Ensemble Filter Research Articles

A GSI-Based Coupled EnSRF–En3DVar Hybrid Data Assimilation System for the Operational Rapid Refresh Model: Tests at a Reduced Resolution

Abstract A coupled ensemble square root filter–three-dimensional ensemble-variational hybrid (EnSRF–En3DVar) data assimilation (DA) system is developed for the operational Rapid Refresh (RAP) forecasting system. The En3DVar hybrid system employs the extended control variable method, and is built on the NCEP operational gridpoint statistical interpolation (GSI) three-dimensional variational data assimilation (3DVar) framework. It is coupled with an EnSRF system for RAP, which provides ensemble perturbations. Recursive filters (RF) are used to localize ensemble covariance in both horizontal and vertical within the En3DVar. The coupled En3DVar hybrid system is evaluated with 3-h cycles over a 9-day period with active convection. All conventional observations used by operational RAP are included. The En3DVar hybrid system is run at ⅓ of the operational RAP horizontal resolution or about 40-km grid spacing, and its performance is compared to parallel GSI 3DVar and EnSRF runs using the same datasets and resolution. Short-term forecasts initialized from the 3-hourly analyses are verified against sounding and surface observations. When using equally weighted static and ensemble background error covariances and 40 ensemble members, the En3DVar hybrid system outperforms the corresponding GSI 3DVar and EnSRF. When the recursive filter coefficients are tuned to achieve a similar height-dependent localization as in the EnSRF, the En3DVar results using pure ensemble covariance are close to EnSRF. Two-way coupling between EnSRF and En3DVar did not produce noticeable improvement over one-way coupling. Downscaled precipitation forecast skill on the 13-km RAP grid from the En3DVar hybrid is better than those from GSI 3DVar analyses.

One‐dimensional soil temperature simulation with Common Land Model by assimilating in situ observations and MODISLST with the ensemble particle filter

AbstractSoil temperature plays an important role in hydrology, agriculture, and meteorology. In order to improve the accuracy of soil temperature simulation, a soil temperature data assimilation system was developed based on the Ensemble Particle Filter (EnPF) and the Common Land Model (CLM), and then applied in the Walnut Gulch Experimental Watershed (WGEW) in Arizona, United States. Surface soil temperature in situ observations and Moderate Resolution Imaging Spectroradiometer Land Surface Temperature (MODIS LST) data were assimilated into the system. In this study, four different assimilation experiments were conducted: (1) assimilating in situ observations of instantaneous surface soil temperature each hour, (2) assimilating in situ observations of instantaneous surface soil temperature once per day, (3) assimilating verified MODIS LST once per day, and (4) assimilating original MODIS LST once per day. These four experiments reflect a transition from high‐quality and more frequent in situ observations to lower quality and less frequent remote sensing data in the data assimilation system. The results from these four experiments show that the assimilated results are better than the simulated results without assimilation at all layers except the bottom layer, while the superiority gradually diminishes as the quality and frequency of the observations decrease. This demonstrates that remote sensing data can be assimilated using the ensemble particle filter in poorly gauged catchments to obtain highly accurate soil variables (e.g., soil moisture, soil temperature). Meanwhile, the results also demonstrate that the ensemble particle filter is effective in assimilating soil temperature observations to improve simulations, but the performance of the data assimilation method is affected by the frequency of assimilation and the quality of the input data.

A Comparison of Ensemble Kalman Filters for Storm Surge Assimilation

Abstract This study evaluates and compares the performances of several variants of the popular ensemble Kalman filter for the assimilation of storm surge data with the advanced circulation (ADCIRC) model. Using meteorological data from Hurricane Ike to force the ADCIRC model on a domain including the Gulf of Mexico coastline, the authors implement and compare the standard stochastic ensemble Kalman filter (EnKF) and three deterministic square root EnKFs: the singular evolutive interpolated Kalman (SEIK) filter, the ensemble transform Kalman filter (ETKF), and the ensemble adjustment Kalman filter (EAKF). Covariance inflation and localization are implemented in all of these filters. The results from twin experiments suggest that the square root ensemble filters could lead to very comparable performances with appropriate tuning of inflation and localization, suggesting that practical implementation details are at least as important as the choice of the square root ensemble filter itself. These filters also perform reasonably well with a relatively small ensemble size, whereas the stochastic EnKF requires larger ensemble sizes to provide similar accuracy for forecasts of storm surge.

Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real-time assimilation of streamflow data into operational hydrologic models

Various data assimilation (DA) methods have been used and are being explored for use in operational streamflow forecasting. For ensemble forecasting, ensemble Kalman filter (EnKF) is an appealing candidate for familiarity and relative simplicity. EnKF, however, is optimal in the second-order sense, only if the observation equation is linear. As such, without an iterative approach, EnKF may not be appropriate for assimilating streamflow data for updating soil moisture states due to the strong nonlinear relationships between the two. Maximum likelihood ensemble filter (MLEF), on the other hand, is not subject to the above limitation. Being an ensemble extension of variational assimilation (VAR), MLEF also offers a strong connection with the traditional single-valued forecast process through the control, or the maximum likelihood, solution. In this work, we apply MLEF and EnKF as a fixed lag smoother to the Sacramento (SAC) soil moisture accounting model and unit hydrograph (UH) for assimilation of streamflow, mean areal precipitation (MAP) and potential evaporation (MAPE) data for updating soil moisture states. For comparative evaluation, three experiments were carried out. Comparison between homoscedastic vs. heteroscedastic modeling of selected statistical parameters for DA indicates that heteroscedastic modeling does not improve over homoscedastic modeling, and that homoscedastic error modeling with sensitivity analysis may suffice for application of MLEF for soil moisture updating using streamflow data. Comparative evaluation with respect to the model errors associated with soil moisture dynamics, the ensemble size and the number of streamflow observations assimilated per cycle showed that, in general, MLEF outperformed EnKF under varying conditions of observation and model errors, and ensemble size, and that MLEF performed well with an ensemble size as small as 5 while EnKF required a much larger ensemble size to perform closely to MLEF. Also, MLEF was not very sensitive to the uncertainty parameters and performed reasonably well over relatively wide ranges of parameter settings, an attribute desirable for operational applications where accurate estimation of such parameters is often difficult.

An Observing System Simulation Experiments framework based on the ensemble square root Kalman Filter for evaluating the concentration of chlorophyll a by multi-source data: A case study in Taihu Lake

Data assimilation is a method to produce a description of the system state, as accurately as possible, under the control of observations by using all the available information and by taking into account the observation and model errors. We developed a framework for Observing System Simulation Experiments (OSSEs) based on the ensemble square root Klaman filter (EnSRF) technique, and the framework could assimilate two data sets of chlorophyll a retrieved from Environmental Satellite 1 (HJ-1) and moderate resolution imaging spectro-radiometer (MODIS) onboard the Terra platform, separately. We assumed that one of the retrieved results was the proxy “truth value” and the other one contained errors. Based on EnSRF technique, combined with the three dimensional numerical model of wind-driven circulation and pollutant transportation in a large-scale lake, we investigated the potential impact of location distributions of simulated observation stations in Taihu Lake (China) on the performance of data assimilation. In addition, the effectiveness of this method for evaluation and prediction of the concentration of chlorophyll a was validated. The results showed that the location of simulated observation stations not only influenced the accuracy of evaluating and forecasting results, but also the performance of data assimilation. We also discuss the impact of assimilation time and background error on the results. This study demonstrated that this method of data assimilation is effective for evaluation and prediction of the concentration of chlorophyll a in highly turbid case 2 waters.

Storm-Centered Ensemble Data Assimilation for Tropical Cyclones

Abstract A significant challenge for tropical cyclone ensemble data assimilation is that storm-scale observations tend to make analyses that are more asymmetric than the prior forecasts. Compromised structure and intensity, such as an increase of amplitude across the azimuthal Fourier spectrum, are a routine property of ensemble-based analyses, even with accurate position observations and frequent assimilation. Storm dynamics in subsequent forecasts evolve these states toward axisymmetry, creating difficulty in distinguishing between model-induced and actual storm asymmetries for predictability studies and forecasting. To address this issue, a novel algorithm using a storm-centered approach is proposed. The method is designed for use with existing ensemble filters with little or no modification, facilitating its adoption and maintenance. The algorithm consists of 1) an analysis of the environment using conventional coordinates, 2) a storm-centered analysis using storm-relative coordinates, and 3) a merged analysis that combines the large-scale and storm-scale fields together at an updated storm location. This algorithm is evaluated in two sets of observing system simulation experiments (OSSEs): first, no-cycling tests of the update step for idealized three-dimensional storms in radiative–convective equilibrium; second, full cycling tests of data assimilation applied to a shallow-water model for a field of interacting vortices. Results are compared against a control experiment based on a conventional ensemble Kalman filter (EnKF) scheme as well as an alternative EnKF scheme proposed by Lawson and Hansen. The storm-relative method yields vortices that are more symmetric and exhibit finer inner-core structure than either approach, with errors reduced by an order of magnitude over a control case with prior spread consistent with the National Hurricane Center (NHC)’s mean 5-yr forecast track error at 12 h. Azimuthal Fourier error spectra exhibit much-reduced noise associated with data assimilation as compared to both the control and the Lawson and Hansen approach. An assessment of free-surface height tendency of model forecasts after the merge step reveals a balanced trend between the storm-centered and conventional approaches, with storm-centered values more closely resembling the reference state.

