The Oikamanai River is a main influent river of the Oikamanai Lagoon in the Tokachi coastal region of southeastern Hokkaido, Japan (Figure 1; [15] [16] ). The river catchment (42˚33'46'' to 42˚40'40''N, 143˚21'47'' to

143˚28'36''E; altitude, 6 m to 330 m asl) upstream of site R1 has the area of 62.6 km², the mean slope angle of 34.7˚ (gradient, 0.692) and the mean riverbed gradient of 0.033 (Figure 1). The distribution of slope angle corresponds to that of the surface geology (Figure 2); the upper, middle and lower regions with relatively steep slope in the northwest to southeast directions are occupied by sedimentary rocks of early to middle Miocene, middle to late Miocene and late Miocene to Pliocene, respectively, and the lowest region with relatively gentle slope just upstream of site R1 by alluvial flood deposits. The sedimentary rocks are composed of conglomerate, sandstone, mudstone, siltstone and tuff, of which the former two exhibit high permeability. The sedimentary rocks in the mountainous regions are accompanied by many faults, which are due to the orogenic movement of the Hidaka Range in Miocene to Pliocene, west of the river catchment. The northern faults are currently active, being adjacent to the Tokachi Median Tectonic Zone to north [17] . The faults tend to frequently produce landslides or collapse in the mountainous region (Tokachi Subprefecture HP; URL: http://www.tokachi.pref.hokkaido.lg.jp/sr/srs/gaiyou/sugata/sugata.htm) (Figure 2). The relatively young sedimentary rocks of Miocene to Pliocene with faults could also leak some groundwater to the other catchments or to the Pacific Ocean. Pyroclastic deposits, loam, sand and gravel in late Pleistocene are distributed along the border of flood plain (Figure 2) and in forest soils. Such porous deposits could make the seepage easy from the forest region to the flood plain.

The catchment upstream of site R1 is covered by 88.3% forest in the mountainous region, 10.6% farmland (mostly, grassland) on the lowest alluvial plain, etc. (Figure 1). The forest is composed of ca. 50% broad-lea- ved and ca. 50% coniferous (mainly, Sakhalin fir; Abies sachalinensis) trees.

River stage at site R1 was recorded at 30 min intervals by an air pressure logger and an air pressure-plus-water pressure logger with temperature sensors (HOBO U20, Onset Computer, Inc., USA; the range of 69 - 207 kPa and the accuracy of ±0.62 kPa for pressure, and the range of −20˚C to 50˚C and the accuracy of ±0.2˚C for temperature). The water pressure logger was set at near the deepest point in the cross-section of site R1 in Novem-

ber 2010. The water level, h (m), at site R1 was changed into river discharge, Q (m³/s), by the h-Q rating curve (Q = 11.72h^1.373, R² = 0.966, P < 0.01). The rating curve was obtained by frequent discharge measurements in April-November of 2011 and 2012 during the stage recording. River discharge was calculated by measuring the depth averaged velocity at about 20 sections partitioned in the cross-section and then summing the sectional discharge defined by the product of the sectional area. Then, the unchanged positions of the two loggers were ascertained by frequent surveys with three benchmarks. The Oikamanai River is frozen in December-March, when the h-Q rating curve is not applicable. Hence, the discharge obtained in the non-frozen season of April-November is applied for discussing the characteristics of discharge. For estimating water balance of the catchment, discharge and meteorological data in the rainfall season in the catchment of no snow cover are utilized, because the snow-covered period in April is very short (about two weeks).

Meteorological data were obtained at site M (altitude, 6 m asl; rainfall and air temperature) near the Oikamanai Lagoon [15] [16] at 4.0 km south-southeast of site R1, at site P (altitude, 142 m asl; rainfall and air temperature) near the water divide of the Oikamanai catchment, at site F (altitude, 34 m asl; air temperature, relative humidity and rainfall) (Figure 1), and at the Taiki Aerospace Research Field (altitude, 21 m asl; rainfall, air temperature, solar radiation, and wind velocity) 10.5 km south-southwest of site R1, and at Taiki town (altitude, 85 m asl; snow depth, rainfall, air temperature, and wind velocity) 18.9 km southwest of site R1. The distinction between rainfall and snowfall in the catchment was made by the air temperature of 0˚C at site M.

