Data Assimilation Method Research Articles

Vertical Localization for Strongly Coupled Data Assimilation: Experiments in a Global Coupled Atmosphere‐Ocean Model

AbstractStrongly coupled data assimilation allows observations of one Earth system component (e.g., the ocean) to directly update another component (e.g., the atmosphere). The majority of the information transfer in strongly coupled atmosphere‐ocean systems is passed through vertical correlations between atmospheric boundary layer and ocean mixed layer fields. In this work we use correlations from a global, coupled model to study vertical observation‐space localization techniques for strongly coupled data assimilation. We generate target correlations using a bootstrapping approach from a single 24 hr forecast from a realistic global, weakly coupled atmosphere‐ocean cycling system with an 80‐member ensemble, which is the ensemble size currently used by the NOAA operational global data assimilation system. We compare data assimilation methods with different localization schemes using single‐update, offline experiments. We develop a new strategy for optimal observation space localization, called Empirical Optimal R‐localization (EORL), to give an upper bound on the improvement we can expect with any localization scheme. We then evaluate Gaspari‐Cohn localization, which is a commonly used parametric localization function and review its performance with respect to the optimal localization scheme. We investigate how the performance of these localization strategies changes with increasing ensemble sizes. Our results show that strongly coupled data assimilation has the potential to be an improvement over weakly coupled data assimilation when large ensembles are used. We also show that the Gaspari‐Cohn localization function does not appear to be a particularly good choice for cross‐fluid vertical localization.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

Beyond assimilation of leaf area index: Leveraging additional spectral information using machine learning for site-specific soybean yield prediction

Assimilating external observations of crop state in cropping system models is essential for making spatially explicit predictions of crop variables relevant in precision agriculture. Satellite-based leaf area index (LAI) estimates have been the most frequent variable used as a proxy of actual crop growth. However, additional information beyond LAI, like canopy N content, water content, and structure, can be retrieved from satellite observations. Including such variables by data assimilation directly is difficult because many crop models do not have corresponding state variables or the relationship between the observations and the process that regulates crop growth is unclear. Therefore, other approaches are required to include such information. In this study, we investigate the improvement in the predicted yield and feature impact on model outputs by using a hybrid approach that combines observations from Sentinel-1 and 2 time-series with the outputs from a process-based model embedded in a data assimilation framework and uses the Gradient-boosted trees regressor (GBTR) as predictive model. We used two regions with soybean fields: the US (13 K points) and Uruguay (400 K points). We found an advantage when using the GBTR as the predictive model (reduced RRMSE by ∼16%) compared to data assimilation. Adding the vegetation indices had a marginal improvement (reduced RRMSE by ∼1%), while the impact of adding reflectance and backscatter values was negative. The satellite-based features had a very small importance score, while features' impact on prediction was predominantly unclear, explaining the marginal predictive power added by satellite-based features. We found that features from the reproductive stages had the highest importance, while the importance of an index related to drought stress (NMDI) across the growing season provided insights for further improvement of data assimilation methods. However, more studies are required to better disentangle pathways towards further improvement in constraining crop models by ingesting satellite observations.

Projection of 4D seismic onto the ensemble observation subspace for data assimilation

Time-lapse (4D) seismic data offer valuable insights into fluid movements and pressure changes within reservoirs, thus aiding the updating of numerical models used in hydrocarbon recovery and geological CO2 storage. However, it is essential to characterize both the uncertainties in the data and the limitations in the forward model to effectively utilize this information. In the context of ensemble-based data assimilation methods, this objective is accomplished through the utilization of the data-error covariance matrix, denoted as Ce. The selection of an appropriate Ce is of paramount importance, as it determines the level of accuracy required to match the data and influences the relative weight assigned to various data sources and prior information during the computation of model updates.Despite significant efforts, the practical estimation of Ce, accounting for both data and model errors, remains a challenging task. This paper presents a novel methodology for estimating Ce within an ensemble-based 4D seismic data assimilation framework. The approach involves projecting observed seismic data onto the subspace defined by predicted data from the prior ensemble and estimating Ce based on the residuals—the difference between observed and projected 4D seismic data. The proposed methodology is tested through application with actual data from three real-world reservoir cases.

