Ensemble Square Root Filter Research Articles

Scale-dependent inflation algorithms for ensemble Kalman filters

Abstract Ensemble-based data assimilation methods often suffer sampling errors due to limited ensemble sizes and model errors, which can result in filter divergence. One method to avoid filter divergence is inflation, which inflates ensemble perturbations to increase ensemble spread and account for model errors. The commonly applied inflation methods, including the multiplicative inflation, relax to prior spread (RTPS), and additive inflation, often use a constant inflation parameter. To capture different error growths at different scales, a scale-dependent inflation is proposed here, which applies different inflation magnitudes for variables associated with different scales. Results from the two-scale Lorenz05 model III show that for the ensemble square-root filter (EnSRF) and integrated hybrid ensemble Kalman filter with ensemble mean updated by hybrid background error covariances (IHEnKF-Mean), scale-dependent inflation is superior to constant inflation. Constant inflation overinflates small-scale variables and results in increased small-scale errors, which then propagate to large-scale variables through the coupling between large- and small-scale variables and lead to increased large-scale errors. Scale-dependent inflation applies larger inflation for large-scale variables and imposes no inflation for small-scale variables, since large-scale errors have larger magnitudes than small-scale ones, and small-scale errors grow faster than large-scale ones. But IHEnKF-Ensemble that updates both the ensemble mean and perturbations with hybrid background error covariances is much less sensitive to scale-dependent inflation, compared to EnSRF and IHEnKF-Mean, because updating ensemble perturbations with hybrid background error covariances can play a role similar to the scale-dependent inflation.

Data assimilation for combustion ignition delay time simulation using schlieren image velocimetry

This study sought to improve the accuracy of simulating spray penetration and combustion ignition delay by means of data assimilation (DA). The simulations were conducted using the Reynolds-averaged Navier–Stokes (RANS) equations and assimilating the schlieren image data. In DA, an ensemble square root filter (EnSRF) was used to build the statistical model, making the simulation results more accurate without any change in the governing equations. Recognizing that the spray-cone injection angle has a large effect on penetration, we created ensemble members with different injection angles. And we applied the two-component velocity distribution calculated via SIV and updated both velocity and temperature by using a DA statistical model derived from RANS ensemble simulations. The ignition delay time is generally known to vary even under the same experimental conditions because it is influenced by many factors. In this study, we attempted the transient DA-assisted RANS simulation to predict the ignition delay time even when the temporal resolution and accuracy of the observation data ware insufficient. Our trials offer an example of how a combination of techniques can be effectively used to assimilate experimental data obtained under restricted conditions.

A Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) for emission estimates: system development and application

Abstract. Top-down atmospheric inversion infers surface–atmosphere fluxes from spatially distributed observations of atmospheric composition in order to quantify anthropogenic and natural emissions. In this study, we developed a Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) based on the Weather Research and Forecasting–Community Multiscale Air Quality (WRF–CMAQ) modeling system model, the three-dimensional variational (3D-Var) algorithm, and the ensemble square root filter (EnSRF) algorithm. This system can simultaneously assimilate hourly in situ CO, SO2, NO2, PM2.5, and PM10 observations to infer gridded emissions of CO, SO2, NOx, primary PM2.5 (PPM2.5), and coarse PM10 (PMC) on a regional scale. In each data assimilation window, we use a “two-step” scheme, in which the emissions are inferred first and then input into the CMAQ model to simulate initial conditions (ICs) of the next window. The posterior emissions are then transferred to the next window as prior emissions, and the original emission inventory is only used in the first window. Additionally, a “super-observation” approach is implemented to decrease the computational costs, observation error correlations, and influence of representative errors. Using this system, we estimated the emissions of CO, SO2, NOx, PPM2.5, and PMC in December and July 2016 over China using nationwide surface observations. The results show that compared to the prior emissions (2016 Multi-resolution Emission Inventory for China – MEIC 2016)), the posterior emissions of CO, SO2, NOx, PPM2.5, and PMC in December 2016 increased by 129 %, 20 %, 5 %, 95 %, and 1045 %, respectively, and the emission uncertainties decreased by 44 %, 45 %, 34 %, 52 %, and 56 %, respectively. With the inverted emissions, the RMSE of simulated concentrations decreased by 40 %–56 %. Sensitivity tests were conducted with different prior emissions, prior uncertainties, and observation errors. The results showed that the two-step scheme employed in RAPAS is robust in estimating emissions using nationwide surface observations over China. This study offers a useful tool for accurately quantifying multi-species anthropogenic emissions at large scales and in near-real time.

