Equivalent Potential Temperature Theta E Calculator
Calculate equivalent potential temperature theta with our free science calculator. Uses standard scientific formulas with unit conversions and
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
theta_e = theta * exp((3.376/T_LCL - 0.00254) * w * (1 + 0.00081*w))
Where theta is potential temperature in Kelvin, T_LCL is the LCL temperature in Kelvin, and w is mixing ratio in g/kg. Theta = T*(1000/P)^0.286. The exponential adds latent heat from condensation.
Worked Examples
Example 1: Tropical Maritime Air Mass
Problem:Calculate theta-e for tropical air at 30 C with dew point 26 C at 1010 hPa.
Solution:T=30C (303.15K), Td=26C es=42.43 hPa, e=33.61 hPa w=21.42 g/kg, theta=302.29K Bolton: theta-e = 358.7 K
Result:Theta-e: 358.7 K | Very Unstable
Example 2: Mid-Latitude Continental Air
Problem:Calculate theta-e for air at 20 C, dew point 10 C, at 950 hPa.
Solution:T=20C (293.15K), Td=10C e=12.27 hPa, w=8.13 g/kg theta=297.38K Bolton: theta-e = 321.5 K
Result:Theta-e: 321.5 K | Moderately Unstable
Frequently Asked Questions
What is equivalent potential temperature and why is it important?
Equivalent potential temperature (theta-e) is the temperature an air parcel would have if all its water vapor were condensed out and the latent heat released was used to warm the parcel, then brought adiabatically to 1000 hPa. It is conserved in both dry and moist adiabatic processes, making it extremely useful for tracking air masses. Meteorologists use theta-e to identify atmospheric instability, predict severe weather, and trace origins of moist air masses. Higher theta-e values indicate warmer and more humid air with greater convective potential energy.
How does theta-e differ from regular potential temperature?
Regular potential temperature only accounts for dry adiabatic lifting to 1000 hPa without considering moisture. Theta-e additionally includes latent heat released if all water vapor were condensed. For dry air they are essentially identical, but in moist tropical air the difference can exceed 20 to 30 Kelvin. Theta is conserved only in dry adiabatic processes while theta-e is conserved in both dry and saturated adiabatic processes. This makes theta-e a more complete thermodynamic variable for weather systems involving moisture.
How is theta-e used to assess severe weather potential?
Forecasters examine theta-e values and spatial distribution to identify regions favorable for severe thunderstorms and tornadoes. High theta-e at the surface above 340 K combined with lower values aloft indicate conditional instability and strong convective potential. Theta-e ridges often mark the warm sector of extratropical cyclones where severe weather is most likely. Sharp horizontal gradients frequently align with fronts and drylines. A rapid decrease of theta-e with height signals explosive convective development potential.
What role does the mixing ratio play in computing theta-e?
The mixing ratio quantifies mass of water vapor per unit mass of dry air in grams per kilogram. It directly determines how much latent heat is available for release during condensation, the key factor distinguishing theta-e from ordinary potential temperature. Higher mixing ratios produce higher theta-e for the same temperature and pressure. In tropical maritime air masses mixing ratios reach 18 to 22 g/kg adding 30 K or more to theta-e compared to dry conditions. Accurate dew point measurement is essential for computing mixing ratio and therefore theta-e.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy