Real Data Assimilation Experiments Research Articles

Estimating geodynamic model parameters from geodetic observations using a particle method

SUMMARY Bayesian-based data assimilation methods integrate observational data into geophysical forward models to obtain the temporal evolution of an improved state vector, including its uncertainties. We explore the potential of a variant, a particle method, to estimate mechanical parameters of the overriding plate during the interseismic period. Here we assimilate vertical surface displacements into an elementary flexural model to estimate the elastic thickness of the overriding plate, and the locations and magnitudes of line loads acting on the overriding plate to produce flexure. Assimilation of synthetic observations sampled from a different forward model than is used in the particle method, reveal that synthetic seafloor data within 150 km from the trench are required to properly constrain parameters for long wavelength solutions of the upper plate (i.e. wavelength ∼500 km). Assimilation of synthetic observations sampled from the same flexural model used in the particle method shows remarkable convergence towards the true parameters with synthetic on-land data only for short to intermediate wavelength solutions (i.e. wavelengths between ∼100 and 300 km). In real-data assimilation experiments we assign representation errors due to discrepancies between our incorrect or incomplete physical model and the data. When assimilating continental data prior to the 2011 Mw Tohoku-Oki earthquake (1997–2000), an unrealistically low effective elastic plate thickness for Tohoku of ∼5–7 km is estimated. Our synthetic experiments suggest that improvements to the physical forward model, such as the inclusion of a slab, a megathrust interface and viscoelasticity of the mantle, including accurate seafloor data, and additional geodetic observations, may refine our estimates of the effective elastic plate thickness. Overall, we demonstrate the potential of using the particle method to constrain geodynamic parameters by providing constraints on parameters and corresponding uncertainty values. Using the particle method, we provide insights into the data network sensitivity and identify parameter trade-offs.

A Sequential Non-Gaussian Approach for Precipitation Data Assimilation

AbstractIn two recent studies, the authors presented a new data assimilation (DA) method for precipitation observations that does not require Gaussianity or linearity assumptions. The method, called localized ensemble mosaic assimilation (LEMA), initializes the new ensemble forecast by relaxing the background ensemble (prior) toward a single analysis composed of different column states taken from the ensemble members with the lowest error in the precipitation forecast. However, a limitation of the LEMA method is that relaxing the background ensemble toward that analysis severely reduces the spread of the ensemble, thus, limiting its usefulness for cycled DA applications. This study presents a new version of LEMA, called localized ensemble mosaic assimilation sequence (LEMAS), suitable for cycled DA operations. LEMAS constructs an ensemble of analysis mosaics using a small group of members closer to the observations instead of only the closest one. The new ensemble forecast is then initialized by recentering the prior ensemble around the mean of the analysis ensemble while scaling the original background perturbations to match the spread of the analysis mosaics. A series of ideal and real DA experiments are used to evaluate the potential of LEMAS for the assimilation of hourly accumulation observations. A comparison of LEMAS with the local ensemble transform Kalman filter (LETKF) using idealized experiments shows that LEMAS produces similar or slightly better forecast quality than the LETKF in temperature, water vapor, winds, and precipitation. Extending this comparison to real DA experiments assimilating Stage-IV precipitation observations shows that both methods produce precipitation forecasts of comparable quality.

A Heuristic Approach for Precipitation Data Assimilation: Effect of Forecast Errors and Assimilation of NCEP Stage IV Precipitation Analyses

