Variational Data Assimilation Method Research Articles

Improving Typhoon Muifa (2022) Forecasts with FY-3D and FY-3E MWHS-2 Satellite Data Assimilation under Clear Sky Conditions

This study investigates the impacts of assimilating the Microwave Humidity Sounder II (MWHS-2) radiance data carried on the FY-3D and FY-3E satellites on the analyses and forecasts of Typhoon Muifa in 2022 under clear-sky conditions. Data assimilation experiments are conducted using the Weather Research and Forecasting (WRF) model coupled with the Three-Dimensional Variational (3D-Var) Data Assimilation method to compare the different behaviors of FY-3D and FY-3E radiances. Additionally, the data assimilation strategies are assessed in terms of the sequence of applying the conventional and MWHS-2 radiance data. The results show that assimilating MWHS-2 data is able to enhance the dynamic and thermal structures of the typhoon system. The experiment with FY-3E MWHS-2 assimilated demonstrated superior performance in terms of simulating the typhoon’s structure and providing a prediction of the typhoon’s intensity and track than the experiment with FY-3D MWHS-2 did. The two-step assimilation strategy that assimilates conventional observations before the radiance data has improved the track and intensity forecasts at certain times, particularly with the FY-3E MWHS-2 radiance. It appears that large-scale atmospheric conditions are more refined by initially assimilating the Global Telecommunication System (GTS) data, with subsequent satellite data assimilation further adjusting the model state. This strategy has also confirmed improvements in precipitation prediction as it enhances the dynamic and thermal structures of the typhoon system.

An Enhanced Long-Term Wind Speed Prediction Using Dynamic Unified Ensemble Learning and Data Assimilation Techniques: A Case Study in Tamil Nadu, India

Reliable wind speed prediction is essential for effective grid management since wind energy is a key component of renewable energy generation. However, controlling wind speed just right is no easy feat since the wind flow changes constantly. This paper presents an innovative method for predicting wind speeds in the future. It uses state-of-the-art data assimilation methods and a dynamic unified ensemble learning model. For efficient wind energy planning and monitoring, WSP accuracy is crucial. Data from a single site limited the accuracy of WSPs in previous research. An improved accuracy of long-term wind speed predictions is achieved by the proposed model via the integration of data assimilation and ensemble learning. To increase forecast accuracy, the model uses sophisticated data assimilation methods like the Kalman filter to combine data from many sources. Specifically, the model employs the Stacked CNN + BiLSTM with Data Assimilator (SCBLSTM+DA) technique, which integrates Wind Speed (WS) data from adjacent areas with the CNN + BiLSTM-based Ensemble Learning Model (ELM) and the Four-Dimensional Variational and Ensemble Kalman Filter (4DVar/EnKF) Data Assimilation method. Using real-world wind speed data from nine meteorological stations in Tamil Nadu, India, we find that current prediction models, including both classical statistical and cutting-edge machine learning models, perform better. Further, unlike standalone models, the suggested model shows less susceptibility to changes in prediction time scales. Promising a solution to improve long-term wind speed predictions accuracy, this study has significant consequences for wind energy management and production.

Hybrid IFDMB/4D-Var inverse modeling to constrain the spatiotemporal distribution of CO and NO2 emissions using the CMAQ adjoint model

We performed a hybrid approach that combines the iterative finite difference mass balance (IFDMB) and four-dimensional variational data assimilation (4D-Var) methods to effectively constrain the spatiotemporal distribution of emissions. To quantitatively compare the performance of inverse modeling in constraining CO and NO2 emissions in South Korea spatiotemporally, we conducted a model-based twin experiment for three inverse modeling methods: IFDMB, 4D-Var, and hybrid inversions. We performed numerical modeling using the Community Multi-scale Air Quality (CMAQ) and its adjoints to calculate the values required for inverse modeling. As a result, the IFDMB inversion can effectively constrain the average spatial distribution of emissions. Meanwhile, the 4D-Var inversion can help estimate temporal variations in emissions, but it is not effective in regions with large prior emission errors. The hybrid inversion showed the best performance in constraining the spatiotemporal distribution of emissions because it combined the strengths of the two aforementioned methods. Furthermore, to compare the performance of the inverse modeling of pollutants with different chemical properties, we conducted additional inverse modeling for highly reactive NO2. After the application of inverse modeling, the emission errors of NO2 (18.339%) were larger than those of CO (10.593%). This difference in inverse modeling errors was due to the greater nonlinear relationship between emissions and concentrations in the inverse modeling process for NO2, which is more reactive compared to CO. In this study, the ideal modeling tests were performed to quantitatively assess the performance of inverse modeling. In future studies, we expect to apply the hybrid inversion approach used in this study to inverse modeling using actual observations.

