A Deep Learning Approach for Forecasting Thunderstorm Gusts in the Beijing–Tianjin–Hebei Region

Thunderstorm gusts are a common form of severe convective weather in the warm season in North China,and it is of great importance to correctly forecast them.At present,the forecasting of thunderstorm gusts is mainly based on traditional subjective methods,which fails to achieve high-resolution and high-frequency gridded forecasts based on multiple observation sources.In this paper,we propose a deep learning method called Thunderstorm Gusts TransU-net(TGTransUnet)to forecast thunderstorm gusts in North China based on multi-source gridded product data from the Institute of Urban Meteorology(IUM)with a lead time of 1 to 6 h.To determine the specific range of thunderstorm gusts,we combine three meteorological variables:radar reflectivity factor,lightning location,and 1-h maximum instantaneous wind speed from automatic weather stations(AWSs),and obtain a reasonable ground truth of thunderstorm gusts.Then,we transform the forecasting problem into an image-to-image problem in deep learning under the TG-TransUnet architecture,which is based on convolutional neural networks and a transformer.The analysis and forecast data of the enriched multi-source gridded comprehensive forecasting system for the period 2021–23 are then used as training,validation,and testing datasets.Finally,the performance of TG-TransUnet is compared with other methods.The results show that TG-TransUnet has the best prediction results at 1–6 h.The IUM is currently using this model to support the forecasting of thunderstorm gusts in North China.

Enhancing Deep Learning Soil Moisture Forecasting Models by Integrating Physics-based Models

Accurate soil moisture(SM)prediction is critical for understanding hydrological processes.Physics-based(PB)models exhibit large uncertainties in SM predictions arising from uncertain parameterizations and insufficient representation of land-surface processes.In addition to PB models,deep learning(DL)models have been widely used in SM predictions recently.However,few pure DL models have notably high success rates due to lacking physical information.Thus,we developed hybrid models to effectively integrate the outputs of PB models into DL models to improve SM predictions.To this end,we first developed a hybrid model based on the attention mechanism to take advantage of PB models at each forecast time scale(attention model).We further built an ensemble model that combined the advantages of different hybrid schemes(ensemble model).We utilized SM forecasts from the Global Forecast System to enhance the convolutional long short-term memory(ConvLSTM)model for 1–16 days of SM predictions.The performances of the proposed hybrid models were investigated and compared with two existing hybrid models.The results showed that the attention model could leverage benefits of PB models and achieved the best predictability of drought events among the different hybrid models.Moreover,the ensemble model performed best among all hybrid models at all forecast time scales and different soil conditions.It is highlighted that the ensemble model outperformed the pure DL model over 79.5%of in situ stations for 16-day predictions.These findings suggest that our proposed hybrid models can adequately exploit the benefits of PB model outputs to aid DL models in making SM predictions.

Seasonal Characteristics of Forecasting Uncertainties in Surface PM_(2.5)Concentration Associated with Forecast Lead Time over the Beijing-Tianjin-Hebei Region

Forecasting uncertainties among meteorological fields have long been recognized as the main limitation on the accuracy and predictability of air quality forecasts.However,the particular impact of meteorological forecasting uncertainties on air quality forecasts specific to different seasons is still not well known.In this study,a series of forecasts with different forecast lead times for January,April,July,and October of 2018 are conducted over the Beijing-Tianjin-Hebei(BTH)region and the impacts of meteorological forecasting uncertainties on surface PM_(2.5)concentration forecasts with each lead time are investigated.With increased lead time,the forecasted PM_(2.5)concentrations significantly change and demonstrate obvious seasonal variations.In general,the forecasting uncertainties in monthly mean surface PM_(2.5)concentrations in the BTH region due to lead time are the largest(80%)in spring,followed by autumn(~50%),summer(~40%),and winter(20%).In winter,the forecasting uncertainties in total surface PM_(2.5)mass due to lead time are mainly due to the uncertainties in PBL heights and hence the PBL mixing of anthropogenic primary particles.In spring,the forecasting uncertainties are mainly from the impacts of lead time on lower-tropospheric northwesterly winds,thereby further enhancing the condensation production of anthropogenic secondary particles by the long-range transport of natural dust.In summer,the forecasting uncertainties result mainly from the decrease in dry and wet deposition rates,which are associated with the reduction of near-surface wind speed and precipitation rate.In autumn,the forecasting uncertainties arise mainly from the change in the transport of remote natural dust and anthropogenic particles,which is associated with changes in the large-scale circulation.

