Root Kalman Filter Research Articles

Real-time optimization control of variable rotor speed based on Helicopter/ turboshaft engine on-board composite system

In order to adequately leverage the advantages of coaxial compound helicopters (CCH) to enhance overall performance and efficiency through variable rotor speed, and to improve the fuel economy of the composite propulsion system, a real-time optimization control method of variable rotor speed based on helicopter/turboshaft engine on-board composite system is proposed. Firstly, a steady-state model of the CCH required power and an on-board inverse model of the turboshaft engine based on an improved deep neural network propulsion system model (AdamDNN-PSM) are established. On this basis, an on-board adaptive model based on adaptive square root Kalman filter (ASRUKF) estimator is employed to correct the precision of the on-board inverse model and to track the real engine state. Finally, by adopting the feasible sequence quadratic programming (FSQP) method, an optimal speed rotor (OSR) is obtained through real-time optimization control, which reduces fuel consumption during cruising while considering both the geometric and aerodynamic constraints of the rotor. The simulation results demonstrate that the accuracy and real-time performance of the on-board inverse model have been significantly improved. The real-time optimization control method for OSR effectively reduces fuel consumption during cruising and enhances the CCH performance of the entire flight envelope.

Estimating Time-Dependent Structures in a Multivariate Causality for Land–Atmosphere Interactions

Abstract The land surface and atmosphere interaction forms an integral part of the climate system. However, this intricate relationship involves many complicated interactions and feedback effects between multiple variables. As a result, relying solely on traditional linear regression analysis and correlation analysis to distinguish between multivariate complex “driver–response” relations can be challenging, since they do not have the needed asymmetry to establish causality. The Liang–Kleeman (LK) information flow theory provides a strict nonparametric causality measurement for identifying the causality between any given time series, and its recent extension from bivariate to multivariate form provides a powerful tool for causal inference in complex multivariate systems. However, the multivariate LK information flow also assumes stationarity in time and requires a sufficiently long time series to ensure statistical sufficiency. To remedy this challenge, we rely on the square-root Kalman filter to estimate the time-varying form of the multivariate LK information flow causality. The results from theoretical and real-world applications show that the new algorithm provides a valuable tool for characterizing time-varying causal relationships in land–atmosphere interactions, even when the time series are short and highly correlated. Significance Statement Causality in land–atmosphere interactions is generally characterized by seasonal and intraseasonal changes that are usually not captured with commonly used approaches, because most approaches assume the time series are stationary. In this study, we extend the recently proposed multivariate Liang–Kleeman information flow causality (MtvLK) to handle nonstationary systems such as those in land–atmosphere interactions. By considering nonstationarity, we aim to unravel time-varying causal structures that are usually masked out in commonly used methods. Validating the MtvLK with synthetic models showed that the MtvLK is able to obtain the expected causal structures. Furthermore, real-world applications reveal novel findings of the time-varying causal structures between soil moisture, vapor pressure deficit, and the gross primary product.

Novel method for modelling and adaptive estimation for SOC and SOH of lithium-ion batteries

Equivalent circuit models of lithium-ion batteries are the foundation of accurately estimating state of charge (SOC) and state of health (SOH). To further describe the performance of the batteries between working and idling states, we present for the first time the analysis of an improved fractional-order model (IFOM). Moreover, an endogenous immune algorithm (EIA) is proposed to identify the parameters of the model. Meanwhile, considering the aging effect, an adaptive dual square root Kalman filtering (ADSRCKF) with the dormancy zone is proposed to achieve the estimation. The first filter in ADSRCKF estimates SOC and SOH in which the SOH is characterised by the ohmic resistance. The second filter adaptively updates the drifted model parameters according to the dormancy zone. Finally, the proposed method is evaluated with the random walk charging and discharging test. The experimental results illustrate that the adaptively updated parameters can better match the battery status in real time, and the proposed ADSRCKF can achieve high accuracy with strong robustness. For the initial SOC error, the root mean square error (RMSE) of SOC is less than 0.3%, and the RMSE is approximately 1% even when the initial capacity is also deviated.

