In recent years, Artificial Intelligence (AI)-based weather prediction models have emerged as powerful tools in meteorology, capable of learning complex dependencies from extensive weather datasets and generating rapid forecasts after training. These models achieve prediction accuracies comparable to state-of-the-art Numerical Weather Prediction (NWP) systems. However, these models remain not fully operational due to their dependence on computationally intensive Data Assimilation (DA) systems for generating accurate initial fields. Recent advances in AI techniques offer a potential pathway to develop more efficient and accurate DA systems, advancing the operational feasibility of end-to-end AI-based weather forecasting. Despite growing interest, research in AI-based DA remains fragmented. Therefore, a comprehensive review is necessary to clarify the current progress, identify challenges, and guide the future development of next-generation AI-based DA systems. This review categorizes AI-based DA research into two primary domains. The first domain is AI-empowered DA, where AI enhances individual components such as observation operators, tangent linear and adjoint models, and uncertainty quantification. It also includes latent DA, which helps reduce computational costs. The second domain is AI-based end-to-end DA models, which integrate observations and short-range weather predictions within unified AI frameworks to generate accurate initial fields. We further discuss key challenges and opportunities, including dataset standardization, model evaluation protocols, assimilation of extended observation types, enforcement of physical constraints, and addressing operational scalability. Finally, we emphasize the importance of interdisciplinary collaboration across AI and meteorology in developing practical and reliable AI solutions to enhance DA processes and support more accurate weather forecasting. This review offers practical insights to the research community to expedite the development and operationalization of AI-based DA and end-to-end weather forecasting systems.

This study evaluated the performance of a Weak-Constraint Four-Dimensional Variational data assimilation (WC_4DVAR) system in simulating the 2024 sudden stratospheric warming (SSW) event, comparing it against the Strong-Constraint Four-Dimensional Variational (SC_4DVAR) approach. For this event, results showed that WC_4DVAR clearly improved the stratospheric analysis, reducing the observation-minus-background (OmB) temperature biases by up to 24.3% at 20 hPa compared to SC_4DVAR. In contrast, SC_4DVAR exhibited systematic biases exceeding 0.3 K throughout the 100-10 hPa layer. In forecasting, WC_4DVAR reduced root-mean-square errors (RMSE) in geopotential height and temperature forecasts, with notable improvements at lead times of 7-9 days, although a slight degradation in temperature RMSE occurred during the first 1-4 days at 10 and 20 hPa. It also mitigated the mid-March temperature underestimation in extended-range forecasts (days 7-10). The system markedly alleviated cold biases during the pre-onset (28 February), onset (4 March), and post-onset (9 March) phases of the SSW. Notably, for forecasts initialized at the onset date (4 March), WC_4DVAR reduced the core temperature bias from -6 to -3 K and cut wind errors by 1-3 m & centerdot;s-1 at 10-5 hPa throughout days 5-10. The improvements were attributed to a more realistic easterly intensity and a refined vertical shear of zonal wind in the initial analysis, which induced a more realistic wave-mean flow interaction. However, for the pre-onset and post-onset initialization, wind improvements were smaller or locally negative, indicating a strong dependence on the background state. In summary, for the 2024 SSW event, WC_4DVAR performed favorably compared to SC_4DVAR for both stratospheric analysis and forecasting, particularly during dynamically critical periods. These findings highlight the potential for operational stratospheric forecasting pending further multicase validation.

The world's first operational early morning-orbit meteorological satellite, Fengyun-3E (FY-3E), launched on 5 July 2021, and has expanded global data coverage for numerical weather prediction (NWP) of 6-h assimilation windows. To determine whether the early morning orbit affects microwave observations and the benefits to NWP, radiance from FY-3E microwave instruments was assimilated into the operational global Yinhe four-dimensional variational assimilation (YH4DVAR) system. The performance of the microwave instruments was first assessed based on the statistics of background departure. The sunlight conditions have little effect on FY-3E microwave observations, and ascending and descending pass observations could be uniformly assimilated for both the Microwave Humidity Sounder-2 (MWHS-2) and the Microwave Temperature Sounder-3 (MWTS-3). The standard deviation of observation minus background (OmB) after variational bias correction increased, indicating slightly reduced performance of MWTS-3 compared with equivalent Advanced Technology Microwave Sounder (ATMS) channels on SNPP/NOAA-20. Based on reduced OmB mean and standard deviation values, FY-3E MWHS-2 performs better than MWHS-2 on predecessor satellites. To test the impact of FY-3E microwave observations on the operational YH4DVAR system, three NWP experiments were performed from June to August 2022. All-sky assimilation of FY-3E MWHS-2 observations in the YH4DVAR system has a neutral to positive impact on forecast skill. Assimilation of FY-3E MWTS-3 under clear-sky conditions provides little benefit to the YH4DVAR system in longer-range forecasts but improves the fit to the background of stratospheric temperature-sounding channels of ATMS and Advanced Microwave Sounding Unit-A (AMSUA) and radiosonde temperature observations over 150-400 hPa in the Northern Hemisphere and humidity observations over 100-850 hPa.