Dates for the start and end of snow cover within the catchment were suggested by using the RGB images of MODIS/Terra or MODIS/Aqua with the resolution of 500 m (URL: http://www.eorc.jaxa.jp/cgi-bin/adeos/modis_frame.cgi?year=2014&month=10&prov=eoc&type=500mchla) and snow depth data at Taiki town. Considering a topographic effect on the solar radiation, the DEM in Figure 1 was applied to know the slope angle and aspect of the basin. The elevation effect on rainfall was explored by using the rainfall data at site M, site F and site P, and analytical rainfall data of 1 km × 1 km mesh by the Japan Meteorological Agency. The mesh data are built up at 1 h intervals by coupling in situ rainfall with radar echo, and the mesh covers the main Japanese islands (Hokkaido, Honshu, Shikoku, Kyushu, etc.) (URL: http://www.jma.go.jp/jma/jma-eng/jma-center/nwp/outline2013-nwp/index.htm).

The time series of discharge and meteorology in Figure 3 and meteorology at site M, site F and site P are utilized as a daily data base for calculating water balance of the Oikamanai River catchment. This calculation is needed for estimating the groundwater leakage to the other catchments or the Pacific Ocean, and simulating the hydrographs at site R1. The accuracy in discharge is relatively very low in the frozen period, and the daily spatial change of snow depth in the catchment in the snowmelt season is unknown. Hence, the frozen and snowmelt seasons are excluded for the calculation.

The DEM and land-use maps of the catchment in Figure 1 were utilized for evapotranspiration calculation, because effects of slope angle, slope aspect and surface condition on the solar radiation should be considered. Figure 4 shows spatial distributions of slope angle and aspect in the catchment (resolution, 0.1 km). As a result, the averaged slope angle and aspect were 34.66˚ and 176.6˚ (clockwise from north at 0˚), respectively. The basin slope thus faces almost south on average. With respect to land use, each value of albedo α and dimensionless bulk transfer coefficient of sensible heat C_H was considered for forest and grassland separately.

Water balance of a catchment for a certain period is given as follows:

where ΔS is groundwater storage change (mm) for the water-balance period Δt (day), P is precipitation (mm/d), E is evapotranspiration (mm/d), R is runoff rate (mm/d) at the “exit” of the catchment (here, site R1 in Figure 1),

and L is groundwater leakage (mm/d). The runoff rate, R, is calculated from daily discharge (m³/d) divided by the catchment area (6.26 × 10⁷ m²). Here, the evapotranspiration, E, is calculated by the one-layer model for the forest or grassland area (Figure 1). In the one-layer model, the leaf-surface temperature, T_e (K), at a certain height in forest or grassland is obtained by the successive approximation method to satisfy the following heat balance equations:

where K_θ↓ is downward shortwave radiation (W/m²) onto the catchment of slope angle θ, α is albedo, L↓ is downward long wave radiation (W/m²), G is soil heat flux (W/m²), σ is the Stefan-Bolzmann constant (=5.670 × 10⁻⁸ W/m²/K⁴), Q_H is sensible heat flux (W/m²), Q_E is latent heat flux (W/m²), λ is vaporization heat (J/kg), c_p is specific heat (J/kg/K) of water at constant pressure, ρ_a is air density (~1.2 kg/m³), ε is the ratio of water vapor density to dry air density (=0.622), C_H is a dimensionless bulk transfer coefficient for sensible heat flux, T_z is air temperature (K) at z, u_z is wind speed (m/s) at the height, z, above the earth surface, p is air pressure (Pa) at z, e_z is the vapor pressure (Pa) at z, e₀(T_e) is saturated vapor pressure (hPa) at leaf-surface temperature T_e, and β is evaporation efficiency (=C_E/C_H; C_E, dimensionless bulk transfer coefficient for latent heat flux).

Here, the albedo α is supposed to be constant at 0.10 or 0.15 for the forested (88.3% area) Oikamanai River catchment, since α = 0.05 - 0.15 for broadleaf forest, α = 0.1 - 0.2 for needleleaf forest and α = 0.15 - 0.25 for grassland (Figure 1; [19] ). Actually, considering these ranges and the ratio of the land use area in Figure 1, the α value can be 0.08 - 0.18. The evaporation efficiency β is given at 0.3 for Equations (3) and (4), because β = 0.26 at the mixed broadleaf and needle leaf forest in summer [20] . When rainfalls at site M and site P was more than 40 mm/d, and relative humidity at site F was 100%, β = 1 was given. The bulk transfer coefficient, C_H, for sensible heat flux is assumed to range from 0.005 to 0.008 for forest and grassland.

