Optimal Interpolation Scheme Research Articles

Data assimilation of partitioned HF radar wave data into Wavewatch III

In this study the assimilation of HF radar data into a high resolution, coastal Wavewatch III model is investigated. An optimal interpolation scheme is used to assimilate the data and the design of a background error covariance matrix which reflects the local conditions and difficulties associated with a coastal domain is discussed. Two assimilation schemes are trialled; a scheme which assimilates mean parameters from the HF radar data and a scheme which assimilates partitioned spectral HF radar data. This study demonstrates the feasibility of assimilating partitioned wave data into a coastal domain. The results show that the assimilation schemes provide satisfactory improvements to significant wave heights but more mixed results for mean periods. The best improvements are seen during a stormy period with turning winds. During this period the model is deficient at capturing the change in wave directions and the peak in the waveheights, while the high sea state ensures good quality HF radar data for assimilation. The study also suggests that there are both physical and practical advantages to assimilating partitioned wave data compared to assimilating mean parameters for the whole spectrum.

Evaluation of ECMWF's soil moisture analyses using observations on the Tibetan Plateau

AbstractAn analysis is carried out for two hydrologically contrasting but thermodynamically similar areas on the Tibetan Plateau, to evaluate soil moisture analysis based on the European Centre for Medium‐Range Weather Forecasts (ECMWF) previous optimum interpolation scheme and the current point‐wise extended Kalman filter scheme. To implement the analysis, this study used two regional soil moisture and soil temperature networks (i.e., Naqu and Maqu) on the Tibetan Plateau. For the cold‐semiarid Naqu area, both ECMWF soil moisture analyses significantly overestimate the regional soil moisture in the monsoon seasons. For the cold‐humid Maqu network area, the ECMWF products have comparable accuracy as reported by previous studies in the humid monsoon period. The comparisons were made among the liquid soil moisture analysis from ECMWF, the ground station's measurements and the satellite estimates from the Advanced Scatterometer sensor. The results show reasonable performances of the ECMWF soil moisture analyses (i.e., both optimum interpolation and extended Kalman filter products) and the Advanced Scatterometer level 2 products, when compared to the in situ measurements.

Assimilation of OMI NO<sub>2</sub> retrievals into the limited-area chemistry-transport model DEHM (V2009.0) with a 3-D OI algorithm

Abstract. Data assimilation is the process of combining real-world observations with a modelled geophysical field. The increasing abundance of satellite retrievals of atmospheric trace gases makes chemical data assimilation an increasingly viable method for deriving more accurate analysed fields and initial conditions for air quality forecasts. We implemented a three-dimensional optimal interpolation (OI) scheme to assimilate retrievals of NO2 tropospheric columns from the Ozone Monitoring Instrument into the Danish Eulerian Hemispheric Model (DEHM, version V2009.0), a three-dimensional, regional-scale, offline chemistry-transport model. The background error covariance matrix, B, was estimated based on differences in the NO2 concentration field between paired simulations using different meteorological inputs. Background error correlations were modelled as non-separable, horizontally homogeneous and isotropic. Parameters were estimated for each month and for each hour to allow for seasonal and diurnal patterns in NO2 concentrations. Three experiments were run to compare the effects of observation thinning and the choice of observation errors. Model performance was assessed by comparing the analysed fields to an independent set of observations: ground-based measurements from European air-quality monitoring stations. The analysed NO2 and O3 concentrations were more accurate than those from a reference simulation without assimilation, with increased temporal correlation for both species. Thinning of satellite data and the use of constant observation errors yielded a better balance between the observed increments and the prescribed error covariances, with no appreciable degradation in the surface concentrations due to the observation thinning. Forecasts were also considered and these showed rather limited influence from the initial conditions once the effects of the diurnal cycle are accounted for. The simple OI scheme was effective and computationally feasible in this context, where only a single species was assimilated, adjusting the three-dimensional field for this compound. Limitations of the assimilation scheme are discussed.

A combined optimal interpolation and nudging scheme to assimilate OSISAF sea-ice concentration into ROMS

AbstractThe Ocean and Sea Ice Satellite Application Facility (OSISAF) of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) distributes satellite observations operationally. In this paper, we describe the development of a combined optimal interpolation and nudging (COIN) scheme in the Norwegian Meteorological Institute that assimilates OSISAF sea-ice concentration (SIC) into a coupled sea-ice–ocean Regional Ocean Modeling System (ROMS). The scheme modifies the modeled SIC at every time-step, based on the difference between observation and forecast as well as on the ratio of observation error to model error. Snow and sea-ice thickness are diagnostically modified to match the ice concentration field. Hindcast experiments of Arctic sea ice are performed for the whole of 2009. The results are compared with OSISAF and Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) SIC, showing a significant improvement in the analyzed sea-ice edge and summer SIC.

