Variational Data Assimilation Scheme Research Articles

Combining neural networks and data assimilation to enhance the spatial impact of Argo floats in the Copernicus Mediterranean biogeochemical model

Abstract. Biogeochemical-Argo (BGC-Argo) float profiles provide substantial information on key vertical biogeochemical dynamics and have been successfully integrated in biogeochemical models via data assimilation approaches. Although BGC-Argo assimilation results have been encouraging, data scarcity remains a limitation with respect to their effective use in operational oceanography. To address availability gaps in the BGC-Argo profiles, an observing system experiment (OSE) that combines a neural network (NN) and data assimilation (DA) was performed here. A NN was used to reconstruct nitrate profiles, starting from oxygen profiles and associated Argo variables (pressure, temperature, and salinity), while a variational data assimilation scheme (3DVarBio) was upgraded to integrate BGC-Argo and reconstructed observations in the Copernicus Mediterranean operational forecast system (MedBFM). To ensure the high quality of oxygen data, a post-deployment quality control method was developed with the aim of detecting and eventually correcting potential sensors drift. The Mediterranean OSE features three different set-ups: a control run without assimilation; a multivariate run with assimilation of BGC-Argo chlorophyll, nitrate, and oxygen; and a multivariate run that also assimilates reconstructed observations. The general improvement in the skill performance metrics demonstrated the feasibility of integrating new variables (oxygen and reconstructed nitrate). Major benefits have been observed with respect to reproducing specific biogeochemical-process-based dynamics such as the nitracline dynamics, primary production, and oxygen vertical dynamics. The assimilation of BGC-Argo nitrate corrects a generally positive bias of the model in most of the Mediterranean areas, and the addition of reconstructed profiles makes the corrections even stronger. The impact of enlarged nitrate assimilation propagates to ecosystem processes (e.g. primary production) at a basin-wide scale, demonstrating the importance of the assimilation of BGC-Argo profiles in forecasting the biogeochemical ocean state.

Assessing the Accuracy of 3D-VAR in Supercell Thunderstorm Forecasting: A Regional Background Error Covariance Study

Data assimilation (DA) integrates observational data with numerical weather predictions to enhance weather forecast accuracy. This study evaluates three regional background error (BE) covariance statistics for numerical weather prediction (NWP) via a variational data assimilation (VAR) scheme. The best practices in DA are highlighted, as well as the impact of BE covariance calculation in DA procedures by employing the Weather Research and Forecasting (WRF) model. Forecasts initialized at different intervals were used to compute distinct regional background error statistics utilizing three control variable (CV) methodologies over a span of 20 days. These statistics are used by the three-dimensional VAR DA process of WRF DA software, producing analysis fields that lead to forecasts for a distinct convective supercell event during the summer of 2019 over northern Greece. This high-impact convective event underscores the importance of selecting appropriate BE over complex terrain areas. The results emphasize the significance of BE usage in DA, proposing the optimal DA approach for simulations of convective systems.

Efficient deep data assimilation with sparse observations and time-varying sensors

Variational Data Assimilation (DA) has been broadly used in engineering problems for field reconstruction and prediction by performing a weighted combination of multiple sources of noisy data. In recent years, the integration of deep learning (DL) techniques in DA has shown promise in improving the efficiency and accuracy in high-dimensional dynamical systems. Nevertheless, existing deep DA approaches face difficulties in dealing with unstructured observation data, especially when the placement and number of sensors are dynamic over time. We introduce a novel variational DA scheme, named Voronoi-tessellation Inverse operator for VariatIonal Data assimilation (VIVID), that incorporates a DL inverse operator into the assimilation objective function. By leveraging the capabilities of the Voronoi-tessellation and convolutional neural networks, VIVID is adept at handling sparse, unstructured, and time-varying sensor data. Furthermore, the incorporation of the DL inverse operator establishes a direct link between observation and state space, leading to a reduction in the number of minimization steps required for DA. Additionally, VIVID can be seamlessly integrated with Proper Orthogonal Decomposition (POD) to develop an end-to-end reduced-order DA scheme, which can further expedite field reconstruction. Numerical experiments in a fluid dynamics system demonstrate that VIVID can significantly outperform existing DA and DL algorithms. The robustness of VIVID is also accessed through the application of various levels of prior error, the utilization of varying numbers of sensors, and the misspecification of error covariance in DA.

