QUANTITATIVE ANALYSIS OF HYDROLOGIC CYCLE IN COLD SNOWY BASIN

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1 QUANTITATIVE ANALYSIS OF HYDROLOGIC CYCLE IN COLD SNOWY BASIN Tomohide USUTANI 1 and Makoto NAKATSUGAWA 2 1 Japan Weather Association, Sapporo, Japan 2 Toyohashi Office of River Works, Ministry of Land, Infrastructure and Transport, Toyohashi, Japan ABSTRACT For comprehensive water management and water environmental planning in large river catchment areas, it is necessary to know the long-term hydrologic cycle. In snowy cold regions, the snow process (falling, accumulation, and melting) plays an important role on the hydrologic cycle. An understanding of snow cover volume and snowmelt volume is essential. Analysis of the water balance of the catchment area also requires accurate estimation of evapotranspiration, which is affected by soil and vegetation. This report applies a two-layer model toward estimating the evapotranspiration, snow cover volume, and snowmelt volume of 1-km meshes. The model incorporates heat balance between the air, the vegetation layer, and the ground surface. These estimates were used to reproduce long-term runoff, in order to examine the validity of the estimates. The estimates were found to accurately reproduce the measurements. This has enabled the quantification of long-term hydrologic factors for snowy cold regions. KEY WORDS: Cold snowy basin; Hydrologic cycle; Two-layer model; Long-term runoff. INTRODUCTION The understanding of long-term hydrologic cycle is important for comprehensive hydrologic management and in formulating environmental plans for large rivers. In the hydrologic cycle, processes related to snow play a particularly important role in snowy cold regions. Therefore, reliable estimates of snow accumulation and snowmelt are needed to estimate the hydrologic cycle. Runoff models that consider snowmelt have been developed, such as those reported by Lu et al. (1998) and Nakayama et al. (2001). However, to consider the long-term hydrologic cycle, it is necessary to evaluate the calculated results of the developed model by comparison with water budget records. Nakatsugawa et al. (2002,2003) have been performing research in an effort to understand such hydrologic variables, including snow. Previous studies have estimated hydrologic variables such as snowmelt and evapotranspiration at dam basins of approximately 100 km 2 in snowy cold regions by using the two-layer model proposed by Kondo et al. (1994). Use of the estimated values as inputs enabled the estimation of long-term runoff in these dam basins. In this study, the methods used for these dam basins were applied in quantitative analysis -45-

2 Uryuu River Wakkanai Hokkaido Sea of Japan Okhotsk Sea Uryu Br. Ishikari River Akabira 44ºN Asahikawa Sorachi River Ishikari-ohasi Br. Kiyohoro Br. Uranosawa Yuubari River Chitose River ;Gauging station in the major tributaries Sapporo Kushiro Ishikari River basin Pacific Ocean Unit: km of hydrologic variables for the Ishikari River basin (14,330 km 2 ), one of the largest river basins in Japan. In quantifying the hydrologic variables in a large river basin, it is important that their distribution be considered, because spatial variations are greater within large basins than within small basins. This study performed estimation of all hydrologic variables for each 1-km-square mesh, and then those estimates were compiled to gain an understanding of the entire basin. Details of the process are as follows. 1) Meteorological data from scattered observation stations are superimposed on a 1-km x 1-km mesh (basic grid square), and hydrologic variables such as evapotranspiration, snow cover distribution, and snowmelt are estimated per mesh for the period from 1998 to The estimation considers various mesh conditions (vegetation, elevation, and slope gradient). 2) The validity of the method is verified by comparing estimated evapotranspiration with evapotranspiration obtained by the two-layer model, and by comparing the estimated snow cover distributions with those from satellite images. 3) From the estimated hydrologic variables, the runoff for the Ishikari River basin is reproduced, and runoff calculations are performed per mesh. The results confirm that it is possible to reproduce the long-term runoff. These results show that by applying the quantification method that was previously applied in dam basins, it is possible to gain an understanding of the hydrologic cycle for the Ishikari River basin. 43ºN 42ºN Hakodate 141ºE 143ºE Figure 1: Study area (In the left figure, gray solid lines show the watershed) STUDY AREA AND OBSERVATION DATA Study area This study targeted the Ishikari River basin in Hokkaido, Japan (Figure 1). The basin is located within the range of 43 N and 44 N. The riverhead is located at Mt. Ishikaridake (elev. 1,967 m) in the Taisetsu Mountains of central Hokkaido, and the river flows into the Sea of Japan through the Ishikari Plain. In the Ishikari River, the length of the mainstream is 268 km, and the catchment area is 14,330 km 2. The highest elevation in the Ishikari Plain less than 50 m and the plain is bordered by mountain ranges with peaks exceeding 1,000 m in elevation. At Sapporo (elev. 17 m) in this basin, monthly air temperature in the warmest month (August) is 22.0 C, and the coldest month (January) is -4.1 C. About four months from December to March are the snow cover durations in Sapporo. Annual snowfall is 630cm, and the year deepest snow depth is 101cm (normal value ). -46-

