Ensemble Kalman Filter Assimilation Research Articles

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.

Data assimilation of PS-InSAR vertical deformation into a frost heave model to analyze subgrade deformation of high-speed railway in northwest China

Temperature changes may cause irregular soil uplift or thawing settlements in frozen soil areas, potentially affecting the safe operation of High-Speed Railways (HSR). Analyzing and predicting these deformation characteristics is thus critical. However, the conventional forecasting and analysis techniques rarely considered factors such as dynamic parameter variations, uncertainties, and measurement errors, which hinder accurate regional scale forecasting. To bridge this gap, this paper introduces a novel time-series coupling method, which integrates post-processing deformation from Interferometric Synthetic Aperture Radar (InSAR) with a frost heave model (FHM), facilitated by the ensemble Kalman filter (EnKF) assimilation algorithm. We obtained deformation observations along the HSR using Persistent Scatterer InSAR (PS-InSAR) technology in combination with time-series post-processing techniques. Considering the causative factors for deformation, we structured the FHM. By integrating FHM with observational data using the EnKF algorithm achieved an efficient upgrade of the posterior distribution of model parameters. This integration significantly improves the predictive accuracy, it facilitates an efficient update to the posterior distribution of model parameters, leading to enhanced prediction accuracy of our model. Our experimental results indicate that the effectiveness of this approach, with observational data assimilation into FHM reducing the average Root Mean Square Error (RMSE) to a mere 0.247 mm. Concurrently, both the Normalized Reduction Error Index (NER) and the Assimilation Efficiency Factor (EFF) values surpassed 0.60 and 0.84 respectively. These underlines signify a successful update of our model parameters, which in turn elevates the accuracy of future deformation predictions, thereby promising safer railway operations.

A Region‐Optional Targeted Observation Method and Its Application in the Sea Surface Temperature Prediction Associated With the Indian Ocean Dipole

AbstractAlthough data assimilation‐based targeted observation approaches have been widely used, obtaining optimal observation sites over a specific region for a prediction target remains a challenge. Hence, this study developed a more practical region‐optional targeted observation method by introducing a projection vector, allowing for the prediction targeted region to be different from the observation one. By minimizing the analysis error variance in a targeted region, the method identified optimal sites through a sequential assimilation framework. This region‐optional method was applied in the targeted observation study of the sea surface temperature (SST) prediction associated with Indian Ocean Dipole (IOD). The first 10 optimal observation sites were identified, with seven sites in the west IO, and three in the east. The results were further validated by conducting observation system simulation experiments using an ensemble adjustment Kalman filter assimilation system in the Community Earth System Model (CESM). The assimilation of observations from the 10 optimal sites was capable of reducing root mean squared errors (RMSEs) by 38.2% when assessing the SST across the IOD key regions, significantly more than the reduction from 10 optimal sites identified via the conventional method, or that from 10 random sites. This improvement was primarily due to the error reduction in the eastern IO, where SST RMSEs were reduced by >50%. The proposed region‐optional targeted observation method can seek optimal sites in any region of interest and is not confined to the targeted region as in conventional algorithms, thus providing a more reasonable method for designing optimal observation networks.

Effect of western Pacific current uncertainties on the forecasting of eddy shedding from the Kuroshio loop into the South China Sea: A case study

The process of eddy shedding from the Kuroshio loop current (LC) into the South China Sea via the Luzon Strait is highly variable and significantly controlled by the uncertainties in the Western Pacific (WP) currents. This study investigates the forecast of a strong eddy shedding event from the Kuroshio LC during the winter 2016–2017 using the regional ocean modeling system and ensemble Kalman filter assimilation method. Experiments are conducted to explore the sensitivity of forecasts to the assimilation of satellite sea surface height anomaly data from different key regions of the WP, such as the subtropical countercurrent (STCC) and Northern Equatorial Current (NEC) regions. The results indicate that the improved forecast performance of the strong Kuroshio LC eddy shedding event is mainly attributed to assimilation in the STCC region and partly owing to assimilation in the NEC region. Specifically, assimilation in the STCC region reproduces a westward-propagating cyclonic eddy that collides with the Kuroshio in the Luzon Strait, blocking the Kuroshio northward flow and causing Kuroshio LC eddy shedding. Furthermore, assimilation in the NEC region enhances the simulation of the weak Kuroshio background current, which further facilitates the formation of a strong Kuroshio background LC and the occurrence of Kuroshio LC eddy shedding.

