In the field of irrigation, drainage and reclamation engineering, we quite often need spacial information such as soil moisture, bearing force, percolation rate, and ups and down of field. However, so far a few reasonable methods for estimating such informations have been established.
In this paper, first of all, we have made a proposal for using the causal stochastic model having separable covariance function for the simulation of three dimensional terrain. And we found that the simulated spacial series had also statistical characteristics such as average, variance and autocorrelation which were equal to those of the original series.
Furthermore, using this simulation model, its peripheral model and its improved version, we estimated the residual water of several types of land classified according to their use (paddy fields, grounds, and reclaimed lands) and its fixed value when the slope of the lands are changed.

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Various formulas for rainfall energy, a basic element for analysis of soil erosion, have been proposed so far. They are, however, empirical formulas derived from the actual measurements. No report studied on the theoretical basis has been found as yet.
The authors examined the studies reported so far and indicated that an exponential formula is more adequate than a logarithmic formula such as Wischmeiers et al's formula for calculation of rainfall energy.
From the result of theoretical analysis using a concept of space drop concentration, the following exponential formula was obtained:
KE=10.7 I^0.22
where unit of KE=J/m².mm and that of r=mm/h.
The validity of the formula was proved by the data of 365 raindrops sampled in Ube in 1983.

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The equation, h=kq^p, is generally used in the kinematic runoff model to express the relation between depth, h, and discharge, q, of a two-dimensional overland flow. In this equation, exponent p is believed to be governed by a state of flow such as p=1/3 for laminar flow and p=3/5 for turbulent flow.
This paper points out that the two-dimensional overland flow is a hypothetical flow transformed by the modeling of a slope in which rainwater flows along rills, and that the value of p is then changed inevitably beyond recognition.
First, the sectional characteristics of a rill are investigated in detail in a field plot over a natural slope. Next, how the depth-discharge relation changes is examined by transforming a shallow flow of laminar or turbulent state along a rill over a slope surface into the imaginal sheet plane flow over the full-width of the rill or the whole-width of the slope surface under a given rate of rainfall.
As a result, it was disclosed that the value of p changes outwardly to 0.40-0.53 for a laminar flow and to 0.67-0.75 for a turbulent flow, and that we may assume p=0.5-0.7=0.6 from a practical engineering view point.

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In relation to the water pollution of the Kasumigaura lake, the water quality and nutrient load of rivers in the lake basin have been investigated. However those investigations did not reveal the water quality and nutrient loads in case of flood runoff, and the problem remained untouched whenever the total nutrient load flowing into the Kasumigaura lake was estimated. Therefore, the water quality and nutrient load of flood runoff have been investigated for three years in the Hanasashi stream which is a small river in agricultural area.
1) When the discharge becomes large, the concentrations of SS, COD and T-P are higher, where as, that of NO₃-N is often low (Figs. 3-6).
2) When the concentration increases with the discharge, usually the peak time of the concentration comes earlier than that of the discharge.
3) In the relation between the discharge and the concentrations, hysteresis is observed. With the decreasing discharge, the concentrations of SS, COD, and T-P become lower as compared with the same dischage value when the discharge is increasing.
4) Hysteresis is also observed in the relation between the discharge and the loads of the nutrients. The loads of SS, COD, and T-P become lower when discharge is decreasing than when it is increasing.
The load of T-N has the inverse tendency (Fig. 14).
5) The loads in period of rainfall are heavily influenced not only by rainfall and discharge but also by the rainless days before the rainfall and manuring period. The loads of SS and COD depend heavily on the rainless days and that of N and P on the manuring period (Table 4).
6) The mean concentration of direct runoff water C_D is usually higher than the concentration of base flow water, C_B. Especially the concentration ratio, f_c of phosphorus is large, hence the load of P flows remarkably during the period of rainfall (Fig. 19).