A simplified Extended Kalman Filter for the global operational soil moisture analysis at ECMWF

AbstractA new land surface analysis system based on a simplified point‐wise Extended Kalman Filter (EKF) was implemented at the European Centre for Medium‐Range Weather Forecasts in the global operational Integrated Forecasting System (IFS) in November 2010. This system will allow consistent and optimal analyses of land surface parameters like soil moisture, surface temperatures, snow and vegetation properties. As part of the system implementation, the surface analysis structure has been revised to permit an independent and parallel computation with the upper‐air 4D‐Var analysis. The new analysis system is used for the soil moisture analysis, replacing the previous Optimal Interpolation (OI) scheme. Similar to the OI system, the simplified EKF uses 2 m air temperature and relative humidity observations from the SYNOP (land surface synoptic report) ground‐based networks to analyse soil moisture. This paper describes the new land surface analysis, its application for analysing soil moisture, and initial verification results which supported its operational implementation at ECMWF. The performance is evaluated based on a set of one‐year analysis experiments. The simplified EKF is compared to the OI, on soil moisture, 2 m temperature and relative humidity, showing a consistent improvement on screen‐level parameters and soil moisture forecasts. To demonstrate the potential of the new analysis scheme, soil moisture derived from ASCAT (Advanced Scatterometer) has been assimilated through the simplified EKF.

Comparison of methods for argo drifters data assimilation into a hydrodynamical model of the ocean

Different data assimilation methods such as an extended Kalman filter, the optimal interpolation method, and a method based on the Fokker-Planck equation applications are considered. Data from the ARGO drifters are assimilated into the HYCOM shallow water model (University of Miami, USA). Throughout the study, the schemes and methods of parallel computations with an MPI library are used. The results of the computations with assimilations are compared between themselves and with independent observations. The method based on the Fokker-Planck equation and the extended Kalman filter are preferable because they give better results than the optimal interpolation scheme. The various model characteristics of the ocean, such as the heat content fields and others, are analyzed after the data assimilation.

Exploring spatiotemporal ecological variations by the multiscale interpolation

We implement the method of wavelet-based, multiscale inversion to tackle the problem of interpolation of spatiotemporal ecological variations from sparse field observations for the purpose of investigating environmental issues such as climate change, pollution, fisheries and others. The merit of the multiscale approach lies mainly in its capability of automatic adapting to the often irregular and sparse sampling. The embedded multiresolution scale hierarchy facilitates the screening of the local density of data constraints to retain large-scale features while enhancing non-stationary local details where dense data constraints are available. To evaluate the efficacy of the multiscale interpolation, we compare dominant interpolation schemes, including especially the popular kriging method. Using spatiotemporal data of squid fisheries near the coast of Argentina in the south Atlantic as an example, we show that the multiscale interpolation encloses the least model variance while compromising locally between the smoothness and the resolution by accommodating the data distribution rather than imposing presumptions of ad hoc fixed-scale correlation. The multiscale interpolation scheme outperforms the kriging scheme in revealing the apt spatial variation in the recovering experiments of a synthesized stochastic pattern. It is highlighted that the kriging scheme is intrinsically an exact interpolator presuming noise-free observations; its estimation variance reflects the degree of lack of resolution rather than the numerical uncertainty. Moreover, an implicitly stationary correlation is established via the empirical variogram irrespective of the non-uniform sampling. Unsatisfactory performance of kriging results indicates that it might not be an optimal interpolation scheme for sparsely sampled data.

Wave spectra assimilation in typhoon wave modeling for the East China Sea

The East China Sea is a hot area for typhoon waves to occur. A wave spectra assimilation model has been developed to predict the typhoon wave more accurately and operationally. This is the first time where wave data from Taiwan have been used to predict typhoon wave along the mainland China coast. The two-dimensional spectra observed in Taiwan northeast coast modify the wave field output by SWAN model through the technology of optimal interpolation (OI) scheme. The wind field correction is not involved as it contributes less than a quarter of the correction achieved by assimilation of waves. The initialization issue for assimilation is discussed. A linear evolution law for noise in the wave field is derived from the SWAN governing equations. A two-dimensional digital low-pass filter is used to obtain the initialized wave fields. The data assimilation model is optimized during the typhoon Sinlaku. During typhoons Krosa and Morakot, data assimilation significantly improves the low frequency wave energy and wave propagation direction in Taiwan coast. For the far-field region, the assimilation model shows an expected ability of improving typhoon wave forecast as well, as data assimilation enhances the low frequency wave energy. The proportion of positive assimilation indexes is over 81% for all the periods of comparison. The paper also finds that the impact of data assimilation on the far-field region depends on the state of the typhoon developing and the swell propagation direction.

