Morphing Ensemble Kalman Filters

A new type of ensemble filter is proposed, which combines an ensemble Kalman filter (EnKF) with the ideas of morphing and registration from image processing. This results in filters suitable for nonlinear problems whose solutions exhibit moving coherent features, such as thin interfaces in wildfire modeling. The ensemble members are represented as the composition of one common state with a spatial transformation, called registration mapping, plus a residual. A fully automatic registration method is used that requires only gridded data, so the features in the model state do not need to be identified by the user. The morphing EnKF operates on a transformed state consisting of the registration mapping and the residual. Essentially, the morphing EnKF uses intermediate states obtained by morphing instead of linear combinations of the states.Comment: 17 pages, 7 figures. Added DDDAS references to the introductio

DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF

Balance conditions in variational data assimilation for a high-resolution forecast model

This paper explores the role of balance relationships for background error covariance modelling as the model's grid box decreases to convective-scales. Data assimilation (DA) analyses are examined from a simplified convective-scale model and DA system (called ABC-DA) with a grid box size of 1.5km in a 2D 540km (longitude), 15km (height) domain. The DA experiments are performed with background error covariance matrices B modelled and calibrated by switching on/off linear balance (LB) and hydrostatic balance (HB), and by observing a subset of the ABC variables, namely v, meridional wind, r', scaled density (a pressure-like variable), and b', buoyancy (a temperature-like variable). Calibration data are sourced from two methods of generating proxies of forecast errors. One uses forecasts from different latitude slices of a 3D parent model (here called the `latitude slice method'), and the other uses sets of differences between forecasts of different lengths but valid at the same time (the National Meteorological Center method). Root-mean-squared errors computed over the domain from identical twin DA experiments suggest that there is no combination of LB/HB switches that give the best analysis for all model quantities. It is frequently found though that the B-matrices modelled with both LB and HB do perform the best. A clearer picture emerges when the errors are examined at different spatial scales. In particular it is shown that switching on HB in B mostly has a neutral/positive effect on the DA accuracy at `large' scales, and switching off the HB has a neutral/positive effect at `small' scales. The division between `large' and `small' scales is between 10 and 100km. Furthermore, one hour forecast error correlations computed between control parameters find that correlations are small at large scales when balances are enforced, and at small scales when balances are not enforced (ideal control parameters have zero cross correlations). This points the way to modelling B with scale-dependent balances

An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations

We present a data assimilation system to estimate surface fluxes of CO2 and other trace gases from observations of their atmospheric abundances. The system is based on ensemble data assimilation methods under development for Numerical Weather Prediction (NWP) and is the first of its kind to be used for CO2 flux estimation. The system was developed to overcome computational limitations encountered when a large number of observations are used to estimate a large number of unknown surface fluxes. The ensemble data assimilation approach is attractive because it returns an approximation of the covariance, does not need an adjoint model or other linearization of the observation operator, and offers the possibility to optimize fluxes of chemically active trace gases (e.g., CH4, CO) in the same framework. We assess the performance of this new system in a pseudodata experiment that resembles the real problem we will apply this system to. The sensitivity of the method to the choice of several parameters such as the assimilation window size and the number of ensemble members is investigated. We conclude that the system is able to provide satisfactory flux estimates for the relatively large scales resolved by our current observing network and that the loss of information in the approximated covariances is an acceptable price to pay for the efficient computation of a large number of surface fluxes. The full potential of this data assimilation system will be used for near–real time operational estimates of North American CO2 fluxes. This will take advantage of the large amounts of atmospheric data that will be collected by NOAA-CMDL in conjunction with the implementation of the North American Carbon Program (NACP)