An inversion model based on GEOS-Chem for estimating global and China's terrestrial carbon fluxes in 2019

The 2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories added the method of assimilating atmospheric CO2 concentrations to invert carbon sources and sinks; however, many global carbon inversion models are not publicly available. In addition, our regional assimilation inversion system, CCMVS-R (China Carbon Monitoring, Verification and Supporting for Regional), needs a global carbon inversion model with higher assimilation efficiency to provide boundary conditions. Here, an inversion model based on the global atmospheric chemistry model GEOS-Chem and a more accurate and easier-to-implement ensemble square root Kalman filter (EnSRF) algorithm is constructed and used to infer global and China's carbon fluxes in 2019. Atmospheric CO2 concentrations from ObsPack sites and five additional CO2 observational sites from China's Greenhouse Gas Observation Network (CGHGNET) were used for data assimilation to improve the estimate. The inverted annual global terrestrial and oceanic carbon uptake is 2.12 and 2.53 Pg C per year, respectively, accounting for 21.1% and 25.1% of global fossil fuel CO2 emissions. The remaining 5.41 Pg C per year in the atmosphere is consistent with the global atmospheric CO2 growth rates of 5.44 Pg C per year reported by the National Oceanic and Atmospheric Administration (NOAA), showing that the inversion model can provide a reasonable estimate of global-scale natural carbon sinks. The inverted terrestrial carbon sink of China is 0.37 Pg C per year, accounting for approximately 13% of China's fossil CO2 emissions.

External force estimation for robot manipulator based on a LuGre-linear-hybrid friction model and an improved square root cubature Kalman filter

PurposeThe sensorless external force estimation of robot manipulator can be helpful for reducing the cost and complexity of the robot system. However, the complex friction phenomenon of the robot joint and uncertainty of robot model and signal noise significantly decrease the estimation accuracy. This study aims to investigate the friction modeling and the noise rejection of the external force estimation.Design/methodology/approachA LuGre-linear-hybrid (LuGre-L) friction model that combines the dynamic friction characteristics of the robot joint and static friction of the drive motor is proposed to improve the modeling accuracy of robot friction. The square root cubature Kalman filter (SCKF) is improved by integrating a Sage Window outer layer and a nonlinear disturbance observer (NDOB) inner layer. In the outer layer, Sage Window is integrated in the square root Kalman filter (W-SCKF) to dynamically adjust noise statistics. NDOB is applied as the inner layer of W-SCKF (NDOB-WSCKF) to obtain the uncertain state variables of the state model.FindingsA peg-in-hole contact experiment conducted on a real robot demonstrates that the average accuracy of the estimated joint torque based on LuGre-L is improved by 4.9% in contrast to the LuGre model. Based on the proposed NDOB-WSCKF, the average estimation accuracy of the external joint torque can reach up to 92.1%, which is improved by 4%–15.3% in contrast to other estimation methods (SCKF and NDOB).Originality/valueA LuGre-L friction model is proposed to handle the coupling of static and dynamic friction characteristics for the robot manipulator. An improved SCKF is applied to estimate the external force of the robot manipulator. To improve the noise rejection ability of the estimation method and make it more resistant to unmodeled state variable, SCKF is improved by integrating a Sage Window and NDOB, and a NDOB-WSCKF external force estimator is developed. Validation results demonstrate that the accuracy of the robot dynamics model and the estimated external force is improved by the proposed method.