Optimizing Parameters in the Common Land Model by Using Gravity Recovery and Climate Experiment Satellite Observations

Terrestrial water storage (TWS) is pivotal in understanding environmental dynamics, climate change, and human impacts. Despite the utility of land surface models, uncertainties persist in their parameterization schemes. This study employs GRACE (Gravity Recovery and Climate Experiment) satellite data to optimize the runoff parameterization scheme within the Common Land Model by a data assimilation and parameter optimization method. The optimization algorithm sets an adjustment factor that varies with time and space for runoff simulation and updates it along with the running of the land surface model. The evaluation reveals that there are improved correlation coefficients and reduced root mean square errors compared to GRACE observations. Independent assessments by using in situ river discharge observations demonstrate enhanced model performance, particularly in mountainous regions such as western North America. This study underscores the efficacy of integrating GRACE data to improve land surface model parameterization, offering more accurate predictions of TWS changes.

Space Weather with Quantified Uncertainties: Improving Space Weather Predictions with Data-Driven Models of the Solar Atmosphere and Inner Heliosphere

To address Objective II of the National Space Weather Strategy and Action Plan “Develop and Disseminate Accurate and Timely Space Weather Characterization and Forecasts” and US Congress PROSWIFT Act 116–181, our team is developing a new set of open-source software that would ensure substantial improvements of Space Weather (SWx) predictions. On the one hand, our focus is on the development of data-driven solar wind models. On the other hand, each individual component of our software is designed to have accuracy higher than any existing SWx prediction tools with a dramatically improved performance. This is done by the application of new computational technologies and enhanced data sources. The development of such software paves way for improved SWx predictions accompanied with an appropriate uncertainty quantification. This makes it possible to forecast hazardous SWx effects on the space-borne and ground-based technological systems, and on human health. Our models include (1) a new, open-source solar magnetic flux model (OFT), which evolves information to the back side of the Sun and its poles, and updates the model flux with new observations using data assimilation methods; (2) a new potential field solver (POT3D) associated with the Wang–Sheeley–Arge coronal model, and (3) a new adaptive, 4-th order of accuracy solver (HelioCubed) for the Reynolds-averaged MHD equations implemented on mapped multiblock grids (cubed spheres). We describe the software and results obtained with it, including the application of machine learning to modeling coronal mass ejections, which makes it possible to improve SWx predictions by decreasing the time-of-arrival mismatch. The tests show that our software is formally more accurate and performs much faster than its predecessors used for SWx predictions.

Optimizing the key parameter to accelerate the recovery of AMOC under a rapid increase of greenhouse gas forcing

Atlantic Meridional Overturning Circulation (AMOC) plays a central role in long-term climate variations through its heat and freshwater transports, which can collapse under a rapid increase of greenhouse gas forcing in climate models. Previous studies have suggested that the deviation of model parameters is one of the major factors in inducing inaccurate AMOC simulations. In this work, with a low-resolution earth system model, the authors try to explore whether a reasonable adjustment of the key model parameter can help to re-establish the AMOC after its collapse. Through a new optimization strategy, the extra freshwater flux (FWF) parameter is determined to be the dominant one affecting the AMOC's variability. The traditional ensemble optimal interpolation (EnOI) data assimilation and new machine learning methods are adopted to optimize the FWF parameter in an abrupt 4×CO2 forcing experiment to improve the adaptability of model parameters and accelerate the recovery of AMOC. The results show that, under an abrupt 4×CO2 forcing in millennial simulations, the AMOC will first collapse and then re-establish by the default FWF parameter slowly. However, during the parameter adjustment process, the saltier and colder sea water over the North Atlantic region are the dominant factors in usefully improving the adaptability of the FWF parameter and accelerating the recovery of AMOC, according to their physical relationship with FWF on the interdecadal timescale.