Abstract Recently, Pérez Hortal et al. introduced a simple data assimilation (DA) technique named localized ensemble mosaic assimilation (LEMA) for the assimilation of radar-derived precipitation observations. The method constructs an analysis by assigning to each model grid point the information from the ensemble member that is locally closest to the precipitation observations. This study explores the effects of the forecasts errors in the performance of the method using a series of observing system simulation experiments (OSSEs) with different magnitudes of forecast errors employing a small ensemble of 20 members. The ideal experiments show that LEMA is able to produce forecasts with considerable and long-lived error reductions in the fields of precipitation, temperature, humidity, and wind. Nonetheless, the quality of the analysis deteriorates with increasing forecast errors beyond the spread of the ensemble. To overcome this limitation, we expand the spread of the ensemble used to construct the analysis mosaic by considering states at different times and states from forecasts initialized at different times (lagged forecasts). The ideal experiments show that the additional information in the expanded ensemble improves the performance of LEMA, producing larger and long-lived improvements in the state variables and in the precipitation forecast quality. Finally, the potential of LEMA is explored in real DA experiments using actual Stage IV precipitation observations. When LEMA uses only the background members, the quality of the precipitation forecast shows small or no improvements. However, the expanded ensemble improves the LEMA’s effectiveness, producing larger and more persistent improvements in precipitation forecasts.

Improved streamflow simulations by coupling soil moisture analytical relationship in EnKF based hydrological data assimilation framework

Abstract The present study investigates the potential of coupled Soil Moisture Analytical Relationship (SMAR) and Ensemble Kalman Filter (EnKF) based surface soil moisture data assimilation for improving the streamflow simulations. For this purpose, synthetic and real data assimilation experiments were carried out using Soil and Water Assessment Tool (SWAT) hydrological model in two different sub-catchments lying in the Krishna River basin, India. Here, the satellite-based surface soil moisture estimates from Soil Moisture and Ocean Salinity (SMOS) and Advanced Scatterometer (ASCAT) are used for assimilation. Results of the synthetic experiment show that the use of physically based SMAR scheme coupled with EnkF for updating profile soil moisture has better ability to improve the surface flow, groundwater flow and consequently streamflow over the covariance-based updates using EnKF only. Likewise, the real data assimilation experiment also shows SMAR-EnKF assimilation strategy performs better than the EnKF only updates for simulating streamflow. However, in both the synthetic as well as real data experiment, the improvements are only moderate. This restricted success in improving streamflow simulations indicate that updating only the soil moisture through any updating scheme adopted here is not sufficient to reduce the effect of the errors in model forcing on subsequent simulation days.

Improving Robustness of Hydrologic Ensemble Predictions Through Probabilistic Pre‐ and Post‐Processing in Sequential Data Assimilation

AbstractData assimilation using the ensemble Kalman filter (EnKF) has been increasingly recognized as a promising tool for probabilistic hydrologic predictions. However, little effort has been made to conduct the pre‐ and post‐processing of assimilation experiments, posing a significant challenge in achieving the best performance of hydrologic predictions. This paper presents a unified data assimilation framework for improving the robustness of hydrologic ensemble predictions. Statistical pre‐processing of assimilation experiments is conducted through the factorial design and analysis to identify the best EnKF settings with maximized performance. After the data assimilation operation, statistical post‐processing analysis is also performed through the factorial polynomial chaos expansion to efficiently address uncertainties in hydrologic predictions, as well as to explicitly reveal potential interactions among model parameters and their contributions to the predictive accuracy. In addition, the Gaussian anamorphosis is used to establish a seamless bridge between data assimilation and uncertainty quantification of hydrologic predictions. Both synthetic and real data assimilation experiments are carried out to demonstrate feasibility and applicability of the proposed methodology in the Guadalupe River basin, Texas. Results suggest that statistical pre‐ and post‐processing of data assimilation experiments provide meaningful insights into the dynamic behavior of hydrologic systems and enhance robustness of hydrologic ensemble predictions.

Limitations of ozone data assimilation with adjustment of NO<sub><i>x</i></sub> emissions: mixed effects on NO<sub>2</sub> forecasts over Beijing and surrounding areas

