Sharanya J. Majumdar

Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects

A suboptimal Kalman filter called the ensemble transform Kalman filter (ET KF) is introduced. Like other Kalman filters, it provides a framework for assimilating observations and also for estimating the effect of observations on forecast error covariance. It differs from other ensemble Kalman filters in that it uses ensemble transformation and a normalization to rapidly obtain the prediction error covariance matrix associated with a particular deployment of observational resources. This rapidity enables it to quickly assess the ability of a large number of future feasible sequences of observational networks to reduce forecast error variance. The ET KF was used by the National Centers for Environmental Prediction in the Winter Storm Reconnaissance missions of 1999 and 2000 to determine where aircraft should deploy dropwindsondes in order to improve 24‐72-h forecasts over the continental United States. The ET KF may be applied to any well-constructed set of ensemble perturbations. The ET KF technique supercedes the ensemble transform (ET) targeting technique of Bishop and Toth. In the ET targeting formulation, the means by which observations reduced forecast error variance was not expressed mathematically. The mathematical representation of this process provided by the ET KF enables such things as the evaluation of the reduction in forecast error variance associated with individual flight tracks and assessments of the value of targeted observations that are distributed over significant time intervals. It also enables a serial targeting methodology whereby one can identify optimal observing sites given the location and error statistics of other observations. This allows the network designer to nonredundantly position targeted observations. Serial targeting can also be used to greatly reduce the computations required to identify optimal target sites. For these theoretical and practical reasons, the ET KF technique is more useful than the ET technique. The methodology is illustrated with observation system simulation experiments involving a barotropic numerical model of tropical cyclonelike vortices. These include preliminary empirical tests of ET KF predictions using ET KF, 3DVAR, and hybrid data assimilation schemes—the results of which look promising. To concisely describe the future feasible sequences of observations considered in adaptive sampling problems, an extension to Ide et al.’s unified notation for data assimilation is suggested.

The North Pacific Experiment (NORPEX-98): Targeted Observations for Improved North American Weather Forecasts

Abstract The objectives and preliminary results of an interagency field program, the North Pacific Experiment (NORPEX), which took place between 14 January and 27 February 1998, are described. NORPEX represents an effort to directly address the issue of observational sparsity over the North Pacific basin, which is a major contributing factor in short-range (less than 4 days) forecast failures for land-falling Pacific winter-season storms that affect the United States, Canada, and Mexico. The special observations collected in NORPEX include approximately 700 targeted tropospheric soundings of temperature, wind, and moisture from Global Positioning System (GPS) dropsondes obtained in 38 storm reconnaissance missions using aircraft based primarily in Hawaii and Alaska. In addition, wind data were provided every 6 h over the entire North Pacific during NORPEX, using advanced and experimental techniques to extract information from multispectral geostationary satellite imagery. Preliminary results of NORPEX dat...

The Pre-Depression Investigation of Cloud-Systems in the Tropics (PREDICT) Experiment: Scientific Basis, New Analysis Tools, and Some First Results

The principal hypotheses of a new model of tropical cyclogenesis, known as the marsupial paradigm, were tested in the context of Atlantic tropical disturbances during the National Science Foundation (NSF)-sponsored Pre-Depression Investigation of Cloud Systems in the Tropics (PREDICT) experiment in 2010. PREDICT was part of a tri-agency collaboration, along with the National Aeronautics and Space Administrations Genesis and Rapid Intensification Processes (NASA GRIP) experiment and the National Oceanic and Atmospheric Administrations Intensity Forecasting Experiment (NOAA IFEX), intended to examine both developing and nondeveloping tropical disturbances. During PREDICT, a total of 26 missions were flown with the NSF/NCAR Gulfstream V (GV) aircraft sampling eight tropical disturbances. Among these were four cases (Fiona, ex-Gaston, Karl, and Matthew) for which three or more missions were conducted, many on consecutive days. Because of the scientific focus on the Lagrangian nature of the tropical cyclogen...

The Effect of Targeted Dropsonde Observations during the 1999 Winter Storm Reconnaissance Program

Abstract In this paper, the effects of targeted dropsonde observations on operational global numerical weather analyses and forecasts made at the National Centers for Environmental Prediction (NCEP) are evaluated. The data were collected during the 1999 Winter Storm Reconnaissance field program at locations that were found optimal by the ensemble transform technique for reducing specific forecast errors over the continental United States and Alaska. Two parallel analysis–forecast cycles are compared; one assimilates all operationally available data including those from the targeted dropsondes, whereas the other is identical except that it excludes all dropsonde data collected during the program. It was found that large analysis errors appear in areas of intense baroclinic energy conversion over the northeast Pacific and are strongly associated with errors in the first-guess field. The “signal,” defined by the difference between analysis–forecast cycles with and without the dropsonde data, propagates at an...

Adaptive sampling with the ensemble transform Kalman filter. Part II: Field program implementation

The practical application of the ensemble transform Kalman filter (ET KF), used in recent Winter Storm Reconnaissance (WSR) programs by the National Centers for Environmental Prediction (NCEP), is described. The ET KF assesses the value of targeted observations taken at future times in improving forecasts for preselected critical events. It is based on a serial assimilation framework that makes it an order of magnitude faster than its predecessor, the ensemble transform technique. The speed of the ET KF enabled several different forecast scenarios to be assessed for targeting during recent WSR programs. Each potential observational network is broken down into idealized routine and adaptive components. The adaptive component represents a predesigned flight track along which GPS dropwindsondes are released. For a large number of flight tracks, the ET KF estimates the forecast error reducing effects of these observations (via the ‘‘signal variance’’). The track that maximizes the average forecast signal variance within a selected verification region is deemed optimal for targeting. Secondary flight tracks can also be chosen using serial assimilation, by calculating the signal variance for each flight track given that the primary track had already been selected. For the second consecutive year the ET KF was able to estimate, via a statistical rescaling, the variance of NCEP signal realizations produced by the dropwindsonde data. A monotonic increasing relationship between the ET KF signal variance and the reduction in NCEP forecast error variance due to the targeted observations was then deduced for the operational 2001 WSR program.

