Difference between revisions of "Sigma-theta"

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<div class="definition"><div class="short_definition">(Used in [[physical oceanography]], symbol ''&#x003c3;<sub>&#x003b8;</sub>''.) The [[density]] ''&#x003c1;'' (<1000 kg m<sup>&minus;3</sup>) that a [[parcel]] of water of [[salinity]] ''S''  and [[temperature]] ''T'' would have if it were raised [[adiabatic process|adiabatically]] to the sea surface, where its [[temperature]]  would change from ''T'' to [[potential temperature]] ''&#x003b8;'' due to [[adiabatic]] decompression. In symbols,</div><br/> <div class="paragraph"><div class="display-formula"><blockquote>[[File:sigma-theta-ocean.gif|link=|center|sigma-theta-ocean]]</blockquote></div></div><br/></div>
 
<div class="definition"><div class="short_definition">(Used in [[physical oceanography]], symbol ''&#x003c3;<sub>&#x003b8;</sub>''.) The [[density]] ''&#x003c1;'' (<1000 kg m<sup>&minus;3</sup>) that a [[parcel]] of water of [[salinity]] ''S''  and [[temperature]] ''T'' would have if it were raised [[adiabatic process|adiabatically]] to the sea surface, where its [[temperature]]  would change from ''T'' to [[potential temperature]] ''&#x003b8;'' due to [[adiabatic]] decompression. In symbols,</div><br/> <div class="paragraph"><div class="display-formula"><blockquote>[[File:sigma-theta-ocean.gif|link=|center|sigma-theta-ocean]]</blockquote></div></div><br/></div>
  
<div class="definition"><div class="short_definition">(Used in [[meteorology]], symbol ''&#x003b8;<sub>&#x003c3;</sub>''.) The [[standard deviation]] of horizontal [[wind direction]] used primarily in [[air pollution]] applications. Sigma-theta can either be computed directly from measured wind direction or with the Yamartino method. Sigma-theta is used as a proxy to characterize the [[dispersion]] capabilities of the lower [[troposphere]] in the Pasquill-Gifford categories. The Yarmartino method is given by:<br/> <div class="paragraph"><div class="display-formula"><blockquote>[[File:sigma-theta-atmos.gif|link=|center|sigma-theta-atmos]]</blockquote></div></div><br/></div>
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<div class="definition"><div class="short_definition">(Used in [[meteorology]], symbol ''&#x003c3;<sub>&#x003b8;</sub>''.) The [[standard deviation]] of horizontal [[wind direction]] used primarily in [[air pollution]] applications. Sigma-theta can either be computed directly from measured wind direction or with the Yamartino method (Yamartino 1984). Sigma-theta is used as a proxy to characterize the [[dispersion]] capabilities of the lower [[troposphere]] with different [[stability categories]]. The Yamartino method is given by:<br/> <div class="paragraph"><div class="display-formula"><blockquote>[[File:sigma-theta-atmos.gif|link=|center|sigma-theta-atmos]]</blockquote></div></div><br/></div>
  
 
<div class="definition"><div class="short_definition">where ''s<sub>a</sub>'' = (1/''n'')&#x3A3;<sub>''i''</sub>sin''&#x003b8;<sub>i</sub>'' and ''c<sub>a</sub>'' = (1/''n'')&#x3A3;<sub>''i''</sub>cos''&#x003b8;<sub>i</sub>'' are computed from a sequence of ''n'' wind angle (''&#x003b8;<sub>i</sub>'') measurements.</div></div><br/>
 
<div class="definition"><div class="short_definition">where ''s<sub>a</sub>'' = (1/''n'')&#x3A3;<sub>''i''</sub>sin''&#x003b8;<sub>i</sub>'' and ''c<sub>a</sub>'' = (1/''n'')&#x3A3;<sub>''i''</sub>cos''&#x003b8;<sub>i</sub>'' are computed from a sequence of ''n'' wind angle (''&#x003b8;<sub>i</sub>'') measurements.</div></div><br/>
  
<p>''Term edited 9 April 2018.''</p>
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<p>Yamartino, R. J., 1984: A comparison of several "single-pass" estimators of the standard deviation of wind direction. ''J. Climate Appl. Meteor.'', '''23''', 1362&ndash;1366, <nowiki>https://doi.org/10.1175/1520-0450(1984)023<1362:ACOSPE>2.0.CO;2</nowiki>.</p><br/>
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<p>''Term edited 16 May 2018.''</p>
  
 
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Latest revision as of 08:36, 22 June 2018



sigma-theta

(Used in physical oceanography, symbol σθ.) The density ρ (<1000 kg m−3) that a parcel of water of salinity S and temperature T would have if it were raised adiabatically to the sea surface, where its temperature would change from T to potential temperature θ due to adiabatic decompression. In symbols,

sigma-theta-ocean

(Used in meteorology, symbol σθ.) The standard deviation of horizontal wind direction used primarily in air pollution applications. Sigma-theta can either be computed directly from measured wind direction or with the Yamartino method (Yamartino 1984). Sigma-theta is used as a proxy to characterize the dispersion capabilities of the lower troposphere with different stability categories. The Yamartino method is given by:
sigma-theta-atmos

where sa = (1/nisinθi and ca = (1/nicosθi are computed from a sequence of n wind angle (θi) measurements.

Yamartino, R. J., 1984: A comparison of several "single-pass" estimators of the standard deviation of wind direction. J. Climate Appl. Meteor., 23, 1362–1366, https://doi.org/10.1175/1520-0450(1984)023<1362:ACOSPE>2.0.CO;2.


Term edited 16 May 2018.