30 research outputs found
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Quantifying the latitudinal representivity of in situ solar wind observations
Advanced space-weather forecasting relies on the ability to accurately predict near-Earth solar wind conditions. For this purpose, physics-based, global numerical models of the solar wind are initialized with photospheric magnetic field and coronagraph observations, but no further observation constraints are imposed between the upper corona and Earth orbit. Data assimilation (DA) of the available in situ solar wind observations into the models could potentially provide additional constraints, improving solar wind reconstructions, and forecasts. However, in order to effectively combine the model and observations, it is necessary to quantify the error introduced by assuming point measurements are representative of the model state. In particular, the range of heliographic latitudes over which in situ solar wind speed measurements are representative is of primary importance, but particularly difficult to assess from observations alone. In this study we use 40+ years of observation-driven solar wind model results to assess two related properties: the latitudinal representivity error introduced by assuming the solar wind speed measured at a given latitude is the same as that at the heliographic equator, and the range of latitudes over which a solar wind measurement should influence the model state, referred to as the observational localisation. These values are quantified for future use in solar wind DA schemes as a function of solar cycle phase, measurement latitude, and error tolerance. In general, we find that in situ solar wind speed measurements near the ecliptic plane at solar minimum are extremely localised, being similar over only 1° or 2° of latitude. In the uniform polar fast wind above approximately 40° latitude at solar minimum, the latitudinal representivity error drops. At solar maximum, the increased variability of the solar wind speed at high latitudes means that the latitudinal representivity error increases at the poles, though becomes greater in the ecliptic, as long as moderate speed errors can be tolerated. The heliospheric magnetic field and solar wind density and temperature show very similar behaviour
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Nonlinear bias correction for satellite data assimilation using Taylor series polynomials
Output from a high-resolution ensemble data assimilation system is used to assess the ability of an innovative nonlinear bias correction (BC) method that uses a Taylor series polynomial expansion of the observation-minus background departures to remove linear and nonlinear conditional biases from all-sky satellite infrared brightness temperatures. Univariate and multivariate experiments were performed in which the satellite zenith angle and variables sensitive to clouds and water vapor were used as the BC predictors. The results showed that even though the bias of the entire observation departure distribution is equal to zero regardless of the order of the Taylor series expansion, there are often large conditional biases that vary as a nonlinear function of the BC predictor. The linear 1st order term had the largest impact on the entire distribution as measured by reductions in variance; however, large conditional biases often remained in the distribution when plotted as a function of the predictor. These conditional biases were typically reduced to near zero when the nonlinear 2nd and 3rd order terms were used. The univariate results showed that variables sensitive to the cloud top height are effective BC predictors especially when higher order Taylor series terms are used. Comparison of the statistics for clear-sky and cloudy-sky observations revealed that nonlinear departures are more important for cloudy-sky observations as signified by the much larger impact of the 2nd and 3rd order terms on the conditional biases. Together, these results indicate that the nonlinear BC method is able to effectively remove the bias from all-sky infrared observation departures
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An idealized study of coupled atmosphere-ocean 4D-Var in the presence of model error
Atmosphere only and ocean only variational data assimilation (DA) schemes are able to use window lengths that are optimal for the error growth rate, non-linearity and observation density of the respective systems. Typical window lengths are 6-12 hours for the atmosphere and 2-10 days for the ocean. However, in the implementation of coupled DA schemes it has been necessary to match the window length of the ocean to that of the atmosphere, which may potentially sacrifice the accuracy of the ocean analysis in order to provide a more balanced coupled state. This paper investigates how extending the window length in the presence of model error affects both the analysis of the coupled state and the initialized forecast when using coupled DA with differing degrees of coupling.
Results are illustrated using an idealized single column model of the coupled atmosphere-ocean system. It is found that the analysis error from an uncoupled DA scheme can be smaller than that from a coupled analysis at the initial time, due to faster error growth in the coupled system. However, this does not necessarily lead to a more accurate forecast due to imbalances in the coupled state. Instead coupled DA is more able to update the initial state to reduce the impact of the model error on the accuracy of the forecast. The effect of model error is potentially most detrimental in the weakly coupled formulation due to the inconsistency between the coupled model used in the outer loop and uncoupled models used in the inner loop
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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
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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
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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
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Nonlinear conditional model bias estimation for data assimilation
In this study, we develop model bias estimators based on an asymptotic expansion of the model dynamics for small time scales and small perturbations in a model parameter, and then use the estimators to improve the performance of a data assimilation system. We employ the well-known Lorenz (1963) model so that we can study all aspects of the dynamical system and model bias estimators in a detailed way that would not be possible with a full physics numerical weather prediction model. In particular, we first work out the asymptotics of the Lorenz model for small changes in one of its parameters and then use statistics from cycled data assimilation experiments to demonstrate that the asymptotics accurately represent the behavior of the model and that the coefficients of the nonlinear asymptotical expansion can be reasonably estimated by solving a least squares minimization problem.
In data assimilation, the background error covariance matrix usually estimates the uncertainty of the model background, which is then used along with the observation error covariance matrix to produce an updated analysis. If the uncertainty of the model background is strongly influenced by time-dependent model biases, then the development of nonlinear bias estimators that also vary with time could improve the performance of the assimilation system and the accuracy of the updated analysis. We demonstrate this improvement through the combination of a constant background error covariance matrix with a dynamically-varying matrix computed using the model bias estimators. Numerical tests using the Lorenz (1963) model illustrate the feasibility of the approach and show that it leads to clear improvements in the analysis and forecast accuracy
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Integration of a 3D Variational data assimilation scheme with a coastal area morphodynamic model of Morecambe Bay
This paper describes the implementation of a 3D variational (3D-Var) data assimilation scheme for a morphodynamic model applied to Morecambe Bay, UK. A simple decoupled hydrodynamic and sediment transport model is combined with a data assimilation scheme to investigate the ability of such methods to improve the accuracy of the predicted bathymetry. The inverse forecast error covariance matrix is modelled using a Laplacian approximation which is calibrated for the length scale parameter required. Calibration is also performed for the Soulsby-van Rijn sediment transport equations. The data used for assimilation purposes comprises waterlines derived from SAR imagery covering the entire period of the model run, and swath bathymetry data collected by a ship-borne survey for one date towards the end of the model run. A LiDAR survey of the entire bay carried out in November 2005 is used for validation purposes. The comparison of the predictive ability of the model alone with the model-forecast-assimilation system demonstrates that using data assimilation significantly improves the forecast skill. An investigation of the assimilation of the swath bathymetry as well as the waterlines demonstrates that the overall improvement is initially large, but decreases over time as the bathymetry evolves away from that observed by the survey. The result of combining the calibration runs into a pseudo-ensemble provides a higher skill score than for a single optimized model run. A brief comparison of the Optimal Interpolation assimilation method with the 3D-Var method shows that the two schemes give similar results
On time-parallel preconditioning for the state formulation of incremental weak constraint 4D-Var
Using a high degree of parallelism is essential to perform data assimilation efficiently. The state formulation of the incremental weak constraint four-dimensional variational data assimilation method allows parallel calculations in the time dimension. In this approach, the solution is approximated by minimising a series of quadratic cost functions using the conjugate gradient method. To use this method in practice, effective preconditioning strategies that maintain the potential for parallel calculations are needed. We examine approximations to the control variable transform (CVT) technique when the latter is beneficial. The new strategy employs a randomised singular value decomposition and retains the potential for parallelism in the time domain. Numerical results for the Lorenz 96 model show that this approach accelerates the minimisation in the first few iterations, with better results when CVT performs well