Hybrid IFDMB/4D-Var inverse modeling to constrain the spatiotemporal distribution of CO and NO2 emissions using the CMAQ adjoint model

We performed a hybrid approach that combines the iterative finite difference mass balance (IFDMB) and four-dimensional variational data assimilation (4D-Var) methods to effectively constrain the spatiotemporal distribution of emissions. To quantitatively compare the performance of inverse modeling in constraining CO and NO2 emissions in South Korea spatiotemporally, we conducted a model-based twin experiment for three inverse modeling methods: IFDMB, 4D-Var, and hybrid inversions. We performed numerical modeling using the Community Multi-scale Air Quality (CMAQ) and its adjoints to calculate the values required for inverse modeling. As a result, the IFDMB inversion can effectively constrain the average spatial distribution of emissions. Meanwhile, the 4D-Var inversion can help estimate temporal variations in emissions, but it is not effective in regions with large prior emission errors. The hybrid inversion showed the best performance in constraining the spatiotemporal distribution of emissions because it combined the strengths of the two aforementioned methods. Furthermore, to compare the performance of the inverse modeling of pollutants with different chemical properties, we conducted additional inverse modeling for highly reactive NO2. After the application of inverse modeling, the emission errors of NO2 (18.339%) were larger than those of CO (10.593%). This difference in inverse modeling errors was due to the greater nonlinear relationship between emissions and concentrations in the inverse modeling process for NO2, which is more reactive compared to CO. In this study, the ideal modeling tests were performed to quantitatively assess the performance of inverse modeling. In future studies, we expect to apply the hybrid inversion approach used in this study to inverse modeling using actual observations.

Data assimilation to determine the electrohydrodynamic force of plasma actuator

The electrohydrodynamic (EHD) force is the main flow control mechanism of plasma actuators (PAs), and a thorough understanding of the EHD force field is important for the practical application of PAs. However, because it is difficult to directly measure the EHD force field, a methodology for determining the unobservable EHD force field is required. In this study, we developed a new methodology using a data assimilation (DA) method which utilizes both experimental data and numerical simulation. The methodology was based on computational fluid dynamics and ensemble four-dimensional variational method and enabled us to determine the unobservable EHD force field from experimentally observable flow field data. Through numerical experiments, we demonstrated that the methodology can inversely estimate the EHD force field using time-series velocity and density field data with sufficient precision. Moreover, the results show that either the velocity or density field data are sufficient to estimate the EHD force field. The proposed DA methodology provides key factors for determining the flow field, such as the maximum value, extent, and vertical position of the maximum value of the EHD force field. Our methodology that estimates EHD force fields from the experimentally observed flow field data is also useful for understanding other EHD flows, which are the phenomena involving plasma and flow.

Dynamic Neural Assimilation: a deep learning and data assimilation model for air quality predictions

Ambient air pollution is known to be a serious issue that has an impact on human health and the environment. Assessing air quality is of the utmost importance to protect human health and the environment. Different tools are available, from monitoring stations to complex models. These systems are capable of accurately predicting air quality levels, but they are often computationally very expensive which makes them poorly efficient. In this paper, we developed a novel model called Dynamic Neural Assimilation (DyNA) integrating Recurrent Neural Networks and Data Assimilation methods to derive a physics-informed system capable of accurately forecasting air pollution tendencies and investigating the relationship with industrial statistics. DyNA is trained in historical data and is fine-tuned as soon as new data comes available. We trained and tested the system on real data provided by the air quality monitoring stations located in Italy from the European Environment Agency and simulated results derived from the air quality modelling system Atmospheric Modelling System-Model to support the International Negotiation on atmospheric pollution on a National Italian level. We analysed air pollution data in Italy from the years 2003–2010 and studied its correlation with nearby industries in some regions where monitoring sensors were available.

Intercomparison of initialization methods for seasonal-to-decadal climate predictions with the NorCPM