Hybrid Assimilation of Snow Cover Improves Land Surface Simulations over Northern China

Abstract Ensemble data assimilation (DA) is an efficient approach to reduce snow simulation errors by combining observation and land surface modeling. However, there is a small spread between ensemble members of simulated snowpack, which typically occurs for a long time with 100% snow cover fraction (SCF) or snow-free conditions. Here, we apply a hybrid DA method, in which direct insertion (DI) is a supplement of the ensemble square root filter (EnSRF), to assimilate the spaceborne SCF into a land surface model, driven by China Meteorological Administration Land Data Assimilation System high-resolution climate forcings over northern China during the snow season in 2021/22. Compared to the open-loop experiment (without SCF assimilation), the root-mean-square error (RMSE) of SCF is reduced by 6% through the original EnSRF and is even lower (by 14%) in the combined DI and EnSRF (EnSRFDI) experiment. The results reveal the ability of both EnSRF and EnSRFDI to improve the SCF estimation over regions where the snow cover is low, while only EnSRFDI is able to efficiently reduce the RMSE over areas with high SCF. Moreover, the SCF assimilation is also observed to improve the snow depth and soil temperature simulations, with the Kling–Gupta efficiency (KGE) increasing at 60% and 56%–70% stations, respectively, particularly under conditions with near-freezing temperature, in which reliable simulations are typically challenging. Our results demonstrate that the EnSRFDI hybrid method can be applied for the assimilation of spaceborne observational snow cover to improve land surface simulations and snow-related operational products. Significance Statement Due to the small spread between the seasonal snowpack of ensemble simulations, ensemble snow cover fraction (SCF) data assimilation (DA) proves to be ineffective. Therefore, we apply a hybrid method that combines the direct insertion (DI) and ensemble square root filter (EnSRF) to assimilate the spaceborne SCF into a land surface model (LSM) driven by high-resolution climate forcings. Our results reveal the applicability of the EnSRFDI to further improve snow cover simulations over regions with high SCF. Furthermore, the DA experiments were validated through a large number of in situ observations from the China Meteorological Administration. The uncertainties of snow depth and soil temperature simulations are also slightly reduced by the SCF DAs, particularly over regions with a poor LSM performance.

An economical assimilation scheme for radar reflectivity in non‐convective region to suppress spurious precipitation

AbstractIncreasing convection information in initial field and weakening spurious convection information are hot topics in numerical weather prediction. How to economically assimilate radar reflectivity in the non‐convective region (NCR) is the focus of this study. This study proposes a new assimilation scheme for the two‐dimensional (2D) composite reflectivity in NCR through the ensemble square‐root filter method. A single‐column observation test and two convective cases are studied to verify the assimilation effect. Three experiments are designed for each test, including a control experiment (Exp_CTL) that only assimilates convective reflectivity and two assimilation experiments that assimilate reflectivity in NCR (one assimilates 3D weak reflectivity [Exp_RF] and the other assimilates 2D composite reflectivity [Exp_CRF]) based on the Exp_CTL. The results of real‐case studies show that the new scheme has two clear advantages. One is that it can save approximately three quarters of the assimilation workload. The other is that the new scheme has the most significant effect on weakening spurious convection and decreasing the false alarm ratios of precipitation and reflectivity.

