Kalman Filter Data Assimilation Research Articles

Ensemble Kalman Filter Data Assimilation into the Surface Flux Transport Model to Infer Surface Flows: An Observing System Simulation Experiment

Knowledge of the global magnetic field distribution and its evolution on the Sun’s surface is crucial for modeling the coronal magnetic field, understanding the solar wind dynamics, computing the heliospheric open flux distribution, and predicting the solar cycle strength. As the far side of the Sun cannot be observed directly and high-latitude observations always suffer from projection effects, we often rely on surface flux transport (SFT) simulations to model the long-term global magnetic field distribution. Meridional circulation, the large-scale north–south component of the surface flow profile, is one of the key components of the SFT simulation that requires further constraints near high latitudes. Prediction of the photospheric magnetic field distribution requires knowledge of the flow profile in the future, which demands reconstruction of that same flow at the current time so that it can be estimated at a later time. By performing Observing System Simulation Experiments, we demonstrate how the ensemble Kalman filter technique, when used with an SFT model, can be utilized to make “posterior” estimates of flow profiles into the future that can be used to drive the model forward to forecast the photospheric magnetic field distribution.

An Enhanced Long-Term Wind Speed Prediction Using Dynamic Unified Ensemble Learning and Data Assimilation Techniques: A Case Study in Tamil Nadu, India

Reliable wind speed prediction is essential for effective grid management since wind energy is a key component of renewable energy generation. However, controlling wind speed just right is no easy feat since the wind flow changes constantly. This paper presents an innovative method for predicting wind speeds in the future. It uses state-of-the-art data assimilation methods and a dynamic unified ensemble learning model. For efficient wind energy planning and monitoring, WSP accuracy is crucial. Data from a single site limited the accuracy of WSPs in previous research. An improved accuracy of long-term wind speed predictions is achieved by the proposed model via the integration of data assimilation and ensemble learning. To increase forecast accuracy, the model uses sophisticated data assimilation methods like the Kalman filter to combine data from many sources. Specifically, the model employs the Stacked CNN + BiLSTM with Data Assimilator (SCBLSTM+DA) technique, which integrates Wind Speed (WS) data from adjacent areas with the CNN + BiLSTM-based Ensemble Learning Model (ELM) and the Four-Dimensional Variational and Ensemble Kalman Filter (4DVar/EnKF) Data Assimilation method. Using real-world wind speed data from nine meteorological stations in Tamil Nadu, India, we find that current prediction models, including both classical statistical and cutting-edge machine learning models, perform better. Further, unlike standalone models, the suggested model shows less susceptibility to changes in prediction time scales. Promising a solution to improve long-term wind speed predictions accuracy, this study has significant consequences for wind energy management and production.

Federal Algorithm Design and Numerical Experiments of Ensemble Kalman Filter Data Assimilation Analysis Process

Based on the federated Kalman filter proposed by Carlson with linear systems, we propose a federated computing scheme for the ensemble Kalman filter (EnKF) assimilation analysis process for nonlinear systems, and give an optimal information fusion estimation algorithm weighted by diagonal matrix under the linear minimum variance criterion, that is, the assimilation analysis values of each variable in the global estimation are linear combinations of the assimilation analysis values of the corresponding variables in the local estimation of sub-filters, and the calculation of the combination coefficients is given. The federated algorithm of the EnKF assimilation analysis process for nonlinear systems is verified by the Lorenz (1963) system.

Are the Noah and Noah-MP land surface models accurate for frozen soil conditions?

The accurate prediction of frozen soil conditions is a critical component of dynamic terrain characterization for engineering operations in cold regions. Currently the trusted resource for dynamic terrain within the US military uses gridded global soil conditions (i.e., temperature and moisture) generated by the Land Information System (LIS) architecture. LIS combines static terrain data with trusted surface weather information into the Noah land surface model to generate a continuous representation of the global surface conditions. Both the input weather data and the model output land surface state are adjusted to match the observed state using an advanced ensemble Kalman filter data assimilation technique to incorporate in situ and remote sensing observations. While this product has been robustly evaluated under unfrozen conditions only sporadic studies have investigated its ability to accurately simulate freeze/thaw cycles, and soil temperature and moisture under frozen conditions. Here, we present a broad comparison and evaluation of the simulated soil state against an in situ network of soil temperature and moisture distributed across the Continental United States that focuses on the winter season. This comparison includes both the Noah and the newer Noah with multi-parameterization (Noah-MP) land surface models. A comparison of the two models reveals substantial differences in simulated soil moisture, frozen content, and frozen soil strength. In general, Noah predicts colder soils with deeper frost depths, and frozen soils that are slightly stronger than Noah-MP. Initial results evaluating Noah and Noah-MP against in situ observations show that both models have significantly degraded model performance for frozen soil conditions compared to their performance for unfrozen soil. In particular, Noah has a significant and persistent cold bias of approximately −3 K when the soil temperature is below freezing. This cold bias is not present in Noah-MP and further analysis shows that this improvement was almost entirely caused by a better representation of thermal conduction through snow in Noah-MP. Specifically, we find that the bulk effective thermal conductivity of a snowpack is 2× greater in Noah, which allows for greater surface heat loss during the winter and, consequently, lower soil temperatures. This analysis reveals that the more advanced multi-layer snow model in Noah-MP substantially improves the representation of soil temperature during the cold season.