State updating in a distributed hydrological model by ensemble Kalman filtering with error estimation

For flood simulation in small- and medium-sized catchments, discharge observations may be used to update model states of a distributed hydrological model to improve performance. The ensemble Kalman filter (EnKF) has been widely used for hydrological assimilation due to its relative simplicity and robustness. An advantage of the EnKF is that it is easy to include different sources of uncertainty, therefore the choice of error model is crucial for the application of the EnKF assimilation. This paper describes an EnKF assimilation scheme for estimating error models using the maximum a posteriori estimation method (MAP). We test this scheme in two small and medium-sized catchments in China with different characteristics, and in addition compared the performance differences under two kinds of rainfall forcing. We show that MAP is beneficial in specifying error models and providing reliable ensemble spread. The assimilation scheme can effectively ameliorate the degradation of distributed hydrological model performance due to uncalibrated model parameters and/or poor quality of input data.

Estimating Maize Yield in the Black Soil Region of Northeast China Using Land Surface Data Assimilation: Integrating a Crop Model and Remote Sensing.

Accurate yield estimation at the regional scale has always been a persistent challenge in the agricultural sector. With the vigorous emergence of remote sensing land surface observations in recent decades, data assimilation methodology has become an effective means to promote the accuracy and efficiency of yield estimation by integrating regional data and point-scale crop models. This paper focuses on the black soil area of Northeast China, a national strategic grain production base, applying the AquaCrop crop growth model to simulate the fractional vegetation cover (FVC) and maize yield from 2000 to 2020 and then forming a reliable FVC optimization dataset based on an ensemble Kalman filter (EnKF) assimilation algorithm with remote sensing products. Using the random forest model, the regression relationship between FVC and yield was established from the long-term time series data, which is crucial to achieve better yield estimation through the optimized FVC. The major findings include the following: (1) The R2 of the assimilated FVC and maize yield can reach 0.557. (2) When compared with the local statistical yield, our method reduced the mean absolute error (MAE) from 1.164 ton/ha (based on GLASS FVC products) to 1.004 ton/ha (based on the calibrated AquaCrop model) and then to 0.888 ton/ha (the result after assimilation). The above results show that we have proposed a yield estimation method to provide accurate yield estimations by combining data assimilation and machine learning. This study provided deep insights into understanding the variations in FVC and revealed the spatially explicit yield prediction ability from the time series land surface parameters, which has significant potential for optimizing water and soil resource management.

The Impact of Perturbing Eddy Diffusion and Upper Boundary on the Ionosphere EnKF Assimilation System

AbstractAccurate representation of ensemble members of coupled Ionosphere‐Thermosphere (I‐T) is crucial to the ionosphere forecast in the ensemble Kalman filter (EnKF) data assimilation system. In this paper, besides the model drivers used in previous studies, including the solar 10.7 cm radio flux (F10.7), auroral hemispheric power (HP) and cross‐tail potential drop (CP), the eddy diffusion coefficient (ED), and nighttime vertical O+ flux at the top boundary are also perturbed to generate ensemble members. Based on our developed EnKF data assimilation system, the impact of perturbing different model external forcing parameters on ensemble generation and forecast capability of ionosphere and thermosphere has been investigated in detail through a series of sensitivity tests and data assimilation experiments. This system uses the National Center for Atmospheric Research (NCAR) Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) as a background model. The findings are summarized as follows: (a) Associated with perturbing two additional model forcing parameters, better ensemble members of ionosphere and thermosphere states of the background model can be generated during both daytime and nighttime. (b) The improvement of the forecast capability of the ionosphere and thermosphere variables can be further enhanced. This study can provide a reference for ensemble generating strategy for the coupled I‐T EnKF data assimilation in the future.

Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

Research on Prediction of Metro Surface Deformation Based on Ensemble Kalman Filter

In order to improve the prediction ability of the statistical model of the subway surface deformation, the equal-dimensional innovation grey system theory model and Kalman filter model are used to predict the surface deformation of the subway. The ensemble Kalman filter (EnKF) algorithm is used to assimilate the two groups of prediction data to improve the accuracy of the prediction data. The absolute difference and the root mean square error between the EnKF assimilation prediction data, the Kalman filter prediction data, and the equal-dimensional and innovation grey model prediction data and the measured data are compared and analysed. The results show that the accuracy of EnKF assimilation prediction data is greatly improved compared with the prediction data of grey system theory model and Kalman filter model, and the short-term prediction effect is better.

Observing System Impact on Ionospheric Specification Over China Using EnKF Assimilation

AbstractAccurate ionospheric specification for the current and future is one of the key tasks in operational space weather. In this work, we have assessed the effect of a dense ground network consisting of different radio instruments either developed or under developing on ionosphere nowcasting and forecasting over China and adjacent region (0–60°N and 70–140°E) through observing system simulation experiments. The data assimilation system is an Ensemble Kalman filter (EnKF) ionosphere and thermosphere data assimilation algorithm. The National Center for Atmospheric Research Thermosphere Ionosphere Electrodynamics General Circulation Model is used as a background model. Effects of different observation types, including the slant total electron content from Beidou System geostationary satellite and Global Position System and electron density observations from ionosondes and incoherent scattering radar on the ionospheric nowcasting and forecasting, are examined by the accurate specification of ionosphere key parameters (total electron content and 3‐D electron density). We found that simultaneously assimilating different observation types can greatly improve the quality of ionosphere specification. Furthermore, updating the thermospheric state variables in the coupled thermosphere‐ionosphere forecast model in the assimilation step plays an important role in improving the ionosphere forecasting. The ionosphere forecasting capability can last longer (>24 hr) in each observing system simulation experiment due to the adjusted thermosphere states. This study can provide a reference for observing system design over the China region and future ionosphere forecasting operation.

A Flow‐Dependent Targeted Observation Method for Ensemble Kalman Filter Assimilation Systems

AbstractIn this study, we developed a flow‐dependent sequential assimilation‐based targeted observation method by minimizing the analysis error variance under the framework of the ensemble Kalman filter (EnKF). This approach considers the flow‐dependent variation in background error statistics when identifying optimal observational sites through the sequential assimilation method. Covariance localization is also introduced in this method, enabling computational efficiency and eliminating impacts from spurious observations. By quantifying the reduction in analysis error variances, the proposed method could estimate the potential improvements by each optimal observation while assimilated. With this method, we design an optimal observational array for sea level anomaly (SLA) prediction in the tropical Indian Ocean (TIO), which is implemented using a fully coupled climate model, the Community Earth System Model (CESM), in conjunction with a coupled assimilation system. The optimal observational array detected from this method was found to theoretically reduce the initial uncertainty by up to approximately 60% of the error variance. An observing system simulation experiment (OSSE) using the CESM and the coupled assimilation system, which was designed for validation purposes, confirms the theoretical reduction in the analysis error variance by the optimal observation array.