Performance comparisons of the three data assimilation methods for improved predictability of PM2·5: Ensemble Kalman filter, ensemble square root filter, and three-dimensional variational methods

To improve the predictability of concentrations of atmospheric particulate matter, a data assimilation (DA) system using ensemble square root filter (EnSRF) has been developed for the Community Multiscale Air Quality (CMAQ) model. The EnSRF DA method is a deterministic variant of the ensemble Kalman filter (EnKF) method, which means that unlike the EnKF method, it does not add random noise to the observations. To compare the performances of the EnSRF with those of other DA methods, such as EnKF and 3DVAR (three-dimensional variational), these three methods were applied to the same CMAQ model simulations with identical experimental settings. This is the first attempt in the field of chemical DA to compare the EnKF and EnSRF methods. An identical set of surface fine particulate matter (PM2.5) were assimilated every 6 h by all the DA methods over a CMAQ domain of East Asia, during the period from 01 May to 11 June 2016. In parallel with ‘reanalysis experiments’, we also carried out ‘48 h prediction experiments’ using the optimized initial conditions produced by the three DA methods. Detailed analyses among the three DA methods were then carried out by comparing both the reanalysis and the prediction outputs with the observed surface PM2.5 over four regions (i.e., South Korea, the Beijing–Tianjin–Hebei (BTH) region, Shandong province, and Liaoning province). The comparison results revealed that the EnSRF produced the best reanalysis and prediction fields in terms of several statistical metrics. For example, when the 3DVAR, EnKF, and EnSRF methods were used, averaged normalized mean biases (NMBs) decreased by (57.6, 85.6, and 91.8) % in reanalyses and (39.7, 87.6, and 91.5) % in first-day predictions, compared to the CMAQ control experiment (i.e., without DA) over South Korea, respectively. Also, over the three Chinese regions, the EnSRF method outperformed the EnKF and 3DVAR methods.

Deep Learning Augmented Data Assimilation: Reconstructing Missing Information with Convolutional Autoencoders

Abstract Remote sensing data play a critical role in improving numerical weather prediction (NWP). However, the physical principles of radiation dictate that data voids frequently exist in physical space (e.g., subcloud area for satellite infrared radiance or no-precipitation region for radar reflectivity). Such data gaps impair the accuracy of initial conditions derived from data assimilation (DA), which has a negative impact on NWP. We use the barotropic vorticity equation to demonstrate the potential of deep learning augmented data assimilation (DDA), which involves reconstructing spatially complete pseudo-observation fields from incomplete observations and using them for DA. By training a convolutional autoencoder (CAE) with a long simulation at a coarse “forecast” resolution (T63), we obtained a deep learning approximation of the “reconstruction operator,” which maps spatially incomplete observations to a model state with full spatial coverage and resolution. The CAE was applied to an incomplete streamfunction observation (∼30% missing) from a high-resolution benchmark simulation and demonstrated satisfactory reconstruction performance, even when only very sparse (1/16 of T63 grid density) observations were used as input. When only spatially incomplete observations are used, the analysis fields obtained from ensemble square root filter (EnSRF) assimilation exhibit significant error. However, in DDA, when EnSRF takes in the combined data from the incomplete observations and CAE reconstruction, analysis error reduces significantly. Such gains are more pronounced with sparse observation and small ensemble size because the DDA analysis is much less sensitive to observation density and ensemble size than the conventional DA analysis, which is based solely on incomplete observations. Significance Statement Data assimilation plays a critical role in improving the skills of modern numerical weather prediction by establishing accurate initial conditions. However, unobservable regions are common in observation data, particularly those derived from remote sensing. The nonlinear relationship between data from observable regions and the physical state of unobservable regions may impede DA efficiency. As a result, we propose that deep learning be used to improve data assimilation in such cases by reconstructing a spatially complete first guess of the physical state with deep learning and then applying data assimilation to the reconstructed field. Such deep learning augmentation is found effective in improving the accuracy of data assimilation, especially for sparse observation and small ensemble size.

Observation system simulation experiments (OSSEs) for assimilation of the planetary boundary‐layer height (PBLH) using the EnSRF technique

