Several models are based on the climate classification scheme developed by C.W. Thornthwaite and J.R. Mather (Thornthwaite 1948; Thornthwaite and Mather 1955). The first quantity required is an annual heat index (HI), which is the sum of the 12 monthly values of I:

(1) I = (MMT/5)1.514

The heat index is next used to calculate a coefficient, a, by the following formula:

(2) a = 6.75x10-7HI3-7.71x10-5HI 2+1.792x10-2HI +4.9239x10-1

Annual potential evapotranspiration (APE) can then be estimated by summing the twelve monthly PE values:

(3) PE = 1.6((10*MMT)/HI)a

With the annual potential evapotranspiration (APE) and mean annual precipitation (MAP) values, a moisture index (MI) can then be calculated (Mather and Yoshioka 1968):

- MI = 100((MAP/APE)-1)

Note that this applies to steady state conditions in which there are no net changes in soil moisture storage from year to year. Negative values represent dry conditions (water demand exceeds supply), positive values represent wet conditions (water demand is less than supply). A value of zero means that water demand equals supply.

Actual evapotranspiration (AE) is limited by precipitation (P) and soil moisture storage (STOR). If PE is less than the sum of P and STOR, then AE is equal to PE, otherwise AE is equal to the sum of P and STOR. The monthly moisture deficit (DEF) is the difference beween PE and AE. There is no deficit (DEF = 0) if AE and PE are equal.

Annual actual evapotranspiration (AAE) is equal to the sum of the twelve monthly AE values. Annual moisture deficit (ADEF) is equal to the sum of the twelve monthly DEF values.

Thornthwaite (1948) developed an elaborate climate classification scheme based on water and energy balances. Four indices are required to run classify climates according to Thornthwaite’s method: a moisture index (an aridity index (ARID); a humidity index (HUMID); and a summer concentration of thermal efficiency (THERM). If DEF > 0, ARID is calculated by the following:

(5) ARID = (100*ADEF)/APE

otherwise ARID = 0. HUMID can then be calculated by:

(6) HUMID = MI + ARID

(7) THERM = MI + ARID

The climate type is determined based on the Thornthwaite (1948) MI:

Climate type |
MI range |

Perhumid (A) Humid (B4) Humid (B3) Humid (B2) Humid (B1) Moist subhumid (C2) Dry subhumid (C1) Semiarid (D) Arid (E) |
100 and above 80 to 100 60 to 80 40 to 60 20 to 40 0 to 20 -20 to 0 -40 to -20 -60 to -40 |

The seasonal moisture regime is determined from the Thornthwaite (1948) ARID and HUMID indices:

Moist climates (A, B, C2) |
ARID range |

r -- little or no water deficiency s -- moderate summer water deficiency w -- moderate winter water deficiency s2 -- large summer water deficiency w2 -- large winter water deficiency |
0-16.7 16.7-33.3 16.7-33.3 33.3 and up 33.3 and up |

Dry climates (C2, D, E) |
HUMID range |

r -- little or no water surplus s -- moderate summer water surplus w -- moderate winter water surplus s2 -- large summer water surplus w2 -- large winter water surplus |
0-10 10-20 10-20 20 and up 20 and up |

Thornthwaite (1948) then classifies climates according to thermal efficiency:

Thermal efficiency type |
APE range |

Megathermal (A’) Mesothermal (B’4) Mesothermal (B’3) Mesothermal (B’2) Mesothermal (B’1) Microthermal (C’2) Microthermal (C’1) Tundra (D’) Frost (E’) |
1140 and up 997-1140 855-997 71.2-855 57.0-71.2 42.7-57.0 28.5-42.7 14.2-28.5 0-14.2 |

The final parameter in a Thornthwaite (1948) climate classification scheme is the summer concentration of thermal efficiency (SCTE). SCTE (in percent) is estimated by:

(8) SCTE = 157.76 - (66.44 * log(APE))

Summer concentration type |
SCTE (percent) |

a’ b’4 b’3 b’2 b’1 c’2 c’1 d’ |
88.0 and up 48.0-51.9 51.9-56.3 56.3-61.6 61.6-68.0 68.0-76.3 76.3-88.0 88.0 and up |

Copyright © 2003-2011, David M. Lawrence

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