Small-Angle X-Ray Scattering- and Nuclear Magnetic Resonance-Derived Conformational Ensemble of the Highly Flexible Antitoxin PaaA2

Antitoxins from prokaryotic type II toxin-antitoxin modules are characterized by a high degree of intrinsic disorder. The description of such highly flexible proteins is challenging because they cannot be represented by a single structure. Here, we present a combination of SAXS and NMR data to describe the conformational ensemble of the PaaA2 antitoxin from the human pathogen E.coli O157. The method encompasses the use of SAXS data to filter ensembles out of a pool of conformers generated by a custom NMR structure calculation protocol and the subsequent refinement by a block jackknife procedure. The final ensemble obtained through the method is validated by an established residual dipolar coupling analysis. We show that the conformational ensemble of PaaA2 is highly compact and that the protein exists in solution as two preformed helices, connected by a flexible linker, that probably act as molecular recognition elements for toxin inhibition.

Joint estimation of soil moisture profile and hydraulic parameters by ground‐penetrating radar data assimilation with maximum likelihood ensemble filter

AbstractGround‐Penetrating Radar (GPR) has recently become a powerful geophysical technique to characterize soil moisture at the field scale. We developed a data assimilation scheme to simultaneously estimate the vertical soil moisture profile and hydraulic parameters from time‐lapse GPR measurements. The assimilation scheme includes a soil hydrodynamic model to simulate the soil moisture dynamics, a full‐wave electromagnetic wave propagation model, and petrophysical relationship to link the state variable with the GPR data and a maximum likelihood ensemble assimilation algorithm. The hydraulic parameters are estimated jointly with the soil moisture using a state augmentation technique. The approach allows for the direct assimilation of GPR data, thus maximizing the use of the information. The proposed approach was validated by numerical experiments assuming wrong initial conditions and hydraulic parameters. The synthetic soil moisture profiles were generated by the Hydrus‐1D model, which then were used by the electromagnetic model and petrophysical relationship to create “observed” GPR data. The results show that the data assimilation significantly improves the accuracy of the hydrodynamic model prediction. Compared with the surface soil moisture assimilation, the GPR data assimilation better estimates the soil moisture profile and hydraulic parameters. The results also show that the estimated soil moisture profile in the loamy sand and silt soils converge to the “true” state more rapidly than in the clay one. Of the three unknown parameters of the Mualem‐van Genuchten model, the estimation of n is more accurate than that of α and Ks. The approach shows a great promise to use GPR measurements for the soil moisture profile and hydraulic parameter estimation at the field scale.

History matching of statistically anisotropic fields using the Karhunen-Loeve expansion-based global parameterization technique

Traditional ensemble-based history matching method, such as the ensemble Kalman filter and iterative ensemble filters, usually update reservoir parameter fields using numerical grid-based parameterization. Although a parameter constraint term in the objective function for deriving these methods exists, it is difficult to preserve the geological continuity of the parameter field in the updating process of these methods; this is especially the case in the estimation of statistically anisotropic fields (such as a statistically anisotropic Gaussian field and facies field with elongated facies) with uncertainties about the anisotropy direction. In this work, we propose a Karhunen-Loeve expansion-based global parameterization technique that is combined with the ensemble-based history matching method for inverse modeling of statistically anisotropic fields. By using the Karhunen-Loeve expansion, a Gaussian random field can be parameterized by a group of independent Gaussian random variables. For a facies field, we combine the Karhunen-Loeve expansion and the level set technique to perform the parameterization; that is, for each facies, we use a Gaussian random field and a level set algorithm to parameterize it, and the Gaussian random field is further parameterized by the Karhunen-Loeve expansion. We treat the independent Gaussian random variables in the Karhunen-Loeve expansion as the model parameters. When the anisotropy direction of the statistically anisotropic field is uncertain, we also treat it as a model parameter for updating. After model parameterization, we use the ensemble randomized maximum likelihood filter to perform history matching. Because of the nature of the Karhunen-Loeve expansion, the geostatistical characteristics of the parameter field can be preserved in the updating process. Synthetic cases are set up to test the performance of the proposed method. Numerical results show that the proposed method is suitable for estimating statistically anisotropic fields.