AbstractThe planetary boundary‐layer height (PBLH) is a key parameter that is very important in numerical weather and air quality predictions. The current LiDAR networks make it possible to provide potential PBLH observations, and assimilating the parameter will be helpful to improve the forecast of variables within the planetary boundary layer (PBL). This study first carried out idealized experiments on PBLH assimilation through observation system simulation experiments (OSSEs). The ensemble square root filter (EnSRF) is applied to assimilate the simulated PBLH based on the Weather Research and Forecast (WRF) model. This study mainly focused on two issues: which variables can be effectively improved by assimilating the PBLH, and whether there are differences in the assimilation effects above and within the PBL in the vertical direction. The results show that during the daytime within the PBL, PBLH assimilation could effectively improve the simulation and forecasting of model variables, including perturbation potential temperature (pt), water vapour mixing ratio (qv) and perturbation geopotential (ph); meanwhile, PBLH assimilation could strengthen turbulence mixing and result in a warmer and drier PBL. While the vertical and horizontal wind speeds (w, u and v) cannot be effectively updated by assimilating the PBLH, they could be indirectly improved by model dynamical adjustment when pt, qv and ph are improved. Above the PBL top, most of the above six variables cannot be effectively improved by assimilating the daytime PBLH. In contrast, at night, only u and v within the PBL could be directly updated by the low nocturnal PBLH. In this study, the simplest and most idealized schemes are selected based on idealized experiments; nevertheless, the results lay a foundation for later vertical and horizontal localization research and for the study of LiDAR‐retrieved PBLH assimilation in the future, which is the ultimate goal of this series of works.

A Scheme to Suppress Spurious Convection by Assimilating the "Zero" Column Maximum Vertical Velocity

AbstractSuppressing spurious precipitation is one of the key issues in numerical weather prediction. To thoroughly suppress spurious convection, it is necessary to both inhibit the development of convection in false convection areas and weaken the heat and momentum exchange between false convection areas and other surrounding regions. In this study, a scheme to suppress spurious convection through cyclically assimilating the "zero" column maximum vertical velocity (wmax) using the ensemble square root filter (EnSRF) method is proposed. The "zero" wmax is the average wmax over the no‐rain echo region in the background field which is normally close to 0 m s−1. Two convective events that exhibit different characteristics are studied. The results show that the assimilation of "zero" wmax can suppress the upward motion and reduce the water vapor and hydrometeors of the background field in the false convection region, which can effectively suppress the development of spurious convection. In addition, the scheme can reduce the water vapor transport from surrounding areas to the spurious convection region and weaken the cold pool on the ground, which is not conducive to the regeneration and maintenance of false convection. The forecasts of reflectivity and precipitation show that the assimilation of "zero" wmax can effectively suppress either the strong false convection band or the weak spurious convection surrounding the true rain band and can decrease the false alarm rate of reflectivity and precipitation.

Length Scale Analyses of Background Error Covariances for EnKF and EnSRF Data Assimilation

Data assimilation (DA) combines incomplete background values obtained via chemical transport model predictions with observational information. Several 3-Dimensional variational (3DVAR) and sequential methods (e.g., ensemble Kalman filter (EnKF)) are used to define model errors and build a background error covariance (BEC) and are important factors affecting the prediction performance of DA. The BEC determines the spatial range, where observation concentration is reflected in the model when DA is applied to an air pollution transport model. However, studies investigating the characteristics of BEC using air quality models remain lacking. In this study, horizontal length scale (HLS) and vertical length scale (VLS) analyses of a BEC were applied to EnKF and ensemble square root filter (EnSRF), respectively, and two ensemble-based DA methods were performed; the characteristics were compared with those of a BEC applied to 3DVAR. The results of 6 h PM2.5 predictions performed for 42 days were evaluated for a control run without DA (CTR), 3DVAR, EnKF, and EnSRF. HLS and VLS respectively exhibited a high correlation with the ground wind speed and with the planetary boundary layer height for diurnal and daily variations; EnKF and EnSRF exhibited superior performances among all the methods. The root mean square errors were 11.9 μg m−3 and 11.7 μg m−3 for EnKF and EnSRF, respectively, while those for 3DVAR and CTR were 12.6 μg m−3 and 18.3 μg m−3, respectively. Thus, we proposed a simple method to find a Gaussian function that best described the error correlation of the BEC based on the physical distance.

