Sequential Data Assimilation Scheme Research Articles

Daily rainfall assimilation based on satellite and weather radar precipitation products along with rain gauge networks

Abstract The analysis of the spatial and temporal distribution of storm events contributes to a better use of water resources, for example, the supply of drinking water, irrigation practices, electricity generation and management of extreme events to control floods and mitigate droughts, among others. The traditional observation of rainfall fields in Mexico has been carried out using rain gauge network data, but their spatial representativeness is unsatisfactory. Therefore, this study reviewed the possibility of obtaining better estimates of the spatial distribution of daily rainfall considering information from three different databases, which include rain gauge measurements and remotely sensed precipitation products of satellite systems and weather radars. In order to determine a two-dimensional rainfall distribution, the information has been merged with a sequential data assimilation scheme up to the diagnostic stage, paying attention to the benefit that the rain gauge network density has on the estimation. With the application of the Barnes method, historical events in the Mexican territory were analyzed using statistical parameters for the validation of the estimates, with satisfactory results because the assimilated rainfalls turned out to be better approximations than the values calculated with the individual databases, even for a not very low density of surface observations.

SIR‐HUXt—A Particle Filter Data Assimilation Scheme for CME Time‐Elongation Profiles

AbstractWe present SIR‐HUXt, the integration of a sequential importance resampling data assimilation scheme with the HUXt solar wind model. SIR‐HUXt assimilates the time‐elongation profiles of Coronal Mass Ejection (CME) fronts in the low heliosphere, like those extracted from heliospheric imager (HI) data. Observing System Simulation Experiments are used to explore SIR‐HUXt's performance for a simple synthetic CME scenario of an Earth directed CME in a uniform solar wind, where the CME is initialized with the average CME speed and width. These experiments are performed for a range of observer locations, from 20° to 90° behind Earth, spanning the L5 point where ESA's Vigil mission will return HI data for operational space weather forecasting. For this idealized scenario, SIR‐HUXt performs well at constraining the CME speed, and has some success at constraining the CME longitude while the CME width is largely unconstrained by SIR‐HUXt. Rank‐histograms suggest the SIR‐HUXt ensembles are well calibrated, with no indications of bias or under/over dispersion. Improved constraints on the initial CME speed lead to improvements in the CME transit time and arrival speed. For an L5 observer, SIR‐HUXt reduced the transit time and arrival speed uncertainties by 69% and 63%. Therefore, SIR‐HUXt could improve the real‐world representivity of HUXt simulations and reduce the uncertainty of CME arrival time forecasts. The idealized scenario studied here likely enhances SIR‐HUXt's performance relative to the challenge of simulating real‐world CMEs and solar wind conditions. Future work should validate SIR‐HUXt with case studies of real CMEs in structured solar wind.

Flow enhancement of tomographic particle image velocimetry measurements using sequential data assimilation

Sequential data assimilation (DA) was performed on three-dimensional flow fields of a circular jet measured by tomography particle image velocimetry (tomo-PIV). The work focused on an in-depth analysis of the flow enhancement and the pressure determination from volumetric flow measurement data. The jet was issued from a circular nozzle with an inner diameter of D= 20 mm. A split-screen configuration including two high-speed cameras was used to capture the particle images from four different views for a tomography reconstruction of the voxels in the tomo-PIV measurement. Planar PIV was also performed to obtain the benchmark two-dimensional velocity fields for validation. The adjoint-based sequential DA scheme was used with the measurement uncertainty implanted using a threshold function to recover the flow fields with high fidelity and fewer measurement errors. The pressure was determined by either the direct mode, with implementation directly in the DA solver, or by the separate mode, which included solving the Poisson equation on the DA-recovered flow fields. Sequential DA recovered high signal-to-noise flow fields that had piecewise-smooth temporal variations due to the intermittent constraints of the observations, while only the temporal sequence of the fields at the observational instances was selected as the DA output. Errors were significantly reduced, and DA improved the divergence condition of the three-dimensional flow fields. DA also enhanced the dynamical features of the vortical structures, and the pressure determined by both modes successfully captured the downstream convection signatures of the vortex rings.