Promising Results Predict Role for Artificial Intelligence in Weather Forecasting

Artificial intelligence(AI)has already demonstrated its proficiency at difficult scientific tasks like predicting how proteins will fold and identifying new astronomical objects in masses of observational data[1].Now,recent results suggest that AI also excels at weather forecasting.For global predictions,GraphCast,an AI system developed by Google subsidiary DeepMind(London,UK),outperforms the state-of-the-art model from the European Centre for Medium-Range Weather Forecasts(ECMWF),providing more accurate projections of variables such as temperature and humidity 90%of the time[2,3].Other AI systems,including Pangu-Weather from the Chinese tech company Huawei(Shenzhen,China)[4],can also match or beat traditional global forecasting models.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Some Modified Equations of the Sine-Hilbert Type

Three modified sine-Hilbert(sH)-type equations, i.e., the modified sH equation, the modified damped sH equation, and the modified nonlinear dissipative system, are proposed, and their bilinear forms are provided.Based on these bilinear equations, some exact solutions to the three modified equations are derived.

Scientific Advances and Weather Services of the China Meteorological Administration’s National Forecasting Systems during the Beijing 2022 Winter Olympics

Since the Beijing 2022 Winter Olympics was the first Winter Olympics in history held in continental winter monsoon climate conditions across complex terrain areas,there is a deficiency of relevant research,operational techniques,and experience.This made providing meteorological services for this event particularly challenging.The China Meteorological Administration(CMA)Earth System Modeling and Prediction Centre,achieved breakthroughs in research on short-and medium-term deterministic and ensemble numerical predictions.Several key technologies crucial for precise winter weather services during the Winter Olympics were developed.A comprehensive framework,known as the Operational System for High-Precision Weather Forecasting for the Winter Olympics,was established.Some of these advancements represent the highest level of capabilities currently available in China.The meteorological service provided to the Beijing 2022 Games also exceeded previous Winter Olympic Games in both variety and quality.This included achievements such as the“100-meter level,minute level”downscaled spatiotemporal resolution and forecasts spanning 1 to 15 days.Around 30 new technologies and over 60 kinds of products that align with the requirements of the Winter Olympics Organizing Committee were developed,and many of these techniques have since been integrated into the CMA’s operational national forecasting systems.These accomplishments were facilitated by a dedicated weather forecasting and research initiative,in conjunction with the preexisting real-time operational forecasting systems of the CMA.This program represents one of the five subprograms of the WMO’s high-impact weather forecasting demonstration project(SMART2022),and continues to play an important role in their Regional Association(RA)II Research Development Project(Hangzhou RDP).Therefore,the research accomplishments and meteorological service experiences from this program will be carried forward into forthcoming highimpact weather forecasting activities.This article provides an overview and assessment of this program and the operational national forecasting systems.

An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields

In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method.

Better use of experience from other reservoirs for accurate production forecasting by learn-to-learn method

To assess whether a development strategy will be profitable enough,production forecasting is a crucial and difficult step in the process.The development history of other reservoirs in the same class tends to be studied to make predictions accurate.However,the permeability field,well patterns,and development regime must all be similar for two reservoirs to be considered in the same class.This results in very few available experiences from other reservoirs even though there is a lot of historical information on numerous reservoirs because it is difficult to find such similar reservoirs.This paper proposes a learn-to-learn method,which can better utilize a vast amount of historical data from various reservoirs.Intuitively,the proposed method first learns how to learn samples before directly learning rules in samples.Technically,by utilizing gradients from networks with independent parameters and copied structure in each class of reservoirs,the proposed network obtains the optimal shared initial parameters which are regarded as transferable information across different classes.Based on that,the network is able to predict future production indices for the target reservoir by only training with very limited samples collected from reservoirs in the same class.Two cases further demonstrate its superiority in accuracy to other widely-used network methods.

Comparison among the UECM Model, and the Composite Model in Forecasting Malaysian Imports

For more than a century, forecasting models have been crucial in a variety of fields. Models can offer the most accurate forecasting outcomes if error terms are normally distributed. Finding a good statistical model for time series predicting imports in Malaysia is the main target of this study. The decision made during this study mostly addresses the unrestricted error correction model (UECM), and composite model (Combined regression—ARIMA). The imports of Malaysia from the first quarter of 1991 to the third quarter of 2022 are employed in this study’s quarterly time series data. The forecasting outcomes of the current study demonstrated that the composite model offered more probabilistic data, which improved forecasting the volume of Malaysia’s imports. The composite model, and the UECM model in this study are linear models based on responses to Malaysia’s imports. Future studies might compare the performance of linear and nonlinear models in forecasting.