The Geostationary Interferometric Infrared Sounder (GIIRS) on board FengYun-4B (FY-4B), a Chinese second-generation hyperspectral infrared, enables the provision of critical data for forecasting high-impact weather events such as typhoons. To evaluate the reliability of FY-4B/GIIRS data, this study conducted three comparative assimilation trials for both Typhoon Gaemi and Typhoon Doksuri, assimilating observations from the Infrared Atmospheric Sounding Interferometer (IASI), Advanced Microwave Sounding Unit-A (AMSU-A), and FY-4B/GIIRS, respectively. Results demonstrate that the assimilation of GIIRS observations yields more stable forecasts of the wind field at 300 hPa and 500 hPa compared to AMSU-A and IASI, with biases within ±6 m/s relative to NCEP FNL data. However, GIIRS assimilation produces systematic underprediction of vertical velocity, whereas AMSU-A forecasts align more closely with reanalysis. For track forecasts, the GIIRS-assimilated trajectory exhibits closer alignment with observations than AMSU-A and IASI experiments, maintaining biases below 50 km throughout 48 h forecast period of Gaemi. This study provides valuable experience for the application of FY-4B/GIIRS data assimilation.

The C-band Advanced Scatterometer (ASCAT) has the advantages of good spatial-temporal coverage and low sensitivity to nonextreme rainfall. While the perceived wind speed underestimation issues of ASCAT sea surface wind (SSW) retrievals can be mitigated using appropriate high wind speed scalings, the low spatial resolution in ASCAT remains a challenge, which implicitly leads to the blurring effect in tropical cyclone (TC) inner-core regions. To overcome this issue, the 2-D variational (2DVAR) analysis method is modified from 12.5 to 1.8 km grid size, where the latter allows super-resolution (SR) spatial structure functions, empirically trained on synthetic aperture radar (SAR) data, to enhance TC structure retrievals of ASCAT. The method first employs triple collocation analysis to estimate observation and background errors under different TC categories. After that, the relevant spatial parameters during the data assimilation process are determined and linked to TC features. These analyses contribute to constructing SAR-learned structure functions, complementing ASCAT-observed TC characteristics, and then achieving TC vortex reconstruction and wind field SR. Validation studies demonstrate that the SR products possess the correct small-scale properties of TC inner-core structures, such as radius of maximum wind (RMW), TC asymmetry, and wind variability. Notably, the proposed SR approach can achieve a significant reduction in error standard deviations (SDs) of ( l,t ) wind components (by 37% and 33%, respectively) when compared to spatial interpolated results. The encouraging results suggest the feasibility of the method in enhancing the abundant but lower resolution scatterometer winds, potentially contributing to future advancements in TC advisories.

Machine Learning (ML) has shown great promise in revolutionizing weather forecasting, yet most ML systems still rely on initial conditions generated by Numerical Weather Prediction (NWP) systems. End-to-end ML models aim to eliminate this dependency, but they often rely on observation-specific encoders and require redesign or retraining when observation sources change, thereby limiting their operational robustness. Here, we introduce XiChen, a global weather observation-to-forecast ML system via four-dimensional variational (4DVar) gradient-guided flexible assimilation. We demonstrate that the gradient of the 4DVar cost function serves as a physically grounded interface that maps heterogeneous observations into a common state space. This novel formulation enables XiChen to flexibly assimilate diverse conventional and raw satellite observations while preserving physical consistency. Experiments show that the system achieves forecasting metrics competitive with operational NWP systems. This work provides a practical and physically consistent route toward operational ML-based global weather forecasting systems with heterogeneous and evolving observations.