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In the previous report individual direct runoffs have been considerd, and in this report the annual variation and total amount of pollutant and nutrients loads have been mentioned. Speaking about eutrophication in lake and pond, the annual amount of load is greater problem than individual runoff. Similar to the previous report, the investigation was carried out in a small agricultural stream, Hanasashi river, and the report is as follows.
1) In respect to the degree of the concentration increase during the period of rainfall, SS and T-P have large values, and T-N not so much. However, in May, during the manuring period, high concentration of T-N is detected (Fig. 2).
2) The specific load is significantly influenced by the discharge. That of N and P have high values in middle ten days of May, during the initial manuring period (Fig. 3). The base flow per day-l_B1 of NO₃-N increases from autumn to winter.
3) The annual total loads-l_T are sriiall, 0.16t/km² in T-N and 0.028 t/km² in T-P, and the loads flowing from agricultural area which has no large point sources are recognized as small (Table 1).
4) The ratios of the annual load of direct runoff l_D to the total load l_T are 79% in SS, 72% in COD, 68% in T-N and 81% in T-P which is the highest. On the other hand, the ratio of annual dischage of direct runoff q_D to the total discharge is 55%, and therefore, discharge has to be taken into consideration (Table 1 and Fig. 5).
5) The ratios of particulate component to the annual total load are 47% in COD, 31% in T-N, and 82% in T-P which is remarkably high (Fig. 4 and 7).

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Novel approximate solutions for the soil water movement during evaporation have been derived by using the characteristics of matric flux potential φ(= ∫Ddθ, D: diffusivity, θ: water content). Under the semi-infinite soil condition, with gravity neglected, the variation of φ during evaporation was approximated in the form of the equation:
φ(x, t) =φ₀ (t) + [φi-φ0 (t)] tanh (ax/√t), where x is depth, t is time, φ₀ and φi are values of φ at x=0 and t=0 respectively. The constant a, and the time function φ₀(_t), could be determined using the “water balance equation” at the evaporating surface. With some limitations, the results compared favorably with the finite-difference solutions especially when D was described as the exponential function of θ. Furthermore, several relationships among the state variables (drying rate, water flux in soil, etc.) were derived using these solutions.

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The effects of differences in drying levels, kinds of soils and concentrations of solution for saturation on the leaching characteristics of soils were studied experimentally using soil columns. Q-C curves representing the relation between volume and concentration of the effluent showed the existence of curves of three types based on the difference in drying level. These types were discussed by the effluent with a constant concentration, and concentration and volume of the effluent and elapsed time at the peak. The other characteristics were determined by the relation between volume of effluent and discharge percentage of salt from the column and water content distribution and concentration of exracted soil solution at the end of the leaching. As a result of discussion, it was recognized that these factors affected the leaching characteristics of soils. Moreover, It was considered that this work would be useful for developing an efficient water control method and improving the desalinization method.

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Authors developed some contrast media for researching the spatial continuity of void in the soils. The continuous void images were photographed by soft X-ray projection after the contrast medium infiltrated in the soils.
The developed contrast media were the following heavy liquids:
Diiodomethane (C medium), Tribromomethane (D medium) and 1, 1, 2, 2-Tetrabromoethane (Emedium).
C and E medium were preferable to D medium (Photo. 1).
In X-ray images, fine pores diameters up to 25μm size could be observed.
The way of photographing X-ray images after infiltration of the heavy liquid in objective was named the “Heavy Liquid Infiltration method”.
The sample soils were the volcanic ash soil from the foot of Mt. Iwate. Pores formed by plant roots were obvious in void images on grass land root zone soil photographed by H. L. I. method. In unplowed sub-soil layer too, the forms of root system remained in detail as micropores. Therefore, the pores formed by plant roots were not only macropores but also micropores (Photos 2-6).
The size of the root bodies found in the sample soils were about 100μm or more in diameter and their total volume was about 10% or less for the volume of noncapillary pores (φ>100μm) in the sample. Therefore, it was evident that the fine funicular images are almost empty capillary pores. So the authors called them the “root formed pores” and presumed that the most fine pores were formed by the root hairs having a size of about 10μm in diameter (Photos 7-9).
The considerations on the root formed pores were as follows;
(1) The capillary net shape of root formed pores is consisted of connectivity between some root systems.
(2) Root formed poresh ave tbe function of percolation and moistu reretention. The energy of retention will reach pF 2.5 (equivalellt diameter is about 10μm).