A Quantile-Conserving Ensemble Filter Framework. Part II: Regression of Observation Increments in a Probit and Probability Integral Transformed Space

Abstract Traditional ensemble Kalman filter data assimilation methods make implicit assumptions of Gaussianity and linearity that are strongly violated by many important Earth system applications. For instance, bounded quantities like the amount of a tracer and sea ice fractional coverage cannot be accurately represented by a Gaussian that is unbounded by definition. Nonlinear relations between observations and model state variables abound. Examples include the relation between a remotely sensed radiance and the column of atmospheric temperatures, or the relation between cloud amount and water vapor quantity. Part I of this paper described a very general data assimilation framework for computing observation increments for non-Gaussian prior distributions and likelihoods. These methods can respect bounds and other non-Gaussian aspects of observed variables. However, these benefits can be lost when observation increments are used to update state variables using the linear regression that is part of standard ensemble Kalman filter algorithms. Here, regression of observation increments is performed in a space where variables are transformed by the probit and probability integral transforms, a specific type of Gaussian anamorphosis. This method can enforce appropriate bounds for all quantities and deal much more effectively with nonlinear relations between observations and state variables. Important enhancements like localization and inflation can be performed in the transformed space. Results are provided for idealized bivariate distributions and for cycling assimilation in a low-order dynamical system. Implications for improved data assimilation across Earth system applications are discussed.

Barents-2.5km v2.0: an operational data-assimilative coupled ocean and sea ice ensemble prediction model for the Barents Sea and Svalbard

Abstract. An operational ocean and sea ice forecast model, Barents-2.5, is implemented for short-term forecasting at the coast off northern Norway, the Barents Sea, and the waters around Svalbard. Primary forecast parameters are sea ice concentration (SIC), sea surface temperature (SST), and ocean currents. The model also provides input data for drift modeling of pollutants, icebergs, and search-and-rescue applications in the Arctic domain. Barents-2.5 has recently been upgraded to include an ensemble prediction system with 24 daily realizations of the model state. SIC, SST, and in situ hydrography are constrained through the ensemble Kalman filter (EnKF) data assimilation scheme executed in daily forecast cycles with a lead time up to 66 h. Here, we present the model setup and validation in terms of SIC, SST, in situ hydrography, and ocean and ice velocities. In addition to the model's forecast capabilities for SIC and SST, the performance of the ensemble in representing the model's uncertainty and the performance of the EnKF in constraining the model state are discussed.

Reconstructing cardiac electrical excitations from optical mapping recordings.

The reconstruction of electrical excitation patterns through the unobserved depth of the tissue is essential to realizing the potential of computational models in cardiac medicine. We have utilized experimental optical-mapping recordings of cardiac electrical excitation on the epicardial and endocardial surfaces of a canine ventricle as observations directing a local ensemble transform Kalman filter data assimilation scheme. We demonstrate that the inclusion of explicit information about the stimulation protocol can marginally improve the confidence of the ensemble reconstruction and the reliability of the assimilation over time. Likewise, we consider the efficacy of stochastic modeling additions to the assimilation scheme in the context of experimentally derived observation sets. Approximation error is addressed at both the observation and modeling stages through the uncertainty of observations and the specification of the model used in the assimilation ensemble. We find that perturbative modifications to the observations have marginal to deleterious effects on the accuracy and robustness of the state reconstruction. Furthermore, we find that incorporating additional information from the observations into the model itself (in the case of stimulus and stochastic currents) has a marginal improvement on the reconstruction accuracy over a fully autonomous model, while complicating the model itself and thus introducing potential for new types of model errors. That the inclusion of explicit modeling information has negligible to negative effects on the reconstruction implies the need for new avenues for optimization of data assimilation schemes applied to cardiac electrical excitation.

