scholarly journals On the Positive Bias of Peak Horizontal Velocity from an Idealized Doppler Profiler

2005 ◽  
Vol 22 (1) ◽  
pp. 98-104
Author(s):  
David A. Short ◽  
Francis J. Merceret
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Vertical Velocity ◽  
Gumbel Distribution ◽  
Extreme Value Distribution ◽  
Value Distribution ◽  
Horizontal Velocity ◽  
Simple Function ◽  
Type I ◽  
Positive Bias

Abstract In the presence of 3D turbulence, peak horizontal velocity estimates from an idealized Doppler profiler are found to be positively biased due to an incomplete specification of the vertical velocity field. The magnitude of the bias was estimated by assuming that the vertical and horizontal velocities can be separated into average and perturbation values and that the vertical and horizontal velocity perturbations are normally distributed. Under these assumptions, properties of the type-I extreme value distribution for maxima, known as the Gumbel distribution, can be used to obtain an analytical solution of the bias. The bias depends on geometric properties of the profiler configuration, the variance in the horizontal velocity, and the unresolved variance in the vertical velocity. When these variances are normalized by the average horizontal velocity, the bias can be mapped as a simple function of the normalized variances.

Determination of the Probability Plotting Position for Type I Extreme Value Distribution

2012 ◽  
Vol 12 (14) ◽  
pp. 1501-1506 ◽  
Author(s):  
Ahmad Shukri Yah ◽  
Norlida Md. Nor ◽  
Nor Rohashikin ◽  
Nor Azam Ramli ◽  
Fauziah Ahmad ◽  
...  
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (04) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (4) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Withdrawal from a reservoir of stratified fluid

1981 ◽  
Vol 376 (1767) ◽  
pp. 499-523
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Vertical Velocity ◽  
Mass Flux ◽  
Laboratory Experiments ◽  
Initial Period ◽  
Horizontal Layer ◽  
Horizontal Velocity ◽  
Viscous Stress ◽  
Similar Flows

A series of laboratory experiments are described in which the following major features of the flow field were observed. Well above the outlet the flow was essentially one of uniform vertical velocity, which is such that the free surface falls at a rate determined by the mass flux through the outlet, the isopycnics remaining horizontal. The small vertical velocity is converted to a considerably larger horizontal velocity in an essentially horizontal layer near the level of the outlet slot. The width of this withdrawal layer was almost constant over a large portion of the tank (except for the region near the outlet), and the velocity field within it was found to be steady after an initial period of establishment. Also the horizontal velocity at a given level in the withdrawal layer was found, to a good approximation, to vary linearly with the distance along the tank, and the velocity distribution, at a given station, was determined principally by the viscous stress, once a representative length had been established. For flows initiated in a uniform tank by suddenly opening a valve in the outlet line, the width of the withdrawal layer seemed to be uniquely determined on a scale, dependent on the flux, that appears to derive from terms that are negligible once the steady flow has been established. By placing suitable obstructions in the tank it was possible to obtain similar flows, but with various widths. We were also able to change the structure of the withdrawal layer by controlling the way the mass flux was brought to its final value, thereby establishing that the width of the withdrawal layer was dependent on its history.

A Note on Estimation from a Type I Extreme-Value Distribution

Technometrics ◽  
1967 ◽  
Vol 9 (2) ◽  
pp. 325-331 ◽  
Author(s):  
H. Leon Harter ◽  
Albert H. Moore
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I
Sign in / Sign up

Export Citation Format

Share Document