Benefits of smoothing backgrounds and radar reflectivity observations for multiscale data assimilation with an ensemble Kalman filter at convective scales: A proof of concept study

In the ensemble Kalman filter (EnKF), the covariance localization radius is usually small when assimilating radar observations because of high density of the radar observations. This makes the region away from precipitation difficult to correct if no other observations are available, as there is no reason to correct the background. To correct errors away from the innovating radar observations, a multiscale localization (MLoc) method adapted to dense observations like those from radar is proposed. In this method, different scales are corrected successively by using the same reflectivity observations, but with different degree of smoothing and localization radius at each step. In the context of observing system simulation experiments, single and multiple assimilation experiments are conducted with the MLoc method. Results show that the MLoc assimilation updates areas that are away from the innovative observations and improves on average the analysis and forecast quality in single cycle and cycling assimilation experiments. The forecast gains are maintained until the end of the forecast period, illustrating the benefits of correcting different scales.

An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation

The covariance matrix estimated from the ensemble data assimilation always suffers from filter collapse because of the spurious correlations induced by the finite ensemble size. The localization technique is applied to ameliorate this issue, which has been suggested to be effective. In this paper, an adaptive scheme for Schur product covariance localization is proposed, which is easy and efficient to implement in the ensemble data assimilation frameworks. A Gaussian-shaped taper function is selected as the localization taper function for the Schur product in the adaptive localization scheme, and the localization radius is obtained adaptively through a certain criterion of correlations with the background ensembles. An idealized Lorenz96 model with an ensemble Kalman filter is firstly examined, showing that the adaptive localization scheme helps to significantly reduce the spurious correlations in the small ensemble with low computational cost and provides accurate covariances that are similar to those derived from a much larger ensemble. The investigations of adaptive localization radius reveal that the optimal radius is model-parameter-dependent, vertical-level-dependent and nearly flow-dependent with weather scenarios in a realistic model; for example, the radius of model parameter zonal wind is generally larger than that of temperature. The adaptivity of the localization scheme is also illustrated in the ensemble framework and shows that the adaptive scheme has a positive effect on the assimilated analysis as the well-tuned localization.

Exploring Assimilation Order to Improve Assimilation with Serial Ensemble Kalman Filter

Serial ensemble Kalman filter (EnKF) is a kind of EnKF which treats observations serially during every assimilation step. The assimilation order can be generated by different rules and has significant impacts on the performance of serial EnKF when localization algorithm is applied. In this study, we seek to examine and better understand the characteristics of various ordering methods when they are applied in the serial EnKF. The results show that different ordering methods demonstrate almost the same changes in analysis as the localization radius changing. Moreover, the optimal parameters of localization radius and forgetting factor of serial EnKF are found varying among different ordering rules. In addition, a novel rule for confirming the assimilation order is proposed to further improve the performance of serial EnKF. The observations are sorted from “better” to “worse” (OBS-BtoW), which are evaluated by estimating the distance of analysis between the prior and observations. Compared with the existing ordering methods, the proposed method can improve the performance at a very small computation cost without needing future forecasts and the truth.

Lagrangian Data Assimilation of Surface Drifters to Support Ocean and Coupled Model Initialization

<p>The air-sea interface is one of the most physically active interfaces of the Earth's environments and significantly impacts the dynamics in both the atmosphere and ocean. In this study, we discuss the data assimilation of surface drifters, of which the dynamic motions are highly relevant to the instant change of both surface wind field and underlying ocean flow fields. We intend to take advantage of this relationship and improve the estimation of the model initialization in both ocean and coupled atmosphere-ocean systems.</p><p>The assimilation of position data from Lagrangian observing platforms is underdeveloped in operational applications because of two main challenges: 1) nonlinear growth of model and observation error in the Lagrangian trajectories, and 2) the high dimensionality of realistic models. In this study, we first propose an augemented-state Lagrangian data assimilation (LaDA) method that is based on the Local Ensemble Transform Kalman Filter (LETKF). The algorithm is tested with “identical twin” approach of Observing System Simulation Experiments (OSSEs) using the ocean model. Examinations on both of the eddy-permitting and the eddy-resolving Modular Ocean Model of the Geophysical Fluid Dynamics Laboratory (GFDL) are tested, which is intended to update the ocean states (T/S/U/V) at both the surface and at depth by directly assimilating the drifter locations. Results show that with a proper choice of localization radius, the LaDA can outperform conventional assimilation of surface in situ temperature and salinity measurements. The improvements are seen not only in the surface state estimate, but also throughout the ocean column to deep layer. The impacts of localization radius and model error in estimating accuracy of both fluid and drifter states are further investigated. In the second section, we investigate the LaDA within a Strongly Coupled Data Assimilation (SCDA) system using the simplified Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), a three-layer truncated quasi-geostrophic model. Results show that assimilating the surface drifter locations directly is capable of improving not only the ocean states but also the atmosphere states as well. We then compare it to the conventional approach to assimilate the approximated velocities instead of the direct drifter locations and it shows that the assimilating drifter locations outperforms the other approach.</p>

