The asymmetrical valleys of Eastern Hokkaido, Northern Japan, are discussed in this paper and it is concluded that they were formed by both periglacial mass-movements and fluvial processes under the permafrost environment of the Last Glacial age.
The Konsen Genya Plain of Eastern Hokkaido consists of hills, uplands, and fans com-posed of unconsolidated deposits (Fig. 1). The Kucharo and Mashu volcanoes are located to the west of the Konsen Genya Plain and have ejected great volumes of pumice, ash, and pyroclastic flows. The age of formation of some of the geomorphic surfaces in the region have been determined by tephrochronology using ¹⁴C dating (Fig. 2). In the Konsen Genya Plain, many streams flow almost parallel to each other in a west-east direction, forming shallow flat-bottomed valleys.
Asymmetrical valleys are distributed in various parts of the Konsen Genya Plain (Fig. 4). However, intense asymmetry of the valley slopes, with the steeper slopes oriented towards the north, is best developed on the Kamishunbetsu surface which is a fan composed of sand and gravel. Since the fan was formed between 30, 000 and 17, 000 years ago, the valleys dissecting the fan were formed during the Last Ice-Age.
The asymmetrical valleys in the study area of the Kamishunbetsu surface were mapped from aerial photographs (Fig. 6). Asymmetry was well developed in the Shunbetsu, Tokotan, and their tributary valleys (Fig. 7). The mean inclinations of the slopes in the asymmetrical valleys were estimated from maps (scale, 1:5, 000) and the maximum angles and transverse profiles were measured in the field by tape and Brunton pocket transits. The results obtained several variations in the asymmetrical features of the valleys from the head to the downstream region (Figs. 8, 9).
The asymmetrical features are less distinctive at the heads of the valleys, where both slopes are gentle but the north-facing slopes are slightly steeper than the others (e. g. Fig. 9, A-1). Asymmetry develops progressively towards downstream as the north-facing slopes gradually increase in angle and the south-facing slopes maintain constantly low angles. At a distance of 5_??_6km from the head, the valleys attain maximum asymmetry. The angles of the steeper north-facing slopes reach l5_??_20°, while the southfacing gentle slopes have uniform angles Isse than 7_??_8°. The cross profiles show a sharp contrast between the steep convex form of the north-facing slopes and the long smooth form of the south-facing gentle slopes. Downstream from the zone of maximum asymmetry, the gentle south-facing slopes increase in angle in response to downcutting and lateral erosion by the streams. Steep meander bluffs are produced on both slopes far down the valleys, so that a symmetrical valley form is established there. The apparent pattern of evolution of the valley profile thus suggests that the steep north-facing slopes are a direct result of the erosive action of the streams.
It has been assumed that the landscape of Eastern Hokkaido represents a “fossil” penglacial one. This idea has been supported by the finding of widespread evidences of fossil periglacial phenomena such as ice-wedge casts. The asymmetrical valleys were apparentry formed under the permafrost environment of the Last Glacial age since the slopes of the valleys are covered by Holocene tephra.
These facts indicate that the stronger erosion occuring at the foot of the north-facing slopes may have been related to microclimatic differences caused by the different attitudes of the two slopes. The microclimatic differences, such as in the intensity of insolation and the extent of snow-drifts driven by northwest winds, accentuated differences in the degree of development of solifiuction processes.

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Municipal and industrial water demands have increased with a rapid economic growth after the Second World War, giving rise to many water problems in our country today. This paper reports the procedures and results of a statistical analysis of residential water demand in Tachikawa City, by using cross-sectional data for the fiscal year of 1974. These data are obtained through a questionaire survey.
Tachikawa City is located to the west of Tokyo (Fig. 1), with an area of 24.2 km² and a population of about 135, 000 in 1975. Municipal water demand in the fiscal year of 1974 is about fifteen million cubic meters. About 39, 000 water-consumptive units (households, department stores, office buildings, etc.) are supplied by the Tachikawa Municipal Waterworks, and confined groundwater is the main water source (Fig. 2). In summer, some water is purchased from the Tokyo Municipal Waterworks because of the seasonal increase of water demand. Roughly 60 percent of the water that is provided by the Tachikawa Municipal Waterworks is used for residential purposes.
The basic demand function for residential water is defined as
RW=f (N, B, T, D, I, S, O)
where RW is residential water demand (m³•household^-1•year^-1), N the number of persons in a household, I income (million yen•household^-1•year^-1), others being dummy variables (Table 1). Three types of models are tested by means of a least squares multiple regression analysis.
_??_
where a₀, b₀, c₀ are constants and a_j, b_j, c_j (_j=1, 2, …, 7) are regression coefficients.
The results (Tables 5 and 6) are summarized as follows:
(1) The model C fits best among the three.
(2) The residential water demand is inelastic to household-size, though each model gives a little different elasticity of the number of persons in a household.
(3) The income does not seem to have any significant impact on residential water demand, because the income elasticities are estimated all around zero.
Recent urbanization with respect to the water demand is characterized by the increase of nuclear families and the spread of flush-toilet. To consider an influence of the urbanization on the residential water demand, averages of the residential water demand per household (_??_res) and of that per capita (_??_rpc) are compared: The spread of flush-toilet increases both _??_res and _??_rpc. The appearance of nuclear families decreases _??_res but increases _??_rpc. Unless the future urbanization changes the structure of residential waterdemand, _??_res and _??_rpc are estimated by Eq. (17) and (18) and are shown in Fig. 7.

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Drought problems are critical aspects of water resources conservation, development, and control at present. Continuous pressure on limited water resources will make drought problems much more serious in the future. Therefore, intensive and systematic investigations on drought problems are urgent and necessary. However, the definition of drought is a controversial subject. Since Yevjevich (1967) introduced the theory of runs as an objective definition of hydrologic drought, several theoretical and experimental studies of runs related to drought problems have been done. Among properties of run-length, runsum, and run-intensity defined in Fig. 1, the run-length has been most widely investigated because the run-length properties are free of underlying distribution of input processes. However, applications of these developed properties of runs are limited to univariate or bivariate stationary series. In this paper, some statistical properties of the runs for an independent nonstationary process (periodic-stochastic process) are studied on some simple but realistic assumptions (Eq. (4) through Eq. (8)). On the assumption of Eq. (7), the properties of deficit or negative run-lengths are free of the underlying distribution as in the case of stationary process. The properties of run-sums are considered with the corresponding variables of run-length and onset time of the run-length. Expected value, variance, conditional expected values, and conditional variances are found analytically. The theoretical values are compared with those of generated data.

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