Initialization is essential for accurate seasonal-to-decadal (S2D) climate predictions. The initialization schemes used differ on the component initialized, the Data Assimilation method, or the technique. We compare five popular schemes within NorCPM following the same experimental protocol: reanalysis from 1980 to 2010 and seasonal and decadal predictions initialized from the reanalysis. We compare atmospheric initialization—Newtonian relaxation (nudging)—against ocean initialization—Ensemble Kalman Filter—(ODA). On the atmosphere, we explore the benefit of full-field (NudF-UVT) or anomaly (NudA-UVT) nudging of horizontal winds and temperature (U, V, and T) observations. The scheme NudA-UV nudges horizontal winds to disentangle the role of wind-driven variability. The ODA+NudA-UV scheme is a first attempt at joint initialization of ocean and atmospheric components in NorCPM. During the reanalysis, atmospheric nudging improves the synchronization of the atmosphere and land components with the observed data. Conversely, ODA is more effective at synchronizing the ocean component with observations. The atmospheric nudging schemes are better at reproducing specific events, such as the rapid North Atlantic subpolar gyre shift. An abrupt climatological change using the NudA-UV scheme demonstrates that energy conservation is crucial when only assimilating winds. ODA outperforms atmospheric-initialized versions for S2D global predictions, while atmospheric nudging is preferable for accurately initializing phenomena in specific regions, with the technique’s benefit depending on the prediction’s temporal scale. For instance, atmospheric full-field initialization benefits the tropical Atlantic Niño at 1-month lead time, and atmospheric anomaly initialization benefits longer lead times, reducing hindcast drift. Combining atmosphere and ocean initialization yields sub-optimal results, as sustaining the ensemble’s reliability—required for ODA’s performance—is challenging with atmospheric nudging.

Comparison of 4-dimensional variational and ensemble optimal interpolation data assimilation systems using a Regional Ocean Modeling System (v3.4) configuration of the eddy-dominated East Australian Current system

Abstract. Ocean models must be regularly updated through the assimilation of observations (data assimilation) in order to correctly represent the timing and locations of eddies. Since initial conditions play an important role in the quality of short-term ocean forecasts, an effective data assimilation scheme to produce accurate state estimates is key to improving prediction. Western boundary current regions, such as the East Australia Current system, are highly variable regions, making them particularly challenging to model and predict. This study assesses the performance of two ocean data assimilation systems in the East Australian Current system over a 2-year period. We compare the time-dependent 4-dimensional variational (4D-Var) data assimilation system with the more computationally efficient, time-independent ensemble optimal interpolation (EnOI) system, across a common modelling and observational framework. Both systems assimilate the same observations: satellite-derived sea surface height, sea surface temperature, vertical profiles of temperature and salinity (from Argo floats), and temperature profiles from expendable bathythermographs. We analyse both systems' performance against independent data that are withheld, allowing a thorough analysis of system performance. The 4D-Var system is 25 times more expensive but outperforms the EnOI system against both assimilated and independent observations at the surface and subsurface. For forecast horizons of 5 d, root-mean-squared forecast errors are 20 %–60 % higher for the EnOI system compared to the 4D-Var system. The 4D-Var system, which assimilates observations over 5 d windows, provides a smoother transition from the end of the forecast to the subsequent analysis field. The EnOI system displays elevated low-frequency (>1 d) surface-intensified variability in temperature and elevated kinetic energy at length scales less than 100 km at the beginning of the forecast windows. The 4D-Var system displays elevated energy in the near-inertial range throughout the water column, with the wavenumber kinetic energy spectra remaining unchanged upon assimilation. Overall, this comparison shows quantitatively that the 4D-Var system results in improved predictability as the analysis provides a smoother and more dynamically balanced fit between the observations and the model's time-evolving flow. This advocates the use of advanced, time-dependent data assimilation methods, particularly for highly variable oceanic regions, and motivates future work into further improving data assimilation schemes.

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This paper describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED . The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This paper provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.

Dynamical Gaussian, lognormal, and reverse lognormal maximum‐likelihood ensemble filter

AbstractWe present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve.

Which data assimilation method to use and when: unlocking the potential of observations in shoreline modelling