On the Choice of Metric to Calibrate Time-Invariant Ensemble Kalman Filter Hyper-Parameters for Discharge Data Assimilation and Its Impact on Discharge Forecast Modelling

An important step when using some data assimilation methods, such as the ensemble Kalman filter and its variants, is to calibrate its parameters. Also called hyper-parameters, these include the model and observation errors, which have previously been shown to have a strong impact on the performance of the data assimilation method. Many metrics can be used to calibrate these hyper-parameters but may not all yield the same optimal set of values. The current study investigated the importance of the choice of metric used during the hyper-parameter calibration phase and its impact on discharge forecasts. The types of metrics used each focused on discharge accuracy, ensemble spread or observation-minus-background statistics. The calibration was performed for the ensemble square root Kalman filter over two catchments in Canada using two different hydrologic models per catchment. Results show that the optimal set of hyper-parameters depended heavily on the choice of metric used during the calibration phase, where data assimilation was applied. These sets of hyper-parameters in turn produced different hydrologic forecasts. This influence was reduced as the forecast lead time increased, because of not applying data assimilation in the forecast mode, and accordingly, convergence of model state ensembles produced in the calibration phase. However, the influence could remain considerable for a few days up to multiple weeks depending on the catchment and the model. As such, a preliminary analysis would be recommended for future studies to better understand the impact that metrics can have within and outside the bounds of hyper-parameter calibration.

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.

A Time-Varying Causality Formalism Based on the Liang–Kleeman Information Flow for Analyzing Directed Interactions in Nonstationary Climate Systems

AbstractThe interaction between the land surface and the atmosphere is of significant importance in the climate system because it is a key driver of the exchanges of energy and water. Several important relations to heat waves, floods, and droughts exist that are based on the interaction of soil moisture and, for instance, air temperature and humidity. Our ability to separate the elements of this coupling, identify the exact locations where they are strongest, and quantify their strengths is, therefore, of paramount importance to their predictability. A recent rigorous causality formalism based on the Liang–Kleeman (LK) information flow theory has been shown, both theoretically and in real-world applications, to have the necessary asymmetry to infer the directionality and magnitude within geophysical interactions. However, the formalism assumes stationarity in time, whereas the interactions within the land surface and atmosphere are generally nonstationary; furthermore, it requires a sufficiently long time series to ensure statistical sufficiency. In this study, we remedy this difficulty by using the square root Kalman filter to estimate the causality based on the LK formalism to derive a time-varying form. Results show that the new formalism has similar properties compared to its time-invariant form. It is shown that it is also able to capture the time-varying causality structure within soil moisture–air temperature coupling. An advantage is that it does not require very long time series to make an accurate estimation. Applying a wavelet transform to the results also reveals the full range of temporal scales of the interactions.

On the Efficiency of Covariance Localisation of the Ensemble Kalman Filter Using Augmented Ensembles

Localisation is one of the main reasons for the success of the ensemble Kalman filter (EnKF) in high-dimensional geophysical data assimilation problems. It is based on the assumption that correlations between variables of a dynamical system decrease at a fast rate with the physical distance. In the EnKF, two types of localisation methods have emerged: domain localisation and covariance localisation. In this article, we explore possible implementations for covariance localisation in the deterministic EnKF using augmented ensembles in the analysis. We first discuss and compare two different methods to construct the augmented ensemble. The first method, known as modulation, relies on a factorisation property of the background covariance matrix. The second method is based on randomised singular value decomposition (svd) techniques, which has not been previously applied to covariance localisation. The qualitative properties of both methods are illustrated using a simple one-dimensional covariance model. We then show how localisation can be introduced in the perturbation update step using this augmented ensemble framework and we derive a generic ensemble square root Kalman filter with covariance localisation (LEnSRF). Using twin simulations of the Lorenz-1996 model we show that the LEnSRF is numerically more efficient when combined with the randomised svd method than with the modulation method. Finally we introduce a realistic extension of the LEnSRF that uses domain localisation in the horizontal direction and covariance localisation in the vertical direction. Using twin simulations of a multilayer extension of the Lorenz-1996 model, we show that this approach is adequate to assimilate satellite radiances, for which domain localisation alone is insufficient.

