Estimating forecast error covariances for strongly coupled atmosphere-ocean 4D-Var data assimilation

Strongly coupled data assimilation emulates the real world pairing of the atmosphere and ocean by solving the assimilation problem in terms of a single combined atmosphere-ocean state. A significant challenge in strongly coupled variational atmosphere-ocean data assimilation is a priori specification of the cross-covariances between the errors in the atmosphere and ocean model forecasts. These covariances must capture the correct physical structure of interactions across the air-sea interface as well as the different scales of evolution in the atmosphere and ocean; if prescribed correctly, they will allow observations in one medium to improve the analysis in the other. Here we investigate the nature and structure of atmosphere-ocean forecast error cross-correlations using an idealised strongly coupled single-column atmosphere-ocean 4D-Var assimilation system. We present results from a set of identical twin experiments that use an ensemble of coupled 4D-Var assimilations to derive estimates of the atmosphere-ocean error cross-correlations. Our results show significant variation in the strength and structure of cross-correlations in the atmosphere-ocean boundary layer between summer and winter and between day and night. These differences provide a valuable insight into the nature of coupled atmosphere-ocean correlations for different seasons and points in the diurnal cycle

The role of cross-domain error correlations in strongly coupled 4D-Var atmosphere-ocean data assimilation

Strongly coupled atmosphere-ocean data assimilation offers the ability to improve information exchange across the modelled air-sea interface by enabling observations in one domain to have a direct influence on the analysis in the other. For incremental 4D-Var assimilation a strongly coupled approach enables both domains to be updated at the beginning of the assimilation window, whether they are observed or not, and is hence more likely to produce consistent initial model states. This is made possible by the explicit inclusion of cross-domain forecast error covariance information in the coupled forecast error covariance matrix. In this study we use an idealised 1D single column coupled atmosphere-ocean model to examine the extent to which explicit cross-domain forecast error covariances play a role in shaping the coupled analysis increments compared to those implicitly generated in the inner-loop of the incremental formulation of the 4D-Var algorithm. This is done via a set of single observation experiments with and without initial cross-domain forecast error covariances prescribed. Using single observations allows us to obtain explicit expressions for the atmosphere and ocean analysis updates, separating out the individual effects of the explicitly prescribed and implicitly generated cross-domain covariances. Our experiments show that when only one domain is observed,including explicit cross-domain error covariances allows more consistent adjustment of the unobserved domain. Neglecting the cross-domain terms and relying solely on the covariances implicitly generated by the coupled tangent linear and adjoint models restricts the ability of the covariance matrix to impose balance between the two domains. In this case the coupling is essentially one-way; the update to the observed domain is independent of the unobserved domain and so is likely to produce atmosphere and ocean updates that are inconsistent with one another. As we show, this has important consequences for the balance of the coupled analysis state

Data assimilation for moving mesh methods with an application to ice sheet modelling

We develop data assimilation techniques for nonlinear dynamical systems modelled by moving mesh methods. Such techniques are valuable for explicitly tracking interfaces and boundaries in evolving systems. The unique aspect of these assimilation techniques is that both the states of the system and the positions of the mesh points are updated simultaneously using physical observations. Covariances between states and mesh points are generated either by a correlation structure function in a variational context or by ensemble methods. The application of the techniques is demonstrated on a one-dimensional model of a grounded shallow ice sheet. It is shown, using observations of surface elevation and/or surface ice velocities, that the techniques predict the evolution of the ice sheet margin and the ice thickness accurately and efficiently. This approach also allows the straightforward assimilation of observations of the position of the ice sheet margin

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis

Decadal climate prediction with a refined anomaly initialisation approach

In decadal prediction, the objective is to exploit both the sources of predictability from the external radiative forcings and from the internal variability to provide the best possible climate information for the next decade. Predicting the climate system internal variability relies on initialising the climate model from observational estimates. We present a refined method of anomaly initialisation (AI) applied to the ocean and sea ice components of the global climate forecast model EC-Earth, with the following key innovations: (1) the use of a weight applied to the observed anomalies, in order to avoid the risk of introducing anomalies recorded in the observed climate, whose amplitude does not fit in the range of the internal variability generated by the model; (2) the AI of the ocean density, instead of calculating it from the anomaly initialised state of temperature and salinity. An experiment initialised with this refined AI method has been compared with a full field and standard AI experiment. Results show that the use of such refinements enhances the surface temperature skill over part of the North and South Atlantic, part of the South Pacific and the Mediterranean Sea for the first forecast year. However, part of such improvement is lost in the following forecast years. For the tropical Pacific surface temperature, the full field initialised experiment performs the best. The prediction of the Arctic sea-ice volume is improved by the refined AI method for the first three forecast years and the skill of the Atlantic multidecadal oscillation is significantly increased compared to a non-initialised forecast, along the whole forecast time.The authors acknowledge funding support for this study from the SPECS (ENV-2012-308378) Project funded by the Seventh Framework Programme (FP7) of the European Commission and the PICA-ICE (CGL2012-31987) Project funded by the Ministry of Economy and Competitiveness of Spain. E.H. was also funded by the UK Natural Environment Research Council and N.K.N. was funded in part by the UK Natural Environment Research Council. D.V. gratefully acknowledges financial support from the University of Reading. The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Red Española de Supercomputación through the Barcelona Supercomputing Center.Peer ReviewedPostprint (author's final draft