Variational Data Assimilation Method Using Parallel Dual Populations Particle Swarm Optimization Algorithm

In recent years, numerical weather forecasting has been increasingly emphasized. Variational data assimilation furnishes precise initial values for numerical forecasting models, constituting an inherently nonlinear optimization challenge. The enormity of the dataset under consideration gives rise to substantial computational burdens, complex modeling, and high hardware requirements. This paper employs the Dual-Population Particle Swarm Optimization (DPSO) algorithm in variational data assimilation to enhance assimilation accuracy. By harnessing parallel computing principles, the paper introduces the Parallel Dual-Population Particle Swarm Optimization (PDPSO) Algorithm to reduce the algorithm processing time. Simulations were carried out using partial differential equations, and comparisons in terms of time and accuracy were made against DPSO, the Dynamic Weight Particle Swarm Algorithm (PSOCIWAC), and the Time-Varying Double Compression Factor Particle Swarm Algorithm (PSOTVCF). Experimental results indicate that the proposed PDPSO outperforms PSOCIWAC and PSOTVCF in convergence accuracy and is comparable to DPSO. Regarding processing time, PDPSO is 40% faster than PSOCIWAC and PSOTVCF and 70% faster than DPSO.

Foundations for Universal Non‐Gaussian Data Assimilation

AbstractIn many applications of data assimilation, especially when the size of the problem is large, a substantial assumption is made: all variables are well‐described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis, and permits physical bounds for the variables. As such, the error distribution can conform better to the underlying statistics, reducing biases introduced by the Gaussian assumption. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model (Lorenz‐63), compared to an all‐Gaussian technique.

Adjoint-based high-order spectral method of wave simulation for coastal bathymetry reconstruction

Bathymetry is an important factor affecting wave propagation in coastal environments but is often challenging to measure in practice. We propose a method for inferring coastal bathymetry from spatial variations in surface waves by combining a high-order spectral method for wave simulation and an adjoint-based variational data assimilation method. Recursion-formed adjoint equations are derived to obtain the sensitivity of the wave surface elevation to the underlying bottom topography to any desired order of nonlinear perturbation. We also develop a multiscale optimisation method to eliminate spurious high-wavenumber fluctuations in the reconstructed bathymetry data caused by sensitivity variations over the different length scales of surface waves. The proposed bottom detection method is validated with a realistic coastal wave environment involving complex two-dimensional bathymetry features, non-periodic incident waves and nonlinear broadband multidirectional waves. In numerical experiments at both laboratory and field scales, the bathymetry reconstructed from our method agrees well with the ground truth. We also show that our method is robust against imperfect surface wave data in the presence of limited sampling frequency and noise.

Conditioning of hybrid variational data assimilation

AbstractIn variational assimilation, the most probable state of a dynamical system under Gaussian assumptions for the prior and likelihood can be found by solving a least‐squares minimization problem. In recent years, we have seen the popularity of hybrid variational data assimilation methods for Numerical Weather Prediction. In these methods, the prior error covariance matrix is a weighted sum of a climatological part and a flow‐dependent ensemble part, the latter being rank deficient. The nonlinear least squares problem of variational data assimilation is solved using iterative numerical methods, and the condition number of the Hessian is a good proxy for the convergence behavior of such methods. In this article, we study the conditioning of the least squares problem in a hybrid four‐dimensional variational data assimilation (Hybrid 4D‐Var) scheme by establishing bounds on the condition number of the Hessian. In particular, we consider the effect of the ensemble component of the prior covariance on the conditioning of the system. Numerical experiments show that the bounds obtained can be useful in predicting the behavior of the true condition number and the convergence speed of an iterative algorithm

Combined assimilation of hourly rainfall data and every 10-min AHI radiance with WRF 4DVar for the short-range heavy rainfall forecast in Eastern China