Generalized load graphical forecasting method based on modal decomposition

In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized loads.From the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal decomposition.First,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest algorithms.Subsequently,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B channels.The generated images are diversified,and an optimized DenseNet neural network was used for training and prediction.Finally,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise algorithm.Based on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.

Theoretical study of particle and energy balance equations in locally bounded plasmas

In this study,new particle and energy balance equations have been developed to predict the electron temperature and density in locally bounded plasmas.Classical particle and energy balance equations assume that all plasma within a reactor is completely confined only by the reactor walls.However,in industrial plasma reactors for semiconductor manufacturing,the plasma is partially confined by internal reactor structures.We predict the effect of the open boundary area(A′_(L,eff))and ion escape velocity(u_(i))on electron temperature and density by developing new particle and energy balance equations.Theoretically,we found a low ion escape velocity(u_(i)/u_(B)≈0.2)and high open boundary area(A′_(L,eff)/A_(T,eff)≈0.6)to result in an approximately 38%increase in electron density and an 8%decrease in electron temperature compared to values in a fully bounded reactor.Additionally,we suggest that the velocity of ions passing through the open boundary should exceedω_(pi)λ_(De)under the condition E^(2)_(0)?(Φ/λ_(De))^(2).

Data-Driven Ai-and Bi-Soliton of the Cylindrical Korteweg-de Vries Equation via Prior-Information Physics-Informed Neural Networks

By the modifying loss function MSE and training area of physics-informed neural networks(PINNs),we propose a neural networks model,namely prior-information PINNs(PIPINNs).We demonstrate the advantages of PIPINNs by simulating Ai-and Bi-soliton solutions of the cylindrical Korteweg-de Vries(cKdV)equation.

CALTM:A Context-Aware Long-Term Time-Series Forecasting Model

Time series data plays a crucial role in intelligent transportation systems.Traffic flow forecasting represents a precise estimation of future traffic flow within a specific region and time interval.Existing approaches,including sequence periodic,regression,and deep learning models,have shown promising results in short-term series forecasting.However,forecasting scenarios specifically focused on holiday traffic flow present unique challenges,such as distinct traffic patterns during vacations and the increased demand for long-term forecastings.Consequently,the effectiveness of existing methods diminishes in such scenarios.Therefore,we propose a novel longterm forecasting model based on scene matching and embedding fusion representation to forecast long-term holiday traffic flow.Our model comprises three components:the similar scene matching module,responsible for extracting Similar Scene Features;the long-short term representation fusion module,which integrates scenario embeddings;and a simple fully connected layer at the head for making the final forecasting.Experimental results on real datasets demonstrate that our model outperforms other methods,particularly in medium and long-term forecasting scenarios.

Dynamic adaptive spatio-temporal graph network for COVID-19 forecasting

Appropriately characterising the mixed space-time relations of the contagion process caused by hybrid space and time factors remains the primary challenge in COVID-19 forecasting.However,in previous deep learning models for epidemic forecasting,spatial and temporal variations are captured separately.A unified model is developed to cover all spatio-temporal relations.However,this measure is insufficient for modelling the complex spatio-temporal relations of infectious disease transmission.A dynamic adaptive spatio-temporal graph network(DASTGN)is proposed based on attention mechanisms to improve prediction accuracy.In DASTGN,complex spatio-temporal relations are depicted by adaptively fusing the mixed space-time effects and dynamic space-time dependency structure.This dual-scale model considers the time-specific,space-specific,and direct effects of the propagation process at the fine-grained level.Furthermore,the model characterises impacts from various space-time neighbour blocks under time-varying interventions at the coarse-grained level.The performance comparisons on the three COVID-19 datasets reveal that DASTGN achieves state-of-the-art results with a maximum improvement of 17.092%in the root mean-square error and 11.563%in the mean absolute error.Experimental results indicate that the mechanisms of designing DASTGN can effectively detect some spreading characteristics of COVID-19.The spatio-temporal weight matrices learned in each proposed module reveal diffusion patterns in various scenarios.In conclusion,DASTGN has successfully captured the dynamic spatio-temporal variations of COVID-19,and considering multiple dynamic space-time relationships is essential in epidemic forecasting.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