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

A Multiscale Four-Dimensional Variational Data Assimilation Scheme: A Squall-Line Case Study

Abstract This study presents a multiscale four-dimensional variational data assimilation (MS-4DVar) scheme that aims to assimilate multiscale information from conventional and radar observations. The MS-4DVar scheme separately assimilates conventional and radar data in different outer loop iterations of an incremental 4DVar with varied resolutions in the tangent linear and adjoint models (TLM/ADM) and time window lengths in the 4DVar. The MS-4DVar scheme was evaluated through a series of single observation tests and several cycled assimilation and forecasting experiments for a real squall-line case. Our results indicated that different TLM/ADM resolutions and time window lengths applied to the conventional and radar observations improved the multiscale analysis. In addition, the MS-4DVar scheme was more efficient than the common 4DVar because of the low-resolution TLM/ADM used for conventional data and the shortened time window length for radar data. Verification of the squall-line forecasts suggested that the MS-4DVar scheme improved the hourly accumulated precipitation and radar reflectivity forecast skills and reduced the forecast errors of both large-scale environmental and convective-scale states. Further diagnosis revealed that the improvement of precipitation forecast skill was attributable to the stronger cold pool, deeper saturated water vapor layer, and stronger updraft of the simulated squall-line system, as well as a more favorable convective environment.

An operational improvement of A-4DEnVar and its application to the estimation of the spatially varying bottom friction coefficients of the M2 constituent in the Bohai and Yellow seas

The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation scheme inherits the advantages of the conventional four-dimensional variational (4D-Var) data assimilation scheme and removes the adjoint model. However, compatible operational improvements such as the reduction of the computational costs and the localization method should be considered when it is used in realistic systems. In this paper, the computational complexity of calculating the inverse of background error covariance (the B matrix) is decreased by a precondition transform method, i.e., introducing a new state variable whose product with the B matrix is the original state variable to be optimized in the cost function. Furthermore, an independent point (IP) scheme is combined to construct an implicit localization method and further decreases the computational cost. Based on the Princeton Ocean Model with the generalized coordinate system (POMgcs), the operational improved A-4DEnVar is applied to optimize the spatially varying bottom friction coefficients (BFCs) of the M2 constituent in the Bohai and Yellow seas. A twin experiment with idealized observations is designed to validate the effectiveness of the proposed method. In practical experiments, with no more than 10 IPs, the algorithm can assimilate observations from the National Astronomical Observatory (NAO) dataset and obtain a good simulation. The experimental performances increase with the increase of either the IPs or observations, which indicates the efficacy of the proposed algorithm.

HUXt—An open source, computationally efficient reduced-physics solar wind model, written in Python

HUXt is an open source numerical model of the solar wind written in Python. It is based on the solution of the 1D inviscid Burger’s equation. This reduced-physics approach produces solar wind flow simulations that closely emulate the flow produced by 3-D magnetohydrodynamic (MHD) solar wind models at a small fraction of the computational expense. While not intended as a replacement for 3-D MHD, the simplicity and computational efficiency of HUXt offers several key advantages that enable experiments and the use of techniques that would otherwise be cost prohibitive. For example, large ensembles of 102–105 members can easily be run with modest computing resources, which are useful for exploring and quantifying the uncertainty in space weather predictions, as well as for the application of some data assimilation methods. In this article we present the developments in the latest version of HUXt, v4.0, and discuss our plans for future developments and applications of the model. The three key developments in v4.0 are: 1) a restructuring of the models solver to enable fully time-dependent boundary conditions, such that HUXt can in principle be initialised with in-situ observations from any of the fleet of heliospheric monitors; 2) new functionality to trace streaklines through the HUXt flow solutions, which can be used to track features such as the Heliospheric Current Sheet; 3) introduction of a small test-suite so that we can better ensure the reliability and reproducibility of HUXt simulations for all users across future versions. Other more minor developments are discussed in the article. Future applications of HUXt are discussed, including the development of both sequential and variational data assimilation schemes for assimilation of both remote sensing and in-situ plasma measures. Finally, we briefly discuss the progress of transitioning HUXt into an operational model at the UK’s Met Office Space Weather Operations Center as part of the UK governments SWIMMR programme.