On the consistency of the local ensemble square root Kalman filter perturbation update

We examine the perturbation update step of the ensemble Kalman filters which rely on covariance localisation, and hence have the ability to assimilate non-local observations in geophysical models. We show that the updated perturbations of these ensemble filters are not to be identified with the main empirical orthogonal functions of the analysis covariance matrix, in contrast with the updated perturbations of the local ensemble transform Kalman filter (LETKF). Building on that evidence, we propose a new scheme to update the perturbations of a local ensemble square root Kalman filter (LEnSRF) with the goal to minimise the discrepancy between the analysis covariances and the sample covariances regularised by covariance localisation. The scheme has the potential to be more consistent and to generate updated members closer to the model’s attractor (showing fewer imbalances). We show how to solve the corresponding optimisation problem and discuss its numerical complexity. The qualitative properties of the perturbations generated from this new scheme are illustrated using a simple one-dimensional covariance model. Moreover, we demonstrate on the discrete Lorenz–96 and continuous Kuramoto–Sivashinsky one-dimensional low-order models that the new scheme requires significantly less, and possibly none, multiplicative inflation needed to counteract imbalance, compared to the LETKF and the LEnSRF without the new scheme. Finally, we notice a gain in accuracy of the new LEnSRF as measured by the analysis and forecast root mean square errors, despite using well-tuned configurations where such gain is very difficult to obtain.

Parallel Direct Solution of the Covariance-Localized Ensemble Square Root Kalman Filter Equations with Matrix Functions

Abstract Recently, the serial approach to solving the square root ensemble Kalman filter (ESRF) equations in the presence of covariance localization was found to depend on the order of observations. As shown previously, correctly updating the localized posterior covariance in serial requires additional effort and computational expense. A recent work by Steward et al. details an all-at-once direct method to solve the ESRF equations in parallel. This method uses the eigenvectors and eigenvalues of the forward observation covariance matrix to solve the difficult portion of the ESRF equations. The remaining assimilation is easily parallelized, and the analysis does not depend on the order of observations. While this allows for long localization lengths that would render local analysis methods inefficient, in theory, an eigenpair-based method scales as the cube number of observations, making it infeasible for large numbers of observations. In this work, we extend this method to use the theory of matrix functions to avoid eigenpair computations. The Arnoldi process is used to evaluate the covariance-localized ESRF equations on the reduced-order Krylov subspace basis. This method is shown to converge quickly and apparently regains a linear scaling with the number of observations. The method scales similarly to the widely used serial approach of Anderson and Collins in wall time but not in memory usage. To improve the memory usage issue, this method potentially can be used without an explicit matrix. In addition, hybrid ensemble and climatological covariances can be incorporated.

Parallel Direct Solution of the Ensemble Square Root Kalman Filter Equations with Observation Principal Components

AbstractThe ensemble square root Kalman filter (ESRF) is a variant of the ensemble Kalman filter used with deterministic observations that includes a matrix square root to account for the uncertainty of the unperturbed ensemble observations. Because of the difficulties in solving this equation, a serial approach is often used where observations are assimilated sequentially one after another. As previously demonstrated, in implementations to date the serial approach for the ESRF is suboptimal when used in conjunction with covariance localization, as the Schur product used in the localization does not commute with assimilation. In this work, a new algorithm is presented for the direct solution of the ESRF equations based on finding the eigenvalues and eigenvectors of a sparse, square, and symmetric positive semidefinite matrix with dimensions of the number of observations to be assimilated. This is amenable to direct computation using dedicated, massively parallel, and mature libraries. These libraries make it relatively simple to assemble and compute the observation principal components and to solve the ESRF without using the serial approach. They also provide the eigenspectrum of the forward observation covariance matrix. The parallel direct approach described in this paper neglects the near-zero eigenvalues, which regularizes the ESRF problem. Numerical results show this approach is a highly scalable parallel method.

Integrated GPS/DR Vehicle Navigation System Based on Sequential and Square Root Kalman Filters

Global Positioning System (GPS) has become part of many applications in life. In mountainous terrains and around buildings, GPS reception is compromised. In dense urban canyons, signals bounce off the buildings creating multipath reception and provide erroneous measurements. To overcome GPS bandwidth and signal fading problems, Navigation solutions are built on GPS measurements fused with inertial sensors to provide dead reckoning (DR) based position solution. Solution for land vehicle Navigation System using GPS, inertial sensor and odometer is presented. The sensors fusion is performed based on conventional, sequential (SKF) and square root Kalman (SRKF) filters. SRKF based on Cheolesky factorization for covariance matrix P. Simulations are performed on real data, with precisely known covariance’s to simulate mathematical stability, performance and processing time required by each method on a high end microprocessor. The results demonstrate integrated system using SRKF has better performance in stability and estimation accuracy than conventional and sequential filter.

