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Alexander Gluhovsky
and
Ernest Agee

Abstract

Statistical issues of atmospheric data analysis are discussed that address the problem of stationarity and homogeneity of data and the problem of inadequate record lengths. Bandpass filtering of observational data is proposed to make possible the reliable comparisons with model output statistics. Another suggestion is box area measurements that offer considerable advantages in terms of the accuracy of estimation over linear flight path data. Records of stationary data of adequate lengths are unavailable for higher-order statistics, but sufficient amounts of box area data can be obtained from limited domains of 20–40 km. The findings are illustrated by the analyses of data from Project LESS (Lake-Effect Snow Studies) and from large eddy simulation (LES) of Project LESS events.

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Ernest Agee
and
Lindsey Taylor

Abstract

The record of tornado fatalities in the United States for over two centuries (1808–2017) and decadal census records have been examined to search for historical trends. Particular attention has been given to the response to population growth and expansion into the tornado-prone regions of the country. The region selected includes the Tornado Alley of the central Great Plains, the Dixie Alley in the southeastern states, and the adjoining states in the Midwest that collectively encompass a 21-state rectangular region. The data record has been divided into two subintervals, Era A (1808–1915) and Era B (1916–2017), each of which consists of three equal-length periods. Era A is characterized by a growing and westward expanding population along with a basic absence of scientific knowledge, technology, and communications (for prediction, detection, and warning). This is followed by a renaissance of discovery and advancement in Era B that contributes to saving lives. The aforementioned periods are defined by a set of notable events that help to define the respective periods. A death per population index (DPI) is used to evaluate the 21 states in each era; there is a rise of mean DPI values to a maximum of 1.50 at the end of Era A and a subsequent fall to 0.21 at the end of Era B. It is also shown for all three periods in Era B that the deadliest tornado states, in ranked order, are Arkansas, Mississippi, Alabama, and Oklahoma. Suggestions are presented for ways to continue the decreasing trend in DPI, which would imply that the death rate increase is not as fast as the rate of population increase (or would even imply a decreasing death rate).

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Ernest Agee
and
Samuel Childs

Abstract

The U.S. tornado record is subject to inhomogeneities that are due to inconsistent practices in counting tornadoes, assessing their damage, and measuring pathlength and path width. Efforts to improve the modern tornado record (1950–2012) have focused on the following: 1) the rationale for removing the years 1950–52, 2) identification of inconsistencies in F0, F1, and F2 counts based on implementation of the Fujita scale (F scale) and Doppler radar, 3) overestimation of backward-extrapolated F-scale intensity, and 4) a change in path-width reporting from mean width (1953–94) to maximum width (1995–2012). Unique adjustments to these inconsistencies are made by analyzing trends in tornado counts, comparing with previous studies, and making an upward adjustment of tornadoes classified by mean width to coincide with those classified by maximum width. Such refinements offer a more homogeneous tornado record and provide the opportunity to better evaluate climatological trends in significant (F/EF2–F/EF5) tornado activity. The median EF-scale (enhanced Fujita scale) wind speeds V med have been adopted for all significant tornadoes from 1953 to 2012, including an adjustment for overestimated intensities from 1953 to 1973. These values are used to calculate annual mean kinetic energy, which shows no apparent trend. The annual mean maximum path width from 1953 to 2012 (adjusted upward from 1953 to 1994 to obtain a common lower threshold), however, displays an increasing trend. Also, the EF-scale median wind speeds are highly correlated with . The quantity (V med × PWmax)2 is proposed as a tornado destruction index, and, when calculated as an annual cumulative value, the three largest years are 2007, 2008, and 2011.