Rainfall observations and geostationary satellite water vapor radiances account for complementary humidity information over rainy areas and large-scale environments, respectively. This study investigates the simultaneous assimilation of China Hourly Merged Precipitation Analysis (CHMPA) data and clear-sky water vapor radiances provided by the Himawari-8 Advanced Himawari Imager (AHI) with Four-Dimensional Variational (4DVar) data assimilation method using Weather Research and Forecasting (WRF) model with an hourly rapid-update cycling data assimilation configuration. The rapid-update 4DVar assimilation is configured as 10-min interval for AHI radiances and 1-h interval for CHMPA rainfall data in a same 1-h assimilation time window. Generally positive impacts from assimilating CHMPA rainfall and AHI water vapor radiance observations are achieved for the 12-h short-term precipitation forecast. Error reductions are found after assimilating CHMPA rainfall and AHI water vapor radiance observations for both analyses and forecasts when compared to ERA5 reanalysis. It is found that combined assimilation of CHMPA rainfall and AHI water vapor radiance data has clearly positive impacts on heavy rainfall forecasts. A heavy rainfall case that occurred in Jiangsu Province on 28 June 2020 is examined in details. The combined assimilation of infrared radiances from AHI water vapor channels together with CHMPA rainfall data improves the vertical and horizontal transport of humidity conditions, which better adjusts the humidity distribution. The over-estimation of rainfall forecast caused by the assimilation of CHMPA is alleviated. This result can provide reference for quantitative precipitation forecasts of regional numerical weather model.

Role of Ocean Initialization in Skillful Prediction of Sahel Rainfall on the Decadal Time Scale

Abstract Sahel summer rainfall has undergone persistent drought from the 1970s to 1980s, causing severe human life and economic losses. Many studies pointed out that the decadal variations of Sahel rainfall are mainly modulated by low-frequency sea surface temperature (SST) variations in different ocean basins. However, how this modulation contributes to the decadal prediction skill of Sahel rainfall remains unknown. This study provided an affirmative response using the decadal hindcasts initialized by a dimensional-reduced projection four-dimensional variational (DRP-4DVar) data assimilation method to incorporate only ocean analysis data into the gridpoint version 2 of the Flexible Global Ocean–Atmosphere–Land System Model (FGOALS-g2). The hindcasts reveal the benefits of the DRP-4DVar approach for improving the Sahel rainfall decadal prediction skill measured by the anomaly correlation coefficient (ACC), root-mean-square error, ACC difference, and mean square skill score. The decadal variations of SSTs in the Atlantic, Mediterranean Sea, Indian Ocean, and Pacific as well as correct representations of the associated Sahel rainfall–SST relationships are well predicted, thus leading to skillful predictions of Sahel rainfall. In particular, the initialization of SSTs in the Atlantic and Mediterranean Sea plays a more important role in skillful Sahel rainfall predictions than in the other basins. The prediction skill of Sahel rainfall by the FGOALS-g2 prediction system is significantly higher than those by most phase 5 and 6 of the Coupled Model Intercomparison Project (CMIP5&6) prediction systems initialized only with ocean analysis data. This result is likely attributed to a more accurate relationship between Sahel rainfall and SST by the FGOALS-g2 prediction system than by the CMIP5&6 prediction systems. Significance Statement Previous studies have shown limited success in predicting Sahel rainfall. By using an advanced coupled data assimilation method constrained only by ocean observational data, we achieve a high decadal prediction skill for Sahel rainfall. The successful prediction is attributed to accurately predicted decadal variations of sea surface temperatures in the Atlantic, Mediterranean Sea, Indian Ocean, and Pacific as well as their relationships with Sahel rainfall. Our results can provide references for future decadal predictions of Sahel rainfall and motivate the need to evaluate the contributions of the initialization of the ocean versus the other climate components (e.g., atmosphere or land) to Sahel rainfall predictions.

Comparison of Deterministic and Probabilistic Variational Data Assimilation Methods Using Snow and Streamflow Data Coupled in HBV Model for Upper Euphrates Basin

