Progress on “Changing coastlines: data assimilation for morphodynamic prediction and predictability”

The task of assessing the likelihood and extent of coastal flooding is hampered by the lack of detailed information on near-shore bathymetry. This is required as an input for coastal inundation models, and in some cases the variability in the bathymetry can impact the prediction of those areas likely to be affected by flooding in a storm. The constant monitoring and data collection that would be required to characterise the near-shore bathymetry over large coastal areas is impractical, leaving the option of running morphodynamic models to predict the likely bathymetry at any given time. However, if the models are inaccurate the errors may be significant if incorrect bathymetry is used to predict possible flood risks. This project is assessing the use of data assimilation techniques to improve the predictions from a simple model, by rigorously incorporating observations of the bathymetry into the model, to bring the model closer to the actual situation. Currently we are concentrating on Morecambe Bay as a primary study site, as it has a highly dynamic inter-tidal zone, with changes in the course of channels in this zone impacting the likely locations of flooding from storms. We are working with SAR images, LiDAR, and swath bathymetry to give us the observations over a 2.5 year period running from May 2003 – November 2005. We have a LiDAR image of the entire inter-tidal zone for November 2005 to use as validation data. We have implemented a 3D-Var data assimilation scheme, to investigate the improvements in performance of the data assimilation compared to the previous scheme which was based on the optimal interpolation method. We are currently evaluating these different data assimilation techniques, using 22 SAR data observations. We will also include the LiDAR data and swath bathymetry to improve the observational coverage, and investigate the impact of different types of observation on the predictive ability of the model. We are also assessing the ability of the data assimilation scheme to recover the correct bathymetry after storm events, which can dramatically change the bathymetry in a short period of time.

Impact of hydrographic data assimilation on the modelled Atlantic meridional overturning circulation

Here we make an initial step toward the development of an ocean assimilation system that can constrain the modelled Atlantic Meridional Overturning Circulation (AMOC) to support climate predictions. A detailed comparison is presented of 1° and 1/4° resolution global model simulations with and without sequential data assimilation, to the observations and transport estimates from the RAPID mooring array across 26.5° N in the Atlantic. Comparisons of modelled water properties with the observations from the merged RAPID boundary arrays demonstrate the ability of in situ data assimilation to accurately constrain the east-west density gradient between these mooring arrays. However, the presence of an unconstrained "western boundary wedge" between Abaco Island and the RAPID mooring site WB2 (16 km offshore) leads to the intensification of an erroneous southwards flow in this region when in situ data are assimilated. The result is an overly intense southward upper mid-ocean transport (0–1100 m) as compared to the estimates derived from the RAPID array. Correction of upper layer zonal density gradients is found to compensate mostly for a weak subtropical gyre circulation in the free model run (i.e. with no assimilation). Despite the important changes to the density structure and transports in the upper layer imposed by the assimilation, very little change is found in the amplitude and sub-seasonal variability of the AMOC. This shows that assimilation of upper layer density information projects mainly on the gyre circulation with little effect on the AMOC at 26° N due to the absence of corrections to density gradients below 2000 m (the maximum depth of Argo). The sensitivity to initial conditions was explored through two additional experiments using a climatological initial condition. These experiments showed that the weak bias in gyre intensity in the control simulation (without data assimilation) develops over a period of about 6 months, but does so independently from the overturning, with no change to the AMOC. However, differences in the properties and volume transport of North Atlantic Deep Water (NADW) persisted throughout the 3 year simulations resulting in a difference of 3 Sv in AMOC intensity. The persistence of these dense water anomalies and their influence on the AMOC is promising for the development of decadal forecasting capabilities. The results suggest that the deeper waters must be accurately reproduced in order to constrain the AMOC.

Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments

During the past 15 years, a number of initiatives have been undertaken at national level to develop ocean forecasting systems operating at regional and/or global scales. The co-ordination between these efforts has been organized internationally through the Global Ocean Data Assimilation Experiment (GODAE). The French MERCATOR project is one of the leading participants in GODAE. The MERCATOR systems routinely assimilate a variety of observations such as multi-satellite altimeter data, sea-surface temperature and in situ temperature and salinity profiles, focusing on high-resolution scales of the ocean dynamics. The assimilation strategy in MERCATOR is based on a hierarchy of methods of increasing sophistication including optimal interpolation, Kalman filtering and variational methods, which are progressively deployed through the Syst`eme d’Assimilation MERCATOR (SAM) series. SAM-1 is based on a reduced-order optimal interpolation which can be operated using ‘altimetry-only’ or ‘multi-data’ set-ups; it relies on the concept of separability, assuming that the correlations can be separated into a product of horizontal and vertical contributions. The second release, SAM-2, is being developed to include new features from the singular evolutive extended Kalman (SEEK) filter, such as three-dimensional, multivariate error modes and adaptivity schemes. The third one, SAM-3, considers variational methods such as the incremental four-dimensional variational algorithm. Most operational forecasting systems evaluated during GODAE are based on least-squares statistical estimation assuming Gaussian errors. In the framework of the EU MERSEA (Marine EnviRonment and Security for the European Area) project, research is being conducted to prepare the next-generation operational ocean monitoring and forecasting systems. The research effort will explore nonlinear assimilation formulations to overcome limitations of the current systems. This paper provides an overview of the developments conducted in MERSEA with the SEEK filter, the Ensemble Kalman filter and the sequential importance re-sampling filter.

Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Four-dimensional variational data assimilation for high resolution nested models

Four-dimensional variational data assimilation (4D-Var) is used in environmental prediction to estimate the state of a system from measurements. When 4D-Var is applied in the context of high resolution nested models, problems may arise in the representation of spatial scales longer than the domain of the model. In this paper we study how well 4D-Var is able to estimate the whole range of spatial scales present in one-way nested models. Using a model of the one-dimensional advection–diffusion equation we show that small spatial scales that are observed can be captured by a 4D-Var assimilation, but that information in the larger scales may be degraded. We propose a modification to 4D-Var which allows a better representation of these larger scales.

A hybrid data assimilation scheme for model parameter estimation: application to morphodynamic modelling

We present a novel algorithm for joint state-parameter estimation using sequential three dimensional variational data assimilation (3D Var) and demonstrate its application in the context of morphodynamic modelling using an idealised two parameter 1D sediment transport model. The new scheme combines a static representation of the state background error covariances with a flow dependent approximation of the state-parameter cross-covariances. For the case presented here, this involves calculating a local finite difference approximation of the gradient of the model with respect to the parameters. The new method is easy to implement and computationally inexpensive to run. Experimental results are positive with the scheme able to recover the model parameters to a high level of accuracy. We expect that there is potential for successful application of this new methodology to larger, more realistic models with more complex parameterisations.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.