Evaluating Ensemble Kalman, Particle, and Ensemble Particle Filters through Soil Temperature Prediction

AbstractData assimilation is a useful tool in hydrologic and agricultural application studies because of its ability to produce predicted results with high accuracy. However, different data-assimilation methods have different performances for a given application. Although the popular ensemble Kalman filter (EnKF) performs well with Gaussian distribution, the error is difficult to conform to the Gaussian distribution. To take advantage of the EnKF, this study presents a new data-assimilation method, ensemble particle filter (EnPF), which is an integration of the EnKF and the particle filter (PF). This new method was evaluated in comparison with two existing methods (EnKF and PF) through soil temperature predictions. The simple biosphere model (SiB2) and the filters were assessed with observations from the Wudaogou experimental area in the Huaihe River basin, China. Results show that when the time interval increases adequately, all the simulated or assimilated results improve significantly. All of these fil...

Assimilation of Doppler radar observations with an ensemble square root filter: A squall line case study

The effectiveness of using an Ensemble Square Root Filter (EnSRF) to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12 July 2005 in midwest Shandong Province using the Weather Research and Forecasting (WRF) model. The experimental results show that: (1) The EnSRF system has the potential to initiate a squall line accurately by assimilation of real Doppler radar data. The convective-scale information has been added into the WRF model through radar data assimilation and thus the analyzed fields are improved noticeably. The model spin-up time has been shortened, and the precipitation forecast is improved accordingly. (2) Compared with the control run, the deterministic forecast initiated with the ensemble mean analysis of EnSRF produces more accurate prediction of microphysical fields. The predicted wind and thermal fields are reasonable and in accordance with the characteristics of convective storms. (3) The propagation direction of the squall line from the ensemble mean analysis is consistent with that of the observation, but the propagation speed is larger than the observed. The effective forecast period for this squall line is about 5–6 h, probably because of the nonlinear development of the convective storm.

Comparisons of Empirical Localization Techniques for Serial Ensemble Kalman Filters in a Simple Atmospheric General Circulation Model

Abstract Two techniques for estimating good localization functions for serial ensemble Kalman filters are compared in observing system simulation experiments (OSSEs) conducted with the dynamical core of an atmospheric general circulation model. The first technique, the global group filter (GGF), minimizes the root-mean-square (RMS) difference between the estimated regression coefficients using a hierarchical ensemble filter. The second, the empirical localization function (ELF), minimizes the RMS difference between the true values of the state variables and the posterior ensemble mean. Both techniques provide an estimate of the localization function for an observation’s impact on a state variable with few a priori assumptions about the localization function. The ELF localizations can have values larger than 1.0 at small distances, indicating that this technique addresses localization but also can correct the prior ensemble spread in the same way as a variance inflation when needed. OSSEs using ELF localizations generally have smaller root-mean-square error (RMSE) than the optimal Gaspari and Cohn (GC) localization function obtained by empirically tuning the GC width. The localization functions estimated by the GGF are broader than those from the ELF, and the OSSEs with the GGF localization generally have larger RMSE than the optimal GC localization function. The GGFs are too broad because of spurious correlation biases that occur in the OSSEs. These errors can be reduced by using a stochastic EnKF with perturbed observations instead of a deterministic EAKF.

Data classification using an ensemble of filters

Ensemble learning has been the focus of much attention, based on the assumption that combining the output of multiple experts is better than the output of any single expert. Many methods have been proposed of which bagging and boosting were the most popular. In this research, the idea of ensembling is adapted for feature selection. We propose an ensemble of filters for classification, aimed at achieving a good classification performance together with a reduction in the input dimensionality. With this approach, we try to overcome the problem of selecting an appropriate method for each problem at hand, as it is overly dependent on the characteristics of the datasets. The adequacy of using an ensemble of filters rather than a single filter was demonstrated on synthetic and real data, paving the way for its final application over a challenging scenario such as DNA microarray classification.