Comparison of temperature and wind observations in the Tropics in a perfect‐model, global EnKF data assimilation system

Flow‐dependent errors in tropical analyses and short‐range forecasts are analysed using global observing‐system simulation experiments assimilating only temperature, only winds, and both data types using the ensemble Kalman filter (EnKF) Data Assimilation Research Testbed (DART) and a perfect model framework. The idealised, homogeneous observation network provides profiles of wind and temperature data from the nature run for January 2018 using the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM) forced by the observed sea‐surface temperature. The results show that the assimilation of abundant wind observations in a perfect model makes the temperature data in the Tropics largely uninformative. Furthermore, the assimilation of wind data reduces the background errors in specific humidity twice as much as the assimilation of temperature observations. In all experiments, the largest analysis uncertainties and the largest short‐term forecast errors are found in regions of strong vertical and longitudinal gradients in the background wind, especially in the upper troposphere and lower stratosphere over the Indian Ocean and Maritime Continent. The horizontal error correlation scales are on average short throughout the troposphere, just several hundred km. The correlation scales of the wind variables in precipitating regions are half of those in nonprecipitating regions. In precipitating regions, the correlations are elongated vertically, especially for the wind variables. Strong positive cross‐correlations between temperature and specific humidity in the precipitating regions are explained using the Clausius–Clapeyron equation.

Dynamic Assimilation of Deep Learning Predictions to a Process-Based Water Budget

A three-step data assimilation (DA) of deep learning (DL) predictions to a process-based water budget is developed and applied to produce an active, operational water balance for groundwater management. In the first step, an existing water budget model provides forward model predictions of aquifer storage from meteorological observations, estimates of pumping and diversion discharge, and estimates of recharge. A Kalman filter DA approach is the second step and generates updated storage volumes by combining a long short-term memory (LSTM) network, a DL method, and predicted “measurements” with forward model predictions. The third “correction” step uses modified recharge and pumping, adjusted to account for the difference between Kalman update storage and forward model predicted storage, in forward model re-simulation to approximate updated storage volume. Use of modified inputs in the correction provides a mass-conservative water budget framework that leverages DL predictions. LSTM predictor “measurements” primarily represent missing observations due to missing or malfunctioning equipment. Pumping and recharge inputs are uncertain and unobserved in the study region and can be adjusted without contradicting measurements. Because DL requires clean and certain data for learning, a common-sense baseline facilitates interpretation of LSTM generalization skill and accounts for feature and outcome uncertainty when sufficient target data are available. DA, in contrast to DL, provides for explicit uncertainty analysis through an observation error model, which allows the integrated approach to address uncertainty impacts from an LSTM predictor developed from limited outcome observations.

An Ensemble Kalman Filter Data Assimilation Method for the Sea Surface Temperature in the China Seas: Implementation and Simulation Experiments

Data assimilation refers to a method of integrating observation data in the dynamic operation of numerical models on the basis of considering the temporal and spatial distribution of data and the error of observation field and background field. The Ensemble Kalman filter (EnKF) as a technology that has been widely used in the field of atmosphere and ocean has been applied to the ROMS (the Regional Ocean Modeling System) for predicting Sea surface temperature in Yellow, and East China Seas. In order to explore the applicability and effectiveness of the EnKF method for improving the accuracy of marine numerical model, the Sea surface temperature (SST) gained from buoy were used to conduct data assimilation process with EnKF method. Twin experiments have been performed to analysis the sensitivity of this system to the ensemble size and errors in model simulation and observations and a real data assimilation scheme has been conducted to hindcast the SST at the Yellow, and East China Seas during the July of year 2014. The updated results after data assimilation indicate that the model simulation fits observation better when the forecast was updated by observations. The result show that EnKF can effectively reduce the simulation error of complex numerical marine models.

