanced forecast accuracy and grid stability, ultimately paving the way for moresustainable energy solutions.

Growth and Interactions of Multi-Source Perturbations in Convection-Allowing Ensemble Forecasts

This study investigated the growth of forecast errors stemming from initial conditions(ICs),lateral boundary conditions(LBCs),and model(MO)perturbations,as well as their interactions,by conducting seven 36 h convectionallowing ensemble forecast(CAEF)experiments.Two cases,one with strong-forcing(SF)and the other with weak-forcing(WF),occurred over the Yangtze-Huai River basin(YHRB)in East China,were selected to examine the sources of uncertainties associated with perturbation growth under varying forcing backgrounds and the influence of these backgrounds on growth.The perturbations exhibited distinct characteristics in terms of temporal evolution,spatial propagation,and vertical distribution under different forcing backgrounds,indicating a dependence between perturbation growth and forcing background.A comparison of the perturbation growth in different precipitation areas revealed that IC and LBC perturbations were significantly influenced by the location of precipitation in the SF case,while MO perturbations were more responsive to convection triggering and dominated in the WF case.The vertical distribution of perturbations showed that the sources of uncertainties and the performance of perturbations varied between SF and WF cases,with LBC perturbations displaying notable case dependence.Furthermore,the interactions between perturbations were considered by exploring the added values of different source perturbations.For the SF case,the added values of IC,LBC,and MO perturbations were reflected in different forecast periods and different source uncertainties,suggesting that the combination of multi-source perturbations can yield positive interactions.In the WF case,MO perturbations provided a more accurate estimation of uncertainties downstream of the Dabie Mountain and need to be prioritized in the research on perturbation development.

Multimodel Ensemble Forecast of Global Horizontal Irradiance at PV Power Stations Based on Dynamic Variable Weight

In the present study,multimodel ensemble forecast experiments of the global horizontal irradiance(GHI)were conducted using the dynamic variable weight technique.The study was based on the forecasts of four numerical models,namely,the China Meteorological Administration Wind Energy and Solar Energy Prediction System,the Mesoscale Weather Numerical Prediction System of China Meteorological Administration,the China Meteorological Administration Regional Mesoscale Numerical Prediction System-Guangdong,and the Weather Research and Forecasting Model-Solar,and observational data from four photovoltaic(PV)power stations in Yangjiang City,Guangdong Province.The results show that compared with those of the monthly optimal numerical model forecasts,the dynamic variable weight-based ensemble forecasts exhibited 0.97%-15.96%smaller values of the mean absolute error and 3.31%-18.40%lower values of the root mean square error(RMSE).However,the increase in the correlation coefficient was not obvious.Specifically,the multimodel ensemble mainly improved the performance of GHI forecasts below 700 W m^(-2),particularly below 400 W m^(-2),with RMSE reductions as high as 7.56%-28.28%.In contrast,the RMSE increased at GHI levels above 700 W m^(-2).As for the key period of PV power station output(02:00-07:00),the accuracy of GHI forecasts could be improved by the multimodel ensemble:the multimodel ensemble could effectively decrease the daily maximum absolute error(AE max)of GHI forecasts.Moreover,with increasing forecasting difficulty under cloudy conditions,the multimodel ensemble,which yields data closer to the actual observations,could simulate GHI fluctuations more accurately.

Building trust for traffic flow forecasting components in intelligent transportation systems via interpretable ensemble learning

Traffic flow forecasting constitutes a crucial component of intelligent transportation systems(ITSs).Numerous studies have been conducted for traffic flow forecasting during the past decades.However,most existing studies have concentrated on developing advanced algorithms or models to attain state-of-the-art forecasting accuracy.For real-world ITS applications,the interpretability of the developed models is extremely important but has largely been ignored.This study presents an interpretable traffic flow forecasting framework based on popular tree-ensemble algorithms.The framework comprises multiple key components integrated into a highly flexible and customizable multi-stage pipeline,enabling the seamless incorporation of various algorithms and tools.To evaluate the effectiveness of the framework,the developed tree-ensemble models and another three typical categories of baseline models,including statistical time series,shallow learning,and deep learning,were compared on three datasets collected from different types of roads(i.e.,arterial,expressway,and freeway).Further,the study delves into an in-depth interpretability analysis of the most competitive tree-ensemble models using six categories of interpretable machine learning methods.Experimental results highlight the potential of the proposed framework.The tree-ensemble models developed within this framework achieve competitive accuracy while maintaining high inference efficiency similar to statistical time series and shallow learning models.Meanwhile,these tree-ensemble models offer interpretability from multiple perspectives via interpretable machine-learning techniques.The proposed framework is anticipated to provide reliable and trustworthy decision support across various ITS applications.