Assessment of ECMWF’s Precipitation Forecasting Performance for China from 2017 to 2022

This study used the China Meteorological Administration(CMA)three-source fusion gridded precipitation analysis data as a reference to evaluate the precipitation forecast performance of the European Centre for Medium-Range Weather Forecasts(ECMWF)model for China from 2017 to 2022.The main conclusions are as follows.The precipitation forecast capability of the ECMWF model for China has gradually improved from 2017 to 2022.Various scores such as bias,equitable threat score(ETS),and Fractions Skill Score(FSS)showed improvements for different categories of precipitation.The bias of light rain forecasts overall adjusted towards smaller values,and the increase in forecast scores was greater in the warm season than in the cold season.The ETS for torrential rain more intense categories significantly increased,although there were large fluctuations in bias across different months.The model exhibited higher precipitation bias in most areas of North China,indicating overprediction,while it showed lower bias in South China,indicating underprediction.The ETSs indicate that the model performed better in forecasting precipitation in the northeastern part of China without the influence of climatic background conditions.Comparison of the differences between the first period and the second period of the forecast shows that the precipitation amplitude in the ECMWF forecast shifted from slight underestimation to overestimation compared to that of CMPAS05,reducing the likelihood of missing extreme precipitation events.The improvement in ETS is mainly due to the reduction in bias and false alarm rates and,more importantly,an increase in the hit rate.From 2017 to 2022,the area coverage error of model precipitation forecast relative to observations showed a decreasing trend at different scales,while the FSS showed an increasing trend,with the highest FSS observed in 2021.The ETS followed a parabolic trend with increasing neighborhood radius,with the better ETS neighborhood radius generally being larger for moderate rain and heavy rain compared with light rain and torrential rain events.

Weather-Driven Solar Power Forecasting Using D-Informer:Enhancing Predictions with Climate Variables

Precise forecasting of solar power is crucial for the development of sustainable energy systems.Contemporary forecasting approaches often fail to adequately consider the crucial role of weather factors in photovoltaic(PV)power generation and encounter issues such as gradient explosion or disappearance when dealing with extensive time-series data.To overcome these challenges,this research presents a cutting-edge,multi-stage forecasting method called D-Informer.This method skillfully merges the differential transformation algorithm with the Informer model,leveraging a detailed array of meteorological variables and historical PV power generation records.The D-Informer model exhibits remarkable superiority over competing models across multiple performance metrics,achieving on average a 67.64%reduction in mean squared error(MSE),a 49.58%decrease in mean absolute error(MAE),and a 43.43%reduction in root mean square error(RMSE).Moreover,it attained an R2 value as high as 0.9917 during the winter season,highlighting its precision and dependability.This significant advancement can be primarily attributed to the incorporation of a multi-head self-attention mechanism,which greatly enhances the model’s ability to identify complex interactions among diverse input variables,and the inclusion of weather variables,enriching the model’s input data and strengthening its predictive accuracy in time series analysis.Additionally,the experimental results confirm the effectiveness of the proposed approach.

Analytical solutions fractional order partial differential equations arising in fluid dynamics

This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.

THE STABILITY OF BOUSSINESQ EQUATIONS WITH PARTIAL DISSIPATION AROUND THE HYDROSTATIC BALANCE

This paper is devoted to understanding the stability of perturbations around the hydrostatic equilibrium of the Boussinesq system in order to gain insight into certain atmospheric and oceanographic phenomena.The Boussinesq system focused on here is anisotropic,and involves only horizontal dissipation and thermal damping.In the 2D case R^(2),due to the lack of vertical dissipation,the stability and large-time behavior problems have remained open in a Sobolev setting.For the spatial domain T×R,this paper solves the stability problem and gives the precise large-time behavior of the perturbation.By decomposing the velocity u and temperatureθinto the horizontal average(ū,θ)and the corresponding oscillation(ū,θ),we can derive the global stability in H~2 and the exponential decay of(ū,θ)to zero in H^(1).Moreover,we also obtain that(ū_(2),θ)decays exponentially to zero in H^(1),and thatū_(1)decays exponentially toū_(1)(∞)in H^(1)as well;this reflects a strongly stratified phenomenon of buoyancy-driven fluids.In addition,we establish the global stability in H^(3)for the 3D case R^(3).