Variational Data Assimilation Scheme Research Articles

An Impact Assessment of GPS Radio Occultation Data on Prediction of a Rapidly Developing Cyclone over the Southern Ocean*

Abstract The impact of global positioning system (GPS) radio occultation (RO) data on an intense synoptic-scale storm that occurred over the Southern Ocean in December 2007 is evaluated, and a synoptic explanation of the assessed impact is offered. The impact is assessed by using the three-dimensional variational data assimilation scheme (3DVAR) of the Weather Research and Forecasting (WRF) Model Data Assimilation system (WRFDA), and by comparing two experiments: one with and the other without assimilating the refractivity data from four different RO missions. Verifications indicate significant positive impacts of the RO data in various measures and parameters as well as in the track and intensity of the Antarctic cyclone. The analysis of the atmospheric processes underlying the impact shows that the assimilation of the RO data yields substantial improvements in the large-scale circulations that in turn control the development of the Antarctic storm. For instance, the RO data enhanced the strength of a 500-hPa trough over the Southern Ocean and prevented the katabatic flow near the coast of East Antarctica from an overintensification. This greatly influenced two low pressure systems of a comparable intensity, which later merged together and evolved into the major storm. The dominance of one low over the other in the merger dramatically changed the track, intensity, and structure of the merged storm. The assimilation of GPS RO data swapped the dominant low, leading to a remarkable improvement in the subsequent storm’s prediction.

Estimation of surface turbulent heat fluxes via variational assimilation of sequences of land surface temperatures from Geostationary Operational Environmental Satellites

Recently, a number of studies have focused on estimating surface turbulent heat fluxes via assimilation of sequences of land surface temperature (LST) observations into variational data assimilation (VDA) schemes. Using the full heat diffusion equation as a constraint, the surface energy balance equation can be solved via assimilation of sequences of LST within a VDA framework. However, the VDA methods have been tested only in limited field sites that span only a few climate and land use types. Hence, in this study, combined-source (CS) and dual-source (DS) VDA schemes are tested extensively over six FluxNet sites with different vegetation covers (grassland, cropland, and forest) and climate conditions. The CS model groups the soil and canopy together as a single source and does not consider their different contributions to the total turbulent heat fluxes, while the DS model considers them to be different sources. LST data retrieved from the Geostationary Operational Environmental Satellites are assimilated into these two VDA schemes. Sensible and latent heat flux estimates from the CS and DS models are compared with the corresponding measurements from flux tower stations. The results indicate that the performance of both models at dry, lightly vegetated sites is better than that at wet, densely vegetated sites. Additionally, the DS model outperforms the CS model at all sites, implying that the DS scheme is more reliable and can characterize the underlying physics of the problem better.

Implementing a variational data assimilation system in an operational 1/4 degree global ocean model

AbstractThis article describes the implementation of an incremental first guess at an appropriate time three‐dimensional variational (3DVAR) data assimilation scheme, NEMOVAR, in the Met Office's operational 1/4 degree global ocean model. NEMOVAR assimilates observations of sea‐surface temperature (SST), sea‐surface height (SSH), in situ temperature and salinity profiles and sea ice concentration. The Met Office is the first centre to implement NEMOVAR at 1/4 degree and the required developments are discussed, with particular focus on the specification of the background‐error covariances.Background‐error correlations in NEMOVAR are modelled using a diffusion operator. The horizontal background‐error correlations for temperature, salinity and sea ice concentration are parametrized using the Rossby radius, which produces relatively short correlation length‐scales at mid to high latitudes, while a flow‐dependent mixed‐layer depth parametrization is used to define the vertical length‐scales for the 3D variables.Results from a one‐year reanalysis with NEMOVAR are presented and compared with the preceding operational data assimilation scheme at the Met Office. NEMOVAR is shown to provide significant improvements to SST, SSH and sea ice concentration fields, with the largest improvements seen in regions of high variability such as eddy shedding and frontal regions and the marginal ice zone. This improvement is associated with shorter correlation length‐scales in the extratropics and an improved fit to observations in NEMOVAR. Some degradation to subsurface temperature and salinity fields where data are sparse is identified and this will be the focus of future improvements to the system.