A nonparametric sequential data assimilation scheme for soil moisture flow

Various of data assimilation methods such as the ensemble Kalman filter (EnKF) have been established in physical science and engineering for the fusion of observed data with physically motivated models. However, there are cases where a physically motivated model is not available. In particular, the unsaturated flow model is often difficult to build due to the intrinsic nonlinearity and heterogeneity of soil flow process. In this paper, a nonparametric sequential data assimilation scheme (Kalman-GP) is introduced based on the filtering equations of EnKF and data-driven modeling with Gaussian process (GP). The method replaces the physical model with GP constructed directly from available multiple-source data and observations of state variables of interest, while using the Kalman update formulation to reconcile real-time observations. We tested the proposed Kalman-GP method in a real-world case study of soil moisture profile simulation. The performance of Kalman-GP was compared with two different data assimilation methods, i.e. the traditional EnKF with a physical model (Kalman-physics) and a hybrid filter which integrated a dynamic GP error model into physics-based EnKF (Kalman-physics-GP, Zhang et al., 2019). Results showed that, without knowledge of any governing equation, the Kalman-GP filter was able to reconstruct soil moisture dynamics to a level comparable with the parametric EnKF, even exhibit superior performance. The Kalman-physics-GP led to a better soil moisture estimation than Kalman-GP, however at the expense of dependence on the underlying physical model and more requirements of prior knowledge. In contrast, the proposed Kalman-GP requires only easy-to-obtain meteorological data and can be a better alternative to achieve good tradeoff between effectiveness and efficiency, especially in areas short of hydrogeological data. When less prior physical knowledge is available, the advantage of the proposed Kalman-GP over the Kalman-Physics was enhanced, while the superiority of the hybrid filter over the Kalman-GP was weakened.

On the incidence of meteorological and hydrological processors: Effect of resolution, sharpness and reliability of hydrological ensemble forecasts

Meteorological and hydrological ensemble prediction systems are imperfect. Their outputs could often be improved through the use of a statistical processor, opening up the question of the necessity of using both processors (meteorological and hydrological), only one of them, or none. This experiment compares the predictive distributions from four hydrological ensemble prediction systems (H-EPS) utilising the Ensemble Kalman filter (EnKF) probabilistic sequential data assimilation scheme. They differ in the inclusion or not of the Distribution Based Scaling (DBS) method for post-processing meteorological forecasts and the ensemble Bayesian Model Averaging (ensemble BMA) method for hydrological forecast post-processing. The experiment is implemented on three large watersheds and relies on the combination of two meteorological reforecast products: the 4-member Canadian reforecasts from the Canadian Centre for Meteorological and Environmental Prediction (CCMEP) and the 10-member American reforecasts from the National Oceanic and Atmospheric Administration (NOAA), leading to 14 members at each time step. Results show that all four tested H-EPS lead to resolution and sharpness values that are quite similar, with an advantage to DBS + EnKF. The ensemble BMA is unable to compensate for any bias left in the precipitation ensemble forecasts. On the other hand, it succeeds in calibrating ensemble members that are otherwise under-dispersed. If reliability is preferred over resolution and sharpness, DBS + EnKF + ensemble BMA performs best, making use of both processors in the H-EPS system. Conversely, for enhanced resolution and sharpness, DBS is the preferred method.

Hindcasting and Forecasting of Surface Flow Fields through Assimilating High Frequency Remotely Sensing Radar Data

In order to improve the forecasting ability of numerical models, a sequential data assimilation scheme, nudging, was applied to blend remotely sensing high-frequency (HF) radar surface currents with results from a three-dimensional numerical, EFDC (Environmental Fluid Dynamics Code) model. For the first time, this research presents the most appropriate nudging parameters, which were determined from sensitivity experiments. To examine the influence of data assimilation cycle lengths on forecasts and to extend forecasting improvements, the duration of data assimilation cycles was studied through assimilating linearly interpolated temporal radar data. Data assimilation nudging parameters have not been previously analyzed. Assimilation of HF radar measurements at each model computational timestep outperformed those assimilation models using longer data assimilation cycle lengths; root-mean-square error (RMSE) values of both surface velocity components during a 12 h model forecasting period indicated that surface flow fields were significantly improved when implementing nudging assimilation at each model computational timestep. The Data Assimilation Skill Score (DASS) technique was used to quantitatively evaluate forecast improvements. The averaged values of DASS over the data assimilation domain were 26% and 33% for east–west and north–south velocity components, respectively, over the half-day forecasting period. Correlation of Averaged Kinetic Energy (AKE) was improved by more than 10% in the best data assimilation model. Time series of velocity components and surface flow fields were presented to illustrate the improvement resulting from data assimilation application over time.