Impact of Ensemble-Variational Data Assimilation in Heavy Rain Forecast over Brazilian Northeast

The Brazilian Northeast (BNE) is located in the tropical region of Brazil. It is bounded by the Atlantic Ocean, and its climate and vegetation are strongly affected by continental plateaus. The plateaus keep the humid air masses to the east and are responsible for the rain episodes, and at the west side the northeastern hinterland and dry air masses are observed. This work is a case study that aims to evaluate the impact of updating the model initial condition using the 3DEnVar (Three-Dimensional Ensemble Variational) system in heavy rain episodes associated with Mesoscale Convective Systems (MCS). The results were compared to 3DVar (Three-Dimensional Variational) and EnSRF (Ensemble Square Root Filter) systems and with no data assimilation. The study enclosed two MCS cases occurring on 14 and 24 January 2017. For that purpose, the RMS (Regional Modeling System) version 3.0.0, maintained by the Center for Weather Forecasting and Climate Studies (CPTEC), used two components: the Weather Research and Forecasting (WRF) mesoscale model and the GSI (Gridpoint Statistical Interpolation) data assimilation system. Currently, the RMS provides the WRF initial conditions by using 3DVar data assimilation methodology. The 3DVar uses a climatological covariance matrix to minimize model errors. In this work, the 3DEnVar updates the RMS climatological covariance matrix through the forecast members based on the errors of the day. This work evaluated the improvements in the detection and estimation of 24 h accumulated precipitation in MCS events. The statistic index RMSE (Root Mean Square Error) showed that the hybrid data assimilation system (3DEnVar) performed better in reproducing the precipitation in the MCS occurred on 14 January 2017. On 24 January 2017, the EnSRF was the best system for improving the WRF forecast. In general, the BIAS showed that the WRF initialized with different initial conditions overestimated the 24 h accumulated precipitation. Therefore, the viability of using a hybrid system may depend on the hybrid algorithm that can modify the weights attributed to the EnSRF and 3DVar matrix in the GSI over the assimilation cycles.

Assimilation of the Maximum Vertical Velocity Converted From Total Lightning Data Through the EnSRF Method

AbstractA total lightning data assimilation (LDA) scheme is developed at the cloud‐resolving scale in this study. The LDA scheme assimilates total lightning data through the ensemble square root filter (EnSRF) method based on the relationship between the maximum vertical velocity and the instantaneous flash rate. To verify the effect of LDA, three assimilation experiments based on a convective activity on July 6, 2019 are performed. The results show that all LDA experiments can improve the forecast. LDA improves the water vapor field and provides a warm and moist environment in which convection can develop. LDA can also increase the convergence at low levels and the divergence at upper levels, which leads to intense convection development. However, the LDA experiment that does not consider vertical localization (LDA_no) shows excessive adjustments of the model variables, which leads to overestimation of precipitation. The LDA experiment which adjusts the state variables in the charge zone (LDA_CZ) underestimates the forecast. The LDA experiment using a global group filter (GGF) localization function (LDA_GGF) is optimal in theory and produces a better forecast. The results of LDA_GGF show that the interaction between the cold pool and the strong low‐level vertical wind shear in front of the cold pool is beneficial for triggering new convection in front of the convection, which leads to a rapid shifting in convective activity. In addition, the LDA_GGF scheme is evaluated further for a rainfall process on August 1, 2020 and obtains similar forecast improvements for composite reflectivity and accumulated precipitation.

Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds

<p style='text-indent:20px;'>Ensemble Kalman Inversion (EnKI) [<xref ref-type="bibr" rid="b23">23</xref>] and Ensemble Square Root Filter (EnSRF) [<xref ref-type="bibr" rid="b36">36</xref>] are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble Kalman Filter [<xref ref-type="bibr" rid="b17">17</xref>,<xref ref-type="bibr" rid="b3">3</xref>]. Despite their popularity, they are, however, not unbiased when the forward map is nonlinear [<xref ref-type="bibr" rid="b12">12</xref>,<xref ref-type="bibr" rid="b16">16</xref>,<xref ref-type="bibr" rid="b25">25</xref>]. Important Sampling (IS), on the other hand, obtains the unbiased sampling at the expense of large variance of weights, leading to slow convergence of high moments.</p><p style='text-indent:20px;'>We propose WEnKI and WEnSRF, the weighted versions of EnKI and EnSRF in this paper. It follows the same gradient flow as that of EnKI/EnSRF with weight corrections. Compared to the classical methods, the new methods are unbiased, and compared with IS, the method has bounded weight variance. Both properties will be proved rigorously in this paper. We further discuss the stability of the underlying Fokker-Planck equation. This partially explains why EnKI, despite being inconsistent, performs well occasionally in nonlinear settings. Numerical evidence will be demonstrated at the end.</p>