Reinforcement of MLLR speaker adaptation using optimal linear interpolation

An optimal linear interpolation scheme applied to MLLR speaker adaptation is presented. The proposed reinforced MLLR method, called α opt -MLLR, regulates the influence of MLLR adaptation when the training data from a new speaker is improper by adequately incorporating prior knowledge of the initial models into adaptation, and thus ensures the robustness of MLLR adaptation. The proposed mechanism is conceptually simple and computationally inexpensive, and is superior to FLC-MLLR in regard to lower computing cost.

Operational sea surface temperature bias adjustment using AATSR data

One objective of the sea surface temperature (SST) component of the Global Monitoring for the Environment and Security (GMES) MERSEA project was to define the combined use of all SST products in an optimal interpolation scheme. Most SST products are now available in a common format but show regional differences between datasets that must be removed before use. We have defined a simple method using the SST derived from the Advanced Along Track Scanning Radiometer (AATSR) onboard the European Space Agency (ESA) ENVISAT platform as a common reference for all SST products. This method is based on an analysis of the differences between a given dataset and the AATSR SST over the 10 preceding days and over a 5° regular grid. These space–time characteristics have been defined empirically in a preliminary experiment. The efficiency of the method has been evaluated on a daily basis for a two year period (2007–2008) based on two SST products from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT): the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) derived SST over the Atlantic and the Advanced Very High Resolution Radiometer (AVHRR) SST derived at fine scale over the North-East Atlantic. They have been compared to the AATSR and buoy SSTs and to the Naval Oceanographic Office (NAVOCEANO) AVHRR global SST product. The SEVIRI SST bias, which was reduced from −0.40K to −0.02K for the 0–20N latitude band by this approach provides a good example of the performance of the method. Reductions in the bias are also demonstrated for the North Atlantic, where cloudiness related problems were expected.

Evaluation of an ocean data assimilation system for Chinese marginal seas with a focus on the South China Sea

Data assimilation is a powerful tool to improve ocean forecasting by reducing uncertainties in forecast initial conditions. Recently, an ocean data assimilation system based on the ensemble optimal interpolation (EnOI) scheme and HYbrid Coordinate Ocean Model (HYCOM) for marginal seas around China was developed. This system can assimilate both satellite observations of sea surface temperature (SST) and along-track sea level anomaly (SLA) data. The purpose of this study was to evaluate the performance of the system. Two experiments were performed, which spanned a 3-year period from January 1, 2004 to December 30, 2006, with and without data assimilation. The data assimilation results were promising, with a positive impact on the modeled fields. The SST and SLA were clearly improved in terms of bias and root mean square error over the whole domain. In addition, the assimilations provided improvements in some regions to the surface field where mesoscale processes are not well simulated by the model. Comparisons with surface drifter trajectories showed that assimilated SST and SLA also better represent surface currents, with drifter trajectories fitting better to the contours of SLA field than that without assimilation. The forecasting capacity of this assimilation system was also evaluated through a case study of a birth-and-death process of an anticyclone eddy in the Northern South China Sea (NSCS), in which the anticyclone eddy was successfully hindcasted by the assimilation system. This study suggests the data assimilation system gives reasonable descriptions of the near-surface ocean state and can be applied to forecast mesoscale ocean processes in the marginal seas around China.

Assimilating Along-Track Altimetric Observations through Local Hydrostatic Adjustment in a Global Ocean Variational Assimilation System