Implementation of Scale-Dependent Background-Error Covariance Localization in the Canadian Global Deterministic Prediction System

Abstract The approach of applying different amounts of horizontal localization to different ranges of background-error covariance horizontal scales as proposed by Buehner and Shlyaeva was recently implemented in the four-dimensional ensemble–variational (4DEnVar) data assimilation scheme of the global deterministic prediction system (GDPS) at Environment and Climate Change Canada operations. To maximize the benefits from this approach to reduce the sampling noise in the ensemble-derived background-error covariances, it was necessary to adopt a new weighting between the climatological and flow-dependent covariances that increases significantly the role of the latter. Thus, in December 2021 the GDPS became the first operational global deterministic medium-range weather forecasting system to rely completely on flow-dependent covariances in the troposphere and the lower stratosphere. The experiments that led to the adoption of these two related changes and their impacts on the forecasts up to 7 days for various regions of the globe during the boreal summer of 2019 and winter of 2020 are presented here. It is also illustrated that relying more on ensemble-derived covariances amplifies the positive impacts on the GDPS when the background ensemble generation strategy is improved.

Non‐Gaussian Detection Using Machine Learning With Data Assimilation Applications

AbstractIn most data assimilation and numerical weather prediction systems, the Gaussian assumption is prevalent for the behavior of the random variables/errors that are involved. At the Cooperative Institute for Research in the Atmosphere theory has been developed for different forms of variational data assimilation schemes that enables the Gaussian assumption to be relaxed. For certain variable types, a lognormally distributed random variable can be combined in a mixed Gaussian‐lognormal distribution to better capture the interactions of the errors of different distributions. However, assuming that a distribution can change in time, then developing techniques to know when to switch between different versions of the data assimilation schemes becomes very important. By dynamically changing the formulation of the data assimilation system we are able to assimilate observations in a way that reflects the flow‐dependent variability of their distribution.In this paper, we present results with a machine learning technique (the support vector machine) to switch between data assimilation methods based on the detection of a change in the Lorenz 1963 model's z component's probability distribution. Given the machine learning technique's detection/prediction of a change in the distribution, then either a Gaussian or a mixed Gaussian‐lognormal 3DVar based cost function is used to minimize the errors in this period of time. It is shown that switching from a Gaussian 3DVar to a lognormal 3DVar at lognormally distributed parts of the attractor improves the data assimilation analysis error compared to using one distribution type for the entire attractor.

The Multigrid Beta Function Approach for Modeling of Background Error Covariance in the Real-Time Mesoscale Analysis (RTMA)

Abstract We describe a method for the efficient generation of the covariance operators of a variational data assimilation scheme, which is suited to implementation on a massively parallel computer. The elementary components of this scheme are what we call “beta filters,” since they are based on the same spatial profiles possessed by the symmetric beta distributions of probability theory. These approximately Gaussian (bell-shaped) polynomials blend smoothly to zero at the ends of finite intervals, which makes them better suited to parallelization than the present quasi-Gaussian “recursive filters” used in operations at NCEP. These basic elements are further combined at a hierarchy of different spatial scales into an overall multigrid structure formulated to preserve the necessary self-adjoint attribute possessed by any valid covariance operator. This paper describes the underlying idea of the beta filter and discusses how generalized Helmholtz operators can be enlisted to weight the elementary contributions additively in such a way that the covariance operators may exhibit realistic negative sidelobes, which are not easily obtained through the recursive filter paradigm. The main focus of the paper is on the basic logistics of the multigrid structure by which more general covariance forms are synthesized from the basic quasi-Gaussian elements. We describe several ideas on how best to organize computation, which led us to a generalization of this structure that made it practical so that it can efficiently perform with any rectangular arrangement of processing elements. Some simple idealized examples of the applications of these ideas are given.

