Dimensional Variational Data Assimilation Research Articles

Scalability analysis of a two level domain decomposition approach in space and time solving data assimilation models

SummaryWe are concerned with the mapping on high performance hybrid architectures of a parallel software implementing a two level overlapping domain decomposition, that is, along space and time directions, of the four dimensional variational data assimilation model. The reference architecture belongs to the SCoPE (Sistema Cooperativo Per Elaborazioni scientifiche multidisciplinari) data center, located at University of Naples Federico II. We consider the initial boundary problem of the shallow water equation and analyse both strong and weak scaling. Keeping the efficiency always greater than and about in most cases, we experimentally find that the isoefficiency function grows a little more than linearly with respect to the number of processes. Results, obtained by using the parallel computing toolbox of MATLABR2013a, are in agreement with the algorithm's performance prevision based on the scale up factor, confirming the appropriate mapping of the algorithm on the hybrid architecture.

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

Comparison of the performance of HYBRID ETKF-3DVAR and 3DVAR data assimilation scheme on the forecast of tropical cyclones formed over the Bay of Bengal

This study compares the performance of hybrid ensemble transform Kalman filter – three dimensional variational data assimilation (HYBRID) system and three dimensional variational (3DVAR) data assimilation system in Weather Research and Forecasting Model (WRF) in simulating tropical cyclones (TC) formed over the Bay of Bengal. An Ensemble Transform Kalman Filter (ETKF) system updates the ensemble system that provides flow-evolving background error covariance for HYBRID data assimilation system. Results indicate that use of flow-evolving ensemble error covariance in 3DVAR system has systematically reduced the TC position and intensity errors in the analysis; however, adding more weights to the ensemble error covariance term in 3DVAR cost function has not made any significant impact. The 3DVAR analysis depicts a stronger TC vortex with a well pronounced warm core structure as compared to that in HYBRID analysis. The forecasts from HYBRID analysis outperform that from 3DVAR in reducing TC track forecast error. The relative improvement in TC landfall position is 43% and 49% for variously configured HYBRID experiments. The forecasts initiated from HYBRID analysis has higher skill in quantitative precipitation forecasts during TC landfall compared to 3DVAR, which may be attributed to improved track prediction in the HYBRID experiments.

Model reduction in space and time for ab initio decomposition of 4D variational data assimilation problems

We present an innovative approach for solving time dependent Four Dimensional Variational Data Assimilation (4D VAR DA) problems. The proposed approach performs a decomposition of the whole physical domain, i.e. both along spatial and temporal directions; a reduction in space and time of both the Partial Differential Equations-based model and the Data Assimilation functional; finally it uses a modified regularization functional describing restricted 4D VAR DA problems on the domain decomposition. Innovation mainly lies in the introduction ab initio, i.e. on the numerical model – of a domain decomposition approach in space and time joining the idea of Schwarz's method and Parallel in Time (PinT)–based approaches. We provide the numerical framework of this method including convergence analysis and error propagation. A validation analysis is performed discussing computational results on a case study relying on Shallow Water Equations.

Enhancing CFD-LES air pollution prediction accuracy using data assimilation

It is recognised worldwide that air pollution is the cause of premature deaths daily, thus necessitating the development of more reliable and accurate numerical tools. The present study implements a three dimensional Variational (3DVar) data assimilation (DA) approach to reduce the discrepancy between predicted pollution concentrations based on Computational Fluid Dynamics (CFD) with the ones measured in a wind tunnel experiment. The methodology is implemented on a wind tunnel test case which represents a localised neighbourhood environment. The improved accuracy of the CFD simulation using DA is discussed in terms of absolute error, mean squared error and scatter plots for the pollution concentration. It is shown that the difference between CFD results and wind tunnel data, computed by the mean squared error, can be reduced by up to three order of magnitudes when using DA. This reduction in error is preserved in the CFD results and its benefit can be seen through several time steps after re-running the CFD simulation. Subsequently an optimal sensors positioning is proposed. There is a trade-off between the accuracy and the number of sensors. It was found that the accuracy was improved when placing/considering the sensors which were near the pollution source or in regions where pollution concentrations were high. This demonstrated that only 14% of the wind tunnel data was needed, reducing the mean squared error by one order of magnitude.