Abstract. This study investigates a cross-variable ozone data assimilation (DA) method based on an ensemble Kalman filter (EnKF) that has been used in the companion study to improve ozone forecasts over Beijing and surrounding areas. The main purpose is to delve into the impacts of the cross-variable adjustment of nitrogen oxide (NOx) emissions on the nitrogen dioxide (NO2) forecasts over this region during the 2008 Beijing Olympic Games. A mixed effect on the NO2 forecasts was observed through application of the cross-variable assimilation approach in the real-data assimilation (RDA) experiments. The method improved the NO2 forecasts over almost half of the urban sites with reductions of the root mean square errors (RMSEs) by 15–36 % in contrast to big increases of the RMSEs over other urban stations by 56–239 %. Over the urban stations with negative DA impacts, improvement of the NO2 forecasts (with 7 % reduction of the RMSEs) was noticed at night and in the morning versus significant deterioration during daytime (with 190 % increase of the RMSEs), suggesting that the negative data assimilation impacts mainly occurred during daytime. Ideal-data assimilation (IDA) experiments with a box model and the same cross-variable assimilation method confirmed the mixed effects found in the RDA experiments. In the same way, NOx emission estimation was improved at night and in the morning even under large biases in the prior emission, while it deteriorated during daytime (except for the case of minor errors in the prior emission). The mixed effects observed in the cross-variable data assimilation, i.e., positive data assimilation impacts on NO2 forecasts over some urban sites, negative data assimilation impacts over the other urban sites, and weak data assimilation impacts over suburban sites, highlighted the limitations of the EnKF under strong nonlinear relationships between chemical variables. Under strong nonlinearity between daytime ozone concentrations and NOx emissions uncertainties (with large biases in the a priori emission), the EnKF may come up with inefficient or wrong adjustments to NOx emissions. The present findings reveal that bias correction is essential for the application of the EnKF in dealing with the data assimilation problem over strong nonlinear system.

The Impact of Assumed Error Variances on Surface Soil Moisture and Snow Depth Hydrologic Data Assimilation

Accurate knowledge of antecedent soil moisture (SM) and snow depth (SD) conditions is often important for obtaining reliable hydrological simulations of stream flow. Data assimilation (DA) methods can be used to integrate remotely sensed (RS) SM and SD retrievals into a hydrology model and improve such simulations. In this paper, we examine the impact of assumed model and observation error variance on stream flow estimates obtained by assimilating RS SM and SD data into a lumped hydrological model. The analysis is based on both synthetic and real DA experiments conducted within the Tuotuo River watershed at the headwaters of the Yangtze River. Synthetic experiments demonstrate that, when the true model error variance is small, DA is more sensitive to the overestimation of the error variance than to its underestimation. Conversely, if the true variance is large, DA is sensitive to the assumed model error variance but not the underestimation of the observation error variance. Given this sensitivity, the maximum a posteriori (MAP) estimation method is applied to accurately estimate model and observation error variances. In general, MAP is able to identify model and observation error parameters associated with an accurate stream flow analysis. However, its utility is somewhat limited by equifinality with regard to observation error statistics.

Comparison of static mesoscale background‐error covariances estimated by three different ensemble data assimilation techniques

AbstractThree ensemble‐based analysis‐error representation techniques are applied and compared with the aim of simulating background errors of the mesoscale limited‐area model (LAM) Aire Limitée Adaptation Dynamique Développement International (ALADIN) and thus computing appropriate mesoscale static background‐error covariances for its three‐dimensional variational (3DVAR) data assimilation system. Real data assimilation experiments are performed for the simulation of the background errors, where uncertainties of the initial conditions and lateral boundary conditions are represented, while model errors are not accounted for. The three analysis error‐simulation techniques compared are as follows: (i) the downscaling of the analysis error represented by the stochastic ensemble data assimilation (EDA) system of a global model (DSC EDA); (ii) the representation of the analysis error by a LAM stochastic ensemble data assimilation (LAM EDA) system; and (iii) the representation of the analysis error by a LAM ensemble transform Kalman filter (LAM ETKF) system. Spectral diagnostics have been developed in the study, allowing an examination of the simulated background errors at different spatial scales. It is shown that LAM EDA provides more realistic simulated background errors than DSC EDA, particularly at mesoscales. This is also partly the case for LAM ETKF at mesoscales (although to a lesser extent than for LAM EDA). The error variance is underestimated by LAM ETKF, which suggests that the applied inflation technique could be improved. Analysis and forecast impact studies using background‐error covariance matrices based on the DSC EDA and LAM EDA error samples confirm the superiority of the latter simulation technique.