Ideal Case Study of Adaptive Localization in Storm-scale Ensemble Kalman Filter Assimilation

This study explores the use of the hierarchical ensemble filter to determine the localized influence of observations in the Weather Research and Forecasting ensemble square root filtering(WRF-EnSRF)assimilation system.With error correlations between observations and background field state variables considered,the adaptive localization approach is applied to conduct a series of ideal storm-scale data assimilation experiments using simulated Doppler radar data.Comparisons between adaptive and empirical localization methods are made,and the feasibility of adaptive localization for storm-scale ensemble Kalman filter assimilation is demonstrated.Unlike empirical localization,which relies on prior knowledge of distance between observations and background field,the hierarchical ensemble filter provides continuously updating localization influence weights adaptively.The adaptive scheme improves assimilation quality during rapid storm development and enhances assimilation of reflectivity observations.The characteristics of both the observation type and the storm development stage should be considered when identifying the most appropriate localization method.Ultimately,combining empirical and adaptive methods can optimize assimilation quality.

Storm-scale ensemble forecast based on breeding of growth modes

How to obtain fast-growth errors, which is comparable to the actual forecast growth error, is a crucial problem in ensemble forecast （EF）. The method, Breeding of Growth Modes （BGM）, which has been used to generate perturbations for medium-range EF at NCEP, simulates the development of fast-growth errors in the analysis cycle, and is a reasonable choice in capturing growing errors modes, especially for extreme weather by BGM. An ideal supercell storm, simulated by Weather Research Forecast model （WRF）, occurred in central Oklahoma on 20 May 1977. This simulation was used to study the application of BGM methods in the meso-scale strong convective Ensemble Prediction System （EPS）. We compared the forecasting skills of EPS by different pertubation methods, like Monte-Carlo and BGM. The results show that the ensemble average forecast based on Monte-Carlo with statistics meaning is superior to the single-deterministic prediction, but a less dynamic process of the method leads to a smaller spread than expected. The fast-growth errors of BGM are comparable to the actual short-range forecast error and a more appropriate ensemble spread. Considering evaluation indexes and scores, the forecast skills of EPS by BGM is higher than Monte-Carlo＇s. Furthermore, various breeding cycles have different effects on precipitation and non-precipitation fields, confirmation of reasonable cycles need consider balance between variables.

The method of residual‑based bootstrap averaging of the forecast ensemble

This paper presents an optimization approach—residual-based bootstrap averaging(RBBA)—for different types of forecast ensembles.Unlike traditional residual-mean-square-error-based ensemble forecast averaging approaches,the RBBA method attempts to find optimal forecast weights in an ensemble and allows for their combi-nation into the most effective additive forecast.In the RBBA method,all the different types of forecasts obtain the optimal weights for ensemble residuals that are statisti-cally optimal in terms of the fitness function of the residuals.Empirical studies have been conducted to demonstrate why and how the RBBA method works.The experi-mental results based on the real-world time series of contemporary stock exchanges show that the RBBA method can produce ensemble forecasts with good generalization ability.

Significant wave height forecasts integrating ensemble empirical mode decomposition with sequence-to-sequence model

As wave height is an important parameter in marine climate measurement,its accurate prediction is crucial in ocean engineering.It also plays an important role in marine disaster early warning and ship design,etc.However,challenges in the large demand for computing resources and the improvement of accuracy are currently encountered.To resolve the above mentioned problems,sequence-to-sequence deep learning model(Seq-to-Seq)is applied to intelligently explore the internal law between the continuous wave height data output by the model,so as to realize fast and accurate predictions on wave height data.Simultaneously,ensemble empirical mode decomposition(EEMD)is adopted to reduce the non-stationarity of wave height data and solve the problem of modal aliasing caused by empirical mode decomposition(EMD),and then improves the prediction accuracy.A significant wave height forecast method integrating EEMD with the Seq-to-Seq model(EEMD-Seq-to-Seq)is proposed in this paper,and the prediction models under different time spans are established.Compared with the long short-term memory model,the novel method demonstrates increased continuity for long-term prediction and reduces prediction errors.The experiments of wave height prediction on four buoys show that the EEMD-Seq-to-Seq algorithm effectively improves the prediction accuracy in short-term(3-h,6-h,12-h and 24-h forecast horizon)and long-term(48-h and 72-h forecast horizon)predictions.