Effects of Flow Dependency Introduced by Background Error in Frequent and Dense Assimilation of Radial Winds Using Observation Error Correlated in Time and Space

Abstract We investigated the effect of flow dependency in the assimilation of high-density, high-frequency observations. Radial winds from a Doppler radar are assimilated using a regional hybrid four-dimensional variational data assimilation (4D-Var) scheme with a flow-dependent background error covariance. To consistently assimilate 5 km × 5.625° cell-averaged radial winds at an interval of 10 min, the spatial and temporal correlations of the observation error are statistically diagnosed to be incorporated into the hybrid 4D-Var. The spatial correlation width is larger than that expected from instrument error, suggesting a contribution from representation error whose propagation is also considered to lead to temporal correlation, the width of which is diagnosed to increase with forecast time. The background error covariance also has an important role in incorporating observational information into the analysis. Single observation experiments show that the hybrid 4D-Var has more small-scale structure in its flow-dependent background error correlation than the 4D-Var limited from the climatological background error covariance mainly in the former part of the assimilation window. This suggests the higher potential of the hybrid 4D-Var to allow more higher-wavenumber components in the increment. A case study shows that the hybrid 4D-Var makes better use of the dense and frequent observations, reflecting more detailed representation of flow throughout the assimilation window, leading to promising results in the forecast. Sensitivity experiments also show that it is important to use the optimal observation error correlation. It is suggested that the flow-dependent background error becomes necessary to effectively use high-resolution, high-frequency observations.

High-Resolution Reanalysis of the Mediterranean Sea Biogeochemistry (1999–2019)

Ocean reanalyses integrate models and observations to provide a continuous and consistent reconstruction of the past physical and biogeochemical ocean states and variability. We present a reanalysis of the Mediterranean Sea biogeochemistry at a 1/24° resolution developed within the Copernicus Marine Environment Monitoring Service (CMEMS) framework. The reanalysis is based on the Biogeochemical Flux Model (BFM) coupled with a variational data assimilation scheme (3DVarBio) and forced by the Nucleus for European Modeling of the Ocean (NEMO)–OceanVar physical reanalysis and European Centre for medium-range weather forecasts (ECMWF) reanalysis ERA5 atmospheric fields. Covering the 1999–2019 period with daily means of 12 published and validated biogeochemical state variables, the reanalysis assimilates surface chlorophyll data and integrates EMODnet data as initial conditions, in addition to considering World Ocean Atlas data at the Atlantic boundary, CO2 atmospheric observations, and yearly estimates of riverine nutrient inputs. With the use of multiple observation sources (remote, in situ, and BGC-Argo), the quality of the biogeochemical reanalysis is qualitatively and quantitatively assessed at three validation levels including the evaluation of 12 state variables and fluxes and several process-oriented metrics. The results indicate an overall good reanalysis skill in simulating basin-wide values and variability in the biogeochemical variables. The uncertainty in reproducing observations at the mesoscale and weekly temporal scale is satisfactory for chlorophyll, nutrient, oxygen, and carbonate system variables in the epipelagic layers, whereas the uncertainty increases for a few variables (i.e., oxygen and ammonium) in the mesopelagic layers. The vertical dynamics of phytoplankton and nitrate are positively evaluated with specific metrics using BGC-Argo data. As a consequence of the continuous increases in temperature and salinity documented in the Mediterranean Sea over the last 20 years and atmospheric CO2 invasion, we observe basin-wide biogeochemical signals indicating surface deoxygenation, increases in alkalinity, and dissolved inorganic carbon concentrations, and decreases in pH at the surface. The new, high-resolution reanalysis, open and freely available from the Copernicus Marine Service, allows users from different communities to investigate the spatial and temporal variability in 12 biogeochemical variables and fluxes at different scales (from the mesoscale to the basin-wide scale and from daily to multiyear scales) and the interaction between physical and biogeochemical processes shaping Mediterranean marine ecosystem functioning.