Improving parameter and state estimation of a hydrological model with the ensemble square root filter

Data assimilation techniques are widely used in hydrology and water resources management to improve model forecast uncertainty by assimilating observations. The big challenge in practical applications is how to describe model uncertainties correctly to avoid the occurrence of spurious covariance during data assimilation. In this study, the ensemble square root filter (EnSRF) is used to estimate parameters and states of a groundwater model in Guantao, China, which updates ensemble means and perturbations separately and avoids the need to perturb observations. The uncertainty in parameters and states decreased with time while assimilating observations. However, incorrect updates of parameters and states were obtained, which could not be corrected by assimilating further observations improving the representation of the hydrological system. To compensate for this effect and reduce other sampling errors introduced during assimilation, localization and two covariance-tuning methods (inflation factor and damping factor) are explored in the study. The results show that alternative scenarios with proper localization length or a large inflation factor or a small damping factor produce better model estimates and improve the filter performance. The scenario with a damping factor of 0.05 shows a distinct gain in model predictive capability. The damping factor method is superior to the inflation factor method and preferable in real field applications. The scenario combining the damping factor with localization further improved the filter performance. The performance of the EnSRF with respect to different amounts of measurement error is also analysed. Even though the increase of observation error can increase the error covariance, a corresponding filter improvement is not observed as in that case, observations are less informative.

Assimilating Observations with Spatially Correlated Errors Using a Serial Ensemble Filter with a Multiscale Approach

AbstractThe serial ensemble square root filter (EnSRF) typically assumes observation errors to be uncorrelated when assimilating the observations one at a time. This assumption causes the filter solution to be suboptimal when the observation errors are spatially correlated. Using the Lorenz-96 model, this study evaluates the suboptimality due to mischaracterization of observation error spatial correlations. Neglecting spatial correlations in observation errors results in mismatches between the specified and true observation error variances in spectral space, which cannot be resolved by inflating the overall observation error variance. As a remedy, a multiscale observation (MSO) method is proposed to decompose the observations into multiple scale components and assimilate each component with separately adjusted spectral error variance. Experimental results using the Lorenz-96 model show that the serial EnSRF, with the help from the MSO method, can produce solutions that approach the solution from the EnSRF with correctly specified observation error correlations as the number of scale components increases. The MSO method is further tested in a two-layer quasigeostrophic (QG) model framework. In this case, the MSO method is combined with the multiscale localization (MSL) method to allow the use of different localization radii when updating the model state at different scales. The combined method (MSOL) improves the serial EnSRF performance when assimilating observations with spatially correlated errors. With adjusted observation error spectral variances and localization radii, the combined MSOL method provides the best solution in terms of analysis accuracy and filter consistency. Prospects and challenges are also discussed for the implementation of the MSO method for more complex models and observing networks.

Potential Impacts of Assimilating All-Sky Satellite Infrared Radiances on Convection-Permitting Analysis and Prediction of Tropical Convection

AbstractGeostationary infrared satellite observations are spatially dense [>1/(20 km)2] and temporally frequent (>1 h−1). These suggest the possibility of using these observations to constrain subsynoptic features over data-sparse regions, such as tropical oceans. In this study, the potential impacts of assimilating water vapor channel brightness temperature (WV-BT) observations from the geostationary Meteorological Satellite 7 (Meteosat-7) on tropical convection analysis and prediction were systematically examined through a series of ensemble data assimilation experiments. WV-BT observations were assimilated hourly into convection-permitting ensembles using Penn State’s ensemble square root filter (EnSRF). Comparisons against the independently observed Meteosat-7 window channel brightness temperature (Window-BT) show that the assimilation of WV-BT generally improved the intensities and locations of large-scale cloud patterns at spatial scales larger than 100 km. However, comparisons against independent soundings indicate that the EnSRF analysis produced a much stronger dry bias than the no data assimilation experiment. This strong dry bias is associated with the use of the simulated WV-BT from the prior mean during the EnSRF analysis step. A stochastic variant of the ensemble Kalman filter (NoMeanSF) is proposed. The NoMeanSF algorithm was able to assimilate the WV-BT without causing such a strong dry bias and the quality of the analyses’ horizontal cloud pattern is similar to EnSRF’s analyses. Finally, deterministic forecasts initiated from the NoMeanSF analyses possess better horizontal cloud patterns above 500 km than those of the EnSRF. These results suggest that it might be better to assimilate all-sky WV-BT through the NoMeanSF algorithm than the EnSRF algorithm.