On improving storm surge forecasting using an adjoint optimal technique

A three-dimensional ocean model and its adjoint model are used to simultaneously optimize the initial conditions (IC) and the wind stress drag coefficient (Cd) for improving storm surge forecasting. To demonstrate the effect of this proposed method, a number of identical twin experiments (ITEs) with a prescription of different error sources and two real data assimilation experiments are performed. Results from both the idealized and real data assimilation experiments show that adjusting IC and Cd simultaneously can achieve much more improvements in storm surge forecasting than adjusting IC or Cd only. A diagnosis on the dynamical balance indicates that adjusting IC only may introduce unrealistic oscillations out of the assimilation window, which can be suppressed by the adjustment of the wind stress when simultaneously adjusting IC and Cd. Therefore, it is recommended to simultaneously adjust IC and Cd to improve storm surge forecasting using an adjoint technique.

Radar Data Assimilation with WRF 4D-Var. Part I: System Development and Preliminary Testing

Abstract The major goal of this two-part study is to assimilate radar data into the high-resolution Advanced Research Weather Research and Forecasting Model (ARW-WRF) for the improvement of short-term quantitative precipitation forecasting (QPF) using a four-dimensional variational data assimilation (4D-Var) technique. In Part I the development of a radar data assimilation scheme within the WRF 4D-Var system (WRF 4D-Var) and the preliminary testing of the scheme are described. In Part II the performance of the enhanced WRF 4D-Var system is examined by comparing it with the three-dimensional variational data assimilation system (WRF 3D-Var) for a convective system over the U.S. Great Plains. The WRF 4D-Var radar data assimilation system has been developed with the existing framework of an incremental formulation. The new development for radar data assimilation includes the tangent-linear and adjoint models of a Kessler warm-rain microphysics scheme and the new control variables of cloud water, rainwater, and vertical velocity and their error statistics. An ensemble forecast with 80 members is used to produce background error covariance. The preliminary testing presented in this paper includes single-observation experiments as well as real data assimilation experiments on a squall line with assimilation windows of 5, 15, and 30 min. The results indicate that the system is able to obtain anisotropic multivariate analyses at the convective scale and improve precipitation forecasts. The results also suggest that the incremental approach with successive basic-state updates works well at the convection-permitting scale for radar data assimilation with the selected assimilation windows.

Assimilating Doppler radar radial velocity and reflectivity observations in the weather research and forecasting model by a proper orthogonal‐decomposition‐based ensemble, three‐dimensional variational assimilation method

Doppler radar observations with high spatial and temporal resolution can effectively improve the description of small‐scale structures in the initial condition and enhance the mesoscale and microscale model skills of numerical weather prediction (NWP). In this paper, Doppler radar radial velocity and reflectivity are simultaneously assimilated into a weather research and forecasting (WRF) model by a proper orthogonal‐decomposition‐based ensemble, three‐dimensional variational assimilation method (referred to as PODEn3DVar), which therefore forms the PODEn3DVar‐based radar assimilation system (referred to as WRF‐PODEn3DVar). The main advantages of WRF‐PODEn3DVar over the standard WRF‐3DVar are that (1) the PODEn3DVar provides flow‐dependent covariances through the evolving ensemble of short‐range forecasts, and (2) the PODEn3DVar analysis can be obtained directly without an iterative process, which significantly simplifies the assimilation. Results from real data assimilation experiments with the WRF model show that WRF‐PODEn3DVar simulation yields better rainfall forecasting than radar retrieval, and radar retrieval is better than the standard WRF‐3DVar assimilation, probably because of the flow‐dependence character embedded in the WRF‐PODEn3DVar.