Development of an ensemble data assimilation system with LMDZ5 AGCM for regional reanalysis

The present study describes a newly developed LMDZ–DART data assimilation system based on the Ensemble Kalman Filter (EnKF) with a stretched grid atmospheric model and evaluates the potential of the system for generating high-resolution reanalysis products over the Indian region. This system is composed using the LMDZ5 (Laboratoire de Meteorologie Dynamique, Zoom, version 5) global atmospheric model, the Data Assimilation Research Testbed (DART), and a set of interface routines. The interface routines enable assimilation of observations with the model using the EnKF assimilation method. The stretched grid capability of the LMDZ5 model has been utilized to generate computationally efficient high-resolution experimental reanalysis data over the Indian region. The assimilation experiments have been conducted for 4 months during the Indian summer monsoon (ISM) period using LMDZ–DART system with two different configurations: REG (1° × 1° regular grid size over the globe) and ZOOM (~ 0.35° × 35° over the Indian region and coarser resolution outside). The results of the assimilation experiments are validated by comparing with observations as well as with an independent atmospheric reanalysis (ERA-Interim). It has been found that LMDZ–DART system is robust and reliable throughout the investigated ISM period for both REG and ZOOM configurations. In the REG experiment, spatial patterns and magnitude of the global fields portray a high degree of resemblance with ERA-Interim. The spatial patterns are also well reproduced in the ZOOM reanalysis. However, at some places outside the zoom area, the differences of the ZOOM reanalysis with ERA-Interim are slightly higher than the regular grid. Over the Indian region, the ZOOM configuration provides higher quality analysis and better regional features than REG. These results thus provide confidence in the stretched grid LMDZ–DART system to serve as a basis for generating computationally economical high-resolution regional reanalysis.

Predictability of Deep Convection in Idealized and Operational Forecasts: Effects of Radar Data Assimilation, Orography, and Synoptic Weather Regime

AbstractWe investigate the practical predictability limits of deep convection in a state-of-the-art, high-resolution, limited-area ensemble prediction system. A combination of sophisticated predictability measures, namely, believable and decorrelation scale, are applied to determine the predictable scales of short-term forecasts in a hierarchy of model configurations. First, we consider an idealized perfect model setup that includes both small-scale and synoptic-scale perturbations. We find increased predictability in the presence of orography and a strongly beneficial impact of radar data assimilation, which extends the forecast horizon by up to 6 h. Second, we examine realistic COSMO-KENDA simulations, including assimilation of radar and conventional data and a representation of model errors, for a convectively active two-week summer period over Germany. The results confirm increased predictability in orographic regions. We find that both latent heat nudging and ensemble Kalman filter assimilation of radar data lead to increased forecast skill, but the impact is smaller than in the idealized experiments. This highlights the need to assimilate spatially and temporally dense data, but also indicates room for further improvement. Finally, the examination of operational COSMO-DE-EPS ensemble forecasts for three summer periods confirms the beneficial impact of orography in a statistical sense and also reveals increased predictability in weather regimes controlled by synoptic forcing, as defined by the convective adjustment time scale.

Application of multigrid NLS-4DVar in radar radial velocity data assimilation with WRF-ARW

The nonlinear least-squares four-dimensional variational assimilation (NLS-4DVar) method introduced here combines the merits of the ensemble Kalman filter and 4DVar assimilation methods. The multig...

Assimilation of Remotely-Sensed LAI into WOFOST Model with the SUBPLEX Algorithm for Improving the Field-Scale Jujube Yield Forecasts

In order to enhance the simulated accuracy of jujube yields at the field scale, this study attempted to employ SUBPLEX algorithm to assimilate remotely sensed leaf area indices (LAI) of four key growth stages into a calibrated World Food Studies (WOFOST) model, and compare the accuracy of assimilation with the usual ensemble Kalman filter (EnKF) assimilation. Statistical regression models of LAI and Landsat 8 vegetation indices at different developmental stages were established, showing a validated R2 of 0.770, 0.841, 0.779, and 0.812, and a validated RMSE of 0.061, 0.144, 0.180, and 0.170 m2 m−2 for emergence, fruit filling, white maturity, and red maturity periods. The results showed that both SUBPLEX and EnKF assimilations significantly improved yield estimation performance compared with un-assimilated simulation. The SUBPLEX (R2 = 0.78 and RMSE = 0.64 t ha−1) also showed slightly better yield prediction accuracy compared with EnKF assimilation (R2 = 0.73 and RMSE = 0.71 t ha−1), especially for high-yield and low-yield jujube orchards. SUBPLEX assimilation produced a relative bias error (RBE, %) that was more concentrated near zero, being lower than 10% in 80.1%, and lower than 20% in 96.1% for SUBPLEX, 72.4% and 96.7% for EnKF, respectively. The study provided a new assimilation scheme based on SUBPLEX algorithm to employ remotely sensed data and a crop growth model to improve the field-scale fruit crops yield estimates.

Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

Ensemble Kalman Filter Assimilation of Polarimetric Radar Observations for the 20 May 2013 Oklahoma Tornadic Supercell Case

Abstract Real polarimetric radar observations are directly assimilated for the first time using the ensemble Kalman filter (EnKF) for a supercell case from 20 May 2013 in Oklahoma. A double-moment microphysics scheme and advanced polarimetric radar observation operators are used together to estimate the model states. Lookup tables for the observation operators are developed based on T-matrix scattering amplitudes for all hydrometeor categories, which improve upon previous curved-fitted approximations of T-matrix scattering amplitudes or the Rayleigh approximation. Two experiments are conducted: one assimilates reflectivity (Z) and radial velocity (Vr) (EXPZ), and one assimilates in addition differential reflectivity (ZDR) below the observed melting level at ~2-km height (EXPZZDR). In the EnKF analyses, EXPZZDR exhibits a ZDR arc that better matches observations than EXPZ. EXPZZDR also has higher ZDR above 2 km, consistent with the observed ZDR column. Additionally, EXPZZDR has an improved estimate of the model microphysical states. Specifically, the rain mean mass diameter (Dnr) in EXPZZDR is higher in the ZDR arc region and the total rain number concentration (Ntr) is lower downshear in the forward flank than EXPZ when compared to values retrieved from the polarimetric observations. Finally, a negative gradient of hail mean mass diameter (Dnh) is found in the right-forward flank of the EXPZZDR analysis, which supports previous findings indicating that size sorting of hail, as opposed to rain, has a more significant impact on low-level polarimetric signatures. This paper represents a proof-of-concept study demonstrating the value of assimilating polarimetric radar data in improving the analysis of features and states related to microphysics in supercell storms.

Comparison of 4DVAR and EnKF state estimates and forecasts in the Gulf of Mexico

An experiment is conducted to compare four‐dimensional variational (4DVAR) and ensemble Kalman filter (EnKF) assimilation systems and their predictability in the Gulf of Mexico (GoM) using the Massachusetts Institute of Technology general circulation model (MITgcm). The quality of the ocean‐state estimates, forecasts, and the contribution of ensemble prediction are evaluated. The MITgcm–Estimating the Circulation and Climate of the Ocean (ECCO) 4DVAR (MITgcm–ECCO) and the MITgcm–Data Assimilation Research Testbed (DART) EnKF (MITgcm–DART) systems were used to compute two‐month hindcasts (March–April, 2010) by assimilating satellite‐derived along‐track sea‐surface height (SSH) and gridded sea‐surface temperature (SST) observations. The estimates from both methods at the end of the hindcast period were then used to initialize forecasts for two months (May–June, 2010). This period was selected because a loop current (LC) eddy (Eddy Franklin: Eddy‐F) detachment event occurred at the end of May 2010, immediately after the Deepwater Horizon (DwH) oil spill. Despite some differences between the setups, both systems produce analyses and forecasts of comparable quality and both solutions significantly outperformed model persistence. A reference forecast initialized from the 1/12° Hybrid Coordinate Ocean Model (HYCOM)/NCODA global analysis also performed well. The EnKF experiments for sensitivity to filter parameters showed enhanced predictability when using more ensemble members and stronger covariance localization, but not for larger inflation. The EnKF experiments varying the number of assimilation cycles showed enhanced short‐term (long‐term) predictability with fewer (more) assimilation cycles. Additional hindcast and forecast experiments at other times of significant LC evolution showed mixed performance of both systems, which depends strongly on the background state of the GoM circulation. The present work demonstrates a practical application of both assimilation methods for the GoM and compares them in a limited number of realizations. The overall conclusion showing improved short‐term (long‐term) predictability for EnKF (4DVAR) carries an important caveat that the results from this study are specific to a few 4DVAR and EnKF LC eddy separation experiments in the GoM and cannot be generalized to conclude the relative performance of both methods, especially in other applications. However, some of the concepts and methods should carry over to other applications.