Shoreline predictions are essential for coastal management. In this era of increasing amounts of data from different sources, it is imperative to use observations to ensure the reliability of shoreline forecasts. Data assimilation has emerged as a powerful tool to bridge the gap between episodic and imprecise spatiotemporal observations and the incomplete mathematical equations describing the physics of coastal dynamics. This research seeks to maximize this potential by assessing the effectiveness of different data assimilation algorithms considering different observational data characteristics and initial system knowledge to guide shoreline models towards delivering results as close as possible to the real world. Two statistical algorithms (stochastic ensemble and extended Kalman filters) and one variational algorithm (4D-Var) are incorporated into an equilibrium cross-shore model and a one-line longshore model. A twin experimental procedure is conducted to determine the observation requirements for these assimilation algorithms in terms of accuracy, length of the data collection campaign and sampling frequency. Similarly, the initial system knowledge needed and the ability of the assimilation methods to track the system nonstationarity are evaluated under synthetic scenarios. The results indicate that with noisy observations, the Kalman filter variants outperform 4D-Var. However, 4D-Var is less restrictive in terms of initial system knowledge and tracks nonstationary parametrizations more accurately for cross-shore processes. The findings are demonstrated at two real beaches governed by different processes with different data sources used for calibration. In this contribution, the coastal processes assimilated thus far in shoreline modelling are extended, the 4D-Var algorithm is applied for the first time in the field of shoreline modelling, and guidelines on which assimilation method can be most beneficial in terms of the available observational data and system knowledge are provided.

A generalized data assimilation architecture of digital twin for complex process industrial systems

As one of the critical cores of digital twin (DT), data assimilation (DA) can maintain consistency and synchronization between DT and physical system. Kalman filtering is a common DA method, but its estimation performance is deteriorated by factors such as model inaccuracy and time-varying noise covariance in practical applications. The errors caused by these multiple uncertainties are all coupled to the measurements, which augments the difficulty for DT to obtain physical system information. In order to tackle the DA problem with multiple uncertainties, this paper proposes a generalized DA architecture for DT in sophisticated process industry. First, by combining Stein variational gradient descent and nonlinear Bayesian filtering paradigm, a recursive estimation framework is established, which has higher accuracy in estimating the noise covariance compared to traditional methods. Second, to effectively deal with model inaccuracy by using filtering residuals containing time-varying noise, we propose a neural network and modified wavelet-based model error compensation (NNMW-MEC) block. Based on the modified wavelet technique, the filtering residual denoising built in NNMW-MEC can better cope with time-varying noise compared to existing wavelets, and extract the low-frequency signal involving model error information from noisy residual smoothly. In addition, because of the neural network-based state-compensation subblock, NNMW-MEC has more outstanding ability in compensating the state deviations with large changing range. Finally, we take the boiler system in a coal-fired power plant as an example to verify the effectiveness of our architecture. Experimental results show that the DA architecture proposed in this paper can improve the estimation performance of DT under inaccurate models and uncertain noise statistics.

Removing the systematic errors of the model in operational oceanography forecasting system using data assimilation method

For the operational oceanography forecast, the synoptic forecast error is partly from the long-term systematic bias of the model, which can be partly counteracted by adjusting the values of the physical parameters. To this end, a four-dimensional optimization system is implemented into the South China Sea operational oceanography forecasting system, to adjust the values of multi-parameters using data assimilation method. By assimilating Argo temperature profiles of 51 days in the model domain, five physical parameters (coefficients of horizontal/vertical diffusion/viscosity and linear bottom drag) of the model have been adjusted simultaneously, and then the optimal values are obtained. The RMSE of temperature simulations in the assimilation window decreases from 1.17 to 0.97 K, when using the optimal values. The validation of the freerun experiments shows that the temperature RMSE decreases from 0.97 to 0.88 K, which indicates that the optimal values are still valid in a longer and independent period. Finally, the validation of the hindcast experiments shows that at the synoptic scale the temperature RMSE decreases from 0.90 to 0.80 K and other variables also present improvements. It hints that it is feasible to reduce the synoptic forecast errors by adjusting the parameter values at the climatological scale to partly counteract the systematic bias of the model. Therefore, it also provides a potential pathway to improve the synoptic forecast skill for the operational oceanography forecasting system.