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Alexander Gluhovsky
and
Ernest Agee

Abstract

This study extends the authors’ earlier work that addresses the importance of bootstrap methods in computing statistical characteristics of meteorological and climatological datasets. Subsampling confidence intervals for the skewness and kurtosis are developed for nonlinear datasets, for which traditional time series techniques are not applicable. It also provides an example of how to apply subsampling to real data when only a single record of limited length is available: aircraft observations of vertical velocity in the wintertime convective boundary layer over Lake Michigan. This demonstrates the value of bootstrap methods in obtaining reliable confidence intervals for turbulent flows with coherent structures (characterized by non-Gaussian skewness and kurtosis).

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Ernest M. Agee

Abstract

Manifestations of both Rayleigh-Taylor instability and Kármán vortices in atmospheric flows are recognized, and existing theory is applied to infer some values for the horizontal and vertical eddy transport coefficients for momentum, Kh , and Kz , respectively.

Periodic protrusions of cloud material from beneath cirrus bands sometimes associated with warm frontal

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Alexander Gluhovsky
and
Ernest Agee

Abstract

Linear parametric models are commonly assumed and used for unknown data-generating mechanisms. This study demonstrates the value of inferring statistics of meteorological and climatological time series by using a computer-intensive subsampling method that allows one to avoid time series analysis anchored in parametric models with imposed perceived physical assumptions. A first-order autoregressive model, typically adopted as the default model for correlated time series in climate studies, has been selected and altered with a nonlinear component to provide insight into possible errors in estimation due to nonlinearities in the real data-generating mechanism. The nonlinearity undetected by basic diagnostic procedures is shown to invalidate statistical inference based on the linear model, whereas the inference derived through subsampling remains valid. It is argued that subsampling and other resampling methods are preferable in complex dependent-data situations that are typical for atmospheric and climatic series when the real data-generating mechanism is unknown.

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Alexander Gluhovsky
and
Ernest Agee

Abstract

Low-order models (LOMs) arising in various popular fluid dynamic and atmospheric problems are shown to be equivalent to coupled three-mode nonlinear systems known in mechanics as Volterra gyrostats. The Volterra equations of the gyrostat differ from the Euler equations of the gyroscope by the presence of linear terms, which, unlike ordinary viscous terms, do not affect the energy or the phase volume conservation. In atmospheric LOMs such linear terms, exerting considerable influence on the dynamics, are caused by various factors peculiar to geophysical fluid dynamics (e.g., stratification, rotation, and topography). The simplest Volterra gyrostat in the forced regime is equivalent to the celebrated Lorenz model. Systems of coupled gyrostats also inherently possess fundamental properties of the hydrodynamic equations. Therefore, gyrostats are proposed as elementary modules for developing LOMs of nonlinear fluid dynamic and atmospheric phenomena.

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Alexander Gluhovsky
and
Ernest Agee

Abstract

No abstracts available.

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Alexander Gluhovsky
and
Ernest Agee

Abstract

A method for comprehensive statistical data analysis is presented. It includes a procedure for selection of segments within a data record, where data can be considered stationary, allowing the computation of statistical parameters (from data over selected segments) and their confidence intervals (estimating the statistical reliability of the parameters). The method is illustrated by analysing the vertical component of the wind velocity data collected by research aircraft flights over Lake Michigan during Project LESS (Lake Effect Snow Studies). The results indicate that for skewness and kurtosis, the requirements for acceptable “averaging distances” are less limiting than the required distances for corresponding third- and forth-order moments.

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Ernest Agee
and
Alexander Gluhovsky

Abstract

This study has employed the concept of bandpass filtering of aircraft field data that are obtained within convective planetary boundary layers, for the purpose of comparing the characteristic turbulence statistics with the results of large eddy simulation (LES) models. Field data from Project LESS (10 January 1984) conducted over Lake Michigan in wintertime cold air outbreaks have been used to demonstrate the validity of the concept presented. These results show excellent agreement in variance statistics for LESS filtered data and LES model simulations; however, agreement in the skewness statistics is unsatisfactory. This is attributed to either the authors’ inability to design a proper bandpass filter or the lack of an adequate dataset for computing third-moment statistics.

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