Operational forecasting centres are currently developing data assimilation systems for coupled atmosphereÁ ocean models. Strongly coupled assimilation, in which a single assimilation system is applied to a coupled model, presents significant technical and scientific challenges. Hence weakly coupled assimilation systems are being developed as a first step, in which the coupled model is used to compare the current state estimate with observations, but corrections to the atmosphere and ocean initial conditions are then calculated independently. In this paper, we provide a comprehensive description of the different coupled assimilation methodologies in the context of four-dimensional variational assimilation (4D-Var) and use an idealised framework to assess the expected benefits of moving towards coupled data assimilation. We implement an incremental 4D-Var system within an idealised single-column atmosphereÁocean model. The system has the capability to run both strongly and weakly coupled assimilations as well as uncoupled atmosphere-or ocean-only assimilations, thus allowing a systematic comparison of the different strategies for treating the coupled data assimilation problem. We present results from a series of identical twin experiments devised to investigate the behaviour and sensitivities of the different approaches. Overall, our study demonstrates the potential benefits that may be expected from coupled data assimilation. When compared to uncoupled initialisation, coupled assimilation is able to produce more balanced initial analysis fields, thus reducing initialisation shock and its impact on the subsequent forecast. Single observation experiments demonstrate how coupled assimilation systems are able to pass information between the atmosphere and ocean and therefore use near-surface data to greater effect. We show that much of this benefit may also be gained from a weakly coupled assimilation system, but that this can be sensitive to the parameters used in the assimilation.

7Accurate inundation forecasting provides vital information about the behaviour of fluvial flood water. 8 Using data assimilation with an Ensemble Transform Kalman Filter we combine forecasts from a numerical 9 hydrodynamic model with synthetic observations of water levels. We show that reinitialising the model 10 with corrected water levels can cause an initialization shock and demonstrate a simple novel solution. In 11 agreement with others, we find that although assimilation can accurately correct water levels at observation 12 times, the corrected forecast quickly relaxes to the open loop forecast. Our new work shows that the time 13 taken for the forecast to relax to the open loop case depends on domain length; observation impact is longer-14lived in a longer domain. We demonstrate that jointly correcting the channel friction parameter as well as 15 water levels greatly improves the forecast. We also show that updating the value of the channel friction 16 parameter can compensate for bias in inflow. 17 Keywords Data assimilation, inundation forecasting, fluvial flooding, observation impact, joint state-parameter 18 estimation, ensemble Kalman filter.Highlights 20 • Data assimilation is applied to simulated flood forecasts and SAR-like observations 21 • Reinitialisation shock due to water level correction is removed using a novel method 22 • Observation impact is linked to domain length when updating only water levels 23 • Updating the channel friction parameter leads to marked improvement in forecast skill 24 • Updating the channel friction parameter can compensate for biased inflow 25 Software Availability 26The inundation simulations in this work were generated using Clawpack 5.2.2, a collection of FORTRAN and 27 python code available from http://www.clawpack.org/. Details of the amended Clawpack source code as used 28 in this work are freely available on request from the corresponding author, as is the python code used to perform 29 data assimilation on the inundation simulation output. Please contact e.s.cooper@pgr.reading.ac.uk for details. 30 1 1 Introduction 31 Data assimilation can improve the accuracy of predictions from flood inundation models by combining forecasts 32 from the model with observations of the system, taking into account uncertainty in both the model predictions 33 and the observations. In this study we use a sequential data assimilation method comprising a forecast-update 34 dynamic feedback loop. During each forecast step, the numerical model runs an inundation simulation. When 35 an observation (or set of observations) is available the simulation is interrupted and the update step is performed; 36 updating combines observational data and model predictions to give a better estimate of the state. The next 37 forecast step then starts, with the adjusted water levels as the initial condition. An update is carried out each 38 time a new observation or set of observations is available. 39There are a number of numerical inundation models that can predict the behaviour o...

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, the nature and structure of atmosphere–ocean forecast error cross correlations are investigated using an idealized strongly coupled single-column atmosphere–ocean 4D-Var assimilation system. Results are presented from a set of identical twin–type experiments that use an ensemble of coupled 4D-Var assimilations to derive estimates of the atmosphere–ocean error cross correlations. The 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.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three-dimensional variational (3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2-year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.