The Advanced Radiative Transfer Modeling System(ARMS),a computationally efficient satellite observation op-erator,has been successfully integrated into the YinHe four-dimensional variational data assimilation(YH4DVAR)system.This study investigates the impacts of assimilating Advanced Microwave Sounding Unit-A(AMSU-A)ob-servations from the Meteorological Operational Satellite-C(MetOp-C)on the performance of YH4DVAR.Through a month-long global statistical analysis and a case study of Typhoon Hinnamnor,we evaluate the benefits of AMSU-A data assimilation under clear sky conditions.Key findings are as follows.(1)ARMS achieves simulation accuracy comparable to RTTOV(Radiative Transfer for the Television and InfraRed Observation Satellite Operational Verti-cal sounder)version 11.2,demonstrating only a 0.5％discrepancy in data retention after quality control.(2)Imple-mentation of ARMS as an operator in YH4DVAR enhances forecast accuracy for the 850-hPa temperature and 500-hPa geopotential height in the tropical region.(3)Compared to RTTOV,ARMS has improved the intensity forecast of Typhoon Hinnamnor and reduced mean wind speed errors by approximately 2％and central pressure errors by ap-proximately 1％.ARMS has now been operationally adopted as an alternative observational operator wi-thin YH4DVAR,demonstrating exceptional numerical stability,computational efficiency,and promising potential for future satellite data assimilation applications.

The oceanic mixed layer is essential for air-sea interactions, influencing energy exchanges, climate dynamics, and marine ecosystems through its depth, and seasonal variability. Currently, the mixed layer depth (MLD) is estimated using in-situ observations or model data, both of which are costly and resource-intensive. This study develops a clustering estimation model utilising multisource ocean data to enable faster and more accurate MLD estimation. The model accounts for the temperature and salinity characteristics of different oceanic regions. The K-means clustering method was employed to partition the Pacific Ocean, and the lightGBM model was applied to estimate the MLD in individual subregions. Alongside commonly used sea surface parameters, wind stress curl and precipitation were included as inputs. Feature analysis was conducted separately for the models in each partition. The estimated MLD was compared with that of the in-situ data, showing consistency with observed trends and effectively capturing the spatiotemporal characteristics of MLD across seasons and geographic locations. The estimation error (RMSE) was less than 11.2 m. To assess practical applicability, comparative experiments using remote sensing data were performed, highlighting the model's feasibility and utility. By integrating clustering analysis with advanced estimation models, this study provides a novel approach for accurately reproducing the Pacific Ocean's MLD, which is useful for better analyzing the changes in ocean heat flux and vertical dynamics of seawater.

Ocean reanalysis data, compared to traditional observational data, possess stronger continuity and higher data accuracy. The globally high-resolution ice-ocean coupled reanalysis product China Ocean ReAnalysis, Version 2.0 (CORA v2.0), independently developed by the National Marine Information Center, has attracted considerable attention since its release in 2020. This study selected six representative points of sound velocity profiles in different global ocean regions and conducted comparative analysis between the 2014 momentary data from CORA v2.0 and Argo data. Additionally, the monthly average data of CORA v2.0 in 2013 were compared and studied against General Digital Environmental Model (GDEM) and World Ocean Atlas (WOA) data. Metrics such as Root Mean Square Error (RMSE) and Mean Error (ME) were introduced to evaluate the differences between datasets. The result reveals that, in a comparison of single moment data, the sound velocity profiles of CORA v2.0 data and Argo data exhibit high consistency, with ME generally within 2 m/s. Regarding a comparison of monthly average data, the consistency between CORA v2.0 data and WOA data is higher, while the error relative to GDEM data is relatively larger, but their RMSE and ME exhibit high similarity in temporal trends. Based on the 2014 data of CORA v2.0, the temporal and spatial evolutionary laws of global seawater sound velocity profiles and sound speed fields were analyzed. On the time scale, the variation of seawater sound speed is mainly influenced by seasons, with significant differences between winter and summer seasons. On the daily scale, there are certain differences in sound velocity profiles mainly in the early morning and afternoon. On the spatial scale, analysis was conducted from both horizontal and vertical perspectives. The distribution of sound speed exhibits evident regularity with latitude, with shallow seawater sound speed being greatly influenced by external factors while deep seawater is relatively stable. Using the Range-dependent Acoustic Model for Geoacoustics (RAMgeo) model to solve the underwater acoustic field at three specific points, the characteristic changes of sound velocity profiles at different times of the day and their impact on under water sound propagation losses were obtained. This paper provides valuable information for the application of CORA v2.0 data products.

