Toward reliable ensemble Kalman filter estimates of CO 2 fluxes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95036/1/jgrd18220.pd

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

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs

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

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed

The TIGGE project and its achievements

TIGGE was a major component of the THORPEX (The Observing System Research and Predictability Experiment) research program, whose aim is to accelerate improvements in forecasting high-impact weather. By providing ensemble prediction data from leading operational forecast centers, TIGGE has enhanced collaboration between the research and operational meteorological communities and enabled research studies on a wide range of topics. The paper covers the objective evaluation of the TIGGE data. For a range of forecast parameters, it is shown to be beneficial to combine ensembles from several data providers in a Multi-model Grand Ensemble. Alternative methods to correct systematic errors, including the use of reforecast data, are also discussed. TIGGE data have been used for a range of research studies on predictability and dynamical processes. Tropical cyclones are the most destructive weather systems in the world, and are a focus of multi-model ensemble research. Their extra-tropical transition also has a major impact on skill of mid-latitude forecasts. We also review how TIGGE has added to our understanding of the dynamics of extra-tropical cyclones and storm tracks. Although TIGGE is a research project, it has proved invaluable for the development of products for future operational forecasting. Examples include the forecasting of tropical cyclone tracks, heavy rainfall, strong winds, and flood prediction through coupling hydrological models to ensembles. Finally the paper considers the legacy of TIGGE. We discuss the priorities and key issues in predictability and ensemble forecasting, including the new opportunities of convective-scale ensembles, links with ensemble data assimilation methods, and extension of the range of useful forecast skill

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)