Multi-model ensemble forecasting of 10-m wind speed over eastern China based on machine learning optimization

风对人类活动和电力运行有重大影响,准确预报短期风速具有深远的社会和经济意义.基于中国东部100个站点,本研究首先评估了5个业务模式对10米风速的预报能力,日本气象厅JMA模式在减少预报误差方面表现最好.进一步,利用5种数值模式和多种机器学习方法,将动力和统计相结合,对每个站点分别进行了特征工程和机器学习算法优选,建立了10米风速多模式集成预报模型。针对24至96小时预报时长,将该方法的预报性能与基于岭回归的多模式集成和JMA单模式进行比较.结果表明,基于机器学习优选的多模型集成方法可以将JMA模式的预报误差降低39%以上,预报效果的提升在11月最明显.此外,该方法优于基于岭回归的多模式集成方法.

Applications of Bias-removed Ensemble Mean in the Gale Forecasts over the Yellow Sea and the Bohai Sea

Based on the daily sea surface wind field prediction data of Japan Meteorological Agency(JMA) forecast model,National Centers for Environmental Prediction(NCEP GFS) model and U.S.Navy Operational Global Atmospheric Prediction System(NOGAPS) model at 12:00 UTC from June 28 to August 10 in 2009,the bias-removed ensemble mean(BRE) was used to do the forecast test on the sea surface wind fields,and the root-mean-square error(RMSE) was used to test and evaluate the forecast results.The results showed that the BRE considerably reduced the RMSEs of 24 and 48 h sea surface wind field forecasts,and the forecast skill was superior to that of the single model forecast.The RMSE decreases in the south of central Bohai Sea and the middle of the Yellow Sea were the most obvious.In addition,the BRE forecast improved evidently the forecast skill of the gale process which occurred during July 13-14 and August 7 in 2009.The forecast accuracy of the wind speed and the gale location was also improved.

Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations

This paper preliminarily investigates the application of the orthogonal conditional nonlinear optimal perturbations(CNOPs)–based ensemble forecast technique in MM5(Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model). The results show that the ensemble forecast members generated by the orthogonal CNOPs present large spreads but tend to be located on the two sides of real tropical cyclone(TC) tracks and have good agreements between ensemble spreads and ensemble-mean forecast errors for TC tracks. Subsequently, these members reflect more reasonable forecast uncertainties and enhance the orthogonal CNOPs–based ensemble-mean forecasts to obtain higher skill for TC tracks than the orthogonal SVs(singular vectors)–, BVs(bred vectors)– and RPs(random perturbations)–based ones. The results indicate that orthogonal CNOPs of smaller magnitudes should be adopted to construct the initial ensemble perturbations for short lead–time forecasts, but those of larger magnitudes should be used for longer lead–time forecasts due to the effects of nonlinearities. The performance of the orthogonal CNOPs–based ensemble-mean forecasts is case-dependent,which encourages evaluating statistically the forecast skill with more TC cases. Finally, the results show that the ensemble forecasts with only initial perturbations in this work do not increase the forecast skill of TC intensity, which may be related with both the coarse model horizontal resolution and the model error.

Ensemble Forecast: A New Approach to Uncertainty and Predictability

Ensemble techniques have been used to generate daily numerical weather forecasts since the 1990s in numerical centers around the world due to the increase in computation ability. One of the main purposes of numerical ensemble forecasts is to try to assimilate the initial uncertainty （initial error） and the forecast uncertainty （forecast error） by applying either the initial perturbation method or the multi-model/multiphysics method. In fact, the mean of an ensemble forecast offers a better forecast than a deterministic （or control） forecast after a short lead time （3-5 days） for global modelling applications. There is about a 1-2-day improvement in the forecast skill when using an ensemble mean instead of a single forecast for longer lead-time. The skillful forecast （65% and above of an anomaly correlation） could be extended to 8 days （or longer） by present-day ensemble forecast systems. Furthermore, ensemble forecasts can deliver a probabilistic forecast to the users, which is based on the probability density function （PDF） instead of a single-value forecast from a traditional deterministic system. It has long been recognized that the ensemble forecast not only improves our weather forecast predictability but also offers a remarkable forecast for the future uncertainty, such as the relative measure of predictability （RMOP） and probabilistic quantitative precipitation forecast （PQPF）. Not surprisingly, the success of the ensemble forecast and its wide application greatly increase the confidence of model developers and research communities.

