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- Author or Editor: Sai Ravela x

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## Abstract

Ensemble prediction is a widely used tool in weather forecasting. In particular, the arithmetic mean (AM) of ensemble members is used to filter out unpredictable features from a forecast. AM is a pointwise statistical concept, providing the best sample-based estimate of the expected value of any single variable. The atmosphere, however, is a multivariate system with spatially coherent features characterized with strong correlations. Disregarding such correlations, the AM of an ensemble of forecasts removes not only unpredictable noise but also flattens features whose presence is still predictable, albeit with somewhat uncertain location. As a consequence, AM destroys the structure, and reduces the amplitude and variability associated with partially predictable features. Here we explore the use of an alternative concept of central tendency for the estimation of the expected feature (instead of single values) in atmospheric systems. Features that are coherent across ensemble members are first collocated to their mean position, before the AM of the aligned members is taken. Unlike earlier definitions based on complex variational minimization (field coalescence of Ravela and generalized ensemble mean of Purser), the proposed feature-oriented mean (FM) uses simple and computationally efficient vector operations. Though FM is still not a dynamically realizable state, a preliminary evaluation of ensemble geopotential height forecasts indicates that it retains more variance than AM, without a noticeable drop in skill. Beyond ensemble forecasting, possible future applications include a wide array of climate studies where the collocation of larger-scale features of interest may yield enhanced compositing results.

## Abstract

Ensemble prediction is a widely used tool in weather forecasting. In particular, the arithmetic mean (AM) of ensemble members is used to filter out unpredictable features from a forecast. AM is a pointwise statistical concept, providing the best sample-based estimate of the expected value of any single variable. The atmosphere, however, is a multivariate system with spatially coherent features characterized with strong correlations. Disregarding such correlations, the AM of an ensemble of forecasts removes not only unpredictable noise but also flattens features whose presence is still predictable, albeit with somewhat uncertain location. As a consequence, AM destroys the structure, and reduces the amplitude and variability associated with partially predictable features. Here we explore the use of an alternative concept of central tendency for the estimation of the expected feature (instead of single values) in atmospheric systems. Features that are coherent across ensemble members are first collocated to their mean position, before the AM of the aligned members is taken. Unlike earlier definitions based on complex variational minimization (field coalescence of Ravela and generalized ensemble mean of Purser), the proposed feature-oriented mean (FM) uses simple and computationally efficient vector operations. Though FM is still not a dynamically realizable state, a preliminary evaluation of ensemble geopotential height forecasts indicates that it retains more variance than AM, without a noticeable drop in skill. Beyond ensemble forecasting, possible future applications include a wide array of climate studies where the collocation of larger-scale features of interest may yield enhanced compositing results.

Hurricanes are lethal and costly phenomena, and it is therefore of great importance to assess the long-term risk they pose to society. Among the greatest threats are those associated with high winds and related phenomena, such as storm surges. Here we assess the probability that hurricane winds will affect any given point in space by combining an estimate of the probability that a hurricane will pass within some given radius of the point in question with an estimate of the spatial probability density of storm winds.

To assess the probability that storms will pass close enough to a point of interest to affect it, we apply two largely independent techniques for generating large numbers of synthetic hurricane tracks. The first treats each track as a Markov chain, using statistics derived from observed hurricane-track data. The second technique begins by generating a large class of synthetic, time-varying wind fields at 850 and 250 hPa whose variance, covariance, and monthly means match NCEP–NCAR reanalysis data and whose kinetic energy follows an *ω*
^{−3} geostrophic turbulence spectral frequency distribution. Hurricanes are assumed to move with a weighted mean of the 850- and 250-hPa flow plus a “beta drift” correction, after originating at points determined from historical genesis data. The statistical characteristics of tracks generated by these two means are compared.

For a given point in space, many (~10^{4}) synthetic tracks are generated that pass within a specified distance of a point of interest, using both track generation methods. For each of these tracks, a deterministic, coupled, numerical simulation of the storm's intensity is carried out, using monthly mean upper-ocean and potential intensity climatologies, together with time-varying vertical wind shear generated from the synthetic time series of 850- and 250-hPa winds, as described above. For the case in which the tracks are generated using the synthetic environmental flow, the tracks and the shear are generated using the same wind fields and are therefore mutually consistent.

The track and intensity data are finally used together with a vortex structure model to construct probability distributions of wind speed at fixed points in space. These are compared to similar estimates based directly on historical hurricane data for two coastal cities.

Hurricanes are lethal and costly phenomena, and it is therefore of great importance to assess the long-term risk they pose to society. Among the greatest threats are those associated with high winds and related phenomena, such as storm surges. Here we assess the probability that hurricane winds will affect any given point in space by combining an estimate of the probability that a hurricane will pass within some given radius of the point in question with an estimate of the spatial probability density of storm winds.

To assess the probability that storms will pass close enough to a point of interest to affect it, we apply two largely independent techniques for generating large numbers of synthetic hurricane tracks. The first treats each track as a Markov chain, using statistics derived from observed hurricane-track data. The second technique begins by generating a large class of synthetic, time-varying wind fields at 850 and 250 hPa whose variance, covariance, and monthly means match NCEP–NCAR reanalysis data and whose kinetic energy follows an *ω*
^{−3} geostrophic turbulence spectral frequency distribution. Hurricanes are assumed to move with a weighted mean of the 850- and 250-hPa flow plus a “beta drift” correction, after originating at points determined from historical genesis data. The statistical characteristics of tracks generated by these two means are compared.

For a given point in space, many (~10^{4}) synthetic tracks are generated that pass within a specified distance of a point of interest, using both track generation methods. For each of these tracks, a deterministic, coupled, numerical simulation of the storm's intensity is carried out, using monthly mean upper-ocean and potential intensity climatologies, together with time-varying vertical wind shear generated from the synthetic time series of 850- and 250-hPa winds, as described above. For the case in which the tracks are generated using the synthetic environmental flow, the tracks and the shear are generated using the same wind fields and are therefore mutually consistent.

The track and intensity data are finally used together with a vortex structure model to construct probability distributions of wind speed at fixed points in space. These are compared to similar estimates based directly on historical hurricane data for two coastal cities.