Since the end of the nineteen-sixties, there has been some controversy concerning the matter of a decrease in the transmission coefficient of the atmosphere and its possible longrange effects on world climate. McCormic and Ludwig (1967) hypothesized that the effects of man's pollution of his environment were monotonically increasing along with the world population, whereas the increase in atmospheric turbidity due to volcanic eruptions might have temporary effects on world climate. According to their hypothesis, the time series curve of the transmission coefficient of the atmosphere must be interpreted as follows; the effects of volcanic eruptions are superimposed on a longer-term tsrend, a trend of decreasing transmission coefficient, which could have man-made pollution as its origin.
In this paper, the author reports the secular variation in the transmission coefficient of the atmosphere at Tosa-Shimi.zu, Japan (32°43'N, 133°01'E), by considering the influence of both these aerosol sources on the radiation measurements. The transmission coefficient of the atmosphere is calculated from surface observations of the total amount of direct solar radiation, which are made on a routine basis at 14 meteorological stations in Japan, including the Tosa-Shimizu Meteorological Station. The Tosa-Shimizu Meteorological Station has been in operation for 48 years since August 1932, and many of the days in each year were clear or partly cloudy. The population within a radius of 20 km around the station is the minimum of all, i, e. approximately 25 thousand, and it is remote from major local sources of pollution in Japan, such as Tokyo, Nagoya, Osaka, Kita-Kyushu, and so on. Therefore, this station is particularly suited for monitoring the solar radiation and for its application to estimate of secular variation in the transmission coefficient of the background atmosphere in Japan.
The number of data collected here reached 1, 627 despite missing data for two periods, i. e. from May 1945 to September 1946 and from July 1973 to February 1974. Fig. 4 shows the plot of the transmission coefficient of the atmosphere against time for the period of 35 year. There exists a discernible trend in the transmission coefficient for the period from 1945 to 1979 despite of the considerable scatter of data. The liner regression line was obtained by the least square method as follows;
A(t)=0.7445-1.822×10^-3(t-1945)
where t is time in year A. D., and A (t) the transmission coefficient in the year t. The transmission coefficient predicted by the formula above decreases from 0.744 in 1945 to 0. 681 in 1980, and the mean rate of its decrease is 0. 018 per decade. This trend is interpreted to have man-made pollution as its origin.
To estimate the periodic character of the departure of the transmission coefficient from the longer-term trend, a harmonic analysis has been carried out. The result of the analysis shows that the pattern of the departure is distinctly periodic with a predominant period of one year. The next most predominant period is six months. The power of the six months harmonic is only 17. 5 percent of that of the one year harmonic, and powers of the other harmonics are less than 4 percent. The range of the annual variation is 0.1289, which is approximately 71-fold compared with the annual decrease due to a longer-term trend. Such a pronounced annual variation must result from the Forbes effect, the annual variation in the amount of water vapor within a whole atmosphere, and the exchange of air masses between cold and hot seasons, but not from the influences of volcanic eruptions. Since volcanic aerosols injected through the tropopause into the stratosphere can remain there for several years, the explosive volcanic eruptions must result in the periodic variation in the transmission coefficient with relatively longer periods.

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The Sendai coastal Plain is located on the Pacific side of northeastern part of Honshu Island, extending about 50 km long from north to south and 10 km wide from east to west. In this paper, the author studied the structure of alluvial formations and depositional processes of the Sendai coastal plain based on the analysis of boringlogs, radiometric datings and field survey. A curve of sea-level changes during the Holocene was restored and the geographical changes of shorelines were considered for the last 10, 000 years.
The Holocene sea-level change in the Sendai region is summarized as follows. The rapid rise of sea-levels continued until 8, 000 yr BP and then rate of rising became slower. The sea-level reached nearly the present level at 4, 500 yr BP. Since then, it has been rather stable with slight fluctuations (Fig. 6).
The Sendai coastal plain is consisted of alluvial formations ca. 60 m in thickness which are clearly divided into two kind of sediments ; marine or terrestrial in origin (Fig. 5). Based on the boundary surface between these two sediments, the geographical changes of shorelines during the Holocene is restored as follows (Fig. 7).
(1) By the period when the sea-level reached about 30 m below the present one (ca. 9, 000 yr BP), the sea invaded landward and it passed the location just below the present shoreline in some places. This transgression continued until about 8, 000 yr BP.
(2) After the period when the sea-level reached about 10 m below the present one (ca. 8, 000 yr BP), the Sendai coastal plain stopped decreasing in extent and began to expand seaward by filling up the shallow sea with terrestrial sediments, although the sea-level was still rising (ca. 8, 000 yr BP-4, 500 yr BP).
(3) Following the former period, the shoreline continued to progress seaward intermittently and reached the present position for the period from 4, 500 yr BP to the present. The author emphasized that the period of the highest sea-level in the Holocene and that of the maximum areal extent of the sea did not coincide with each other in time. This time-gap is considered to depend on the conditions of the amount of loads supplied from nearby rivers. The beginning time of a seaward expansion of the coastal plain was earlier in the area supplied with larger amount of loads than in the area with smaller amount.

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The purpose of this paper is to test theoretically one of mathematical models for longitudinal river profiles and to evaluate it by a numerical simulation of terrace development of the Tama River. Significance of mathematical model describing the change of height with time in landform profiles developed by Hirano (1976),
U_t=aU_xx+bU_x
was tested with the view of clarifying flow rate of sediment,
J=(aU_x+bU) where U_xx is curvature, U_x gradient and U height of river bed. The first term of the equation expresses deposition and the second does erosion in the concave river profile. This second order differential equation is the same one that describes the diffusion process having drift.
The analogy of river profile development to diffusion process is basically justified either by the existence of Brownian motion of particles in the river system or by a presumption apriori that the flow rate of sediment is proportional to the gradient of river bed. But it is difficult to identify what is the drift under constraint in the river system, because the flow by the forced drift is opposite in direction of the gradient of river bed and the diffusion flow. Although this model has these weak points in physical basis, it has a big advantage that its steady solution;
U=C_lexp(-rx)+C₂ (r=b/a)
shows an exponential curve which is accepted empirically to be the most suitable one for the longitudinal river profile.
This dynamic model was applied to simulate the terrace development of the Tama River. The Tama River is originated from Kanto Mountains, enters the depositional hanto Plain and ends at Tokyo Bay. Its ca. 1000km² drainage basin is roughly estimated to discharge ca. 1.5×10^-4km³/yr of sediment. And well developed terraces has been studied so in detail that the area has been a type area of Japanese late Pleistocene and Holocene.
The values of coefficient a and b in the equation are estimated from the flow rate of sediment of present River in grade. A shape index r=b/a determines the shape of graded profile, and the flow rate gives a rate of asymptotic convergence to the graded form. The profile (Juen, 1965b) of the Musashino Terrace (60×10³ yr PP) was given as an initial value of simulation. The gradient at the upper boundary was given as a function of time. Another boundary condition was given by the sea level as a function of time. But it is assumed that the river mouth (the lower boundary) has been so conservative there in gradient that the position of the river mouth was floating horizontally in response both to the change of sea level and the profile itself (as a free boundary problem).
The results of simulation well represent the actual development of river profile, which is stated by the early Wi rm fill-strathing in the upper-most reach of the River, the latest Pleistocene over-flowing on the older surfaces in the upper-middle reach, the forming of valley-topography in the lower reach due to the maximum sea level lowering and of drowned valley-topography due to the postglacial sea level rising, and then river mouth advancing toward sea caused by fluvial accretion during the last seven thousand years.

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