Lagrangian Data Assimilation of Surface Drifters in a Double-Gyre Ocean Model Using the Local Ensemble Transform Kalman Filter

The assimilation of position data from Lagrangian observing platforms is underdeveloped in operational applications because of two main challenges: 1) nonlinear growth of model and observation error in the Lagrangian trajectories, and 2) the high dimensionality of realistic models. In this study, we propose a localized Lagrangian data assimilation (LaDA) method that is based on the local ensemble transform Kalman filter (LETKF). The algorithm is tested with an “identical twin” approach in observing system simulation experiments (OSSEs) using a simple double-gyre configuration of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model. Results from the OSSEs show that with a proper choice of localization radius, the LaDA can outperform conventional assimilation of surface in situ temperature and salinity measurements. The improvements are seen not only in the surface state estimate, but also throughout the ocean column to 1000 m depth. The impacts of localization radius and model error in estimating accuracy of both fluid and drifter states are further investigated.

On the Selection of Localization Radius in Ensemble Filtering for Multiscale Quasigeostrophic Dynamics

Covariance localization remedies sampling errors due to limited ensemble size in ensemble data assimilation. Previous studies suggest that the optimal localization radius depends on ensemble size, observation density and accuracy, as well as the correlation length scale determined by model dynamics. A comprehensive localization theory for multiscale dynamical systems with varying observation density remains an active area of research. Using a two-layer quasigeostrophic (QG) model, this study systematically evaluates the sensitivity of the best Gaspari–Cohn localization radius to changes in model resolution, ensemble size, and observing networks. Numerical experiment results show that the best localization radius is smaller for smaller-scale components of a QG flow, indicating its scale dependency. The best localization radius is rather insensitive to changes in model resolution, as long as the key dynamical processes are reasonably well represented by the low-resolution model with inflation methods that account for representation errors. As ensemble size decreases, the best localization radius shifts to smaller values. However, for nonlocal correlations between an observation and state variables that peak at a certain distance, decreasing localization radii further within this distance does not reduce analysis errors. Increasing the density of an observing network has two effects that both reduce the best localization radius. First, the reduced observation error spectral variance further constrains prior ensembles at large scales. Less large-scale contribution results in a shorter overall correlation length, which favors a smaller localization radius. Second, a denser network provides more independent pieces of information, thus a smaller localization radius still allows the same number of observations to constrain each state variable.

Impact of MPEX Upsonde Observations on Ensemble Analyses and Forecasts of the 31 May 2013 Convective Event over Oklahoma

This study examines the impact of assimilating three radiosonde profiles obtained from ground-based mobile systems during the Mesoscale Predictability Experiment (MPEX) on analyses and convection-permitting model forecasts of the 31 May 2013 convective event over Oklahoma. These radiosonde profiles (in addition to standard observations) are assimilated into a 36-member mesoscale ensemble using an ensemble Kalman filter (EnKF) before embedding a convection-permitting (3 km) grid and running a full ensemble of 9-h forecasts. This set of 3-km forecasts is compared to a control run that does not assimilate the MPEX soundings. The analysis of low- to midlevel moisture is impacted the most by the assimilation, but coherent mesoscale differences in temperature and wind are also seen, primarily downstream of the location of the soundings. The ensemble of forecasts of convection on the 3-km grid are improved the most in the first three hours of the forecast in a region where the analyzed position of low-level frontal convergence and midlevel moisture was improved on the mesoscale grid. Later forecasts of the upscale growth of intense convection over central Oklahoma are improved somewhat, but larger ensemble spread lowers confidence in the significance of the improvements. Changes in the horizontal localization radius from the standard value applied to the MPEX sounding assimilation alters the specific times that the forecasts are improved in the first three hours of the forecasts, while changes to the vertical localization radius and specified temperature and wind observation error result in little to no improvements in the forecasts.