Evaluating a mesoscale atmosphere model and a satellite-based algorithm in estimating extreme rainfall events in northwestern Turkey

Abstract. Quantitative precipitation estimates are obtained with more uncertainty under the influence of changing climate variability and complex topography from numerical weather prediction (NWP) models. On the other hand, hydrologic model simulations depend heavily on the availability of reliable precipitation estimates. Difficulties in estimating precipitation impose an important limitation on the possibility and reliability of hydrologic forecasting and early warning systems. This study examines the performance of the Weather Research and Forecasting (WRF) model and the Multi Precipitation Estimates (MPE) algorithm in producing the temporal and spatial characteristics of the number of extreme precipitation events observed in the western Black Sea region of Turkey. Precipitation derived from WRF model with and without the three-dimensional variational (3DVAR) data assimilation scheme and MPE algorithm at high spatial resolution (5 km) are compared with gauge precipitation. WRF-derived precipitation showed capabilities in capturing the timing of precipitation extremes and to some extent the spatial distribution and magnitude of the heavy rainfall events, whereas MPE showed relatively weak skills in these aspects. WRF skills in estimating such precipitation characteristics are enhanced with the application of the 3DVAR scheme. Direct impact of data assimilation on WRF precipitation reached up to 12% and at some points there is a quantitative match for heavy rainfall events, which are critical for hydrological forecasts.

An examination of a multi-scale three-dimensional variational data assimilation scheme in the Kuroshio Extension using the naval coastal ocean model

The implementation of a multi-scale three dimensional variational (MS3DVAR) data assimilation scheme for use with the Navy Coastal Ocean Model (NCOM) in the Kuroshio Extension western boundary current region is presented here. This work leverages on Li et al. (2013), who initially developed this method. MS3DVAR data assimilation allows for the effective assimilation of both spatially coarse and dense collections of observations. Traditional 3DVAR produces an inherent filtering of dynamical features smaller than the decorrelation length. The MS3DVAR allows for a scale selective background error covariance capable of handling a wider range of ocean scales. Here the MS3DVAR is examined in an energetic coastal regime using simulated and real observations. The results show that the MS3DVAR reduces analysis errors when compared to a traditional 3DVAR scheme. Forecast errors appear to be similar for both systems and are most likely due to the coarse resolution of the surface forceing being applied.

Analysis and numerical study of a hybrid BGM-3DVAR data assimilation scheme using satellite radiance data for heavy rain forecasts

A fine heavy rain forecast plays an important role in the accurate flood forecast, the urban rainstorm waterlogging and the secondary hydrological disaster preventions. To improve the heavy rain forecast skills, a hybrid Breeding Growing Mode (BGM)- three-dimensional variational (3DVAR) Data Assimilation (DA) scheme is designed on running the Advanced Research WRF (ARW WRF) model using the Advanced Microwave Sounder Unit A (AMSU-A) satellite radiance data. Results show that: the BGM ensemble prediction method can provide an effective background field and a flow dependent background error covariance for the BGM- 3DVAR scheme. The BGM-3DVAR scheme adds some effective mesoscale information with similar scales as the heavy rain clusters to the initial field in the heavy rain area, which improves the heavy rain forecast significantly, while the 3DVAR scheme adds information with relatively larger scales than the heavy rain clusters to the initial field outside of the heavy rain area, which does not help the heavy rain forecast improvement. Sensitive experiments demonstrate that the flow dependent background error covariance and the ensemble mean background field are both the key factors for adding effective mesoscale information to the heavy rain area, and they are both essential for improving the heavy rain forecasts.

