Abstract
1. Theoretical analyses on the formation of perennial snow patches in Japanese untains based on heat and mass balances are made in this article. Mass balance of a glacier and/or a perennial snow patch is illustrated in Fig. 1. In the upper reach of a glacier, the amount of snow fall exceeds the ablation. The glacier developes in this part. The position on a glacier where the amount of annual ablation (A) equals to annual snow fall (F0) is defined as “equilibrium line”. Mass balance at this line is expressed by the following equation, in which the amounts are reduced to water equivalent.
A=F0
In the lower half of a glacier, ablation exceeds the snow fall. In this part of a glacier or at the lower limit of perennial snow patch, the mass balance equation takes the following form by introducing lateral supply of snow or ice such as glacial flow, ava-lanche and wind drift (F1).
A=F0
+F1 This is the basic equation for the analysis of this report.
The amount of ablation is calculated by heat balance at the snow surface, but more simple method is desired for the general solution of the problem. This is made by use of degree-day factor (f or _??_), then the amount of annual ablation is represented by the following form.
A=Σf•Θa=n•_??_•_??_a
In this, n is the number of days in the ablation period (Θa>0), _??_ is the mean degree-day factor for the period and _??_a represents the mean air temperature during the period. The balance equation for the terminus of perennial snow patch is expressed by Eq. 7, where n* denotes the number of months in the ablation period (n*=30n).
F0
+F1=n•_??_•_??_a
2. The physical meaning of degree-day factor is represented by Eq. 3.
f=_??_•_??_ (Eq.3)
In this equation, Rn is the net-radiation on snow surface, H and LE denote sensible and latent heat exchanges. Each term in the equation is estimated by the followings.
Rn=(1-a)I-R
H=h•Θa
LE=1.5h (ea-6.11)
Albedo for the snow surface (a) is assumed to be 0.45 and the heat transfer coefficient (h) is 15.6cal/cm•day•°C. I denotes the incoming solar radiation and R is the effective outgoing long wave radiation.
Observed values of _??_ are listed in Table 1, in which it is shown that the value lies between 0.4 and 0.5cm/day•°C (water equivalent) in low altitude. The factor varies . with the direction and gradient of slope and altitude, and may also vary with latitude. Numerical values of f and _??_ calculated by heat balance method at ψ=36°N (representing main island of Japan : Honshu) and at ψ=43°N(Hokkaido) are shown in Table 3. The calculations were made for horizontal plane and slopes of twenty degrees. The incoming solar radiation on slopes was calculated by Eqs. 9, 10, 11 and 12. The ratio of solar radiation on slope to that on horizontal plane (m=∫sin h' •dt/∫sin h•dt) is shown in Fig. 2. From the results of the above calculations, it may be concluded that the numerical value off for Honshu is between 0.4 and 0.5cm/day. C, and that for Hokkaido is 0.5 and 0.6 cm/day. °C.
Writing f by use of the Bowen ratio (B),
f=_??_°_??_(Eq 11)
it is assumed that the factor varies depending on the value of (Rn/Θa), because the Bowen ratio for the ablation period does not change greatly with the altitude (Fig. 3).