Evapotranspiration prediction for European forest sites does not improve with assimilation of in situ soil water content data

Abstract. Land surface models (LSMs) are an important tool for advancing our knowledge of the Earth system. LSMs are constantly improved to represent the various terrestrial processes in more detail. High-quality data, freely available from various observation networks, are being used to improve the prediction of terrestrial states and fluxes of water and energy. To optimize LSMs with observations, data assimilation methods and tools have been developed in the past decades. We apply the coupled Community Land Model version 5 (CLM5) and Parallel Data Assimilation Framework (PDAF) system (CLM5-PDAF) for 13 forest field sites throughout Europe covering different climate zones. The goal of this study is to assimilate in situ soil moisture measurements into CLM5 to improve the modeled evapotranspiration fluxes. The modeled fluxes will be evaluated using the predicted evapotranspiration fluxes with eddy covariance (EC) systems. Most of the sites use point-scale measurements from sensors placed in the ground; however, for three of the forest sites we use soil water content data from cosmic-ray neutron sensors, which have a measurement scale closer to the typical land surface model grid scale and EC footprint. Our results show that while data assimilation reduced the root-mean-square error for soil water content on average by 56 % to 64 %, the root-mean-square error for the evapotranspiration estimation is increased by 4 %. This finding indicates that only improving the soil water content (SWC) estimation of state-of-the-art LSMs such as CLM5 is not sufficient to improve evapotranspiration estimates for forest sites. To improve evapotranspiration estimates, it is also necessary to consider the representation of leaf area index (LAI) in magnitude and timing, as well as uncertainties in water uptake by roots and vegetation parameters.

Regional Comparison of Performance between EnKF and EnOI in the North Pacific

Abstract The North Pacific is divided into different regions based on ocean currents and sea surface temperature (SST) distribution. Data assimilation is a useful tool for generating accurate ocean estimates because of the limited availability of observational data. This study compared the performances of two data assimilation methods, ensemble optimal interpolation (EnOI) and ensemble Kalman filter (EnKF), in various North Pacific subregions using an ocean model configured with the Regional Ocean Modeling System (ROMS). Both methods assimilated spaceborne SST observations, and the simulation results varied by subregion. The study found that EnKF and EnOI methods performed better than the control model in all regions when compared against satellite SST. EnOI reproduced SST as well as EnKF and required fewer computational resources. However, EnOI performed worse than the control model at sea surface height (SSH) in the equatorial region, while EnKF’s performance improved. This was due to the crushed mean state in the EnOI, which used long-term historical data as an ensemble member. El Niño–Southern Oscillation at the equator drove substantial interannual variability that crushed the ensemble mean of SSH in the EnOI. It is crucial to use a suitable assimilation method for the target area, considering the regional properties of ocean variables. Otherwise, the performance of the assimilated model may be even worse than that of the control model. While EnKF is better suited for regions with high variability in ocean variables, EnOI requires fewer computational resources. Thus, it is crucial to use a suitable assimilation method for accurately predicting and understanding the dynamics of the North Pacific.

A Hybrid Data‐Driven and Data Assimilation Method for Spatiotemporal Forecasting: PM2.5 Forecasting in China

AbstractSpatiotemporal forecasting involves generating temporal forecasts for system state variables across spatial regions. Data‐driven methods such as Convolutional Long Short‐Term Memory (ConvLSTM) are effective in capturing both spatial and temporal correlations, but they suffer from error accumulation and accuracy loss as forecasting time increases due to the nonlinearity and uncertainty in physical processes. To address this issue, we propose to combine data‐driven and data assimilation (DA) methods for spatiotemporal forecasting. The accuracy of the data‐driven ConvLSTM model can be improved by periodically assimilating real‐time observations using the ensemble Kalman filter (EnKF) approach. This proposed hybrid ConvLSTM‐EnKF method is demonstrated through PM2.5 forecasting in China, which is a challenging task due to the complexity of topographical and meteorological conditions in the region, the need for high‐resolution forecasting over a large study area, and the scarcity of observations. The results show that the ConvLSTM‐EnKF method outperforms conventional methods and can provide satisfactory operational PM2.5 forecasts for up to 1 month with spatially averaged RMSE below 20 μg/m3 and correlation coefficient (R) above 0.8. In addition, the ConvLSTM‐EnKF method shows a substantial reduction in CPU time when compared to the commonly used NAQPMS‐EnKF method, up to three orders of magnitude. Overall, the use of data‐driven models provides efficient forecasts and speeds up DA. This hybrid ConvLSTM‐EnKF is a novel operational forecasting technique for spatiotemporal forecasting and is used in real spatiotemporal forecasting for the first time.