Numerical weather prediction (NWP) is the core technology for weather forecast and disaster prevention and mitigation. The research and operational applications of NWP have always been highly valued in China, and have achieved great progress with an appreciable international influence in the theories, algorithms, and operational system developments. This paper first summarizes the scientific and technological evolution of NWP in China, and then focuses on the current status and recent updates of the two homemade global NWP systems: GRAPES (Global/Regional Assimilation and PrEdiction System) and YHGSM (YinHe Global Spectral Model). (1) GRAPES possesses both deterministic and ensemble forecast systems, with global (regional) model versions running on 12–50-km (3–10-km) resolutions. Significant improvements have been made on its dynamic core, four-dimensional variational (4D-Var) assimilation, satellite and radar data assimilation, ensemble forecast, and cloud microphysics schemes, and so on. It is capable to perform subseasonal to seasonal forecast and has incorporated an atmospheric chemistry model, typhoon numerical forecast model, and ocean wave model. (2) YHGSM continues to follow the development route of spectral models, featured prominently with a dry-mass conserved spectral dynamical core, ensemble 4D-Var assimilation, coupled ocean–land–atmosphere ensemble forecast, and the medium-term and monthly-extended global high-resolution forecast as the baseline. These NWP systems autonomouly developed by the China Meteorological Administration and the national defense insitution benefit from long-term adherence to the national science and technology development strategies and close research to operation practices.

Numerical weather prediction (NWP) is the core technology for weather forecast and disaster prevention and mitigation. The research and operational applications of NWP have always been highly valued in China, and have achieved great progress with an appreciable international influence in the theories, algorithms, and operational system developments. This paper first summarizes the scientific and technological evolution of NWP in China, and then focuses on the current status and recent updates of the two homemade global NWP systems: GRAPES (Global/Regional Assimilation and PrEdiction System) and YHGSM (YinHe Global Spectral Model). (1) GRAPES possesses both deterministic and ensemble forecast systems, with global (regional) model versions running on 12u201350-km (3u201310-km) resolutions. Significant improvements have been made on its dynamic core, four-dimensional variational (4D-Var) assimilation, satellite and radar data assimilation, ensemble forecast, and cloud microphysics schemes, and so on. It is capable to perform subseasonal to seasonal forecast and has incorporated an atmospheric chemistry model, typhoon numerical forecast model, and ocean wave model. (2) YHGSM continues to follow the development route of spectral models, featured prominently with a dry-mass conserved spectral dynamical core, ensemble 4D-Var assimilation, coupled oceanu2013landu2013atmosphere ensemble forecast, and the medium-term and monthly-extended global high-resolution forecast as the baseline. These NWP systems autonomouly developed by the China Meteorological Administration and the national defense insitution benefit from long-term adherence to the national science and technology development strategies and close research to operation practices.

Accurate knowledge of Tropical Cyclone (TC) inner-core structures contributes to a better understanding of TC thermodynamics. The Advanced Scatterometer (ASCAT) can measure ocean surface winds at a good spatial-temporal coverage, but the TC inner structures are largely blurred by its 20-km footprint. In this study, the Two-Dimensional Variational (2DVAR) scheme is considered to enhance the TC inner-core structure, by "learning" background spatial error covariances from high-resolution Synthetic Aperture Radar (SAR) winds. We find that the length scales of the stream function are close to the radii of maximum wind speeds and length scales of the velocity potential are dependent on TC asymmetry scales. All these parameters can be provided by ASCAT data. Experimental results prove that the proposed method can enhance TC inner-core structures and thus achieve super-resolution. The promising results contribute to our long-term goal of developing a general method for providing TC inner-core structures from all scatterometer winds available for nowcasting, allowing temporal monitoring of TC winds.