Improved boundary values of ocean wave fields using a data assimilation scheme

The objective of this study was to assess the accuracy of numerical wave forecasts through data assimilation of boundary values. A sequential data assimilation scheme was adopted to utilise altimeter data. The performance of the system in terms of operational applications, specifically for typhoon waves, was investigated. Two typhoons that occurred in 2006 around Taiwan (Kaemi and Shanshan) were used as case studies. The proposed data assimilation increased the forecast accuracy of the boundary values in terms of the wave parameters, such as the wave heights and periods. The results showed that after the assimilation, the assimilation model was significantly improved, especially the peak value of the wave and time of occurrence of the peak value.

Data assimilation of time under-sampled measurements using observers, the wave-like equation example

We propose a sequential data assimilation scheme using Luenberger type observers when only some space restricted time under-sampled measurements are available. More precisely, we consider a wave-like equation for which we assume known the restriction of the solution to an open non-empty subset of the spatial domain and for some time samples (typically the sampling step in time is much larger than the time discretization step). To assimilate the available data, two strategies are proposed and analyzed. The first strategy consists in assimilating data only if they are available and the second one in assimilating interpolation of the available data at all the discretization times. In order to tackle the spurious high frequencies which appear when we discretize the wave equation, for both strategies, we introduce a numerical viscous term. In this case, we prove some error estimates between the exact solution and our observers. Numerical simulations illustrate the theoretical results in the case of the one dimensional wave equation.

A global water cycle reanalysis (2003–2012) merging satellite gravimetry and altimetry observations with a hydrological multi-model ensemble

Abstract. We present a global water cycle reanalysis that merges water balance estimates derived from the Gravity Recovery And Climate Experiment (GRACE) satellite mission, satellite water level altimetry and off-line estimates from several hydrological models. Error estimates for the sequential data assimilation scheme were derived from available uncertainty information and the triple collocation technique. Errors in four GRACE storage products were estimated to be 11–12 mm over land areas, while errors in monthly storage changes derived from five global hydrological models were estimated to be 17–28 mm. Prior and posterior water storage estimates were evaluated against independent observations of river water level and discharge, snow water storage and glacier mass loss. Data assimilation improved or maintained agreement overall, although results varied regionally. Uncertainties were greatest in regions where glacier mass loss and subsurface storage decline are both plausible but poorly constrained. We calculated a global water budget for 2003–2012. The main changes were a net loss of polar ice caps (−342 Gt yr−1) and mountain glaciers (−230 Gt yr−1), with an additional decrease in seasonal snowpack (−18 Gt yr−1). Storage increased due to new impoundments (+16 Gt yr−1), but this was compensated by decreases in other surface water bodies (−10 Gt yr−1). If the effect of groundwater depletion (−92 Gt yr−1) is considered separately, subsurface water storage increased by +202 Gt yr−1 due particularly to increased wetness in northern temperate regions and in the seasonally wet tropics of South America and southern Africa. The reanalysis results are publicly available via www.wenfo.org/wald/.

An adaptive hybrid EnKF-OI scheme for efficient state-parameter estimation of reactive contaminant transport models

Reactive contaminant transport models are used by hydrologists to simulate and study the migration and fate of industrial waste in subsurface aquifers. Accurate transport modeling of such waste requires clear understanding of the system’s parameters, such as sorption and biodegradation. In this study, we present an efficient sequential data assimilation scheme that computes accurate estimates of aquifer contamination and spatially variable sorption coefficients. This assimilation scheme is based on a hybrid formulation of the ensemble Kalman filter (EnKF) and optimal interpolation (OI) in which solute concentration measurements are assimilated via a recursive dual estimation of sorption coefficients and contaminant state variables. This hybrid EnKF-OI scheme is used to mitigate background covariance limitations due to ensemble under-sampling and neglected model errors. Numerical experiments are conducted with a two-dimensional synthetic aquifer in which cobalt-60, a radioactive contaminant, is leached in a saturated heterogeneous clayey sandstone zone. Assimilation experiments are investigated under different settings and sources of model and observational errors. Simulation results demonstrate that the proposed hybrid EnKF-OI scheme successfully recovers both the contaminant and the sorption rate and reduces their uncertainties. Sensitivity analyses also suggest that the adaptive hybrid scheme remains effective with small ensembles, allowing to reduce the ensemble size by up to 80% with respect to the standard EnKF scheme.

Assimilation of decomposed in situ directional wave spectra into a numerical wave model of typhoon waves

Abstract. The purpose of this study was to enhance the accuracy of numerical wave forecasts through data assimilation during typhoon periods. A sequential data assimilation scheme was modified to enable its use with partitions of directional wave spectra. The performance of the system was investigated with respect to operational applications, specifically for typhoon waves. Two typhoons that occurred in 2006 around Taiwan (Kaemi and Shanshan) were used for this case study. The proposed data assimilation method increased the forecast accuracy in terms of wave parameters, such as wave height and period. After assimilation, the shapes of directional spectra were much closer to those reported from independent observations.

