From AMS Glossary
As used by C. W. Thornthwaite in his 1948 climatic classification, an index of the degree of water surplus over water need at any given station. It is calculated, independent of the opposing aridity index, as follows:
where s (the water surplus) is the sum of the monthly differences between precipitation and potential evapotranspiration for those months when the normal precipitation exceeds the latter, and n (the water need) is the sum of monthly potential evapotranspiration for those months of surplus.
The humidity index has two uses in Thornthwaite's classification: 1) as a component of the moisture index; and 2) as a basis for detailed classification of dry climates.
Thornthwaite, C. W. 1948. An approach toward a rational classification of climate. Geogr. Rev.. 38. 55–94.