Assimilation of radar‐derived refractivity and radar data in the context of ensemble Kalman filter: Cases study of the Southwest Monsoon Experiment

AbstractRadar‐derived refractivity provides moisture information near the surface, which plays a crucial role in convective initiation and of heavy rain. In this study, the high‐resolution Weather Research and Forecasting local ensemble transform Kalman filter data assimilation system was employed for two cases in the Southwest Monsoon Experiment to conduct two experimental sets. The first set was applied in both cases to investigate the effects of assimilating radar‐retrieved refractivity along with reflectivity and radial wind. The second set was conducted in the second case to examine the benefit of increasing the frequency of refractivity assimilation and investigate the optimal strategy to assimilate refractivity. Results of the two cases revealed that assimilating reflectivity and radial velocity modified near‐surface humidity on the basis of the flow‐dependent error correlation estimated by the ensemble, but the spatial distribution may not be fully accurate, causing underestimation of rainfall. With further refractivity assimilation, stronger convergence and more accurate low‐level moisture, temperature, and wind field corrections were obtained, leading to superior forecasts for both light and heavy rainfall during six hours. The results of the second set indicated that increasing the assimilation interval of refractivity enabled capturing the dramatic moisture variation and enhancing wind convergence, resulting in short‐term forecast improvement. The strategy that solely assimilated refractivity before the appearance of the convection system optimized the correction of environmental moisture, then accurately represented the humidity and strengthened the wind convergence when precipitation occurred. Consequently, the achieved improvement of the short‐term forecast was most noteworthy, particularly for heavy rain.

Flow-induced vibration modeling of bluff bodies with data assimilation

Vortex-induced vibration (VIV) and galloping are two typical flow-induced vibration (FIV) problems of bluff bodies, which often cause fatigue damage or destruction of structures. Therefore, the accurate and effective FIV prediction has become a requirement of the industry in order to prevent structural damage and guide design. Although the semi-empirical model (such as the wake oscillator model) is an efficient FIV prediction tool, the precision ability of existing models is constrained due to empirical parameters and unideal mathematical equations. Generally, the numerical simulation and wind tunnel experiments are relatively accurate methods, but for complex fluid–structure interaction problems, their cost is too high. As a result, a data-driven FIV prediction model is proposed to accomplish effective and high-precision prediction in this study. The Ensemble Kalman filter (ENKF) data assimilation (DA) technique is used to combine the experimental data with a semi-empirical model. First, the sensitivity of empirical parameters is analyzed, and the most sensitive ones are selected as the target parameters for data assimilation. The mean deviation of ensemble (MDE) is proposed to represent the sensitivity of parameters. Then DA-based model is used to predict the galloping and VIV of a rectangular cylinder. The results indicate that the accuracy of the DA-based model is up to 10 times greater than that of the initial semi-empirical model. With the data-driven technology, the typical ‘quasi-steady’ theory of galloping has been improved for low Scruton number values. For the wake oscillator model, assimilating the parameters of the acceleration and velocity coupled terms can improve the prediction accuracy of VIV. Also, this modeling procedure can be regarded as a new parameter identification method from forced and free vibration.

Direct Assimilation of All-Sky GOES-R ABI Radiances in GSI EnKF for the Analysis and Forecasting of a Mesoscale Convective System

Abstract In this study, all-sky GOES-R ABI infrared radiances at their native resolution are assimilated using an enhanced GSI ensemble Kalman filter (EnKF) data assimilation (DA) system, and the impacts of the data on the analysis and forecast of a mesoscale convective system (MCS) are explored. Results show that all-sky ABI BT data can correctly build up observed storms within the model and effectively remove spurious storms in model background through frequent DA cycles. Both bias and root-mean-squared innovation of the background and analysis are significantly reduced during the DA cycles, and free forecasts are improved when verified subjectively and objectively against observed ABI BTs and independent radar reflectivity observations. A horizontal localization radius of 30 km is found to produce the best results while 5-min DA cycles improve the storm analyses over 15-min cycles, but the differences in forecasts are small. Further analyses show that the clearing of spurious clouds by ABI radiance is correctly accompanied by reduction in moisture through background error cross covariance, but overdrying often occurs, which can cause spurious storm decay in the forecast. The problem is reduced when the ensemble mean of observation prior instead of observation prior of the ensemble mean state is used in the ensemble mean state update equation of EnKF. The significant difference between the two ways that the ensemble mean of observation prior is calculated when the observational operator is very nonlinear has not been recognized in earlier cloudy radiance DA studies. Significance Statement Satellite observations in cloudy regions are not used in most current operational weather prediction systems due to complex nonlinear relations between satellite-observed quantities, the radiances, and model state in such regions. The models also must predict clouds reasonably well for cloudy observations to be effectively assimilated. The latest NOAA geostationary satellites can provide radiance observations at high spatial and temporal resolutions and such data in both cloudy- and clear-air regions are assimilated using an advanced data assimilation method into a model that explicitly represents convection. Forecasts up to 4 h are improved by the assimilation while several issues associated with the assimilation are discussed. The study contributes to the eventual use of all-sky satellite radiance data in operational models.