Improving Large-Domain Convection-Allowing Forecasts with High-Resolution Analyses and Ensemble Data Assimilation

Analyses with 20-km horizontal grid spacing were produced from continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems over a domain spanning the conterminous United States. These analyses initialized 36-h Weather Research and Forecasting Model forecasts containing a large convection-allowing 4-km nested domain, where downscaled 20-km 3DVAR, EnSRF, and hybrid analyses initialized the 4-km forecasts. Overall, hybrid analyses initialized the best 4-km precipitation forecasts. Furthermore, whether 4-km precipitation forecasts could be improved by initializing them with true 4-km analyses was assessed. As it was computationally infeasible to produce 4-km continuously cycling ensembles over the large 4-km domain, several “dual-resolution” hybrid DA configurations were adopted where 4-km backgrounds were combined with 20-km ensembles to produce 4-km hybrid analyses. Additionally, 4-km 3DVAR analyses were produced. In both hybrid and 3DVAR frameworks, initializing 4-km forecasts with true 4-km analyses, rather than downscaled 20-km analyses, yielded superior precipitation forecasts over the first 12 h. Differences between forecasts initialized from 4-km and downscaled 20-km hybrid analyses were smaller for 18–36-h forecasts, but there were occasionally meaningful differences. Continuously cycling the 4-km backgrounds and using static background error covariances with larger horizontal length scales in the hybrid led to better forecasts. All hybrid-initialized forecasts, including those initialized from downscaled 20-km analyses, were more skillful than forecasts initialized from 4-km 3DVAR analyses, suggesting the analysis method was more important than analysis resolution.

Using an ensemble smoother to evaluate parameter uncertainty of an integrated hydrological model of Yanqi basin

Model uncertainty needs to be quantified to provide objective assessments of the reliability of model predictions and of the risk associated with management decisions that rely on these predictions. This is particularly true in water resource studies that depend on model-based assessments of alternative management strategies. In recent decades, Bayesian data assimilation methods have been widely used in hydrology to assess uncertain model parameters and predictions. In this case study, a particular data assimilation algorithm, the Ensemble Smoother with Multiple Data Assimilation (ESMDA) (Emerick and Reynolds, 2012), is used to derive posterior samples of uncertain model parameters and forecasts for a distributed hydrological model of Yanqi basin, China. This model is constructed using MIKESHE/MIKE11software, which provides for coupling between surface and subsurface processes (DHI, 2011a; DHI, 2011b; DHI, 2011c ; DHI, 2011d). The random samples in the posterior parameter ensemble are obtained by using measurements to update 50 prior parameter samples generated with a Latin Hypercube Sampling (LHS) procedure. The posterior forecast samples are obtained from model runs that use the corresponding posterior parameter samples. Two iterative sample update methods are considered: one based on an a perturbed observation Kalman filter update and one based on a square root Kalman filter update. These alternatives give nearly the same results and converge in only two iterations. The uncertain parameters considered include hydraulic conductivities, drainage and river leakage factors, van Genuchten soil property parameters, and dispersion coefficients. The results show that the uncertainty in many of the parameters is reduced during the smoother updating process, reflecting information obtained from the observations. Some of the parameters are insensitive and do not benefit from measurement information. The correlation coefficients among certain parameters increase in each iteration, although they generally stay below 0.50.

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.

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

Abstract 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.