The operation of upstream reservoirs in mountainous regions fed by snowmelt is highly challenging. This is partly due to scarce information given harsh topographic conditions and a lack of monitoring stations. In this sense, snow observations from remote sensing provide additional and relevant information about the current conditions of the basin. This information can be used to improve the model states of a forecast using data assimilation techniques, therefore enhancing the operation of reservoirs. Typical data assimilation techniques can effectively reduce the uncertainty of forecast initialization by merging simulations and observations. However, they do not take into account model, structural, or parametric uncertainty. The uncertainty intrinsic to the model simulations introduces complexity to the forecast and restricts the daily work of operators. The novel Multi-Parametric Variational Data Assimilation (MP-VarDA) uses different parameter sets to create a pool of models that quantify the uncertainty arising from model parametrization. This study focuses on the sensitivity of the parametric reduction techniques of MP-VarDA coupled in the HBV hydrological model to create model pools and the impact of the number of parameter sets on the performance of streamflow and Snow Cover Area (SCA) forecasts. The model pool is created using Monte Carlo simulation, combined with an Aggregated Distance (AD) Method, to create different model pool instances. The tests are conducted in the Karasu Basin, located at the uppermost part of the Euphrates River in Türkiye, where snowmelt is a significant portion of the yearly runoff. The analyses were conducted for different thresholds based on the observation exceedance probabilities. According to the results in comparison with deterministic VarDA, probabilistic MP-VarDA improves the m-CRPS gains of the streamflow forecasts from 57% to 67% and BSS forecast skill gains from 52% to 68% when streamflow and SCA are assimilated. This improvement rapidly increases for the first additional model parameter sets but reaches a maximum benefit after 5 parameter sets in the model pool. The improvement is notable for both methods in SCA forecasts, but the best m-CRPS gain is obtained for VarDA (31%), while the best forecast skill is detected in MP-VarDA (12%).

Development of an integrated machine-learning and data assimilation framework for NOx emission inversion

As major air pollutants, nitrogen oxides (NOx, mainly comprising NO and NO2) not only have adverse effects on human health but also contribute to the formation of secondary pollutants, such as ozone and particulate nitrate. To acquire reasonable NOx simulation results for further analysis, a reasonable emission inventory is needed for three-dimensional chemical transport models (3D-CTMs). In this study, a comprehensive emission adjustment framework for NOx emission, which integrates the simulation results of the 3D-CTM, surface NO2 measurements, the three-dimensional variational data assimilation method, and an ensemble back propagation neural network, was proposed and applied to correct NOx emissions over China for the summers of 2015 and 2020. Compared with the simulation using prior NOx emissions, the root-mean-square error, normalized mean error, and normalized mean bias decreased by approximately 40 %, 40 %, and 60 % in NO2 simulation using posterior NOx emissions corrected by the framework proposed in this work. Compared with the emissions for 2015, the NOx emission generally decreased by an average of 5 % in the simulation domain for 2020, especially in Henan and Anhui provinces, where the percentage reductions reached 24 % and 19 %, respectively. The proposed framework is sufficiently flexible to correct emissions in other periods and regions. The framework can provide reliable and up-to-date emission information and can thus contribute to both scientific research and policy development relating to NOx pollution.

A real-time variational data assimilation method with data-driven model enrichment for time-dependent problems

We propose an extension of the Parameterized-Background-Data-Weak (PBDW) formulation, introduced in Maday et al. (2015), to the time-dependent context for state reconstruction and prediction-in-time purposes. This method provides a non-intrusive, real-time, and in-situ data assimilation framework for physical systems modeled by parameterized Partial Differential Equations. Given a sequential set of M measurements at acquisition time tk, the key idea of the proposed formulation is to seek an approximation uN,Mk=zN,Mk+ηN,Mk of the true state utruek employing projection-by-data; the first term comes from a background estimate zN,Mk computed from a reduced-basis N-dimensional linear space informed by the parameterized mathematical model, while the second term comes from an update state ηN,Mk informed by experimental observations (hybrid modeling with correction of model bias). The contributions of this work are twofold. First, we present a new formulation adapted to time-dependent parameterized problems of the classical PBDW strategy. In particular, the N-dimensional linear space is here constructed using a space/time/parameter decomposition. Furthermore, we exploit the evolution features to enrich the biased model with previous updates, and to extrapolate in time the estimated states in order to predict and monitor the physical system. We set up and analyze a synthetic numerical example of thermal diffusion with different biases to assess and compare performance of three formulations of the proposed approach.