A Regional Ensemble Forecast System for Stratiform Precipitation Events in the Northern China Region.Part Ⅱ:Seasonal Evaluation for Summer 2010

In this study, the Institute of Atmospheric Physics, Chinese Academy of Sciences - regional ensemble forecast system （IAP-REFS） described in Part I was further validated through a 65-day experiment using the summer season of 2010. The verification results show that IAP-REFS is skillful for quantitative precipitation forecasts （QPF） and probabilistic QPF, but it has a systematic bias in forecasting near-surface variables. Applying a 7-day running mean bias correction to the forecasts of near-surface variables remarkably improved the reliability of the forecasts. In this study, the perturbation extraction and inflation method （proposed with the single case study in Part I） was further applied to the full season with different inflation factors. This method increased the ensemble spread and improved the accuracy of forecasts of precipitation and near-surface variables. The seasonal mean profiles of the IAP-REFS ensemble indicate good spread among ensemble members and some model biases at certain vertical levels.

A Regional Ensemble Forecast System for Stratiform Precipitation Events in Northern China.Part I:A Case Study

A single-model, short-range, ensemble forecasting system （Institute of Atmospheric Physics, Regional Ensemble Forecast System, IAP REFS） with 15-km grid spacing, configured with multiple initial conditions, multiple lateral boundary conditions, and multiple physics parameterizations with 11 ensemble members, was developed using the Weather and Research Forecasting Model Advanced Research modeling system for prediction of stratiform precipitation events in northern China. This is the first part of a broader research project to develop a novel cloud-seeding operational system in a probabilistic framework. The ensemble perturbations were extracted from selected members of the National Center for Environmental Prediction Global Ensemble Forecasting System （NCEP GEFS） forecasts, and an inflation factor of two was applied to compensate for the lack of spread in the GEFS forecasts over the research region. Experiments on an actual stratiform precipitation case that occurred on 5-7 June 2009 in northern China were conducted to validate the ensemble system. The IAP REFS system had reasonably good performance in predicting the observed stratiform precipitation system. The perturbation inflation enlarged the ensemble spread and alleviated the underdispersion caused by parent forecasts. Centering the extracted perturbations on higher-resolution NCEP Global Forecast System forecasts resulted in less ensemble mean root-mean-square error and better accuracy in probabilistic quantitative precipitation forecasts （PQPF）. However, the perturbation inflation and recentering had less effect on near-surface-level variables compared to the mid-level variables, and its influence on PQPF resolution was limited as well.

Improvement of 6–15 Day Precipitation Forecasts Using a Time-Lagged Ensemble Method

A time-lagged ensemble method is used to improve 6-15 day precipitation forecasts from the Beijing Climate Center Atmospheric General Circulation Model,version 2.0.1.The approach averages the deterministic predictions of precipitation from the most recent model run and from earlier runs,all at the same forecast valid time.This lagged average forecast （LAF） method assigns equal weight to each ensemble member and produces a forecast by taking the ensemble mean.Our analyses of the Equitable Threat Score,the Hanssen and Kuipers Score,and the frequency bias indicate that the LAF using five members at time-lagged intervals of 6 h improves 6-15 day forecasts of precipitation frequency above 1 mm d-1 and 5 mm d-1 in many regions of China,and is more effective than the LAF method with selection of the time-lagged interval of 12 or 24 h between ensemble members.In particular,significant improvements are seen over regions where the frequencies of rainfall days are higher than about 40％-50％ in the summer season; these regions include northeastern and central to southern China,and the southeastem Tibetan Plateau.

AN ENSEMBLE FORECAST EXPERIMENT OF A LANDING TYPHOON

Based on the Global Regional Assimilation and Prediction System-Tropical Cyclone Model(GRAPES-TCM),an ensemble forecast experiment was performed,in which Typhoon Wipha during the period immediately prior to landfall was selected for the study and the breeding of growing mode(BGM) method was used to perturb the initial conditions of the vortex field and the environment field.The results of the experiment indicate that each member had a different initial status in BGM processing and they show a reasonable spread among members along with the forecast phase.Changes in the large-scale field,thermodynamic structure,and spread among members took place when Wipha made landfall.The steering effect of the large-scale field and the interaction between the thermodynamics and the dynamics resulted in different tracks of the members.Meanwhile,the forecast uncertainty increased.In summary,the ensemble mean did not perform as well as the control forecast,but the cluster mean provided some useful information,and performed better than the control in some instances.The position error was 34 km for 24 h forecast,153 km for 48 h forecast,and 191 km for 66 h forecast.The strike probability chart qualitatively described the forecast uncertainty.