The continuous monitoring of Tropical Cyclones (TCs) plays a crucial role in exploring TC dynamics and enabling more timely disaster responses by coastal communities. However, a mature and widely recognized dataset depicting long-term TC development is still lacking, whether in terms of satellite observations or reanalyses. The Marine Atmosphere eXtreme Satellite Synergy (MAXSS) project recently released a new global merged wind product, offering hourly 10-m stress-equivalent wind maps on a 0.25 ◦ grid. The project aims to enhance understanding of multi-scale air-sea interactions under extreme conditions, making the new wind product an excellent option for long-term TC research. In this study, the quality of MAXSS winds under TC conditions was assessed through statistical analysis, morphological analysis, and spatial variance evaluation. The statistical comparison among SAR, ASCAT, and MAXSS winds indicates a good consistency between SAR and MAXSS wind speeds, but an apparent overestimation of MAXSS winds compared to ASCAT results, aligning with our expectations. Notably, the wind sensitivity of MAXSS winds can be up to approximately 45m/s meanwhile in relatively lower noise or uncertainties. It suggests the great potential of the MAXSS products in TC research. However, the blurring effects persist in the products, behaving as the extension of TC eyewall structures and the loss of small-scale information. In summary, MAXSS has introduced a new and powerful global merged wind product suitable for TC studies. The preliminary quality assessment presented in the paper proves the value of these products. Nevertheless, some further improvements in TC inner structures could contribute to the more effective application of these products in the future.

Defining the background error covariance matrix accurately is currently a research hotspot in variational data assimilation. The balance relationship is a highly significant physical quantity in the background error covariance matrix, as it characterizes the dynamical constraint relationships among control variables and determines how incremental information propagates in the analysis space. Hence, it is crucial for constructing dynamically coordinated analysis fields. In this paper, we analyze the three main balance coefficients that represent the geostrophic balance relationship, quasi-geostrophic balance relationship, and the relationship between the mass field and velocity field. We investigate the impact of ridge regression methods, sample size, and sampling months on the balance coefficients. The results show that ridge regression coefficients are an effective approach to address multicollinearity issues, although they may introduce systematic biases. Additionally, the statistical results of the balance coefficients are significantly influenced by the sample size and sampling months, which cannot be neglected.

Atmospheric motion vectors, which can be used to infer wind speed and direction based on the trajectory of cloud movement, are instrumental in enhancing atmospheric wind-field insights, contributing notably to wind-field optimization and forecasting. However, a widespread problem with vector data is their inaccuracy, which, when coupled with the mediocre effectiveness of existing correction methods, limits their practical utility in forecasting, often falling short of expectations. Deep-learning techniques are used to refine atmospheric motion vector data from the FY-4A satellite, notably enhancing data quality. Post-training data undergoes a thorough analysis using a quality evaluation function, followed by its integration into a numerical weather prediction system in order to conduct forecasting experiments. Results indicate a marked improvement in data quality post-error correction by the model, characterized by a significant reduction in root mean square error and a notable increase in correlation coefficients. Furthermore, refined data demonstrate a considerable enhancement in the accuracy of meteorological element forecasts, particularly for Asian and Western Pacific regions.

Sea surface wind (SSW) is a crucial parameter for meteorological and oceanographic research, and accurate observation of SSW is valuable for a wide range of applications. However, most existing SSW data products are at a coarse spatial resolution, which is insufficient, especially for regional or local studies. Therefore, in this paper, to derive finer-resolution estimates of SSW, we present a novel statistical downscaling approach for satellite SSW based on generative adversarial networks and dual learning scheme, taking WindSat as a typical example. The dual learning scheme performs a primal task to reconstruct high resolution SSW, and a dual task to estimate the degradation kernels, which form a closed loop and are simultaneously learned, thus introducing an additional constraint to reduce the solution space. The integration of a dual learning scheme as the generator into the generative adversarial network structure further yield better downscaling performance by fine-tuning the generated SSW closer to high-resolution SSW. Besides, a model adaptation strategy was exploited to enhance the capacity for downscaling from low-resolution SSW without high-resolution ground truth. Comprehensive experiments were conducted on both the synthetic paired and unpaired SSW data. In the study areas of the East Coast of North America and the North Indian Ocean, in this work, the downscaling results to 0.25° (high resolution on the synthetic dataset), 0.03125° (8× downscaling), and 0.015625° (16× downscaling) of the proposed approach achieve the highest accuracy in terms of root mean square error and R-Square. The downscaling resolution can be enhanced by increasing the basic blocks in the generator. the highest downscaling reconstruction quality in terms of peak signal-to-noise ratio and structural similarity index was also achieved on the synthetic dataset with high-resolution ground truth. The experimental results demonstrate the effectiveness of the proposed downscaling network and the superior performance compared with the other typical advanced downscaling methods, including bicubic interpolation, DeepSD, dual regression networks, and adversarial DeepSD.