УЧЕТ СКОРРЕЛИРОВАННОСТИ ОШИБОК СПУТНИКОВЫХ ДАННЫХ НАБЛЮДЕНИЙ AMV В АНСАМБЛЕВОЙ СИСТЕМЕ УСВОЕНИЯ ДАННЫХ

The effect of considering correlated errors in AMV (Atmospheric Motion Vectors) satellite observations of wind in the local ensemble transform Kalman filter data assimilation system is studied. It is customary to use a diagonal covariance matrix of errors in observations taking part in assimilation. When assimilating satellite data with correlated errors, the data are thinned, and the values of diagonal elements of the error covariance matrix are often overestimated. This is accompanied by the loss of useful information about the correlation between the errors. The present study uses a different method: the elements of the error covariance matrix for AMV satellite observations are simulated using a second-order autoregressive function. It is shown that such approach reduces the root-mean-square error in initial data for a numerical weather prediction model, in particular on small scales, and improves the forecast quality. It is found that the application of the non-diagonal AMV observation error covariance matrix increases the accuracy of analysis and forecast fields.

Extending ensemble Kalman filter algorithms to assimilate observations with an unknown time offset

Abstract. Data assimilation (DA), the statistical combination of computer models with measurements, is applied in a variety of scientific fields involving forecasting of dynamical systems, most prominently in atmospheric and ocean sciences. The existence of misreported or unknown observation times (time error) poses a unique and interesting problem for DA. Mapping observations to incorrect times causes bias in the prior state and affects assimilation. Algorithms that can improve the performance of ensemble Kalman filter DA in the presence of observing time error are described. Algorithms that can estimate the distribution of time error are also developed. These algorithms are then combined to produce extensions to ensemble Kalman filters that can both estimate and correct for observation time errors. A low-order dynamical system is used to evaluate the performance of these methods for a range of magnitudes of observation time error. The most successful algorithms must explicitly account for the nonlinearity in the evolution of the prediction model.

A Multi‐Model Ensemble Kalman Filter for Data Assimilation and Forecasting

AbstractData assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi‐model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the minimum variance linear unbiased estimator. Here, we formulate and implement a multi‐model ensemble Kalman filter (MM‐EnKF) based on this framework. The MM‐EnKF can combine multiple model ensembles for both DA and forecasting in a flow‐dependent manner; it uses adaptive model error estimation to provide matrix‐valued weights for the separate models and the observations. We apply this methodology to various situations using the Lorenz96 model for illustration purposes. Our numerical experiments include multiple models with parametric error, different resolved scales, and different fidelities. The MM‐EnKF results in significant error reductions compared to the best model, as well as to an unweighted multi‐model ensemble, with respect to both probabilistic and deterministic error metrics.

The effects of estimating a photoionization parameter within a physics-based model using data assimilation

Data assimilation (DA) is the process of merging information from prediction models with noisy observations to produce an estimate of the state of a physical system. In ionospheric physics-based models, the solar ionizing irradiance is commonly estimated from a solar index like F10.7. The goal of this work is to provide the fundamental understanding necessary to appreciate how a DA algorithm responds to estimating an external parameter driving the model’s interpretation of this solar ionizing irradiance. Therefore, in this work we allow the DA system to find the F10.7 value that delivers the degree of photoionization that leads to a predicted electron density field that best matches the observations. To this end, we develop a heuristic model of the ionosphere along the magnetic equator that contains physics from solar forcing and recombination/plasma diffusion, which allows us to explore the impacts of strongly forced system dynamics on DA. This framework was carefully crafted to be both linear and Gaussian, which allows us to use a Kalman filter to clearly see how: (1) while recombination acts as a sink on the information in the initial condition for ionospheric field variables, recombination does not impact the information in parameter estimates in the same way, (2) when solar forcing dominates the electron density field, the prior covariance matrix becomes dominated by its leading eigenvector whose structure is directly related to that of the solar forcing, (3) estimation of parameters for forcing terms leads to a time-lag in the state estimate relative to the truth, (4) the performance of a DA system in this regime is determined by the relative dominance of solar forcing and recombination to that of the smaller-scale processes and (5) the most impactful observations on the electron density field and on the solar forcing parameter are those observations on the sunlit side of the ionosphere. These findings are then illustrated in a full physics-based ionospheric model using an ensemble Kalman filter DA scheme.