Evaluating the Impact of Assimilating Aerosol Optical Depth Observations on Dust Forecasts Over North Africa and the East Atlantic Using Different Data Assimilation Methods.

This study evaluates the impact of assimilating moderate resolution imaging spectroradiometer (MODIS) aerosol optical depth (AOD) data using different data assimilation (DA) methods on dust analyses and forecasts over North Africa and tropical North Atlantic. To do so, seven experiments are conducted using the Weather Research and Forecasting dust model and the Gridpoint Statistical Interpolation analysis system. Six of these experiments differ in whether or not AOD observations are assimilated and the DA method used, the latter of which includes the three‐dimensional variational (3D‐Var), ensemble square root filter (EnSRF), and hybrid methods. The seventh experiment, which allows us to assess the impact of assimilating deep blue AOD data, assimilates only dark target AOD data using the hybrid method. The assimilation of MODIS AOD data clearly improves AOD analyses and forecasts up to 48 hr in length. Results also show that assimilating deep blue data has a primarily positive effect on AOD analyses and forecasts over and downstream of the major North African source regions. Without assimilating deep blue data (assimilating dark target only), AOD assimilation only improves AOD forecasts for up to 30 hr. Of the three DA methods examined, the hybrid and EnSRF methods produce better AOD analyses and forecasts than the 3D‐Var method does. Despite the clear benefit of AOD assimilation for AOD analyses and forecasts, the lack of information regarding the vertical distribution of aerosols in AOD data means that AOD assimilation has very little positive effect on analyzed or forecasted vertical profiles of backscatter.

An ensemble square root filter for the joint assimilation of surface soil moisture and leaf area index within the Land Data Assimilation System LDAS-Monde: application over the Euro-Mediterranean region

Abstract. This paper introduces an ensemble square root filter (EnSRF) in the context of jointly assimilating observations of surface soil moisture (SSM) and the leaf area index (LAI) in the Land Data Assimilation System LDAS-Monde. By ingesting those satellite-derived products, LDAS-Monde constrains the Interaction between Soil, Biosphere and Atmosphere (ISBA) land surface model (LSM), coupled with the CNRM (Centre National de Recherches Météorologiques) version of the Total Runoff Integrating Pathways (CTRIP) model to improve the reanalysis of land surface variables (LSVs). To evaluate its ability to produce improved LSVs reanalyses, the EnSRF is compared with the simplified extended Kalman filter (SEKF), which has been well studied within the LDAS-Monde framework. The comparison is carried out over the Euro-Mediterranean region at a 0.25∘ spatial resolution between 2008 and 2017. Both data assimilation approaches provide a positive impact on SSM and LAI estimates with respect to the model alone, putting them closer to assimilated observations. The SEKF and the EnSRF have a similar behaviour for LAI showing performance levels that are influenced by the vegetation type. For SSM, EnSRF estimates tend to be closer to observations than SEKF values. The comparison between the two data assimilation approaches is also carried out on unobserved soil moisture in the other layers of soil. Unobserved control variables are updated in the EnSRF through covariances and correlations sampled from the ensemble linking them to observed control variables. In our context, a strong correlation between SSM and soil moisture in deeper soil layers is found, as expected, showing seasonal patterns that vary geographically. Moderate correlation and anti-correlations are also noticed between LAI and soil moisture, varying in space and time. Their absolute value, reaching their maximum in summer and their minimum in winter, tends to be larger for soil moisture in root-zone areas, showing that assimilating LAI can have an influence on soil moisture. Finally an independent evaluation of both assimilation approaches is conducted using satellite estimates of evapotranspiration (ET) and gross primary production (GPP) as well as measures of river discharges from gauging stations. The EnSRF shows a systematic albeit moderate improvement of root mean square differences (RMSDs) and correlations for ET and GPP products, but its main improvement is observed on river discharges with a high positive impact on Nash–Sutcliffe efficiency scores. Compared to the EnSRF, the SEKF displays a more contrasting performance.

