An Application of Statistics to Meteorology: Estimation of Motion

Brillinger, David R.

doi:10.1007/978-1-4612-1880-7_6

Cited by 5 publications

(4 citation statements)

References 21 publications

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“… Since then, few works have built upon it. Among those that have are Little and Ekers's work in astrophysics or Brillinger's work in meteorology. Extensions of the corresponding model have been considered, e.g., Cuzol et al and Prevosto et al and the references therein.…”

Section: An Alternative Definition Of Propagationmentioning

confidence: 99%

“…In equation , the propagation speed is supposed to be fixed or specified, but of course, it is unknown and must be estimated simultaneously to the estimation of

f ({\overset{v}{true}}_{t})

. Following Brillinger, we seek the speed vector, which maximizes the fraction of variance of

{scriptE}_{t} MathClass-rel= {((), ε_{t MathClass-bin+ h MathClass-rel| t}^{p})}_{p MathClass-rel\in scriptP MathClass-punc, h MathClass-rel= 1 MathClass-punc, MathClass-op\dots MathClass-punc, H}

explained by the planar wave

\overset{f}{true} ({\overset{v}{true}}_{t})

. We thus maximize

R^{2} ({\overset{v}{true}}_{t}) MathClass-rel= 1 MathClass-bin- \frac{{MathClass-op\sum}_{h MathClass-rel= 1}^{H} {MathClass-op\sum}_{p MathClass-rel\in scriptP} {([], ε_{t MathClass-bin+ h MathClass-rel| t}^{p} MathClass-bin- {\overset{f}{true}}_{t} (p MathClass-bin- {\overset{v}{true}}_{t} (h MathClass-bin- 15)))}^{2}}{{MathClass-op\sum}_{h MathClass-punc, p} {((), ε_{t MathClass-bin+ h MathClass-rel| t}^{p} MathClass-bin- {\overset{ε}{true}}_{t MathClass-bin+ MathClass-punc. MathClass-rel| t}^{MathClass-punc.})}^{2}}

where

{\overset{ε}{true}}_{t MathClass-bin+ MathClass-punc. MathClass-rel| t}

.…”

Section: An Alternative Definition Of Propagationmentioning

confidence: 99%

“…In equation (9), the propagation speed is supposed to be fixed or specified, but of course, it is unknown and must be estimated simultaneously to the estimation of f .E v t /. Following Brillinger, 16 we seek the speed vector, which maximizes the fraction of variance of E t D p tChjt Á p2P; hD1;:::;H explained by the planar wave O f .E v t /. We thus maximize…”

Section: Estimation Of Speedmentioning

confidence: 99%

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Spatio‐temporal propagation of wind power prediction errors

Girard

Allard

2012

Wind Energy

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International audienceThe increasing concentration of wind farms in some parts of the world calls for a new descriptive framework of power fluctuation that can summarize spatio-temporal characteristics of the wind power production process. In the mean time, this high number of measurement devices has great potential for informing or alerting about upcoming front or phase errors. In this paper, we shed light on the spatio-temporal characteristics of wind power forecast errors. We justify and use two strategies for obtaining the main direction and the speed of propagation. The first of these relies on an analysis of the local maxima of the correlation structure, and the second builds upon a planar wave modeling. The connection is made with meteorological parameters. Our analysis is presented so as to be easily reproducible in other cases

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Section: An Alternative Definition Of Propagationmentioning

confidence: 99%

“…In equation , the propagation speed is supposed to be fixed or specified, but of course, it is unknown and must be estimated simultaneously to the estimation of

f ({\overset{v}{true}}_{t})

. Following Brillinger, we seek the speed vector, which maximizes the fraction of variance of

{scriptE}_{t} MathClass-rel= {((), ε_{t MathClass-bin+ h MathClass-rel| t}^{p})}_{p MathClass-rel\in scriptP MathClass-punc, h MathClass-rel= 1 MathClass-punc, MathClass-op\dots MathClass-punc, H}

explained by the planar wave

\overset{f}{true} ({\overset{v}{true}}_{t})

. We thus maximize

R^{2} ({\overset{v}{true}}_{t}) MathClass-rel= 1 MathClass-bin- \frac{{MathClass-op\sum}_{h MathClass-rel= 1}^{H} {MathClass-op\sum}_{p MathClass-rel\in scriptP} {([], ε_{t MathClass-bin+ h MathClass-rel| t}^{p} MathClass-bin- {\overset{f}{true}}_{t} (p MathClass-bin- {\overset{v}{true}}_{t} (h MathClass-bin- 15)))}^{2}}{{MathClass-op\sum}_{h MathClass-punc, p} {((), ε_{t MathClass-bin+ h MathClass-rel| t}^{p} MathClass-bin- {\overset{ε}{true}}_{t MathClass-bin+ MathClass-punc. MathClass-rel| t}^{MathClass-punc.})}^{2}}

where

{\overset{ε}{true}}_{t MathClass-bin+ MathClass-punc. MathClass-rel| t}

.…”

Section: An Alternative Definition Of Propagationmentioning

confidence: 99%

Section: Estimation Of Speedmentioning

confidence: 99%

See 1 more Smart Citation

Spatio‐temporal propagation of wind power prediction errors

Girard

Allard

2012

Wind Energy

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show abstract

“…It is important to estimate the velocity with which the heat front is advancing, for then one can interchange time with location, albeit approximately. In a paper that considers the case of location x on the surface of a sphere, Brillinger () provided a review of various methods to estimate velocity of motion given data { Y ( x , t ), t = 0,…, T − 1, x = 0,…, X − 1}. Projection pursuit regression (PPR) is one method.…”

Section: Some Time‐side Eda Analysesmentioning

confidence: 99%

An exploratory data analysis of the temperature fluctuations in a spreading fire

Brillinger

Finney

2014

Environmetrics

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A series of fire experiments were carried out in a wind tunnel at the United States Forest Service's Fire Science Laboratory in Missoula, Montana. The experiments involved tines cut out of pieces of cardboard. The pieces were laid out in comb‐like strips parallel to each other along a testbed. They were ignited at the windward end of the testbed. The progress of the fire was monitored by thermocouples, recording temperature, set out equidistantly up the middle of the testbed. Goals of the experiment included improved understanding of wildfire spread and the development of practical tools for wild land fire managers to employ. There was to be a search for regular pulsing in the series and any other interesting phenomena. This paper presents the results of a variety of exploratory data analyses meant to elicit information concerning the series before commencing probability modeling. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

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Random Process Methods and Environmental Data: The 1996 Hunter Lecture

Brillinger

1997

Environmetrics

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An Application of Statistics to Meteorology: Estimation of Motion

Cited by 5 publications

References 21 publications

Spatio‐temporal propagation of wind power prediction errors

Spatio‐temporal propagation of wind power prediction errors

An exploratory data analysis of the temperature fluctuations in a spreading fire

Random Process Methods and Environmental Data: The 1996 Hunter Lecture

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