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The authors proposed the “Coefficient of structural development (C_sd) ” as the index to evaluate numerically the structural development of clayey soils in the previous papers. In this paper, the significance of C_sd from a viewpoint of soil physical properties was investigated for thiry-five clayey soils in which eighteen were nonvolcanic ash soils and seventeen volcanic ash soils. The relations between the soil structural development and factors such as clay content, humus content etc were investigated, and the methods to improve soil structure were discussed. Results obtained are summarized as follows.
1) C_sd showed positive correlations (significant at 0.01 or 0.05 level) with saturated hydraulic conductivity, water content under pF 3, gravitational water content (under pF 1.8) and available water content (pF 1.8-3).(Figs. 1-3, Table 2)
2) On the basis of desirable soil physical conditions for upland field, the following relations betweenC_sd values and the degree of soil structural development were obtained: for C_sd value <1. 5, ill-developed: for C_sd value 1.5-1.8, normal; and for C_sd value >1. 8, well-developed.(Figs. 1-4)
3) A positive proportional relation between C_sd value and structural pore volume was recognized.(Fig. 5)
4) Clay content showed a negative correlation with structural pore volume, and especially, the structure of nonvolcanic ash soils with clay contens above 40% was ill-developed.(Fig. 6)
5) Humus contens showed a positive correlation with structural pore volume, and the humus content required to contribute positively to structural development was above 7%.(Fig. 7)
6) Saturation degree at pF 1.8 showed a negative correlation with structural pore volume, this means that the drying-wetting process is important for the structural development.(Table 3)
7) Two kinds of soils with ill-developed structure were recognized, and drainage improvement, subsoil improvement, soil softening, addition of organic materials (compost and green manure). and so on were discussed as the methods for improving the soil structure.(Table 4 and 5)

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Experimental and theoretical investigations were made to determine the obtainable accuracy degree of the evaporation amount estimated by the application of the energy balance method to the farm land having a limited and complex space like the most cases in Japan. To put it simply, a method for examining the degree of coincidence between measured soil temperature soil profiles and computed ones was obtained from the solution of Eq.(13) based on its boundary condition Eq.(12) containing an energy balance term (latent heat flux) related to the estimated evaporation.
Prior carrying out above calculations, the problems contained within the terms of the energy balance were made clear to a certain degree. Especially thermal diffusivity of the soil thermal properties was evaluated as accurately as possible. In this case, since the Eq.(20), the solution of the differential equation of conduction of heat contained the thermal diffusivity only and not any other soil thermal properties, it became possible to search for optimum thermal diffusivity where good coincidence existed between the measured soil temperature profiles and the computed ones provided that the rough values of thermal diffusivity could be evaluated from the relations between the thermal diffusivity and soil moisture content obtained from an indoor experiment.
The main results obtained are summarized as follows.
The estimated amount of evaporation is influenced mainly by the soil moisture content in the surface stratum. Namely, it is shown that in cases of high moisture content of the soil, appropriate values of evaporation can be estimated provided that, in Eq.(6), air temperature θ_a1 and water vapor pressure P_w1 are chosen down on the field surface, and the saturation values are adopted as vapor pressure P_w1. But in cases of rather dry, low moisture content of the soil, the saturation vapor pressures on the surface should be multiplied by the correction factor less than one.