Downward shortwave radiation K_θ↓onto the basin slope is calculated by the following equations [21] :

where K_d is direct shortwave radiation onto a normal surface, K_s is scattered shortwave radiation onto a plane, K↓ = K_d sinh + K_s, i is an incident angle of shortwave radiation onto the slope, h is solar elevation, A_s is solar azimuth, and A is slope aspect (clockwise from A = 0˚ for the south-facing slope). K_d and K_s in Equation (5) were obtained by the following equations.

where J₀ is the solar constant (=1353 W/m² as annual average), ζ is atmospheric transmissivity, and here is assumed to be constant at 0.7. The downward shortwave radiation K_θ↓ onto basin slope was calculated by using hourly K↓ data (θ = 0˚) at the Taiki Aerospace Research Field. Here, K_θ↓ in Equation (5) was calculated at θ = 34.66˚ (averaged slope angle) and A = 356.6˚ (averaged slope aspect) (Figure 4).

Daily mean values (L_d↓) of downward long wave radiation L↓ in Equation (2) were calculated by the following equations [20] :

where B = K_d ↓/K_df ↓ (K_d ↓and K_df ↓, daily mean shortwave radiation observed on the plane and in fair weather, respectively), L_df ↓ is daily mean longwave radiation in fair weather, and T is daily mean air temperature (K) at z. C is a factor of cloud effect with C = 1 in fair weather. L_df ↓ is calculated as follows:

where w is total amount (cm) of effective water vapor, and T_dew is daily mean dew point temperature (˚C) at z, respectively. Daily mean shortwave radiation K_df↓ in fair weather is calculated by using a relation with daily mean downward shortwave radiation K_0d↓on a horizontal surface in the upper end of atmosphere [20] .

When Equations (2)-(4) are applied at the daily base, the soil heat flux G could then be negligibly small compared with the other heat fluxes. Here, the daily mean K_θ↓ calculated and the wind speed, U₁₀ (U_z at z = 10 m) at the Taiki Aerospace Research Field, and daily mean air temperature and relative humidity at site F are adopted to obtain daily mean T₁₀ and e₁₀ values and the T_dew values at z = 10 m. Then, for daily mean air temperature, its spatial distribution or the elevation effect in the catchment should be taken into account. However, the daily mean air temperature at sites M, R1, F and P (Figure 1) did not indicate such a clear environmental lapse rate as −0.65˚C/100m, and the difference of the daily air temperature was abs(ΔT) < 0.5℃ between site F and the other sites. This is probably due to the usual prevalence of sea wind from the Pacific Ocean (Figure 1). Finally, the T_e value obtained by the successive approximation method yields:

where ρ_w is water density (kg/m³) at T_e, and E is evapotranspiration (mm/day).

The groundwater leakage, L, in Equation (1) is estimated, since the catchment has many faults in addition to the relatively porous sedimentary bedrock (Figure 2). The (E + L) in Equation (1) is obtained by the short-term water balance method, where a time period covering one or more rainfall runoff events (Table 1) is adopted to satisfy Q_t1 = Q_t2 for river discharge at the initial time t₁, and the final time t₂ (Figure 5). In the method, it is assumed that the groundwater storage occurs at any time in the same underground zone. Then, the river discharge Q corresponding to the baseflow is proportional to groundwater storage, S, and ΔS = 0 at between t₁ and t₂. Here, mean daily rainfall, P, at site P and mean daily runoff rate, R, at site R1 over a time period giving ΔS = 0 (Figure 1), and mean daily evapotranspiration, E, for the days nearly equal to the time period are applied to Equation (1) to numerically obtain the leakage L. A spatial distribution of the daily rainfall in the catchment should then be considered.

Figure 6 shows four examples of daily rainfall distributed in the catchment. These plots are based on the analytical rainfall data of 1 km × 1 km mesh by the Japan Meteorological Agency. The statistical F-test was performed for the slopes in the linear models for rainfalls of more than 10 mm/d. As a result, the hypothesis of no trend was rejected for the rainfalls. However, the correlation was consistently small (R² < 0.2) as in Figure 6. Hence, the elevation effect on rainfalls is almost negligible in this catchment. The utility of the rainfall data at site P (142 m asl in altitude) can thus be reasonable for estimating the leakage.