Dynamic State Estimation for Synchronous Machines Based on Adaptive Ensemble Square Root Kalman Filter

Dynamic state estimation (DSE) for generators plays an important role in power system monitoring and control. Phasor measurement unit (PMU) has been widely utilized in DSE since it can acquire real-time synchronous data with high sampling frequency. However, random noise is unavoidable in PMU data, which cannot be directly used as the reference data for power grid dispatching and control. Therefore, the data measured by PMU need to be processed. In this paper, an adaptive ensemble square root Kalman filter (AEnSRF) is proposed, in which the ensemble square root filter (EnSRF) and Sage–Husa algorithm are utilized to estimate measurement noise online. Simulation results obtained by applying the proposed method show that the estimation accuracy of AEnSRF is better than that of ensemble Kalman filter (EnKF), and AEnSRF can track the measurement noise when the measurement noise changes.

The 2015 and 2016 wintertime air pollution in China: SO<sub>2</sub> emission changes derived from a WRF-Chem/EnKF coupled data assimilation system

Abstract. Ambient pollutants and emissions in China have changed significantly in recent years due to strict control strategies implemented by the government. It is of great interest to evaluate the reduction of emissions and the air quality response using a data assimilation (DA) approach. In this study, we updated the WRF-Chem/EnKF (Weather Research and Forecasting – WRF, model coupled with the chemistry/ensemble Kalman filter – Chem/EnKF) system to directly analyze SO2 emissions instead of using emission scaling factors, as in our previous study. Our purpose is to investigate whether the WRF-Chem/EnKF system is capable of detecting the emission deficiencies in the bottom-up emission inventory (2010-MEIC, Multi-resolution Emission Inventory for China), dynamically updating the spatial–temporal emission changes (2010 to 2015/2016) and, most importantly, locating the “new” (emerging) emission sources that are not considered in the a priori emission inventory. The 2010 January MEIC emission inventory was used as the a priori inventory (to generate background emission fields). The 2015 and 2016 January emissions were obtained by assimilating the hourly surface SO2 concentration observations for January 2015 and 2016. The SO2 emission changes for northern, western, and southern China from 2010 to 2015 and from 2015 to 2016 (for the month of January) from the EnSRF (ensemble square root filter) approach were investigated, and the emission control strategies during the corresponding period were discussed. The January 2010–2015 differences showed inhomogeneous change patterns in different regions, including (1) significant emission reductions in southern China; (2) significant emission reductions in larger cities with a wide increase in the surrounding suburban and rural regions in northern China, which may indicate missing raw coal combustion for winter heating that was not taken into account in the a priori emission inventory; and (3) significantly large emission increases in western China due to the energy expansion strategy. The January 2015–2016 differences showed wide emission reductions from 2015 to 2016, indicating stricter control strategies having been fully executed nationwide. These derived emission changes coincided with the period of the energy development national strategy in northwestern China and the regulations for the reduction of SO2 emissions, indicating that the updated DA system was possibly capable of detecting emission deficiencies, dynamically updating the spatial–temporal emission changes (2010 to 2015/2016), and locating newly added sources. Forecast experiments using the a priori and updated emissions were conducted. Comparisons showed improvements from using updated emissions. The improvements in southern China were much larger than those in northern and western China. For the Sichuan Basin, central China, the Yangtze River Delta, and the Pearl River Delta, the BIAS (bias, equal to the difference between the modeled value and the observational value, representing the overall model tendency) decreased by 61.8 %–78.2 % (for different regions), the RMSE decreased by 27.9 %–52.2 %, and CORR values (correlation coefficient, equal to the linear relationship between the modeled values and the observational values) increased by 12.5 %–47.1 %. The limitation of the study is that the analyzed emissions are still model-dependent, as the ensembles are conducted using the WRF-Chem model; therefore, the performances of the ensembles are model-dependent. Our study indicated that the WRF-Chem/EnSRF system is not only capable of improving the emissions and forecasts in the model but can also evaluate realistic emission changes. Thus, it is possible to apply the system for the evaluation of emission changes in the future.