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The operation of discharge and the delay of response in the open channel irrigation system were discussed with mathematical analyses and computer simulations. The analytical treatments were made based on the theories of the infinitesimal wave and the monoclinical rising wave.
It was clarified that the obtained parameter α as the results of the analyses was an effective factor to describe the response of operation, and a was denoted
α=√W₀x/4μ₀=√W₀²t/4μ₀in which
μ₀= (hV) _e/2i,
x; distance, t; time, W₀; velocity of hydraulic bore, (hV)_e; discharge per unit breadth of channel at the final stage of response, and i; bottom slope. Also, the phenomena of response in the operations were transferred to down stream as dynamic wave, dynamic-kinematic wave and kinematic wave for α<<1 α=1 and α>>1, respectively.

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For the purpose of the water-use and flood control, a number of discharge-measuring-stations are set on the comparatively wide river basin. It seems that the records of the discharge obtained from these observatories are not all accurate. But these records have not so far been verified for their accuracy and have not been adjusted in relation to each other.
Lagrange's Method of Undeterminate Coefficient, which was used to obtain the most probable values from conditional observations, was applied to estimate more accurate values of river discharge. As this method can not be used for unsteady flow when the objective basin is comparatively wide, the method should be applied to comparatively long term average discharge. It was found that there was need to give 1/M (M: observation) as weight of each of the observatories.
As far as the result of applications to average yearly discharge and five days mean discharge of S River is concerned, although small error rates were found in case of application to yearly average discharge but large error rates were recognized on some observatories for the case of five days mean discharge application. In these observatories, significant correlation between discharge and error rate was recognized, and error rates which were small in the range of middle discharge, were large in the ranges of small and large discharges. Hence it seemed that error rates were small in case of application to yearly average discharge. It was concluded that discharge errors were caused by the inaccuracy of H-Q Curve.
Consequently, it was found that this method could be effectively used to verify the accuracy of discharge records and to estimate more accurate values of river discharge when H-Q Curve accuracy was doubtful.

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The phenomenon of the hydraulic jump has been well known as an efficient method to dissipate the energy of high velocity flow and has been widely studied for a long time. However, as almost all Japanese rivers are very steep, particularly at points where dams are constructed, and cannot keep a reasonable tail-water depth to contain the free jump, it is usual to provide stilling basins with appurtenances such as chute blocks, sills and baffle piers to produce such tail-water depth. But, these appurtenances are very susceptible to serious damage under high velocity flow.
This study investigates the possibility of controlling the hydraulic jump by an abrupt-rise-and-leveledreverse jet (Fig. 1) where in this jet system is suggested for the prevention of cavitation of appurtenances used widely in energy dissipators, for the reduction of stilling basins construction, for an increased effect of energy dissipators, and for the effective utilization of spillways.
The results of this study can be summarized as follows
1. It is possible to form a hydraulic jump on a horizontal floor in a stilling basin so that the ratio of the tail-water depth to initial-flow depth (ψ) decreases as the leveled-reverse jet-flow parameter increases. The analytical depth ratio computed from Eq.(6) agrees closely with the experimental depth ratio to the extent of 0 to 70% of the β_L (Fig. 10).
2. The energy dissipation agrees closely with the analytical result computed from Eq.(20) to the extent of 0 to 70% of the β_L, the same as ψ(Fig. 11)
3. The analytical value (β_L) obtained by the boundary condition of Eq.(13)' agrees fairly closely with the experimental reverse jet-flow parameter (β_Lexp) (Fig. 12).
4. The height of the abrupt rise decreases as the reverse jet-flow parameter increases for a constant δ and F_r1. A reduction of stilling basins construction is possible (Fig. 15).
5. When the Froude number of the initial flow increases for a constant α and β, the hydraulic jump forms as the aperture parameter of the reverse jets (δ) increases (Fig. 16). The more the β value increases, the more remarkable the effect of this parameter will be.
This paper presents the results of an analytical and experimental study of the control of the hydraulic jump by an abrupt-rise-and-leveled-reverse jet instead of chute blocks and baffle piers. It can be concluded that this jet system is an effective method to control the hydraulic jump. Further study of this system is needed under different conditions.

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