# Sigma-theta

From AMS Glossary

## sigma-theta

(Used in physical oceanography, symbol

*σ*.) The density_{θ}*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,(Used in meteorology, symbol

*σ*.) 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:_{θ}where

*s*= (1/_{a}*n*)Σ_{i}sin*θ*and_{i}*c*= (1/_{a}*n*)Σ_{i}cos*θ*are computed from a sequence of_{i}*n*wind angle (*θ*) measurements._{i}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.*