A Comparison of Adaptive Observing Guidance for Atlantic Tropical Cyclones

Abstract Airborne adaptive observations have been collected for more than two decades in the neighborhood of tropical cyclones, to attempt to improve short-range forecasts of cyclone track. However, only simple subjective strategies for adaptive observations have been used, and the utility of objective strategies to improve tropical cyclone forecasts remains unexplored. Two objective techniques that have been used extensively for midlatitude adaptive observing programs, and the current strategy based on the ensemble deep-layer mean (DLM) wind variance, are compared quantitatively using two metrics. The ensemble transform Kalman filter (ETKF) uses ensembles from NCEP and the ECMWF. Total-energy singular vectors (TESVs) are computed by the ECMWF and the Naval Research Laboratory, using their respective global models. Comparisons of 78 guidance products for 2-day forecasts during the 2004 Atlantic hurricane season are made, on both continental and localized scales relevant to synoptic surveillance missions. ...

Intercomparison of Targeted Observation Guidance for Tropical Cyclones in the Northwestern Pacific

Abstract This study compares six different guidance products for targeted observations over the northwest Pacific Ocean for 84 cases of 2-day forecasts in 2006 and highlights the unique dynamical features affecting the tropical cyclone (TC) tracks in this basin. The six products include three types of guidance based on total-energy singular vectors (TESVs) from different global models, the ensemble transform Kalman filter (ETKF) based on a multimodel ensemble, the deep-layer mean (DLM) wind variance, and the adjoint-derived sensitivity steering vector (ADSSV). The similarities among the six products are evaluated using two objective statistical techniques to show the diversity of the sensitivity regions in large, synoptic-scale domains and in smaller domains local to the TC. It is shown that the three TESVs are relatively similar to one another in both the large and the small domains while the comparisons of the DLM wind variance with other methods show rather low similarities. The ETKF and the ADSSV usua...

New Ocean Winds Satellite Mission to Probe Hurricanes and Tropical Convection

AbstractThe Cyclone Global Navigation Satellite System (CYGNSS) is a new NASA earth science mission scheduled to be launched in 2016 that focuses on tropical cyclones (TCs) and tropical convection. The mission’s two primary objectives are the measurement of ocean surface wind speed with sufficient temporal resolution to resolve short-time-scale processes such as the rapid intensification phase of TC development and the ability of the surface measurements to penetrate through the extremely high precipitation rates typically encountered in the TC inner core. The mission’s goal is to support significant improvements in our ability to forecast TC track, intensity, and storm surge through better observations and, ultimately, better understanding of inner-core processes. CYGNSS meets its temporal sampling objective by deploying a constellation of eight satellites. Its ability to see through heavy precipitation is enabled by its operation as a bistatic radar using low-frequency GPS signals. The mission will depl...

On the Ability of Global Ensemble Prediction Systems to Predict Tropical Cyclone Track Probabilities

The ability of ensemble prediction systems to predict the probability that a tropical cyclone will fall within a certain area is evaluated. Ensemble forecasts of up to 5 days issued by the European Centre for MediumRange Weather Forecasts (ECMWF) and the Met Office (UKMET) were evaluated for the 2008 Atlantic and western North Pacific seasons. In the Atlantic, the ECMWF ensemble mean was comparable in skill to a consensus of deterministic models. Dynamic ‘‘probability circles’’ that contained 67% of the ECMWF ensemble captured the best track in ;67% of all cases for 24‐84-h forecasts, and were slightly underdispersive beyond 96 h. In contrast, the Goerss predicted consensus error (GPCE) was overdispersive. The addition of the UKMET ensemble yielded improvements in the short range and degradations for longer-range forecasts. The ECMWF ensemble performed similarly when the size was reduced from 50 to 20. On average, it produced a lower measure of independence between its members than an ensemble comprising different deterministic models. The 67% circles normally captured the best track during straight-line motion, but less so for sharply turning tracks. In contrast to the Atlantic, the ECMWF ensemble (and GPCE) was unable to capture sufficient verifications within the 67% probability circles in the western North Pacific, in part because of a less skillful ensemble mean (and consensus). Though further evaluations are necessary, the results demonstrate the potential for ensemble prediction systems to enhance probabilistic forecasts, and for The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) to be embraced by the operational and research communities.

Using TIGGE Data to Diagnose Initial Perturbations and Their Growth for Tropical Cyclone Ensemble Forecasts

Abstract Ensemble initial perturbations around Typhoon Sinlaku (2008) produced by ECMWF, NCEP, and the Japan Meteorological Agency (JMA) ensembles are compared using The Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) data, and the dynamical mechanisms of perturbation growth associated with the tropical cyclone (TC) motion are investigated for the ECMWF and NCEP ensembles. In the comparison, it is found that the vertical and horizontal distributions of initial perturbations as well as the amplitude are quite different among the three NWP centers before, during, and after the recurvature of Sinlaku. In addition, it turns out that those variations cause a difference in the TC motion not only at the initial time but also during the subsequent forecast period. The ECMWF ensemble exhibits relatively large perturbation growth, which results from 1) the baroclinic energy conversion in a vortex, 2) the baroclinic energy conversion associated with the mid...