Abstract A global ocean three-dimensional variational data assimilation system was developed with the aim of assimilating along-track sea level anomaly observations, along with in situ observations from bathythermographs and conventional sea stations. All the available altimetric data within the period October 1992–January 2006 were used in this study. The sea level corrections were covariated with vertical profiles of temperature and salinity according to the bivariate definition of the background-error vertical covariances. Sea level anomaly observational error variance was carefully defined as a sum of instrumental, representativeness, observation operator, and mean dynamic topography error variances. The mean dynamic topography was computed from the model long-term mean sea surface height and adjusted through an optimal interpolation scheme to account for observation minus first-guess biases. Results show that the assimilation of sea level anomaly observations improves the model sea surface height skill scores as well as the subsurface temperature and salinity fields. Furthermore, the estimate of the tropical and subtropical surface circulation is clearly improved after assimilating altimetric data. Nonnegligible impacts of the mean dynamic topography used have also been found: compared to a gravimeter-based mean dynamic topography the use of the mean dynamic topography discussed in this paper improves both the consistency with sea level anomaly observations and the verification skill scores of temperature and salinity in the tropical regions. Furthermore, the use of a mean dynamic topography computed from the model long-term sea surface height mean without observation adjustments results in worsened verification skill scores and highlights the benefits of the current approach for deriving the mean dynamic topography.

A new methodology for using buoy measurements in sea wave data assimilation

One of the main drawbacks in modern sea wave data assimilation models is the limited temporal and spatial improvement obtained in the final forecasting products. This is mainly due to deviations coming either from the relevant atmospheric input or from the dynamics of the wave model, resulting to systematic errors of the forecasted fields of numerical wave models, when no observation is available for assimilation. A potential solution is presented in this work, based on a combination of advanced statistical techniques, data assimilation systems, and wave models. More precisely, Kalman filtering algorithms are implemented into the wave model WAM and the results are assimilated by an Optimum Interpolation Scheme, in order to extend the beneficial influence of the latter in time and space. The case studied concerns a 3-month period in an open sea area near the South-West coast of the USA (Pacific Ocean).

An Adaptive Approach to Mitigate Background Covariance Limitations in the Ensemble Kalman Filter

Abstract A new approach is proposed to address the background covariance limitations arising from undersampled ensembles and unaccounted model errors in the ensemble Kalman filter (EnKF). The method enhances the representativeness of the EnKF ensemble by augmenting it with new members chosen adaptively to add missing information that prevents the EnKF from fully fitting the data to the ensemble. The vectors to be added are obtained by back projecting the residuals of the observation misfits from the EnKF analysis step onto the state space. The back projection is done using an optimal interpolation (OI) scheme based on an estimated covariance of the subspace missing from the ensemble. In the experiments reported here, the OI uses a preselected stationary background covariance matrix, as in the hybrid EnKF–three-dimensional variational data assimilation (3DVAR) approach, but the resulting correction is included as a new ensemble member instead of being added to all existing ensemble members. The adaptive approach is tested with the Lorenz-96 model. The hybrid EnKF–3DVAR is used as a benchmark to evaluate the performance of the adaptive approach. Assimilation experiments suggest that the new adaptive scheme significantly improves the EnKF behavior when it suffers from small size ensembles and neglected model errors. It was further found to be competitive with the hybrid EnKF–3DVAR approach, depending on ensemble size and data coverage.

Assimilation of sea surface temperature into CECOM by flux correction

Sea surface temperature (SST) from a near real-time data set produced from satellites data has been assimilated into a coupled ice–ocean forecasting model (Canadian East Coast Ocean Model) using an efficient data assimilation method. The method is based on an optimal interpolation scheme by which SST is melded into the model through the adjustment of surface heat flux. The magnitude and space–time variation of the adjustment depend on the depth of heat diffusion into the water column in response to changes in surface flux, the correlation time scale of the data, and model and data errors. The diffusion depth is scaled by the eddy diffusivity for temperature. The ratio of the model and data errors is treated as an adjustable parameter. To evaluate the quality of the assimilation, the results from the model with and without assimilation are compared to independent ship data from the Atlantic Zone Monitoring Program and the World Ocean Circulation Experiment. It is shown that the assimilation has a significant impact on the modeled SST, reducing the root mean square difference (RMSD) between the model SST and the ship SST by 0.63°C or 37%. The RMSD of the assimilated SST is smaller than that of the satellite SST by 0.23°C. This suggests that model simulations or predictions with data assimilation can provide the best estimate of the true SST. A sensitivity study is performed to examine the change of the model RMSD with the adjustable parameter in the assimilation equation. The results show that there is an optimal value of the parameter and the model SST is not very sensitive to the parameter.