Assimilating aerosol observations with a “hybrid” variational‐ensemble data assimilation system

AbstractTotal 550 nm aerosol optical depth, surface fine particulate matter (PM2.5), and meteorological observations were assimilated with continuously cycling three‐dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and hybrid variational‐ensemble data assimilation systems. The hybrid system's background error covariances (BECs) were a blend of those in 3DVAR and produced by the cycling EnSRF system, and the 3DVAR, EnSRF, and hybrid systems differed almost exclusively by their BECs. New analyses were produced every 6 h between 0000 UTC 1 June and 1800 UTC 14 July 2010 over a domain encompassing the contiguous United States (CONUS) and adjacent areas. Additionally, a control experiment that only assimilated meteorological observations was performed. Each 1800 UTC analysis initialized a 48 h Weather Research and Forecasting with Chemistry model forecast. These forecasts were evaluated with a focus on air quality prediction. The ensemble aerosol spread was generally insufficient, particularly over the western CONUS. However, despite the suboptimal ensemble spread, the hybrid system performed quite well and usually produced the best aerosol forecasts. Additionally, both the 3DVAR‐ and EnSRF‐initialized forecasts typically outperformed the control. These results are encouraging and suggest the resiliency of the hybrid method. Improved aerosol ensembles should translate into even better future hybrid forecasts.

Convection-Permitting Forecasts Initialized with Continuously Cycling Limited-Area 3DVAR, Ensemble Kalman Filter, and “Hybrid” Variational–Ensemble Data Assimilation Systems

Abstract Analyses with 20-km horizontal grid spacing were produced from parallel continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems between 0000 UTC 6 May and 0000 UTC 21 June 2011 over a domain spanning the contiguous United States. Beginning 9 May, the 0000 UTC analyses initialized 36-h Weather Research and Forecasting Model (WRF) forecasts containing a large convection-permitting 4-km nest. These 4-km 3DVAR-, EnSRF-, and hybrid-initialized forecasts were compared to benchmark WRF forecasts initialized by interpolating 0000 UTC Global Forecast System (GFS) analyses onto the computational domain. While important differences regarding mean state characteristics of the 20-km DA systems were noted, verification efforts focused on the 4-km precipitation forecasts. The 3DVAR-, hybrid-, and EnSRF-initialized 4-km precipitation forecasts performed similarly regarding general precipitation characteristics, such as timing of the diurnal cycle, and all three forecast sets had high precipitation biases at heavier rainfall rates. However, meaningful differences emerged regarding precipitation placement as quantified by the fractions skill score. For most forecast hours, the hybrid-initialized 4-km precipitation forecasts were better than the EnSRF-, 3DVAR-, and GFS-initialized forecasts, and the improvement was often statistically significant at the 95th percentile. These results demonstrate the potential of limited-area continuously cycling hybrid DA configurations and suggest additional hybrid development is warranted.

A Regional GSI-Based Ensemble Kalman Filter Data Assimilation System for the Rapid Refresh Configuration: Testing at Reduced Resolution

Abstract A regional ensemble Kalman filter (EnKF) system is established for potential Rapid Refresh (RAP) operational application. The system borrows data processing and observation operators from the gridpoint statistical interpolation (GSI), and precalculates observation priors using the GSI. The ensemble square root Kalman filter (EnSRF) algorithm is used, which updates both the state vector and observation priors. All conventional observations that are used in the operational RAP GSI are assimilated. To minimize computational costs, the EnKF is run at ⅓ of the operational RAP resolution or about 40-km grid spacing, and its performance is compared to the GSI using the same datasets and resolution. Short-range (up to 18 h, the RAP forecast length) forecasts are verified against soundings, surface observations, and precipitation data. Experiments are run with 3-hourly assimilation cycles over a 9-day convectively active retrospective period from spring 2010. The EnKF performance was improved by extensive tuning, including the use of height-dependent covariance localization scales and adaptive covariance inflation. When multiple physics parameterization schemes are employed by the EnKF, forecast errors are further reduced, especially for relative humidity and temperature at the upper levels and for surface variables. The best EnKF configuration produces lower forecast errors than the parallel GSI run. Gilbert skill scores of precipitation forecasts on the 13-km RAP grid initialized from the 3-hourly EnKF analyses are consistently better than those from GSI analyses.