Actual evapotranspiration E evaluated by the one-layer model (α = 0.1, C_H = 0.008), the daily rainfall P at site P and the runoff rate R at site R1 are shown in Figure 7. The evapotranspiration E in the rainfall season of 12 April-30 November 2011 and 20 April-30 November 2012 was calculated using the shortwave radiation at θ = 34.66˚ and A = 356.6˚. As a result, Total E, P and R over the periods were 348.1 mm, 971.5 mm and 418.4 mm for 2011, and 324.4 mm, 1039.5 mm and 839.1 mm for 2012, respectively. Calculated shortwave radiation K_θ↓ onto the basin slope of θ = 34.66˚ and A = 356.6˚ was by 24% larger than the solar radiation K↓ at the Taiki Aerospace Research Field, and consequently actual evapotranspiration increased by 33% and 30% in 2011 and 2012, respectively, compared with that from the K↓ values. For a period of 1 May-31 October with no snow cover in the catchment, total E, P and Rare 296.2 mm, 815.5 mm and 325.7 mm for 2011, and 290.6 mm, 797.5 mm and 609.3 mm for 2012, respectively. Potential evapotranspiration, PE, by the Hamon method [22] indicates 428.5 mm and 438.6 mm for 1 May-31 October of 2011 and 2012, respectively. The evapotranspiration ratio E/PE is thus given at 0.69 and 0.66 in 2011 and 2012, respectively. These values are reasonable to calculated results, E/PE = 0.65, in the upper Ishikari River catchment, Hokkaido [23] . The E, P and R values averaged over 1 May-31 October are 1.61 mm/d, 4.43 mm/d and 1.77 mm/d for 2011, and 1.58 mm/d, 4.33 mm/d and 3.31 mm/d for 2012, respectively. Thus, in the non-snow-covered season, the runoff rate R corresponds to 40% and 76% of P for 2011 and 2012, respectively. The ratio of R/(P ? E) is then 0.63 and 1.20 for 2011 and 2012. The great difference of the R/(P ? E) ratio suggests that the groundwater storage, contributing to river discharge, greatly changes year by year. After the snowmelt in April 2012, the runoff rate during non-rainfall was consistently higher than that in 2011 (Figure 3) and the E values in 2012 (Figure 7). This causes the R/(P ? E) ratio to be more than unity in 2012. This suggests that in addition to the groundwater storage by snowmelt in April, large groundwater storage was produced by the heavy rainfall in early May (total rainfall, 221 mm in Table 1).

Relations between the leakage, L, and the effective rainfall (or infiltration), (P ? E), are shown in Figure 8. As a result, for the application of the short-term water balance method to the (E + L) estimate, 20 time periods with the duration of 38 to 649 hrs (14 and 6 time periods in 2011 and 2012, respectively) were selected. Each of all the time periods covered the period of one or more rainfall events (Figure 5). In 2012, relatively small runoff events for the 6 time periods (Table 1) were suitable for the application. In 2011 (white circles in Figure 8), it is evident that the groundwater leakage to the other catchments linearly increases with the effective rainfall. The groundwater leakage then occupies ca. 50% - 75% of the effective rainfall, but, when (P ? E) is 1.3 mm/d or less, the leakage is nearly zero or a little negative. The large leakage is likely due to the young sedimentary bedrocks with many faults (Figure 2), where the deep percolation of rainwater prevails. Such large deep percolation could be connected to the restraint of river flood in the catchment. In 2012 (black circles in Figure 8), the leakage is negative for the 4 time periods, when the effective rainfall is less than 2.1 mm/d.

The application of the short-term water balance method in 2012 was limited to the small effective rainfalls, and the leakage was then negative for the 4 time periods. The negative values are probably due to large variability of the actual evapotranspiration estimated and the relatively high runoff rate during non-rainfall in 2012 (Figure 7(b)), as reflected by R/(P ? E) = 1.20 averaged over 1 May-31 October. For small runoff events, the leakage from the short-term water balance method seems to partially exclude discharge from the relatively large groundwater storage. For modelling discharge time series of the Oikamanai River, it is important to consider if the leakage and groundwater storage is considerably large or not.