Ensemble optimal interpolation schemes for assimilating Argo profiles into a hybrid coordinate ocean model

Abstract To develop a capable ensemble-based scheme for operationally assimilating Argo profile observations into a hybrid coordinate ocean model (HYCOM), we compared some different ensemble optimal interpolation (EnOI) schemes, which can be divided into two different kinds. The first kind is straightforward, i.e., updating the model variables (i.e., layer thickness, layer velocity and layer temperature/salinity) at the same time from the temperature and salinity profiles observed from Argo floats. In the second kind of schemes (will be referred as the modified schemes), which are based on Thacker and Esenkov (2002) , the Argo profiles are first converted to the “observations” of layer thicknesses and they are assimilated to adjust the model layer thickness and model velocity fields. Then the T (or S ) profiles are assimilated to adjust the model layer temperatures (or salinities), followed by deriving the model layer salinity (or temperature) from the equation of seawater state. In this study we showed that the two kinds of EnOI schemes can be implemented in various setups. Firstly for the straightforward schemes an analysis can be done using the thinned (to model layers) observations of Argo profiles or using the full vertical information provided by the Argo profiles. Secondly one can make an analysis applying or not applying localization vertically. Thirdly for the modified schemes either the temperature or the salinity field can be diagnosed. Then we designed six assimilation experiments, each is attached to a different setup in order to test and compare their performances. In all experiments, Argo profiles were assimilated into HYCOM in the Pacific for a four-year period (January, 2004–December, 2007). A large amount of Argo profiles were withheld to validate the assimilation results. The results show the significant improvement by the modified schemes over the straightforward schemes. The best setup of the modified scheme is to diagnose the temperature and to apply the vertical localization at the step of assimilating the layer temperatures.

An Ocean Reanalysis System for the Joining Area of Asia and Indian-Pacific Ocean

AbstractAn ocean reanalysis system for the joining area of Asia and Indian-Pacific Ocean (AIPO) has been developed and is currently delivering reanalysis data sets for study on the air-sea interaction over AIPO and its climate variation over China in the inter-annual time scale. This system consists of a nested ocean model forced by atmospheric reanalysis, an ensemble-based multivariate ocean data assimilation system and various ocean observations. The following report describes the main components of the data assimilation system in detail. The system adopts an ensemble optimal interpolation scheme that uses a seasonal update from a free running model to estimate the background error covariance matrix. In view of the systematic biases in some observation systems, some treatments were performed on the observations before the assimilation. A coarse resolution reanalysis dataset from the system is preliminarily evaluated to demonstrate the performance of the system for the period 1992 to 2006 by comparing th...

The CMCC-INGV Global Ocean Data Assimilation System (CIGODAS)

Centro Euro-Mediterraneo per i Cambiamenti Climatici, Bologna, Italy Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy

Reference crop evapotranspiration estimate using high-resolution meteorological network's data

Abstract. Water management authorities need detailed information about each component of the hydrological balance. This document presents a method to estimate the evapotranspiration rate, initialized in order to obtain the reference crop evapotranspiration rate (ET0). By using an Optimal Interpolation (OI) scheme, the hourly observations of several meteorological variables, measured by a high-resolution local meteorological network, are interpolated over a regular grid. The analysed meteorological fields, containing detailed meteorological information, enter a model for turbulent heat fluxes estimation based on Monin-Obukhov surface layer similarity theory. The obtained ET0 fields are then post-processed and disseminated to the users.

The theoretical impact of remotely sensed sea surface salinity observations in a multi-variate assimilation system

The global ocean observing system is soon to be expanded to include two satellite missions SMOS and Aquarius that will provide the first global observations of sea surface salinity (SSS). Since the ocean responds to gradients in mass the need to more adequately observe salinity is not debatable. Previous studies for these missions have estimated that SSS observations will have a large expected error. Large observation error variance limits the potential impact for analyses of the full ocean state and even SSS itself. Estimating the impact of remotely sensed SSS on an ocean data assimilation system must be cast in the context of multi-variate contributions from both sea surface temperature and sea level anomaly. A simple analytical formulation for a multi-variate analysis of SSS is presented and used to derive diagnostics that estimate the magnitude of observation error variance that can be expected to contribute to the analysis of SSS. The diagnostics assess the likely impact of new observations in a multi-variate scheme where the forecast error covariance and observation error covariance have been estimated. As an example the diagnostics are applied to a specific ensemble optimal interpolation scheme, which has been used for eddy resolving reanalyses and operational predictions in the Asian–Australian region. This scheme dependent result indicates that sea surface temperature and sea level anomalies effectively constrain the forecast error variance of SSS in the mid- to high-latitudes. We conclude that remotely sensed SSS observations are expected to positively contribute to a multi-variate analysis in the tropical Indo–Pacific, but more modestly in the mid- to high-latitudes.