The Effect of Assimilating AMSU-A Radiance Data from Satellites and Large-Scale Flows from GFS on Improving Tropical Cyclone Track Forecast

This study aimed to investigate the effect of assimilating either AMSU-A radiance data from satellites, large-scale flows from the Global Forecast System (GFS), or both together, on improving the track forecast of tropical cyclone (TC). The scale-selective data assimilation (SSDA) approach was employed for the assimilation of large-scale GFS flows, while the conventional 3D variational data assimilation (3DVAR) method was used for that of AMSU-A radiance data. The results show that assimilating either AMSU-A radiance data or large-scale GFS flows has a significant improvement on TC track forecast, but the improvement occurs within the first 72 h and after 72 h, respectively. When assimilating both AMSU-A radiance data and large-scale GFS flows, the forecast can take advantage of both data and thus lead to the smallest 5-day mean errors of the track forecast. These results are instructive to future operational TC track forecasting.

Impacts of FY-4A AGRI Radiance Data Assimilation on the Forecast of the Super Typhoon “In-Fa” (2021)

This study assessed the impact of assimilating the Fengyun-4A (FY-4A) Advanced Geosynchronous Radiation Imager (AGRI) observations on the Super Typhoon “In-Fa” event based on the Weather Research and Forecasting Data Assimilation (WRFDA) system of the three-dimensional variational data assimilation (3DVAR) method. It was found that the two water vapor channels 9–10 from the full-disk AGRI datasets yield relatively stable results in terms of the track forecast of In-Fa. A new cloud-detection method using a Particle Filter (PF) was firstly employed to remove the cloud-affected observations by identifying the channel’s weighting function. Compared to the other cloud-detection schemes based on the AGRI “Cloud_Binary_Mask” (CLM) products, the PF method is conducive to reducing the track error of typhoon prediction after improving the utilization of observations under clear-sky conditions. Furthermore, the proposed cycling assimilation scheme has a potential positive effect on the intensity forecast of In-Fa. It seems that assimilating the FY-4A AGRI radiance data improves the predictability of Typhoon In-Fa by adjusting the atmospheric environment.

A Mini‐Batch Stochastic Optimization‐Based Adaptive Localization Scheme and Its Implementation in NLS‐i4DVar

AbstractThis paper proposes a mini‐batch stochastic optimization‐based adaptive localization scheme for computing the “optimal” localization radius in data assimilation (DA) applications. After constructing a cost function of the localization radius by estimating forecast and observation error statistics, a mini‐batch stochastic gradient descent method with a novel sampling strategy is proposed to minimize the cost function. The proposed stochastic optimization algorithm is further incorporated into the DA method NLS‐i4DVar (the nonlinear least squares integral correcting four‐dimensional variational DA method), which was developed by the authors in Tian et al. (2021, https://doi.org/10.1029/2021EA001767). It is utilized to compute the “optimal” covariance localization radii adaptively and flow‐dependently inside NLS‐i4DVar. The computational cost of NLS‐i4DVar with the proposed adaptive localization scheme only increases slightly due to the use of the mini‐batch stochastic optimization algorithm. Numerical experimental results using the shallow‐water equations demonstrate that NLS‐i4DVar with the proposed adaptive localization scheme shows substantial performance improvement over the standard NLS‐i4DVar method.

Integral correction of initial and model errors in system of multigrid NLS‐4DVar data assimilation for numerical weather prediction (SNAP)

AbstractModel error has a marked influence on forecast error, and integral correction of the initial and model errors in a novel four‐dimensional variational data assimilation (4DVar) method (i4DVar) has recently been developed. Unlike traditional 4DVar, in which the analysis increment focuses only on the initial time point, i4DVar introduces an averaged integral correction term to correct the error evolution at multiple times with the same time interval in the assimilation window; that is, the assimilation window is divided into several sub‐windows. In this study, we incorporated i4DVar into the System of Multigrid Nonlinear Least‐squares‐4DVar Data Assimilation for Numerical Weather Prediction (NWP) (SNAP), hereafter referred to as SN‐i4DVar, and explored its impacts on NWP. The effectiveness and performance of SN‐i4DVar were evaluated using two extreme rainstorm cases assimilating conventional and satellite observations, respectively. The results indicated that integral correction of the initial and model errors reduced analysis error and forecast error growth rates. SN‐i4DVar performed better in precipitation forecasting than the original SNAP and exhibited generally better forecasting capability in terms of the horizontal wind speed (u and v), temperature, and humidity variables, indicating that SN‐i4DVar simultaneously countered initial model errors to improve NWP capability. Meanwhile, the 4DEnVar method, which considers the optimal analysis in the ensemble space, benefits from the improved ensemble space generated according to the formulas of i4DVar, and the observation information can be more effectively absorbed and a more accurate analysis can be obtained by SN‐i4DVar.

