Rainfall in Forest

Abstract

The amount of the precipition in forest and stem flow have been measured many times in the past but theoretical considerations of the relations between the amount of rainfall and the precipitation in forest or the stem flow seems to be lacking. The author tries to treat the problem theoretically and deduces some formulae.
The author first makes clear the idea of the precipitaiton in forest. i. e he distinguishes between the part of precipitation that reaches the ground directly (including the drops of rain which touch the forest canopy but not caught by it and fall to the ground at once, probably splitting) and the other part which is caught by the leaves or twigs and then drips from them when their water retaining capacity exceeds a certain limit. He denotes the former by (1-α)r_e, r_e being the rainfall intensity and αr_e its fraction caught by the crown, and the latter by β(φ-φ₀), φ being the amount of water retained by the crown, φ₀ its threshold value for dripping, and β a proportional factor. He further denotes the stem flow by β'(φ-φ₀'), where φ₀ is a threshold value for stem flow and β' is another proportional facor. He then obtains the following equation for the time variation of the amount of water retained by the crown:
(1)
where γφ is the amount of evaporation assumed to be proportional to φ. Assuming α, β, β', γ, φ₀ and φ₀' are all constants, the equation gives a solution
There are many experimental results of the precipitation in forest in which stem flow was not measured simultaneously, so it may be of value to duduce a formula for the total amount of precipitation that reaches the ground directly plus the total amount of dripping (=R_i'=R_i-S). This can be obtained at once from (16) and (18) as follows:
(19)
To see the behavier of the relations (16), (18) and (19) we can use the following approximations. If we assume R_e is large or amall (and nearly equal to r_et₁), we can ezpand the second term on the right side of these equations and adopt the first two terms respectively. Then we have,
The form of curves which are expected from these equations are shown in Figs. 3_??_7.
Comparison with experiments may be done in many ways. Here the agreement of the equation (19) with the equation (24) was tested. αa₃ and b₃ in equation (24) were obtained from Japanese pecipitation measurements, where appropriate values were selected for α, φ₀, t₁ and β'/β. The agreement is good as is seen from Figs. 8 and 9. A similar comparison of (18) with the stem flow measurements by Kittredge, Laughead and Mazurak was done and was also found to be in good agreement as is seen in Figs. 12 and 13.
There are, however, some uncertainties in the order of magntude of each constant, which will be the subject of a future article.