Observation operators for assimilation of satellite observations in fluvial inundation forecasting

Images from satellite-based synthetic aperture radar (SAR) instruments contain large amounts of information about the position of flood water during a river flood event. This observational information typically covers a large spatial area, but is only relevant for a short time if water levels are changing rapidly. Data assimilation allows us to combine valuable SAR derived observed information with continuous predictions from a computational hydrodynamic model and thus to produce a better forecast than using the model alone. In order to use observations in this way a suitable observation operator is required. In this paper we show that different types of observation operator can produce very different corrections to predicted water levels; this impacts on the quality of the forecast produced.We discuss the physical mechanisms by which different observation operators update modelled water levels and introduce a novel observation operator for inundation forecasting. The performance of the new operator is compared in synthetic experiments with that of two more conventional approaches. The conventional approaches both use observations of water levels derived from SAR to correct model predictions. Our new operator is instead 10 designed to use backscatter values from SAR instruments as observations; such an approach has not been used before in an ensemble Kalman filtering framework. Direct use of backscatter observations opens up the possibility of using more information from each SAR image and could potentially speed up the time taken to produce observations needed to update model predictions. We compare the strengths and weaknesses of the three different approaches with reference to the physical mechanisms by which each of the observation operators allow data assimilation to update water levels in synthetic twin experiments in an idealised domain

Observation error statistics for Doppler radar radial wind superobservations assimilated into the DWD COSMO-KENDA system

Currently in operational numerical weather prediction (NWP) the density of high-resolution observations, such as Doppler radar radial winds (DRWs), is severely reduced in part to avoid violating the assumption of uncorrelated observation errors. To improve the quantity of observations used and the impact that they have on the forecast requires an accurate specification of the observation uncertainties. Observation uncertainties can be estimated using a simple diagnostic that utilises the statistical averages of observation-minus-background and observation-minus-analysis residuals. We are the first to use a modified form of the diagnostic to estimate spatial correlations for observations used in an operational ensemble data assimilation system. The uncertainties for DRW superobservations assimilated into the Deutscher Wetterdienst convection-permitting NWP model are estimated and compared to previous uncertainty estimates for DRWs. The new results show that most diagnosed standard deviations are smaller than those used in the assimilation, hence it may be feasible assimilate DRWs using reduced error standard deviations. However, some of the estimated standard deviations are considerably larger than those used in the assimilation; these large errors highlight areas where the observation processing system may be improved. The error correlation length scales are larger than the observation separation distance and influenced by both the superobbing procedure and observation operator. This is supported by comparing these results to our previous study using Met Office data. Our results suggest that DRW error correlations may be reduced by improving the superobbing procedure and observation operator; however, any remaining correlations should be accounted for in the assimilation

Observation impact, domain length and parameter estimation in data assimilation for flood forecasting

Accurate inundation forecasting provides vital information about the behaviour of fluvial flood water. Using data assimilation with an Ensemble Transform Kalman Filter we combine forecasts from a numerical hydrodynamic model with synthetic observations of water levels. We show that reinitialising the model with corrected water levels can cause an initialisation shock and demonstrate a simple novel solution. In agreement with others, we find that although assimilation can accurately correct water levels at observation times, the corrected forecast quickly relaxes to the open loop forecast. Our new work shows that the time taken for the forecast to relax to the open loop case depends on domain length; observation impact is longer-lived in a longer domain. We demonstrate that jointly correcting the channel friction parameter as well as water levels greatly improves the forecast. We also show that updating the value of the channel friction parameter can compensate for bias in inflow

Efficient hyper-parameter determination for regularised linear BRDF parameter retrieval

Linear kernel driven models of the surface Bidirectional Reflectance Distribution Function (BRDF) are valuable tools for exploiting Earth observation data acquired at different sun–sensor geometries. Here we present a method that efficiently determines linear BRDF model weights using Tikhonov smoothing where the smoothing parameter λ is determined via a Generalized Singular Value Decomposition with the root mean square error prescribed depending on the MODIS band. We applied this method to twenty-six different deciduous broadleaf sites across an entire year using the MODIS Terra and Aqua reflectance data products. Kernel weights and white sky albedo derived from this GSVD method were generally consistent with those provided by the MCD43 data products. The GSVD derived results had less sample variability compared to the MCD43 data products, attributable to the assumed smoothness between kernel weights in the Tikhonov smoothing method. The GSVD technique consistently outperforms MCD43 in the reconstruction of observed MODIS reflectance data, of which retrievals from this method will do a better job of estimating albedo and normalizing data to specified geometries