Technical Note: Comparison of ensemble Kalman filter and variational approaches for CO<sub>2</sub> data assimilation

Abstract. Data assimilation (DA) approaches, including variational and the ensemble Kalman filter methods, provide a computationally efficient framework for solving the CO2 source–sink estimation problem. Unlike DA applications for weather prediction and constituent assimilation, however, the advantages and disadvantages of DA approaches for CO2 flux estimation have not been extensively explored. In this study, we compare and assess estimates from two advanced DA approaches (an ensemble square root filter and a variational technique) using a batch inverse modeling setup as a benchmark, within the context of a simple one-dimensional advection–diffusion prototypical inverse problem that has been designed to capture the nuances of a real CO2 flux estimation problem. Experiments are designed to identify the impact of the observational density, heterogeneity, and uncertainty, as well as operational constraints (i.e., ensemble size, number of descent iterations) on the DA estimates relative to the estimates from a batch inverse modeling scheme. No dynamical model is explicitly specified for the DA approaches to keep the problem setup analogous to a typical real CO2 flux estimation problem. Results demonstrate that the performance of the DA approaches depends on a complex interplay between the measurement network and the operational constraints. Overall, the variational approach (contingent on the availability of an adjoint transport model) more reliably captures the large-scale source–sink patterns. Conversely, the ensemble square root filter provides more realistic uncertainty estimates. Selection of one approach over the other must therefore be guided by the carbon science questions being asked and the operational constraints under which the approaches are being applied.

Error Covariance Estimation for Coupled Data Assimilation Using a Lorenz Atmosphere and a Simple Pycnocline Ocean Model

Abstract Coupled data assimilation uses a coupled model consisting of multiple time-scale media to extract information from observations that are available in one or more media. Because of the instantaneous exchanges of information among the coupled media, coupled data assimilation is expected to produce self-consistent and physically balanced coupled state estimates and optimal initialization for coupled model predictions. It is also expected that applying coupling error covariance between two media into observational adjustments in these media can provide direct observational impacts crossing the media and thereby improve the assimilation quality. However, because of the different time scales of variability in different media, accurately evaluating the error covariance between two variables residing in different media is usually very difficult. Using an ensemble filter together with a simple coupled model consisting of a Lorenz atmosphere and a pycnocline ocean model, which characterizes the interaction of multiple time-scale media in the climate system, the impact of the accuracy of coupling error covariance on the quality of coupled data assimilation is studied. Results show that it requires a large ensemble size to improve the assimilation quality by applying coupling error covariance in an ensemble coupled data assimilation system, and the poorly estimated coupling error covariance may otherwise degrade the assimilation quality. It is also found that a fast-varying medium has more difficulty being improved using observations in slow-varying media by applying coupling error covariance because the linear regression from the observational increment in slow-varying media has difficulty representing the high-frequency information of the fast-varying medium.

Empirical Localization of Observation Impact in Ensemble Kalman Filters

Abstract Localization is a method for reducing the impact of sampling errors in ensemble Kalman filters. Here, the regression coefficient, or gain, relating ensemble increments for observed quantity y to increments for state variable x is multiplied by a real number α defined as a localization. Localization of the impact of observations on model state variables is required for good performance when applying ensemble data assimilation to large atmospheric and oceanic problems. Localization also improves performance in idealized low-order ensemble assimilation applications. An algorithm that computes localization from the output of an ensemble observing system simulation experiment (OSSE) is described. The algorithm produces localizations for sets of pairs of observations and state variables: for instance, all state variables that are between 300- and 400-km horizontal distance from an observation. The algorithm is applied in a low-order model to produce localizations from the output of an OSSE and the computed localizations are then used in a new OSSE. Results are compared to assimilations using tuned localizations that are approximately Gaussian functions of the distance between an observation and a state variable. In most cases, the empirically computed localizations produce the lowest root-mean-square errors in subsequent OSSEs. Localizations derived from OSSE output can provide guidance for localization in real assimilation experiments. Applying the algorithm in large geophysical applications may help to tune localization for improved ensemble filter performance.