Global Gridded Ionospheric Electron Density Derivation During 2006–2016 by Assimilating COSMIC TEC and Its Validation

AbstractThe long‐term accurate specification of the Earth's ionospheric states is crucial to scientific research and applications in the space weather community. In the current work, a global monthly mean three‐dimensional (3‐D) ionospheric electron density product has been obtained during one solar cycle from 2006 to 2016. Specifically, an accurate 3‐D product is reconstructed monthly by assimilating the Constellation Observing System for Meteorology, Ionosphere and Climate slant total electron content (TEC) into an empirical background model via the Kalman filter data assimilation algorithm. The outputs of the results have spatial resolutions of 2° in latitude, 5° in longitude, and 20 km in height, and temporal resolution of 1 hr in universal time. The accuracy and reliability of the results are systematically validated by the critical frequency at the F2 layer from global ionosonde stations, the in situ electron density from the CHAllenging Minisatellite Payload Planar Langmuir Probe, the TEC from the Massachusetts Institute of Technology, and Gravity Recovery and Climate Experiment. We found that the products agree well with the independent observations. Some well‐known ionospheric climatological patterns, including the solar and seasonal variation, annual asymmetry, the Weddell Sea Anomaly, and the longitudinal wave structure, can be well illustrated. The advantages of the products are its 3‐D and gridded electron density and continuous one solar cycle time series (2006–2016). It is useful to study the spatial‐temporal variations in ionospheric states from seasons to decades, which can also be used as the background parameters for atmospheric and ionospheric‐related scientific research and applications.

Spatiotemporal estimation of model error to improve soil moisture analysis in ensemble Kalman filter data assimilation

As a key variable in the surface hydrological cycle and energy balance, soil moisture is often analyzed using data assimilation to improve precise and high spatiotemporal resolution from multisource data. However, accurate estimation of model error in soil moisture data assimilation is not sufficient in spatial and temporal dimensions. This paper proposes a spatiotemporal error estimation method that integrates the spatial and temporal dimensions of the study area into model error estimation. The in-situ data was regarded as the “true value” for the temporal dimensions model error estimation. The triple collocation (TC) technique was used to estimate the spatial error of the model. Based on the aforementioned estimation, a linear method to construct the relationship between spatial and temporal information was proposed to fuse the spatiotemporal model error. Result from the proposed method was compared against the overall model error estimation and spatial estimation methods in ensemble Kalman filter (EnKF) data assimilation. The ERA-Interim reanalysis data and in-situ soil moisture data from Washington State in 2016 were used to evaluate the performance of EnKF data assimilation. Using statistical metrics, including the root mean square error (RMSE), the mean bias error (MBE), and the Pearson correlation coefficient (i.e., R-value), the results show that our proposed approach, which uses spatiotemporal approach to model error estimation in EnKF data assimilation, yielded more accurate soil moisture estimates. When ERA-Interim reanalysis soil moisture data was used as the reference data, compared with the overall model error estimation EnKF Data Assimilation Experiment, RMSE and MBE of spatiotemporal model error estimation EnKF Data Assimilation Experiment were reduced by 0.0062 and 0.0061 m3 / m3, respectively, and R remained basically unchanged. When using in-situ measurements as reference data, RMSE and MBE decreased by 0.0034 and 0.0038 m3 / m3, respectively, and R increased by 0.0365. Compared with the other estimation approaches in the experiments, the spatiotemporal error estimation approach greatly improved the estimation accuracy of soil moisture analysis, yielding the closest values and variation trends with the in-situ measurements. Fully considering the temporal and spatial variation of model error and improving the estimation accuracy of model error can provide more accurate model information for data assimilation. The proposed method and framework in this paper can be used in model error estimation and data assimilation, particularly in the fields of numerical weather forecasting, natural environment monitoring, and geographical environment research.

Calibration of RANS model constant based on data assimilation and accurate simulation of separated flow

To improve the prediction accuracy of separated flow based on the Reynolds Averaged Navier–Stokes model, the model constants of the baseline Reynolds stress model are calibrated by the ensemble Kalman filter data assimilation method. The separated flow in a diffuser is taken as the object, and the wall pressure coefficients of the diffuser are used as the driving data. The results show that the method that recalibrates the model constants based on data assimilation is easy to implement and is an effective method. The wall pressure coefficients and the separation regions of the diffuser predicted by the baseline Reynolds stress model with the default model constants deviate greatly from the experimental observations. By recalibrating the model constants, the prediction accuracy of separated flow based on the baseline Reynolds stress model is improved. This provides an idea for the accurate simulation of separated flow based on the Reynolds Averaged Navier–Stokes model in engineering applications.