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

A new robust discharge estimation method applied in the context of SWOT satellite data processing

Knowing river discharge is vital for monitoring the fresh water cycle at the global scale. The Surface Water and Ocean Topography (SWOT) satellite mission will map river water surface elevations and inundated areas for rivers wider than one hundred meters worldwide. These observations can be used for estimating the river discharge. It is the global coverage which makes these observations particularly valuable, however in many cases there will be no data on the bathymetry and river bed properties available. That is why the problem of discharge estimation using solely the SWOT-type observations has received a noticeable attention recently.The attempts to solve this problem have expectedly confirmed that it is highly ill-posed and, therefore, additional data is useful. In particular, the use of the mean discharge estimates retrieved from the global scale hydrological databases (e.g. the Global Water Balance Model) have been accepted. However, taking into account the accuracy of such estimates and the issue of their relevance to the current time period, the problem is still posing a serious challenge. For example, in the results obtained by different methods reported up to date, the estimated hydrograph may suffer from a significant bias, which often makes a major contribution to the total estimation error.In this paper a new estimation method is suggested, which is specially designed to reduce the solution bias. The concept of this method is similar to the one of the Variational Expectation–Maximization method, however its perception and implementation are original and problem-oriented. In our method, the mean values of the unknown variables are obtained using the Bayesian estimator, whereas the ‘shape’ functions are updated using the variational data assimilation or generated directly using the inverted simplified hydraulic model. The two steps constitute an estimation cycle, which can be repeated after information exchange.The method has been validated using two available testing sets including 51 cases in total. It has demonstrated a much better robustness and reliability than the variational data assimilation method, and quite a promising performance in terms of accuracy. Since the proof of the concept was in the focus of this study, the issue of computational feasibility was not a priority. Nevertheless, the method in its current form can be applied at local/regional or basin scales. For a possible global scale application, a generalized discharge estimator is suggested, where the major computational burden falls on the ‘learning’ stage, which is separated from the discharge prediction algorithm.

4D-Var data assimilation using satellite sea surface temperature to improve the tidally-driven interior ocean dynamics estimates in the Indo-Australian Basin

Estimating ocean processes in regions with sparse observations, and where dynamics are dominated by strong barotropic and baroclinic tides, poses a significant modelling challenge. In this study, a Four-Dimensional Variational (4D-Var) data assimilation method, incorporating remotely sensed sea surface temperature (SST) data observations only, was used to improve estimates of the internal tide dynamics in the ocean between Australia and Indonesia. In this region, local internal tide generation, propagation and interference of the internal tides is highly variable and dependent on the 3D density field and mesoscale dynamics. The results of this study show that assimilation of remotely sensed SST data not only reduced the surface temperature root mean squared error (RMSE) from 0.8 °C to 0.3 °C, and removed a 0.4 °C cold bias (compared to a non-assimilative model), but also improved estimates of through-water-column variables — with the latter evaluated against ARGO profiling floats and two independent mooring sites. Overall, the depth-averaged temperature RMSE was reduced by as much as 38%, and ocean currents by ∼20% at the two mooring sites. The improvements were most significant in the top 100 m, where the internal tide signature was significantly corrected despite no depth-varying variables being assimilated. The study also showed that assimilating 2 km resolution SST observations resulted in more realistic SST wavenumber power spectral density estimates than those without assimilating data; in particular, the scheme reduced the energy at mesoscale length scales and improved the spectral slope towards the smaller submesoscale dynamics. It is concluded that 4D-Var assimilation using only SST improves estimates of upper 100 m ocean dynamics in tropical regions where there is sensitivity to the air–sea fluxes.

Addressing dynamics in radio frequency tomography

Tomographic imaging of a dynamic scene is addressed for the first time in this article. The effect of dynamics of the imaged object is studied for some deformation scenarios using the conventional truncated singular value decomposition (TSVD) method, which is applied in numerous static inverse scattering problems, together with variational data assimilation (DA) methods including three-dimensional variational (3D-VAR) and four-dimensional variational (4D-VAR) techniques. Results show that the DA frameworks outperform the TSVD method, which assumes the scene static, especially for objects with higher contrast. Also, it is seen that applying the conventional TSVD method makes the image blurred and distorts it for high-speed dynamic changes, particularly when the contrast is increased. However, the proposed DA methods seem to be robust against large deformation distortions and can still detect the object.