A Probabilistic Approach to Adaptive Covariance Localization for Serial Ensemble Square Root Filters

This study proposes a variational approach to adaptively determine the optimum radius of influence for ensemble covariance localization when uncorrelated observations are assimilated sequentially. The covariance localization is commonly used by various ensemble Kalman filters to limit the impact of covariance sampling errors when the ensemble size is small relative to the dimension of the state. The probabilistic approach is based on the premise of finding an optimum localization radius that minimizes the distance between the Kalman update using the localized sampling covariance versus using the true covariance, when the sequential ensemble Kalman square root filter method is used. The authors first examine the effectiveness of the proposed method for the cases when the true covariance is known or can be approximated by a sufficiently large ensemble size. Not surprisingly, it is found that the smaller the true covariance distance or the smaller the ensemble, the smaller the localization radius that is needed. The authors further generalize the method to the more usual scenario that the true covariance is unknown but can be represented or estimated probabilistically based on the ensemble sampling covariance. The mathematical formula for this probabilistic and adaptive approach with the use of the Jeffreys prior is derived. Promising results and limitations of this new method are discussed through experiments using the Lorenz-96 system.

The Impact of Data Assimilation Length Scales on Analysis and Prediction of Convective Storms

An idealized convective test bed for the local ensemble transform Kalman filter (LETKF) is set up to perform storm-scale data assimilation of simulated Doppler radar observations. Convective systems with lifetimes exceeding 6 h are triggered in a doubly periodic domain. Perfect-model experiments are used to investigate the limited predictability in precipitation forecasts by comparing analysis schemes that resolve different length scales. Starting from a high-resolution reference scheme with 8-km covariance localization and observations with 2-km resolution on a 5-min cycle, an experimental hierarchy is set up by successively choosing a larger covariance localization radius of 32 km, observations that are horizontally averaged by a factor of 4, a coarser resolution in the calculation of the analysis weights, and a cycling interval of 20 min. After 3 h of assimilation, the high-resolution analysis scheme is clearly superior to the configurations with coarser scales in terms of RMS error and field-oriented measures. The difference is associated with the observation resolution and a larger localization radius required for filter convergence with coarse observations. The high-resolution analysis leads to better forecasts for the first hour, but after 3 hours, the forecast quality of the schemes is indistinguishable. The more rapid error growth in forecasts from the high-resolution analysis appears to be associated with a limited predictability of the small scales, but also with gravity wave noise and spurious convective cells. The latter suggests that the field is in some sense less balanced, or less consistent with the model dynamics, than in the coarser-resolution analysis.

On the Choice of an Optimal Localization Radius in Ensemble Kalman Filter Methods

In data assimilation applications using ensemble Kalman filter methods, localization is necessary to make the method work with high-dimensional geophysical models. For ensemble square root Kalman filters, domain localization (DL) and observation localization (OL) are commonly used. Depending on the localization method, appropriate values have to be chosen for the localization parameters, such as the localization length and the weight function. Although frequently used, the properties of the localization techniques are not fully investigated. Thus, up to now an optimal choice for these parameters is a priori unknown and they are generally found by expensive numerical experiments. In this study, the relationship between the localization length and the ensemble size in DL and OL is studied using twin experiments with the Lorenz-96 model and a two-dimensional shallow-water model. For both models, it is found that the optimal localization length for DL and OL depends linearly on an effective local observation dimension that is given by the sum of the observation weights. In the experiments no influence of the model dynamics on the optimal localization length was observed. The effective observation dimension defines the degrees of freedom that are required for assimilating observations, while the ensemble size defines the available degrees of freedom. Setting the localization radius such that the effective local observation dimension equals the ensemble size yields an adaptive localization radius. Its performance is tested using a global ocean model. The experiments show that the analysis quality using the adaptive localization is similar to the analysis quality of an optimally tuned constant localization radius.