Compared with traditional microwave humidity sounding capabilities at 183 GHz, new channels at 118 GHz have been mounted on the second generation of the Microwave Humidity Sounder (MWHS-2) onboard the Chinese FY-3C and FY-3D polar orbit meteorological satellites, which helps to perform moisture sounding. In this study, as the all-sky approach can manage non-linear and non-Gaussian behavior in cloud- and precipitation-affected satellite radiances, the MWHS-2 radiances in all-sky conditions were first assimilated in the Yinhe four-dimensional variational data assimilation (YH4DVAR) system. The data quality from MWHS-2 was evaluated based on observation minus background statistics. It is found that the MWHS-2 data of both FY-3C and FY-3D are of good quality in general. Six months of MWHS-2 radiances in all-sky conditions were then assimilated in the YH4DVAR system. Based on the forecast scores and observation fits, we conclude that the all-sky assimilation of the MWHS-2 at 118- and 183-GHz channels on FY-3C/D is beneficial to the analysis and forecast fields of the temperature and humidity, and the impact on the forecast skill scores is neutral to positive. Additionally, we compared the impacts of assimilating the 118-GHz channels and the equivalent Advanced Microwave Sounding Unit-A (AMSUA) channels on global forecast accuracy in the absence of other satellite observations. Overall, the impact of the 118-GHz channels on the forecast accuracy is not as large as that for the equivalent AMSUA channels. Nevertheless, all-sky radiance assimilation of MWHS-2 in the YH4DVAR system has indeed benefited from the 118-GHz channels.

Increasing the spatial coverage and temporal resolution of Earth surface monitoring can significantly improve forecasting or monitoring capabilities in the context of smart city, such as extreme weather forecasting, ecosystem monitoring and anthropogenic impact monitoring. As an essential data source for Earth’s surface monitoring, most satellite observations exist data gaps due to various factors like the limitations of measuring equipment, the interferences of environments, and the delay or loss of data updates. Although many efforts have been conducted to fill the gaps in the last decade, the existing techniques cannot efficiently address the problem. In this paper, we extensively study the gap-filling problem of satellite observations using imbalanced learning. Specifically, we propose a framework called Reanalysis to Satellite (R2S) to simulate satellite observations with reanalysis data. In the R2S framework, we propose a generic method called Spatial Temporal Match (STM), matching reanalysis data and satellite observations to construct the Reanalysis-Satellite (R-S) dataset used to train the model. Based on the R-S dataset, we propose a novel method called Semi-imbalanced (SIMBA) to handle the imbalance problem of gap-filling by taking advantages of traditional machine learning and imbalanced learning. We construct a hybrid model in the R2S framework for the Soil Moisture Active Passive (SMAP) satellite observations of the tropical cyclone wind speed. Extensive experiments demonstrate the hybrid model outperforms the traditional machine learning model and closely approximates in situ observations.

In order to improve the humidity analysis of the WRF model, a new multivariable balance constraint scheme has been introduced to estimate wet variable's background error information from a series of historical forecasts. The new scheme consists of three critical procedures: physical transformation, vertical transformation and horizontal transformation. By removing the balanced part associated with other control variables, the unbalanced part of relative humidity is used as the new wet control variable. Statistical results show that relative humidity's background error structure appears an obviously localized characterization, which has a large negative value on model high level in the vertical direction and a stable characteristic length scales about 20km in the horizontal direction.

A more efficient noise filtering technique is needed in ensemble data assimilation, to improve traditional spectral filtering methods that cannot reflect the local characteristics of spatial scales. In this paper, we present the design of a novel constrained wavelet threshold denoising method (CWTDNM) by introducing an improved threshold value and a new constraining parameter. The proposed method aims to filter noise swamped over different scales. We prepared an ideal experiment object based on the two-dimensional barotropic vorticity equation. A suitable wavelet basis function (i.e., Db11) and the optimal number of decomposition levels (i.e., five) were first selected. The results show that, given the wavelet coefficients are constrained by the parameter, the CWTDNM can produce better filtering results with the smallest root mean square error (RMSE) compared to similar methods. In addition, the filtering accuracy of 10 ensemble sample variances using the CWTDNM is equivalent to that estimated directly from 80 ensemble samples, but with the runtime reduced to approximately one-seventh. Furthermore, a large peak signal-to-noise ratio, which implies a low RMSE, suggests that the proposed method suitably preserves most of the information after denoising.