A High Resolution Reanalysis for the Mediterranean Sea

In order to be able to forecast the weather and estimate future climate changes in the ocean, it is crucial to understand the past and the mechanisms responsible for the ocean variability. This is particularly true in a complex area such as the Mediterranean Sea with diverse dynamics like deep convection and overturning circulation. To this end, effective tools are ocean reanalyses or reconstructions of the past ocean state. Here we present a new physical reanalysis of the Mediterranean Sea at high resolution, developed in the Copernicus Marine Environment Monitoring Service (CMEMS) framework. The hydrodynamic model is based on the Nucleus for European Modelling of the Ocean (NEMO) combined with a variational data assimilation scheme (OceanVar). The model has a horizontal resolution of 1/24° and 141 unevenly distributed vertical z* levels. It provides daily and monthly temperature, salinity, current, sea level and mixed layer depth as well as hourly fields for surface velocities and sea level. ECMWF ERA-5 atmospheric fields force the model and daily boundary conditions in the Atlantic are taken from a global reanalysis. The reanalysis covers the 33 years from 1987 to 2019. Initialized from SeaDataNet climatology in January 1985, it reaches a nominal state after a 2-years spin-up. In-situ data from CTD, ARGO floats and XBT are assimilated into the model in combination with satellite altimetry observations. This reanalysis has been validated and assessed through comparison to in-situ and satellite observations as well as literature climatologies. The results show an overall improvement of the comparison with observations and a better representation of the main dynamics of the region compared to a previous, lower resolution (1/16°), reanalysis. Temperature and salinity RMSD are decreased by respectively 14 and 18%. The salinity biases at depth of the previous version are corrected. Climate signals show continuous increase of the temperature and salinity, confirming estimates from observations and other reanalysis. The new reanalysis will allow the study of physical processes at multi-scales, from the large scale to the transient small mesoscale structures and the selection of climate indicators for the basin.

Representations of Precipitation Diurnal Cycle in the Amazon as Simulated by Observationally Constrained Cloud‐System Resolving and Global Climate Models

AbstractThe ability of an observationally‐constrained cloud‐system resolving model (Weather Research and Forecasting; WRF, 4‐km grid spacing) and a global climate model (Energy Exascale Earth System Model; E3SM, 1‐degree grid spacing) to represent the precipitation diurnal cycle over the Amazon basin during the 2014 wet season is assessed. The WRF model coupled with a 3‐D variational data assimilation scheme reproduces the spatial variability of the precipitation diurnal cycle over the basin and the lifecycle of westward propagating MCSs initiated by the coastal sea‐breeze front. In contrast, a single morning peak in rainfall is produced by E3SM for simulations despite the nudging of large‐scale winds toward global reanalysis, indicating precipitation in E3SM is largely controlled by local convection associated with diurnal heating. The role of propagating MCS on the environment are discussed by using a multivariate perturbation analysis. We also find that the advection of moisture perturbations from ocean to inland regions have a higher correlation with the occurrence of MCSs in the Amazon than the intensity of colder air intrusion associated with sea breezes along the coast. Moreover, the presence of large cold pools over the central Amazon basin are responsible for the maintenance of propagating deep convection.

Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

Impacts of the Assimilation of Satellite Sea Surface Temperature Data on Volume and Heat Budget Estimates for the North Sea

AbstractMechanisms controlling the heat budget of the North Sea are investigated based on a combination of satellite sea surface temperature measurements and numerical model simulations. Lateral heat fluxes across the shelf edge and into the Baltic Sea as well as vertical ocean‐atmosphere heat exchange are considered. A 3‐D variational (3DVAR) data assimilation (DA) scheme is applied, which contains assumed model error correlations that depend on the mixed layer depth derived from a coupled circulation/ocean wave model. The analysis balances pressure gradients introduced by temperature modifications. Significant hydrodynamic model response to DA was found, which should be considered in the heat budget estimations. The observed change of the current velocity field decreases the lateral advective volume/heat exchanges between the North Sea and the Atlantic, yielding an increased heat flux from the Atlantic into the North Sea and more heat flux from the sea to the atmosphere. The largest DA impact on volume/heat transport is in the Norwegian Channel, where the dominant process is Eulerian transport, followed by tidal pumping and wind pumping. Further analysis reveals an acceleration of the along‐shelf current at the northern edge of the North Sea, a decrease in the horizontal pressure gradient from the Atlantic to the North Sea, and a reduction of the Eulerian transport of volume/heat outward the North Sea. Furthermore, the coupling between the circulation model and the wave model has significant impacts on lateral heat advection in the DA run, which is due to the wave impact on the mixed layer depth.