Background-error correlation model based on the implicit solution of a diffusion equation

An efficient implementation of background-error correlation modeling for ocean data assimilation based on the implicit solution of a diffusion equation is presented in this work. This study is an extension of Weaver and Courtier (2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is unconditionally stable, therefore larger time steps can be used in the calculation than in the explicit solution, which needs smaller time steps to maintain stability. This is especially true when modeling anisotropic correlations, or when using a non-uniform model grid (e.g. curvilinear grid spacing). Both implicit and explicit methods are tested in terms of numerical efficiency and practical implementation. To that end, a set of simulated and real data assimilation experiments are carried out using a three-dimensional variational (3D-Var) algorithm that has been developed as a test-bed for these correlation models. The results of both the implicit and explicit method are compared to show that while the implicit method provides the same correlation shape, size, and magnitude as the explicit, it does so at a much lower computational cost. For the experiments shown here the implicit solution can be up to five times as efficient in terms of CPU time than the explicit, while also providing a nearly identical analysis and forecast in terms of deviation from independent observations.

Ensemble data assimilation with the CNMCA regional forecasting system

AbstractThe Ensemble Kalman Filter (EnKF) is likely to become a viable alternative to variational methods for the next generation of meteorological and oceanographic data assimilation systems. In this work we present results from real‐data assimilation experiments using the CNMCA regional numerical weather prediction (NWP) forecasting system and compare them to the currently operational variational‐based analysis. The set of observations used is the same as the one ingested in the operational data stream, with the exception of satellite radiances and scatterometer winds. Results show that the EnKF‐based assimilation cycle is capable of producing analyses and forecasts of consistently superior skill in the root mean square error metric than CNMCA operational 3D‐Var.One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. To combat this problem a number of different parametrizations of the model error unaccounted for in the assimilation cycle have been proposed. In the CNMCA system a combination of adaptive multiplicative and additive background covariance inflations has been found to give adequate results and to be capable of avoiding filter divergence in extended assimilation trials. The additive component of the covariance inflation has been implemented through the use of scaled forecast differences.Following suggestions that ensemble square‐root filters can violate the gaussianity assumption when used with nonlinear prognostic models, the statistical distribution of the forecast and analysis ensembles has been studied. No sign of the ensemble collapsing onto one or a few model states has been found, and the forecast and analysis ensembles appear to stay remarkably close to the assumed probability distribution functions. Copyright © 2010 Royal Meteorological Society

Application of a SEEK filter to a 1D biogeochemical model of the Ligurian Sea: Twin experiments and real in-situ data assimilation

The Singular Evolutive Extended Kalman (SEEK) filter has been implemented to assimilate in-situ data in a 1D coupled physical-ecosystem model of the Ligurian Sea. The biogeochemical model describes the partly decoupled nitrogen and carbon cycles of the pelagic food web. The GHER hydrodynamic model (1D version) is used to represent the physical forcings. The data assimilation scheme (SEEK filter) parameterizes the error statistics by means of a set of empirical orthogonal functions (EOFs). Twin experiments are first performed with the aim to choose the suitable experimental protocol (observation and estimation vectors, number of EOFs, frequency of the assimilation,…) and to assess the SEEK filter performances. This protocol is then applied to perform real data assimilation experiments using the DYFAMED data base. By assimilating phytoplankton observations, the method has allowed to improve not only the representation of the phytoplankton community, but also of other variables such as zooplankton and bacteria that evolve with model dynamics and that are not corrected by the data assimilation scheme. The validation of the assimilation method and the improvement of model results are studied by means of suitable error measurements.

Assimilation de données dans un modèle d'écosystème marin de la mer Ligure

The objective is to explore the potentialities of sequential statistical estimation methods to assimilate observations in a primary production biological model coupled to a vertical 1D hydrodynamical model characterised by a k-l turbulent closure. The assimilation method is derived from the SEEK filter (Singular Evolutive Extended Kalman filter), which uses an error subspace represented by multivariate empirical orthogonal functions (EOFs). Real data assimilation experiments collected at sea have been realised to reconstruct the variability of the Ligurian Sea ecosystem during the FRONTAL field experiment.