Simulation of heavy rainfall event along east coast of India using WRF modeling system: impact of 3DVAR data assimilation

The study is evaluated the impact of WRF three dimensional Variational (3DVAR) data assimilation for simulation of a heavy rainfall event due to the presence of the monsoon depression (MD) along the east coast of India. In this purpose, two numerical experiments are carried out such as CNTL (without data assimilation) and 3DV (with assimilation of observations from Global Telecommunication System) for simulation of the heavy rainfall event occurred during 16–21 August 2016 over Indian region. The model is integrated upto 120 h starting at 00 UTC of 16th August 2016 in both the experiments. The results demonstrate that the model with resulting high-resolution reanalyses from 3DV produced reasonably well simulated the location and intensity of rainfall due to the presence of the MD. The model simulated mean sea level pressure (MSLP), vertical structure, track and direct position errors (DPEs) of the MD reasonably well represented in the assimilation experiment (3DV). The statistical skill scores viz. Equitable Thereat Score (ETS) and bias with various thresholds of the rainfall are improved in the 3DV experiment as compared to the CNTL experiment. The present study clearly suggested that the data assimilation (3DVAR) has a positive impact on the simulation of the heavy rainfall event.

Tests of observation error variance tuning with multiple regularization parameters method for typhoon initialization with microwave radiances

Based on the Tikhonov regularization inversion problem theory, a Tikh-4D-Var data assimilation method, which using multiple regularization parameters as a weak constraint for four dimensional variational data assimilation (4D-Var), has been developed by the authors recently. We have shown that the new method is effective in improving the typhoon prediction compared with traditional 4D-Var for the assimilation of bogus observations. In this study, the new method is first applied to the typhoon initialization with microwave radiance observations assimilation, and the results are compared with 4D-Var for typhoon Chaba (2010). Results show that compared with 4D-Var experiment, Tikh-4D-Var experiment can effectively reduce the iterations to accelerate the convergence, and obviously improve the initial structure, the simulated structure, and the intensity and track prediction when radiance observations assimilated. Meanwhile, due to the optimal use of the radiance observations, the warm-core structure and secondary circulation of Tikh-4D-Var experiments improve more significant than the experiments without radiance observations. Moreover, the regularization parameters for different observations are un-correlated, and increasing or decreasing observation type don’t influence the calculation of regularization parameters.

Assimilating observations to simulate marine layer stratocumulus for solar forecasting

Integration of solar energy forecasts into the electric network is becoming essential because of the continually increasing penetration level of solar energy. Three-dimensional numerical weather prediction (NWP) models predict the weather based on the current weather conditions (called initialization) and simulate the ensuing atmospheric processes. The accuracy of forecasts therefore depends, in part, on the accuracy of the model initializations. Data assimilation is recognized as the most widely used technique to improve the initialization into NWP models. In this study, meteorological observations from the surface and upper-air in-situ networks over the southern California coast are assimilated into the advanced research version of the Weather Research and Forecasting (WRF) model using a three dimensional variational data assimilation technique (3DVAR). A single observation test was conducted to tune-up the length scale and variance scale along with the regional domain-dependent background error statistics. A customized version of 3DVAR data assimilation was deployed with two sets of cyclic data assimilation with 6-h and 1-h assimilation windows along with the cold-start mode. The cyclic data assimilation experiments consistently outperformed the cold-start data assimilation and WRF for intra-day Global Horizontal Irradiance (GHI) and Clear Sky Index (CSI) forecast. Hourly cyclic assimilation showed the highest forecast skill score against ground measurements and satellite measurements. Even at the coastal stations with more challenging meteorological conditions, the hourly cyclic assimilation consistently outperformed the 24-h persistence forecast. The average (mean of four case studies) hourly cyclic data assimilation showed the highest forecast skill score in GHI and CSI intra-day forecast with reference to 24-h persistence forecast up to 39.4% and 40.7% respectively at the coastal stations. The spatial distributions of GHI biases estimated against SolarAnywhere satellite measurements showed that the hourly cyclic assimilation consistently improved the stratocumulus cloud coverage, thickness, and life time over the coastal region, but biases are still present further inland.