Evaluation of the Global Ocean Data Assimilation System at INCOIS: The Tropical Indian Ocean

A new version of NCEP’s Global Ocean Data Assimilation System (GODAS), which is based on the Geophysical Fluid Dynamics Laboratory (GFDL) Modular ocean Model version 4.0 (MOM4.0) and a three-dimensional variational (3D-VAR) data assimilation scheme, was configured and operationalized at Indian National Centre for Ocean Information Services (INCOIS). The primary objective of the GODAS at INCOIS (INCOIS–GODAS) is to provide an accurate estimate of the ocean state, which will be used to initialize a coupled model for the seasonal monsoon forecast and also to understand the variability of the ocean at different time scales. In this paper, we assess the quality of ocean analyses in the Tropical Indian Ocean (TIO) obtained from the operational INCOIS–GODAS. In addition to this, we examined the sensitivity of INCOIS–GODAS to different momentum forcing and to the assimilation of temperature and synthetic salinity based on the experiments carried out with different wind products: NCEP2 and QuikSCAT and a free run respectively. The present study reveals that the model with assimilation simulates most of the observed features of temperature, SSHA and currents with reasonably good accuracy in the TIO at both intra-seasonal and inter-annual time scales. The analysis further shows that there was a considerable improvement in the ocean current field, when the model was forced with QuikSCAT winds.

A theoretical study of the multigrid three-dimensional variational data assimilation scheme using a simple bilinear interpolation algorithm

In order to solve the so-called “bull-eye” problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational (3DVAR) data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of “bull-eye”, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional (1D) case, and two idealized data assimilation experiments (one- and two-dimensional (2D) cases). By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.

Variational assimilation of land surface temperature and the estimation of surface energy balance components

Recently, numerous studies have focused on the estimation of surface energy flux components, based on the assimilation of land surface temperature (LST) within a variational data assimilation (VDA) framework. Unlike the previous investigations based on the force-restore equation, in this study, the full heat diffusion equation is employed in the VDA scheme as an adjoint (constraint). In addition, a model error term is added to the surface energy balance (SEB) equation and the VDA scheme to include the model uncertainty. Both VDA schemes (with and without the model uncertainty) are tested over the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site. The comprehensive comparisons between the present model (with heat diffusion equation) and previous model (with the force-restore equation) demonstrate that the present model will decrease the phase error associated with the ground heat flux diurnal cycle, and improve the evaporative fraction and heat fluxes estimation. The numerical examples also conclude that the errors caused by model structures and noisy data in the SEB equation can be detected and quantified in the present model (with model uncertainty).

Control of lateral boundary conditions in four-dimensional variational data assimilation for a limited area model

ABSTRACTThe limited area model forecasting problem is a lateral boundary condition (LBC) problem in addition to the initial condition problem. The data assimilation has traditionally been considered as a process for estimation of the initial condition only, while for the limited area data assimilation this estimation may be extended to include also the LBCs, at least during the data assimilation time window when observations are available. A procedure for such a control of the LBCs has been included in the four-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system. A description of this procedure is provided together with results from idealised as well as real data experiments. The results indicate that control of LBCs may be important with small forecast domains and in particular for weather disturbances moving quickly into and through the forecast domain.

Four-dimensional variational data assimilation for a limited area model

ABSTRACTA 4-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system is described in this article. The innovative approaches to the multi-incremental formulation, the weak digital filter constraint and the semi-Lagrangian time integration are highlighted with some details. The implicit dynamical structure functions are discussed using single observation experiments, and the sensitivity to various parameters of the 4D-Var formulation is illustrated. To assess the meteorological impact of HIRLAM 4D-Var, data assimilation experiments for five periods of 1 month each were performed, using HIRLAM 3D-Var as a reference. It is shown that the HIRLAM 4D-Var consistently out-performs the HIRLAM 3D-Var, in particular for cases with strong mesoscale storm developments. The computational performance of the HIRLAM 4D-Var is also discussed.The review process was handled by Subject Editor Abdel Hannachi

Integration of a 3D variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay

This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby–van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast–assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