Four-Dimensional Variational Data Assimilation of Heterogeneous Mesoscale Observations for a Strong Convective Case

Abstract On 19 September 1996, a squall line stretching from Nebraska to Texas with intense embedded convection moved eastward across the Kansas–Oklahoma area, where special observations were taken as part of a Water Vapor Intensive Observing Period sponsored by the Atmospheric Radiation Measurement program. This provided a unique opportunity to test mesoscale data assimilation strategies for a strong convective event. In this study, a series of real-data assimilation experiments is performed using the MM5 four-dimensional variational data assimilation (4DVAR) system with a full physics adjoint. With a grid size of 20 km and 15 vertical layers, the MM5-4DVAR system successfully assimilated wind profiler, hourly rainfall, surface dewpoint, and ground-based GPS precipitable water vapor data. The MM5-4DVAR system was able to reproduce the observed rainfall in terms of precipitation pattern and amount, and substantially reduced the model errors when verified against independent observations. Additional data a...

Impact of Assimilating SSM/I Rainfall Rates on Numerical Prediction of Winter Cyclones

Abstract A series of observing system simulation experiments (OSSE) and real data assimilation experiments were conducted to assess the impact of assimilating Special Sensor Microwave/Imager (SSM/I)-estimated rainfall rates on limited-area model predictions of intense winter cyclones. For the OSSE, the slow-moving, fronto- and cyclogenesis along the cast coast of United States during the second intensive observation period (IOP 2) of the Genesis of Atlantic Lows Experiment (GALE) (26-28 January 1986) was selected as the test case. The perfect “observed” rainfall rates were obtained by an integration of a version of the Naval Research Laboratory (NRL) limited-area model, whereas the “forecast” was generated by a degraded version of the NRL model. A number of OSSEs were conducted in which the “observed” rainfall rates were assimilated into the “forecast” model. Rainfall rates of various data frequencies, different vertical beating profiles, various assimilation windows, and prescribed systematic errors were...

Variational Assimilation of XBT Data. Part II. Sensitivity Studies and Use of Smoothing Constraints

A linear reduced-gravity model of the tropical pacific is used to assimilate XBT data. The model cannot fit the data in the eastern equatorial Pacific for the whole assimilation period. Several experiments with real and simulated data are performed to investigate the source of this deficiency, which may be in the model or the wind stress used to force the model. It is shown that on the basis of the simple model physics we cannot unambiguously partition the error between model and forcing in the real data assimilation experiments although simulated data experiments do permit discrimination between model and forcing errors. Because the data is incomplete and does not permit a unique determination of the initial state, the use of prior information in the form of first-guess fields and/or smoothing constraints is examined. The filtering characteristics of the optimization algorithm are also discussed by looking at the evolution of the initial conditions as a function of the iteration number.

The Analysis Sensitivity to Tropical Winds from the Global Weather Experiment

The global scale divergent and rotational flow components of the Global Weather Experiment (GWE) are diagnosed from three different analyses of the data. The rotational flow shows closer agreement between the analyses than does the divergent flow. Although the major outflow and inflow centers are similarly placed in all analyses, the global kinetic energy of the divergent wind varies by about a factor of 2 between different analyses while the global kinetic energy of the rotational wind varies by only about 10 percent between the analyses. A series of real data assimilation experiments has been performed with the GLA general circulation model using different amounts of tropical wind data during the First Special Observing Period of the Global Weather Experiment. In exeriment 1, all available tropical wind data were used; in the second experiment, tropical wind data were suppressed; while, in the third and fourth experiments, only tropical wind data with westerly and easterly components, respectively, were assimilated. The rotational wind appears to be more sensitive to the presence or absence of tropical wind data than the divergent wind. It appears that the model, given only extratropical observations, generates excessively strong upper tropospheric westerlies. These biases are sufficiently pronounced to amplify the globally integrated rotational flow kinetic energy by about 10 percent and the global divergent flow kinetic energy by about a factor of 2. Including only easterly wind data in the tropics is more effective in controlling the model error than including only westerly wind data. This conclusion is especially noteworthy because approximately twice as many upper tropospheric westerly winds were available in these cases as easterly winds.