Impact Study of FY-3B MWRI Data Assimilation in WRFDA

In the first attempt to configure the Fengyun-3B satellite’s Microwave Radiation Imager (MWRI) radiance data in the Weather Research Forecast (WRF) model’s Data Assimilation system (WRFDA), the impact of MWRI data assimilation on the analysis and forecast of Typhoon Son-Tinh in 2012 was evaluated with WRFDA’s three-dimensional variational (3DVAR) data-assimilation scheme. Compared to a benchmark experiment with no MWRI data, assimilating MWRI radiances improved the analyses of typhoon central sea level pressure (CSLP), warm core structure, and wind speed. Moreover, verified with European Center for Medium-Range Weather Forecasts (ECMWF) analysis data, significant improvements in model variable forecast, such as geopotential height and specific humidity, were produced. Substantial error reductions in track, CSLP, and maximum-wind-speed forecasts with MWRI assimilation was also obtained from analysis time to 48 h forecast.

Validation and analysis of a 1-D variational assimilation scheme for bathymetry inversion

Results are presented from a variational data assimilation and nearshore bathymetry inversion scheme based on depth and wave-phase averaged surfzone hydrodynamics for a narrow-banded wave spectrum. 1-D Cross shore bathymetry is inverted based on 17-min-averaged significant wave height and longshore current observations made during the Duck94 field experiment. An inversion scenario is considered in which inversion is carried out separately for each 17-min-averaged set of observations. Results are used to quantify the inversion scheme's accuracy depending on time dependent wave and bathymetry conditions. The model generally produced a root-mean-square error of 0.46 m between modelled and actual bathymetry when both wave height observations and alongshore current observations were assimilated. The RMS error reduced to 0.44 m when only wave height observations were assimilated and increased to 0.69 m when only alongshore current observations were assimilated, suggesting that wave height is a more informative variable for bathymetry inversion. The model performed consistently in inverting bathymetry and thereby tracking morphologic change in varied wave conditions, including during large storm events.

Variational assimilation of surface wave data for bathymetry reconstruction. Part I: algorithm and test cases

Accurate mapping of ocean bathymetry is needed for effective modelling of ocean dynamics, such as tsunami prediction. Available bathymetry data does not always provide the resolution to model such nonlinear waves accurately, and collection of accurate data is logistically challenging. As an alternative, in this study we develop and evaluate a variational data assimilation scheme for the one-dimensional nonlinear shallow water equations that estimates bathymetry using a finite set of observations of surface wave height. We demonstrate that convergence to exact bathymetry is improved by including more observation locations and by implementing a low-pass filter in the data assimilation algorithm to remove small-scale noise. A necessary condition for convergence of the bathymetry reconstruction is that the amplitude of the initial conditions is less than 1% of the bathymetry height. We use density-based global sensitivity analysis (GSA) to assess the sensitivity of the surface wave and reconstruction error to model parameters. By demonstrating low sensitivity of the surface wave to the reconstruction error, we show that reconstructing the bathymetry with a relative error of about 10% is sufficiently accurate for surface wave modelling in most cases. These results can be used to guide the development of similar assimilation schemes in higher dimensions and more realistic geometries.

A Multi-Time-Scale Four-Dimensional Variational Data Assimilation Scheme and Its Application to Simulated Radial Velocity and Reflectivity Data

AbstractIn this study, a multi-time-scale four-dimensional variational data assimilation (MTS-4DVar) scheme is developed and applied to the assimilation of radar observations. The MTS-4DVar employs multitime windows with various time lengths in the framework of incremental 4DVar in the Weather Research and Forecasting Data Assimilation (WRFDA). The objective of MTS-4DVar is to enable the 4DVar data assimilation system to extract multiscale information from radar observations, and the algorithm of MTS-4DVar is first discussed in detail. Using a heavy rainfall case, it is shown that the nonlinearity growth of reflectivity is faster than that of radial velocity, suggesting that the time window for assimilating reflectivity in the incremental 4DVar should be shorter than that of radial velocity. A series of single observation tests and observing system simulation experiments (OSSEs) are then presented to examine the physical characteristics and performance of MTS-4DVar. These experiments demonstrate that the MTS-4DVar is capable of combining the larger-scale information from a longer time window and the local-scale features from a shorter time window. With the OSSEs it is shown that the value of the cost function is reduced properly in the minimization of the MTS-4DVar with a combination of longer and shorter time windows. By assimilating the radar radial velocity alone, we found that the MTS-4DVar reduces the analysis and forecast errors and improves the precipitation forecasts in comparison with the normal incremental 4DVar. Additional assimilation of reflectivity further improved the precipitation forecasts, and the results show that the radar reflectivity can also be well assimilated by using MTS-4DVar.