AbstractData assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

A 3DVAR-Based Dynamical Initialization Scheme for Tropical Cyclone Predictions*

Abstract A combined tropical cyclone dynamic initialization–three-dimensional variational data assimilation scheme (TCDI–3DVAR) is proposed. The specific procedure for the new initialization scheme is described as follows. First, a first-guess vortex field derived from a global analysis will be spun up in a full-physics mesoscale regional model in a quiescent environment. During the spinup period, the weak vortex is forced toward the observed central minimum sea level pressure (MSLP). The so-generated balanced TC vortex with realistic MSLP and a warm core is then merged into the environmental field and used in the subsequent 3DVAR data assimilation. The observation system simulation experiments (OSSEs) demonstrate that this new TC initialization scheme leads to much improved initial MSLP, warm core, and asymmetric temperature patterns compared to those from the conventional 3DVAR scheme. Forecasts of TC intensity with the new initialization scheme are made, and the results show that the new scheme is able to predict the “observed” TC intensity change, compared to runs with the conventional 3DVAR scheme or the TCDI-only scheme. Sensitivity experiments further show that the intensity forecasts with knowledge of the initial MSLP and wind fields appear more skillful than do the cases where the initial MSLP, temperature, and humidity fields are known. The numerical experiments above demonstrate the potential usefulness of the proposed new initialization scheme in operational applications. A preliminary test of this scheme with a navy operational model shows encouraging results.

Variational assimilation of albedo in a snowpack model and reconstruction of the spatial mass-balance distribution of an alpine glacier

AbstractAccurate knowledge of the spatial distribution of the mass balance of temperate glaciers is essential for a better understanding of the physical processes controlling the mass balance and for the monitoring of water resources. In relation to albedo variations, the shortwave radiation budget is a controlling variable of the surface energy balance of glaciers. Remotely sensed albedo observations are here assimilated in a snowpack model to improve the modeling of the spatial distribution of the glacier mass balance. The albedo observations are integrated in the snowpack simulation using a variational data assimilation scheme that modifies the surface grain conditions. The study shows that mesoscale meteorological variables and MODIS-derived albedo maps can be used to obtain a good reconstruction of the annual mass balance on Glacier de Saint-Sorlin, French Alps, on a 100 m × 100m grid. Five hydrological years within the 2000-10 decade are tested. The accuracy of the method is estimated from comparison with field measurements. Sensitivity to roughness lengths and winter precipitation fields is investigated. Results demonstrate the potential contribution of remote-sensing data and variational data assimilation to further improve the understanding and monitoring of the mass balance of snowpacks and temperate glaciers.

Targeted observations of a polar low in the Norwegian Sea

AbstractA developing polar low is targeted with dropsonde observations to improve the forecast of its landfall. Accurately forecasting a polar low's strength and location remains a challenge; polar lows form over the ocean in poorly observed regions, therefore initial condition errors may contribute significantly to forecast error. The targeted polar low formed in the Norwegian Sea on 3 March 2008, during the Norwegian IPY‐THORPEX field campaign. Two flights, six hours apart, released dense networks of dropsondes into a sensitive region covering the polar low and Arctic front to its west. The impact of the targeted observations is assessed using the limited‐area Met Office Unified Model and three‐dimensional variational (3D‐Var) data assimilation scheme. Forecasts were verified using ECMWF analysis data, which show good agreement with both dropsonde data from a flight through the mature polar low, and 10 m QuikSCAT winds. The impact of the targeted data moved southwards with the polar low as it developed and then hit the Norwegian coast after 24 hours. The results show that the forecast of the polar low is sensitive to the initial conditions; targeted observations from the first flight did not improve the forecast, but those from the second flight clearly improved the forecast polar low position and intensity. However, caution should be applied to attributing the forecast improvement to the assimilation of the targeted observations from a single case‐study, especially in this case as the forecast improvement is moderate relative to the spread from an operational ensemble forecast. Copyright © 2011 Royal Meteorological Society

Impact of ATOVS Radiance on the Analysis and Forecasts of a Mesoscale Model over the Indian Region During the 2008 Summer Monsoon