An Evaluation of the EnKF vs. EnOI and the Assimilation of SMAP, SMOS and ESA CCI Soil Moisture Data over the Contiguous US

A number of studies have shown that assimilation of satellite derived soil moisture using the ensemble Kalman Filter (EnKF) can improve soil moisture estimates, particularly for the surface zone. However, the EnKF is computationally expensive since an ensemble of model integrations have to be propagated forward in time. Here, assimilating satellite soil moisture data from the Soil Moisture Active Passive (SMAP) mission, we compare the EnKF with the computationally cheaper ensemble Optimal Interpolation (EnOI) method over the contiguous United States (CONUS). The background error–covariance in the EnOI is sampled in two ways: (i) by using the stochastic spread from an ensemble open-loop run, and (ii) sampling from the model spinup climatology. Our results indicate that the EnKF is only marginally superior to one version of the EnOI. Furthermore, the assimilation of SMAP data using the EnKF and EnOI is found to improve the surface zone correlation with in situ observations at a 95 % significance level. The EnKF assimilation of SMAP data is also found to improve root-zone correlation with independent in situ data at the same significance level; however this improvement is dependent on which in situ network we are validating against. We evaluate how the quality of the atmospheric forcing affects the analysis results by prescribing the land surface data assimilation system with either observation corrected or model derived precipitation. Surface zone correlation skill increases for the analysis using both the corrected and model derived precipitation, but only the latter shows an improvement at the 95 % significance level. The study also suggests that assimilation of satellite derived surface soil moisture using the EnOI can correct random errors in the atmospheric forcing and give an analysed surface soil moisture close to that of an open-loop run using observation derived precipitation. Importantly, this shows that estimates of soil moisture could be improved using a combination of assimilating SMAP using the computationally cheap EnOI while using model derived precipitation as forcing. Finally, we assimilate three different Level-2 satellite derived soil moisture products from the European Space Agency Climate Change Initiative (ESA CCI), SMAP and SMOS (Soil Moisture and Ocean Salinity) using the EnOI, and then compare the relative performance of the three resulting analyses against in situ soil moisture observations. In this comparison, we find that all three analyses offer improvements over an open-loop run when comparing to in situ observations. The assimilation of SMAP data is found to perform marginally better than the assimilation of SMOS data, while assimilation of the ESA CCI data shows the smallest improvement of the three analysis products.

Real-Time Forecasting of Hand-Foot-and-Mouth Disease Outbreaks using the Integrating Compartment Model and Assimilation Filtering

Hand-foot-and-mouth disease (HFMD) is a highly contagious viral infection, and real-time predicting of HFMD outbreaks will facilitate the timely implementation of appropriate control measures. By integrating a susceptible-exposed-infectious-recovered (SEIR) model and an ensemble Kalman filter (EnKF) assimilation method, we developed an integrated compartment model and assimilation filtering forecast model for real-time forecasting of HFMD. When applied to HFMD outbreak data collected for 2008–11 in Beijing, China, our model successfully predicted the peak week of an outbreak three weeks before the actual arrival of the peak, with a predicted maximum infection rate of 85% or greater than the observed rate. Moreover, dominant virus types enterovirus 71 (EV-71) and coxsackievirus A16 (CV-A16) may account for the different patterns of HFMD transmission and recovery observed. The results of this study can be used to inform agencies responsible for public health management of tailored strategies for disease control efforts during HFMD outbreak seasons.