## Description

Used in Aspen through V3.4.4 (May 2020), later replaced with simpler version.

The potential temperature $$\Theta$$ (K) calculated from temperature $$t$$ (K) and pressure $$p$$ (mb). A Taylor series expansion about the midpoint of the pressure range is used for pressures greater than 125 mb.

## Formula

$$u = \frac {1000} {p} \\$$ $$\delta = \left\{ \begin{array} {lr} \delta = 0, & \text{for } p \le 125 \\ \delta = u - \frac{1000} {175}, & \text{for } 125 \lt p \le 250 \\ \delta = u - \frac{1000}{350}, & \text{for } 250 \lt p \le 500 \\ \delta = u - \frac{1000}{700}, & \text{for } 500 \lt p \\ \end{array} \right\}\\$$ $$\Theta = \left\{ \begin{array} {lr} \\ t u^{0.28537338} , & \text{for } p \le 125 \\ t (1.64443524 + 0.08212365 \delta - 0.00513518 {\delta}^2 + 0.00051362 {\delta}^3 \\ \quad - 0.00006100 {\delta}^4 + 0.00000793 {\delta}^5 - 0.00000109 {\delta}^6), & \text{for } 125 \lt p \le 250 \\ t (1.34930719 + 0.13476972 \delta - 0.01685425 {\delta}^2 + 0.00337152 {\delta}^3 \\ \quad - 0.00080084 {\delta}^4 + 0.00020824 {\delta}^5 - 0.00005727 {\delta}^6), & \text{for } 250 \lt p \le 500 \\ t (1.10714599 + 0.22116497 \delta - 0.05531763 {\delta}^2 + 0.02213146 {\delta}^3 \\ \quad - 0.01051376 {\delta}^4 + 0.00546766 {\delta}^5 - 0.00300743 {\delta}^6), & \text{for } 500 \lt p \\ \end{array} \right\}$$

## Source

The Aspen source file (MetFormulas.cpp) says that this comes from PAM II Derived Parameters. However, this Taylor series approach is not described in the 1985 document, and so it must have been a later addition in Herzegh (18 March 1988).

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