Assimilation experiments are performed with the Weather Research and Forecasting (WRF) models’ three-dimensional variational data assimilation (3D-Var) scheme to evaluate the impact of directly assimilating the Advanced Television and Infrared Observation Satellite Operational Vertical Sounder (ATOVS) radiance, including AMSU-A, AMSU-B and HIRS, on the analysis and forecasts of a mesoscale model over the Indian region. The present study is, to our knowledge, the first where the impact of ATOVS radiance has been evaluated on the analysis and forecasts of a mesoscale model over the Indian region. The control (without ATOVS radiance) as well as experimental (which assimilated ATOVS radiance) run were made for 48 h starting at 0000 UTC during the entire July 2008. The impacts of assimilating the radiances from different instruments (e.g., AMSU-A, AMSU-B and HIRS) were measured in comparison to the control run. The assimilation experiments for July 2008 (30 cases) demonstrated a positive impact of the assimilated ATOVS radiance on both the analysis state as well as subsequent short-range forecasts. Relative to the control run, the moisture analysis was improved with the assimilation of AMSU-B and HIRS radiance, while AMSU-A was mainly responsible for improved temperature analysis. The comparison of the model-predicted temperature, moisture and wind with NCEP analysis indicated that a positive forecast impact is achieved from each of the three instruments. HIRS and AMSU-A radiance yielded only a slight positive forecast impact, while AMSU-B radiance had the largest positive forecast impact for moisture, temperature and wind. The comparison of model-predicted rainfall with observed rainfall indicates that ATOVS radiance, particularly AMSU-B and HIRS, impacted the rainfall positively. This study clearly shows that the improved analysis of mid-tropospheric moisture, due to the assimilation of AMSU-B radiances, is a key factor to improve the short-term forecast skill of a mesoscale model.

Adaptive Ensemble Covariance Localization in Ensemble 4D-VAR State Estimation

Abstract An adaptive ensemble covariance localization technique, previously used in “local” forms of the ensemble Kalman filter, is extended to a global ensemble four-dimensional variational data assimilation (4D-VAR) scheme. The purely adaptive part of the localization matrix considered is given by the element-wise square of the correlation matrix of a smoothed ensemble of streamfunction perturbations. It is found that these purely adaptive localization functions have spurious far-field correlations as large as 0.1 with a 128-member ensemble. To attenuate the spurious features of the purely adaptive localization functions, the authors multiply the adaptive localization functions with very broadscale nonadaptive localization functions. Using the Navy’s operational ensemble forecasting system, it is shown that the covariance localization functions obtained by this approach adapt to spatially anisotropic aspects of the flow, move with the flow, and are free of far-field spurious correlations. The scheme is made computationally feasible by (i) a method for inexpensively generating the square root of an adaptively localized global four-dimensional error covariance model in terms of products or modulations of smoothed ensemble perturbations with themselves and with raw ensemble perturbations, and (ii) utilizing algorithms that speed ensemble covariance localization when localization functions are separable, variable-type independent, and/or large scale. In spite of the apparently useful characteristics of adaptive localization, single analysis/forecast experiments assimilating 583 200 observations over both 6- and 12-h data assimilation windows failed to identify any significant difference in the quality of the analyses and forecasts obtained using nonadaptive localization from that obtained using adaptive localization.

The AROME-France Convective-Scale Operational Model

Abstract After six years of scientific, technical developments and meteorological validation, the Application of Research to Operations at Mesoscale (AROME-France) convective-scale model became operational at Météo-France at the end of 2008. This paper presents the main characteristics of this new numerical weather prediction system: the nonhydrostatic dynamical model core, detailed moist physics, and the associated three-dimensional variational data assimilation (3D-Var) scheme. Dynamics options settings and variables are explained. The physical parameterizations are depicted as well as their mutual interactions. The scale-specific features of the 3D-Var scheme are shown. The performance of the forecast model is evaluated using objective scores and case studies that highlight its benefits and weaknesses.

Efficient Ensemble Covariance Localization in Variational Data Assimilation

Abstract Previous descriptions of how localized ensemble covariances can be incorporated into variational (VAR) data assimilation (DA) schemes provide few clues as to how this might be done in an efficient way. This article serves to remedy this hiatus in the literature by deriving a computationally efficient algorithm for using nonadaptively localized four-dimensional (4D) or three-dimensional (3D) ensemble covariances in variational DA. The algorithm provides computational advantages whenever (i) the localization function is a separable product of a function of the horizontal coordinate and a function of the vertical coordinate, (ii) and/or the localization length scale is much larger than the model grid spacing, (iii) and/or there are many variable types associated with each grid point, (iv) and/or 4D ensemble covariances are employed.