D. J. Patil

A local ensemble Kalman filter for atmospheric data assimilation

In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earths surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region. Ensemble Kalman Filters, in general, assume that the analysis resulting from the data assimilation lies in the same subspace as the expected forecast error. Under our hypothesis the dimension of this subspace is low. This implies that operations only on relatively low dimensional matrices are required. Thus, the data analysis is done locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. The method, its potential advantages, properties, and implementation requirements are illustrated by numerical experiments on the Lorenz-96 model. It is found that accurate analysis can be achieved at a cost which is very modest compared to that of a full global ensemble Kalman Filter.

Four-dimensional ensemble Kalman filtering

Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations, whether they occur at the assimilation time or at some earlier or later time, can be effectively accounted for at low computational expense. In the case of linear dynamics, the technique is equivalent to instantaneously assimilating data as they are measured. The results of numerical tests of the technique on a simple model problem are shown.

Assessing a local ensemble Kalman filter: perfect model experiments with the National Centers for Environmental Prediction global model

The accuracy and computational efficiency of the recently proposed local ensemble Kalman filter (LEKF) data assimilation scheme is investigated on a state-of-the-art operational numerical weather prediction model using simulated observations. The model selected for this purpose is the T62 horizontaland 28-level vertical-resolution version of the Global Forecast System (GFS) of the National Center for Environmental Prediction. The performance of the data assimilation system is assessed for different configurations of the LEKF scheme. It is shown that a modest size (40-member) ensemble is sufficient to track the evolution of the atmospheric state with high accuracy. For this ensemble size, the computational time per analysis is less than 9 min on a cluster of PCs. The analyses are extremely accurate in the mid-latitude storm track regions. The largest analysis errors, which are typically much smaller than the observational errors, occur where parametrized physical processes play important roles. Because these are also the regions where model errors are expected to be the largest, limitations of a real-data implementation of the ensemble-based Kalman filter may be easily mistaken for model errors. In light of these results, the importance of testing the ensemble-based Kalman filter data assimilation systems on simulated observations is stressed.

Extracting Envelopes of Rossby Wave Packets

Abstract Packets of Rossby waves play an important role in the transfer of kinetic energy in the extratropics. The ability to locate, track, and detect changes in the envelope of these wave packets is vital to detecting baroclinic downstream development, tracking the impact of the analysis errors in numerical weather forecasts, and analyzing the forecast effects of targeted weather observations. In this note, it is argued that a well-known technique of digital signal processing, which is based on the Hilbert transform, should be used for extracting the envelope of atmospheric wave packets. This technique is robust, simple, and computationally inexpensive. The superiority of the proposed algorithm over the complex demodulation technique (the only technique previously used for this purpose in atmospheric studies) is demonstrated by examples. The skill of the proposed algorithm is also demonstrated by tracking wave packets in operational weather analyses from the National Centers for Environmental Prediction...

Mechanisms for the Development of Locally Low-Dimensional Atmospheric Dynamics

The complexity of atmospheric instabilities is investigated by a combination of numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well-established analysis of the local energetics of the atmospheric flow and the recently introduced ensemble dimension (E dimension). The E dimension is a local measure that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions over a geographically localized region. The E dimension is maximal, that is, equal to the number of ensemble members (k), when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E dimension. Numerical experiments with the state-of-the-art operational Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) at a reduced resolution are carried out to investigate the spatiotemporal evolution of the E dimension. This evolution is characterized by an initial transient phase in which coherent regions of low dimensionality develop through a rapid local decay of the E dimension. The typical duration of the transient is between 12 and 48 h depending on the flow; after the initial transient, the E dimension gradually increases with time. The main goal of this study is to identify processes that contribute to transient local low-dimensional behavior. Case studies are presented to show that local baroclinic and barotropic instabilities, downstream development of upper-tropospheric wave packets, phase shifts of finite amplitude waves, anticyclonic wave breaking, and some combinations of these processes can all play crucial roles in lowering the E dimension. The practical implication of the results is that a wide range of synoptic-scale weather events may exist whose prediction can be significantly improved in the short and early medium range by enhancing the prediction of only a few local phase space directions. This potential is demonstrated by a reexamination of the targeted weather observations missions from the 2000 Winter Storm Reconnaissance (WSR00) program.

Assessing Predictability with a Local Ensemble Kalman Filter

Abstract In this paper, the spatiotemporally changing nature of predictability is studied in a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Atmospheric predictability is assessed in the perfect model scenario for which forecast uncertainties are entirely due to uncertainties in the estimates of the initial states. Uncertain initial conditions (analyses) are obtained by assimilating simulated noisy vertical soundings of the “true” atmospheric states with the local ensemble Kalman filter (LEKF) data assimilation scheme. This data assimilation scheme provides an ensemble of initial conditions. The ensemble mean defines the initial condition of 5-day deterministic model forecasts, while the time-evolved members of the ensemble provide an estimate of the evolving forecast uncertainties. The observations are randomly distributed in space to ensure that the geographical distribution of t...

Local Low Dimensionality and Relation to Effects Of Targeted Weather Observations

A statistic, the BV (bred vector) dimension, is introduced to measure the effective local finite‐time dimensionality of a spatiotemporally chaotic system. It is shown that the Earth’s atmosphere often has low BV‐dimension. The implications for improving weather forecasting through data assimilation and targeted observations are discussed.