Assimilating AOD retrievals from GOCI and VIIRS to forecast surface PM2.5 episodes over Eastern China

In this study, Geostationary Ocean Color Imager (GOCI) AOD and Visible Infrared Imaging Radiometer Suite (VIIRS) AOD data were assimilated to forecast surface PM2.5 concentrations over Eastern China, by using the three–dimensional variational (3DAVR) data assimilation (DA) system, to compare DA impacts by assimilating AOD retrievals from these two types of satellites. Three experiments were conducted, including a CONTROL without the AOD assimilation, and GOCIDA and VIIRSDA with the assimilation of AOD retrievals from GOCI and VIIRS, respectively. By utilizing the Weather Research and Forecasting with Chemistry (WRF/Chem) model, 48-h forecasts were initialized at each 06 UTC from 19 November to 06 December 2013. These forecasts were evaluated with 248 ground-based measurements from the air quality monitoring network across 67 China cities. The results show that overall the CONTROL underestimated surface PM2.5 concentrations, especially over Jing–Jin–Ji (JJJ) region and Yangtze River Delta (YRD) region. Both the GOCIDA and VIIRSDA produced higher surface PM2.5 concentrations mainly over Eastern China, which fits well with the PM2.5 measurements at these eastern sites, with more than 8% error reductions (ER). Moreover, compared to CONTROL, GOCIDA reduced 14.0% and 6.4% error on JJJ region and YRD region, respectively, while VIIRSDA reduced respectively 2.0% and 13.4% error over the corresponding areas. During the heavy polluted period, VIIRSDA improved all sites within YRD region, and GOCIDA enhanced 84% sites. Meanwhile, GOCIDA improved 84% sites on JJJ region, while VIIRSDA did not affect that region. These geographic distinctions might result from spatial dissimilarity between GOCI AOD and VIIRS AOD at time intervals. Moreover, the larger increment produced by AOD DA under stable meteorological conditions could lead to a longer duration (e.g., 1–2 days, > 2 days) of AOD DA impacts. Even though with AOD DA, surface PM2.5 concentrations were still underestimated clearly over heavy polluted periods. And 3% sites performed worse, where low PM2.5 values were observed and CONTROL performed well. With this study, the results indicate that AOD DA can partially improve the accuracy of PM2.5 forecasts. And the obvious geographic differences on forecasts emphasize the potential and importance of combining AOD retrievals from GOCI and VIIRS into data assimilation.

Impact of Assimilation of Conventional and Satellite Radiance GTS Observations on Simulation of Mesoscale Convective System Over Southeast India Using WRF-3DVar

The primary goal of present study is to investigate the impact of assimilation of conventional and satellite radiance observations in simulating the mesoscale convective system (MCS) formed over south east India. An assimilation methodology based on Weather Research and Forecasting model three dimensional variational data assimilation is considered. Few numerical experiments are carried out to examine the individual and combined impact of conventional and non-conventional (satellite radiance) observations. After the successful inclusion of additional observations, strong analysis increments of temperature and moisture fields are noticed and contributed to significant improvement in model’s initial fields. The resulting model simulations are able to successfully reproduce the prominent synoptic features responsible for the initiation of MCS. Among all the experiments, the final experiment in which both conventional and satellite radiance observations assimilated has showed considerable impact on the prediction of MCS. The location, genesis, intensity, propagation and development of rain bands associated with the MCS are simulated reasonably well. The biases of simulated temperature, moisture and wind fields at surface and different pressure levels are reduced. Thermodynamic, dynamic and vertical structure of convective cells associated with the passage of MCS are well captured. Spatial distribution of rainfall is fairly reproduced and comparable to TRMM observations. It is demonstrated that incorporation of conventional and satellite radiance observations improved the local and synoptic representation of temperature, moisture fields from surface to different levels of atmosphere. This study highlights the importance of assimilation of conventional and satellite radiances in improving the models initial conditions and simulation of MCS.

Comparison between 3D-Var and 4D-Var data assimilation methods for the simulation of a heavy rainfall case in central Italy

Abstract. This work aims to provide a comparison between three dimensional and four dimensional variational data assimilation methods (3D-Var and 4D-Var) for a heavy rainfall case in central Italy. To evaluate the impact of the assimilation of reflectivity and radial velocity acquired from Monte Midia Doppler radar into the Weather Research Forecasting (WRF) model, the quantitative precipitation forecast (QPF) is used.The two methods are compared for a heavy rainfall event that occurred in central Italy on 14 September 2012 during the first Special Observation Period (SOP1) of the HyMeX (HYdrological cycle in Mediterranean EXperiment) campaign. This event, characterized by a deep low pressure system over the Tyrrhenian Sea, produced flash floods over the Marche and Abruzzo regions, where rainfall maxima reached more than 150 mm 24 h−1.To identify the best QPF, nine experiments are performed using 3D-Var and 4D-Var data assimilation techniques. All simulations are compared in terms of rainfall forecast and precipitation measured by the gauges through three statistical indicators: probability of detection (POD), critical success index (CSI) and false alarm ratio (FAR). The assimilation of conventional observations with 4D-Var method improves the QPF compared to 3D-Var. In addition, the use of radar measurements in 4D-Var simulations enhances the performances of statistical scores for higher rainfall thresholds.