Ensemble Forecasting of Tropical Cyclone Motion Using a Baroclinic Model

The purpose of this study is to investigate the effectiveness of two different ensemble forecasting （EF） techniques-the lagged-averaged forecast （LAF） and the breeding of growing modes （BGM）. In the BGM experiments, the vortex and the environment are perturbed separately （named BGMV and BGME）. Tropical cyclone （TC） motions in two difficult situations are studied： a large vortex interacting with its environment, and an apparent binary interaction. The former is Typhoon Yancy and the latter involves Typhoon Ed and super Typhoon Flo, all occurring during the Tropical Cyclone Motion Experiment TCM- 90. The model used is the baroclinic model of the University of New South Wales. The lateral boundary tendencies are computed from atmospheric analysis data. Only the relative skill of the ensemble forecast mean over the control run is used to evaluate the effectiveness of the EF methods, although the EF technique is also usecl to quantify forecast uncertainty in some studies. In the case of Yancy, the ensemble mean forecasts of each of the three methodologies are better than that of the control, with LAF being the best. The mean track of the LAF is close to the best track, and it predicts landfall over Taiwan. The improvements in LAF and the full BGM where both the environment and vortex are perturbed suggest the importance of combining the perturbation of the vortex and environment when the interaction between the two is appreciable. In the binary interaction case of Ed and Flo, the forecasts of Ed appear to be insensitive to perturbations of the environment and/or the vortex, which apparently results from erroneous forecasts by the model of the interaction between the subtropical ridge and Ed, as well as from the interaction between the two typhoons, thus reducing the effectiveness of the EF technique. This conclusion is reached through sensitivity experiments on the domain of the model and by adding or eliminating certain features in the model atmosphere. Nevertheless, the forecast tracks in some of the cases are improved over that of the control. On the other hand, the EF technique has little impact on the forecasts of Flo because the control forecast is already very close to the best track. The study provides a basis for the. future development of the EF technique. The limitations of this study are also addressed. For example, the above results are based on a small sample, and the study is actually a simulation, which is different than operational forecasting. Further tests of these EF techniques are proposed.

A STUDY ON THE ENSEMBLE FORECAST REAL-TIME CORRECTION METHOD

Using real-time correction technology for typhoons, this paper discusses real-time correction for forecasting the track of four typhoons during 2009 and 2010 in Japan, Beijing, Guangzhou, and Shanghai. It was determined that the short-time forecast effect was better than the original objective mode. By selecting four types of integration schemes after multiple mode path integration for those four objective modes, the forecast effect of the multi-mode path integration is better, on average, than any single model. Moreover, multi-mode ensemble forecasting has obvious advantages during the initial 36 h.

Evaluation of WRF-based Convection-Permitting Multi-Physics Ensemble Forecasts over China for an Extreme Rainfall Event on 21 July 2012 in Beijing

On 21 July 2012,an extreme rainfall event that recorded a maximum rainfall amount over 24 hours of 460 mm,occurred in Beijing,China. Most operational models failed to predict such an extreme amount. In this study,a convective-permitting ensemble forecast system（CEFS）,at 4-km grid spacing,covering the entire mainland of China,is applied to this extreme rainfall case. CEFS consists of 22 members and uses multiple physics parameterizations. For the event,the predicted maximum is 415 mm d^-1 in the probability-matched ensemble mean. The predicted high-probability heavy rain region is located in southwest Beijing,as was observed. Ensemble-based verification scores are then investigated. For a small verification domain covering Beijing and its surrounding areas,the precipitation rank histogram of CEFS is much flatter than that of a reference global ensemble. CEFS has a lower（higher） Brier score and a higher resolution than the global ensemble for precipitation,indicating more reliable probabilistic forecasting by CEFS. Additionally,forecasts of different ensemble members are compared and discussed. Most of the extreme rainfall comes from convection in the warm sector east of an approaching cold front. A few members of CEFS successfully reproduce such precipitation,and orographic lift of highly moist low-level flows with a significantly southeasterly component is suggested to have played important roles in producing the initial convection. Comparisons between good and bad forecast members indicate a strong sensitivity of the extreme rainfall to the mesoscale environmental conditions,and,to less of an extent,the model physics.