A global ocean reanalysis product in the China Ocean Reanalysis (CORA) project

The first version of a global ocean reanalysis over multiple decades (1979–2008) has been completed by the National Marine Data and Information Service within the China Ocean Reanalysis (CORA) project. The global ocean model employed is based upon the ocean general circulation model of the Massachusetts Institute of Technology. A sequential data assimilation scheme within the framework of 3D variational (3DVar) analysis, called multi-grid 3DVar, is implemented in 3D space for retrieving multiple-scale observational information. Assimilated oceanic observations include sea level anomalies (SLAs) from multi-altimeters, sea surface temperatures (SSTs) from remote sensing satellites, and in-situ temperature/salinity profiles. Evaluation showed that compared to the model simulation, the annual mean heat content of the global reanalysis is significantly approaching that of World Ocean Atlas 2009 (WOA09) data. The quality of the global temperature climatology was found to be comparable with the product of Simple Ocean Data Assimilation (SODA), and the major ENSO events were reconstructed. The global and Atlantic meridional overturning circulations showed some similarity as SODA, although significant differences were found to exist. The analysis of temperature and salinity in the current version has relatively larger errors at high latitudes and improvements are ongoing in an updated version. CORA was found to provide a simulation of the subsurface current in the equatorial Pacific with a correlation coefficient beyond about 0.6 compared with the Tropical Atmosphere Ocean (TAO) mooring data. The mean difference of SLAs between altimetry data and CORA was less than 0.1 m in most years.

The impact of mean dynamic topography on a sea-level anomaly assimilation in the South China Sea based on an eddy-resolving model

The sea-level anomaly (SLA) from a satellite altimeter has a high accuracy and can be used to improve ocean state estimation by assimilation techniques. However, the lack of an accurate mean dynamic topography (MDT) is still a bothersome issue in an ocean data assimilation. The previous studies showed that the errors in MDT have significant impacts on assimilation results, especially on the time-mean components of ocean states and on the time variant parts of states via nonlinear ocean dynamics. The temporal-spatial differences of three MDTs and their impacts on the SLA analysis are focused on in the South China Sea (SCS). The theoretical analysis shows that even for linear models, the errors in MDT have impacts on the SLA analysis using a sequential data assimilation scheme. Assimilation experiments, based on EnOI scheme and HYCOM, with three MDTs from July 2003 to June 2004 also show that the SLA assimilation is very sensitive to the choice of different MDTs in the SCS with obvious differences between the experimental results and observations in the centre of the SCS and in the vicinity of the Philippine Islands. A new MDT for assimilation of SLA data in the SCS was proposed. The results from the assimilation experiment with this new MDT show a marked reduction (increase) in the RMSEs (correlation coefficient) between the experimental and observed SLA. Furthermore, the subsurface temperature field is also improved with this new MDT in the SCS.

A data assimilation tool for the Pagasitikos Gulf ecosystem dynamics: Methods and benefits

Within the framework of the European INSEA project, an advanced assimilation system has been implemented for the Pagasitikos Gulf ecosystem. The system is based on a multivariate sequential data assimilation scheme that combines satellite ocean sea color (chlorophyll-a) data with the predictions of a three-dimensional coupled physical–biochemical model of the Pagasitikos Gulf ecosystem presented in a companion paper. The hydrodynamics are solved with a very high resolution (1/100°) implementation of the Princeton Ocean Model (POM). This model is nested within a coarser resolution model of the Aegean Sea which is part of the Greek POSEIDON forecasting system. The forecast of the Aegean Sea model, itself nested and initialized from a Mediterranean implementation of POM, is also used to periodically re-initalize the Pagatisikos hydrodynamics model using variational initialization techniques. The ecosystem dynamics of Pagasitikos are tackled with a stand-alone implementation of the European Seas Ecosystem Model (ERSEM). The assimilation scheme is based on the Singular Evolutive Extended Kalman (SEEK) filter, in which the error statistics are parameterized by means of a suitable set of Empirical Orthogonal Functions (EOFs).The assimilation experiments were performed for year 2003 and additionally for a 9-month period over 2006 during which the physical model was forced with the POSEIDON-ETA 6-hour atmospheric fields. The assimilation system is validated by assessing the relevance of the system in fitting the data, the impact of the assimilation on non-observed biochemical processes and the overall quality of the forecasts. Assimilation of either GlobColour in 2003 or SeaWiFS in 2006 chlorophyll-a data enhances the identification of the ecological state of the Pagasitikos Gulf. Results, however, suggest that subsurface ecological observations are needed to improve the controllability of the ecosystem in the deep layers.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