A Water Quality Model with Three Dimensional Variational Data Assimilation for Contaminant Transport

The safety of water delivery and water quality in the South to North Water Transfer Project is important to China. When sudden pollution accidents happen in this project, a high-accuracy water quality model is needed to simulate contaminant transport. Data assimilation algorithm can be used to improve the accuracy of model, and a water quality model with three dimensional variational data assimilation (3DVAR-WQM), are developed in this paper. A contaminant transport experiment has been conducted for verifying the feasibility and accuracy of this model. After analyzing the simulated results in 3DVAR-WQM and the standard water quality model without assimilation, it has been found that the model with simulation estimates the arrival time and value of the peak concentration more accurately, and that the error between the simulated and observed data in this model is little. At the same time, the root mean square error of this model are smaller. This paper increases forecasting skills through data assimilation techniques, and it provides a tool for improving water quality management in the South to North Water Transfer Project of China.

Numerical simulation of rainfall with assimilation of conventional and GPS observations over north of Iran

<p>In this work, the effect of assimilation of synoptic, radiosonde and ground-based GPS precipitable water vapor (PWV) data has been investigated on the short-term prediction of precipitation, vertical relative humidity and PWV fields over north of Iran. We selected two rainfall events (i.e. February 1, 2014, and September 17, 2014) caused by synoptic systems affecting the southern coasts of the Caspian Sea. These systems are often associated with a shallow and cold high pressure located over Russia that extends towards the southern Caspian Sea. The three dimensional variational (3DVAR) data assimilation system of the weather research and forecasting (WRF) model is used in two rainfall cases. In each case, three numerical experiments, namely CTRL, CONVDA and GPSCONVDA, are performed. The CTRL experiment uses the global analysis as the initial and boundary conditions of the model. In the second experiment, surface and radiosonde observations are inserted into the model. Finally, the GPSCONVDA experiment uses the GPS PWV data in the assimilation process in addition to the conventional observations. It is found that in CONVDA experiment, the mean absolute error (MAE) of the accumulated precipitation is reduced about 5 and 13 percent in 24h model simulation of February and September cases, respectively, when compared to CTRL. Also, the results in both cases suggest that the assimilation of GPS data has the greatest impact on model PWV simulations, with maximum root mean squares error (RMSE) reduction of 0.7 mm. In the GPSCONVDA experiment, comparison of the vertical profiles of 12h simulated relative humidity with the corresponding radiosonde observations shows a slight improvement in the lower levels.</p>

A forward operator and its adjoint for GPS slant total delays

AbstractIn a recent study we developed a fast and accurate algorithm to compute Global Positioning System (GPS) Slant Total Delay (STDs) utilizing numerical weather model data. Having developed a forward operator we construct in this study the tangent linear (adjoint) operator by application of the chain rule of differential calculus in forward (reverse) mode. Armed with these operators we show in a simulation study the potential benefit of GPS STDs in inverse modeling. We conclude that the developed operators are tailored for three (four)‐dimensional variational data assimilation and/or travel time tomography.

POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush–Kuhn–Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for proper orthogonal decomposition (POD) ROM data assimilation using both Galerkin and Petrov–Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov–Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.

Long‐term inverse modeling of Asian dust: Interannual variations of its emission, transport, deposition, and radiative forcing

AbstractInverse modeling of Asian dust over the 8 year period 2005–2012 was performed with the Spectral Radiation‐Transport Model for Aerosol Species/four‐dimensional variational (SPRINTARS/4D‐Var) data assimilation system and satellite‐measured aerosol optical thickness over the ocean. We validated the inversion results with independent measurements provided by ground‐based and space‐based lidar and various in situ measurements. The inversion results were used to analyze interannual variations of Asian dust fluxes and relationships of these fluxes with climate indices. Dust emissions from central China and the Mongolian Plateau were 229–384 Tg yr−1. The standard deviation of 55.3 Tg yr−1 reflected large interannual variability. The frequency of dust storms and the beginning of the dust season in the source region also showed interannual variations. There was a meridional shift of the outflow path from the continent; the transport core was centered at 40–45°N during southern transport years (2006–2007) and at 35–40°N during northern transport years (2005 and 2008–2012). The fact that dust deposition showed a significant positive correlation with satellite‐measured chlorophyll concentrations indicated that settled Asian dust enhanced phytoplankton blooms in the eastern North Pacific. Dust emissions were positively and negatively correlated with the Far Eastern Zonal and Dynamical Normalized Seasonality indices, respectively, the implication being that a strong meridional pressure gradient over the source region and a strong winter monsoon favor dust emission. The fact that the Southern Oscillation Index was positively correlated with dust emission, transport, and deposition suggests that Asian dust is affected by the El Niño–Southern Oscillation cycle and is enhanced during the La Niña phase.