Assimilating AMSU-A Radiances in the TC Core Area with NOAA Operational HWRF (2011) and a Hybrid Data Assimilation System: Danielle (2010)

Abstract A regional hybrid variational–ensemble data assimilation system (HVEDAS), the maximum likelihood ensemble filter (MLEF), is applied to the 2011 version of the NOAA operational Hurricane Weather Research and Forecasting (HWRF) model to evaluate the impact of direct assimilation of cloud-affected Advanced Microwave Sounding Unit-A (AMSU-A) radiances in tropical cyclone (TC) core areas. The forward components of both the gridpoint statistical interpolation (GSI) analysis system and the Community Radiative Transfer Model (CRTM) are utilized to process and simulate satellite radiances. The central strategies to allow the use of cloud-affected radiances are (i) to augment the control variables to include clouds and (ii) to add the model cloud representations in the observation forward models to simulate the microwave radiances. The cloudy AMSU-A radiance assimilation in Hurricane Danielle's (2010) core area has produced encouraging results with respect to the operational cloud-cleared radiance preprocessing procedures used in this study. Through the use of the HVEDAS, ensemble covariance statistics for a pseudo-AMSU-A observation in Danielle's core area show physically meaningful error covariances and statistical couplings with hydrometeor variables (i.e., the total-column condensate in Ferrier microphysics). The cloudy radiance assimilation in the TC core region (i.e., ASR experiment) consistently reduced the root-mean-square errors of the background departures, and also generally improved the forecasts of Danielle's intensity as well as the quantitative cloud analysis and prediction. It is also indicated that an entropy-based information content quantification process provides a useful metric for evaluating the utility of satellite observations in hybrid data assimilation.

Joint state and parameter estimation with an iterative ensemble Kalman smoother

Abstract. Both ensemble filtering and variational data assimilation methods have proven useful in the joint estimation of state variables and parameters of geophysical models. Yet, their respective benefits and drawbacks in this task are distinct. An ensemble variational method, known as the iterative ensemble Kalman smoother (IEnKS) has recently been introduced. It is based on an adjoint model-free variational, but flow-dependent, scheme. As such, the IEnKS is a candidate tool for joint state and parameter estimation that may inherit the benefits from both the ensemble filtering and variational approaches. In this study, an augmented state IEnKS is tested on its estimation of the forcing parameter of the Lorenz-95 model. Since joint state and parameter estimation is especially useful in applications where the forcings are uncertain but nevertheless determining, typically in atmospheric chemistry, the augmented state IEnKS is tested on a new low-order model that takes its meteorological part from the Lorenz-95 model, and its chemical part from the advection diffusion of a tracer. In these experiments, the IEnKS is compared to the ensemble Kalman filter, the ensemble Kalman smoother, and a 4D-Var, which are considered the methods of choice to solve these joint estimation problems. In this low-order model context, the IEnKS is shown to significantly outperform the other methods regardless of the length of the data assimilation window, and for present time analysis as well as retrospective analysis. Besides which, the performance of the IEnKS is even more striking on parameter estimation; getting close to the same performance with 4D-Var is likely to require both a long data assimilation window and a complex modeling of the background statistics.

An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state.Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.

Ensemble square root filter assimilation of near-surface soil moisture and reference-level observations into a coupled land surface-boundary layer model

The potential for using the ensemble square root filter data assimilation technique to estimate soil moisture profiles, surface heat fluxes, and the state of the planetary boundary layer (PBL) is explored. An observing system simulation experiment is designed to mimic the assimilation of near-surface soil moisture observations (θ°) and in-situ measurements of 2-m temperature (T°), 2-m specific humidity (Q°), and 10-m horizontal winds [V°=(U°, V°)]. The background forecasts are generated by a one-dimensional coupled land surface-boundary layer model (CLS-BLM) with soil, surface-layer and PBL parameterization schemes similar to those used in the Weather Research and Forecasting (WRF) model. Soil moisture, surface heat fluxes, and the state of the PBL evolve on different characteristic timescales, so the minimum assimilation time intervals required for skillful estimates of each target component are different. Correct estimates of the soil moisture profile are obtained effectively when a 6-h update time interval is used, while skillful estimates of surface fluxes and the PBL state require more frequent updates. The CLS-BLM requires a shorter assimilation time interval to correctly estimate the soil moisture profile than previously indicated by experiments using an off-line land surface model (LSM). Results from assimilating different subsets of observations show that θ° makes a larger contribution to soil moisture estimates, while T°, θ°, and V° are more important for estimates of surface heat fluxes and the PBL state. It is therefore necessary to combine these variables to accurately estimate the states of both the land surface and the PBL. Experimentation with different prescribed observational errors shows that the assimilation system is more sensitive to increases in observational errors than to reductions in observational errors.