Abstract Roy, S., Platt, T., and Sathyendranath, S. 2011. Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing. – ICES Journal of Marine Science, 68: 719–728. A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

Ionospheric nowcasting via assimilation of GPS measurements of ionospheric electron content in a global physics‐based time‐dependent model

AbstractWe present the rationale for having accurate nowcast and forecast ionospheric conditions, and a brief overview of recent work on assimilation of ionospheric measurements in physics‐based models. This manuscript describes the results of a project aimed at generating accurate operational specifications of ionospheric electron content by the assimilation of Global Positioning System (GPS) ionospheric measurements in a relatively complex first‐principles forecast model. We describe: the overall design of the model, the implemented sequential data assimilation scheme, the specifics of GPS data processing, and the on‐line scheme for estimation of instrumental biases inherent in GPS measurements of ionospheric electron content. Performance of the designed ionospheric specification system is illustrated via common statistical tests, comparisons with data withheld from the assimilation process and comparisons with independent non‐GPS measurements. Web‐based access to the system results is provided athttp://fusionnumerics.com/ionosphere. Copyright © 2005 Royal Meteorological Society

A Kalman filter application to a spectral wave model

Abstract. A sequential time dependent data assimilation scheme based on the Kalman filter is applied to a spectral wave model. Usually, the first guess covariance matrices used in optimal interpolation schemes are exponential spreading functions, which remain constant. In the present work the first guess correlation errors evolve in time according to the dynamic constraints of the wave model. A system error noise is deduced and used to balance numerical errors. The assimilation procedure is tested in a standard situation of swell propagation, where the Kalman filter is used to assimilate the significant wave height. The evolution of the wave field is described by a linear two-dimensional advection equation and the propagation of the error covariance matrix is derived according to Kalman's linear theory. Model simulations were performed in a 2-dimensional domain with deep-water conditions, a relatively small surface area and without wind forcing or dissipation. A true state simulation and a first guess simulation were used to illustrate the assimilation outcome, showing a reasonable performance of the Kalman filter.

Error covariance modeling in sequential data assimilation

The efficiency of a sequential data assimilation scheme relies on the capability to describe the error covariance. This aspect is all the more relevant if one needs accurate statistics on the estimation error. Frequently an ad hoc function depending on a few parameters is proposed, and these parameters are tuned, estimated or updated. This usually requires that the covariance is second-order stationary (i.e. depends only on the distance between two points). In this paper, we discuss this feature and show that even in simple applications (such as one-dimensional hydrodynamics), this assumption does not hold and may lead to poorly described estimation errors. We propose a method relying on the analysis of the error term and the use of the hydrodynamical model to generate one part of the covariance function, the other part being modeled using a second-order stationary approach. This method is discussed using a twin experiment in the case where a physical parameter is erroneous, and improves significantly the results: the model bias is strongly reduced and the estimation error is well described. Moreover, it enables a better adaptation of the Kalman gain to the actual estimation error.

Horizontal and Vertical Structure of the Representer Functions for Sea Surface Measurements in a Coastal Circulation Model

Abstract The representer functions used to propagate the information from observations onto model variables in a sequential data assimilation scheme are calculated with a statistical method. The Princeton Ocean Model is used in a simple configuration simulating the North Current flowing along the French coasts in the northwestern Mediterranean Sea. The influence of sea level measurements on the models’ three-dimensional temperature and velocity fields is investigated. Inhomogeneities and directions of anisotropy are evidenced. A comparison with simplified reduced order assimilation methods suggests that such schemes will not allow for consistent assimilation of nearshore altimetric data.

Data assimilation with a Martian atmospheric GCM: An example using thermal data

Data assimilation is a technique for the analysis of atmospheric observations which combines current information with prior knowledge from previous observations, summarized and forecast in time via the use of a numerical model. A sequential data assimilation scheme has been implemented with a full general circulation model (GCM) of the martian atmosphere for the first time, and has been adapted for the types of atmospheric data which might be expected in the near future, e.g. remote-sensed temperature profiles from a polar orbiter mission such as Mars Surveyor '96 and '98. Tests demonstrate the performance of the scheme using artificial data generated from independent model experiments.