Multigrid methods for improving the variational data assimilation in numerical weather prediction

Two conditions are needed to solve numerical weather prediction models: initial condition and boundary condition. The initial condition has an especially important bearing on the model performance. To get a good initial condition, many data assimilation techniques have been developed for the meteorological and the oceanographical fields. Currently, the most commonly used technique for operational applications is the 3 dimensional (3-D) or 4 dimensional variational data assimilation method. The numerical method used for the cost function minimising process is usually an iterative method such as the conjugate gradient. In this paper, we use the multigrid method based on the cell-centred finite difference on the variational data assimilation to improve the performance of the minimisation procedure for 3D-Var data assimilation.

Application of surface pressure measurements of O2-band differential absorption radar system in three-dimensional data assimilation on hurricane: Part II — A quasi-observational study

This is the second part on assessing the impacts of assimilating various distributions of sea-level pressure (SLP) on hurricane simulations, using the Weather and Research Forecast (WRF) three dimensional variational data assimilation system (3DVAR). One key purpose of this series of study is to explore the potential of using remotely sensed sea surface barometric data from O2-band differential absorption radar system currently under development for server weather including hurricane forecasts. In this part II we further validate the conclusions of observational system simulation experiments (OSSEs) in the part I using observed SLP for three hurricanes that passed over the Florida peninsula. Three SLP patterns are tested again, including all available data near the Florida peninsula, and a band of observations either through the center or tangent to the hurricane position. Before the assimilation, a vortex SLP reconstruction technique is employed for the use of observed SLP as discussed in the part I. In agreement with the results from OSSEs, the performance of assimilating SLP is enhanced for the two hurricanes with stronger initial minimum SLP, leading to a significant improvement in the track and position relative to the control where no data are assimilated. On the other hand, however, the improvement in the hurricane intensity is generally limited to the first 24–48h of integration, while a high resolution nested domain simulation, along with assimilation of SLP in the coarse domain, shows more profound improvement in the intensity. A diagnostic analysis of the potential vorticity suggests that the improved track forecasts are attributed to the combined effects of adjusting the steering wind fields in a consistent manner with having a deeper vortex, and the associated changes in the convective activity.

The four dimensional variational data assimilation with multiple regularization parameters as a weak constraint (Tikh-4D-Var) and its preliminary application on typhoon initialization

Traditional variational data assimilation (VDA) with only one regularization parameter constraint cannot produce optimal error tuning for all observations. In this paper, a new data assimilation method of “four dimensional variational data assimilation (4D-Var) with multiple regularization parameters as a weak constraint (Tikh-4D-Var)” is proposed by imposing different regularization parameters for different observations. Meanwhile, a new multiple regularization parameters selection method, which is suitable for actual high-dimensional data assimilation system, is proposed based on the posterior information of 4D-Var system. Compared with the traditional single regularization parameter selection method, computation of the proposed multiple regularization parameters selection method is smaller. Based on WRF3.3.1 4D-Var data assimilation system, initialization and simulation of typhoon Chaba (2010) with the new Tikh-4D-Var method are compared with its counterpart 4D-Var to demonstrate the effectiveness of the new method. Results show that the new Tikh-4D-Var method can accelerate the convergence with less iterations. Moreover, compared with 4D-Var method, the typhoon track, intensity (including center surface pressure and maximum wind speed) and structure prediction are obviously improved with Tikh-4D-Var method for 72-h prediction. In addition, the accuracy of the observation error variances can be reflected by the multiple regularization parameters.

Low-rank approximations for computing observation impact in 4D-Var data assimilation

We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of observation impact matrix. This novel technique is illustrated in what follows on important applications such as data pruning and the identification of faulty sensors for a two dimensional shallow water test system.