3 Observation data In this analysis, two kinds of data sets were used: meteorological data, and topographical data (Table 1). The meteorological data used the value having been observed by the Japan Meteorological Agency. The meteorological data have seven items as showing in Table 1. The daily observation values were gathered for the four years from The Ishikari River Area Landscape Intelligences (1998) data book was used as the topographic data source. The data book uses third-order mesh (approximately 1-km 2 grid) topographic data from the Digital National Land Information. For the entire Ishikari River basin, the Table 1: Data item Item Remark Meteorological Air temperature, Wind velocity, 28 stations Sunshine duration Humidity 3 stations Solar radiation 28 stations (Including the station where solar radiation was calculated by using the sunshine duration.) Precipitation 43 stations Snow depth 19 stations Topographical Elevation, Ground Ishikari River Area cover, Inflow and Landscape Intelligences runoff mesh codes (1998) Gradient Digital national land information mesh) (250-m LAI (leaf area index) Results of analysis by Ishii et al. (1999) number of meshes is 15,303. The gradients are obtained as the average gradient (in the east-west and north-south directions) from the third-order mesh data in the Digital National Land Information (250-m mesh elevation). The LAI values are the values for each month, estimated by Ishii et al.(1999). ESTIMATION OF HYDROLOGIC VARIABLES Interpolation meteorological data Methods for the interpolation of meteorological data are four kinds: a Kriging method for air temperature, sunshine durations and solar radiation; a distance-weighted method for humidity; a mass-consistent atmospheric flux model (MASCON) for interpolating wind velocity; a distanceweighted method that takes the influence of elevation into consideration for precipitation. A concrete procedure for interpolating it by using the distance-weighted method that takes the influence of elevation into consideration is as follows. 1) First, a linear regression equation is made with precipitation as the response variable and the location (latitude and longitude) and elevation of the observation station as the predictor variable. With this regression equation, the mesh values of the area to be analyzed are estimated to obtain estimated regression values. 2) Next, errors in the estimated regression values can be identified by comparing them with values measured at observation stations. Therefore, errors in the estimated regression values are interpolated using a distance-weighted method, and errors in all the meshes are estimated (error distribution value). 3) Finally, by subtracting the error distribution values from the estimated regression values, the mesh values are obtained. This process is performed for each day to obtain the mesh values of the period to be analyzed. -47-

4 Estimation of evapotranspiration, and snowmelt Evapotranspiration is dependent on the conditions of ground and vegetation cover. To estimate the heat flux with greater accuracy, heat balance at the soil surface or at the snow cover surface (hereafter: ground surface) and at the vegetation cover is formulated as follows (Kuchizawa et al., 2002), according to a two-layer model proposed by Kondo (1994): ( 1 ) σ ( ) f R + f T Q + Q + Q = εσt + H + le (1) 4 4 v v v M B R g g g 4 4 ( 1 f )( R εσt ) 2( 1 f ) σt H l( E I) + = (2) v g v v v v where Equations (1) and (2) are heat balance equations for the ground surface (i.e., the atmospheric layer from the ground surface to the lowest limit of canopy) and vegetation cover (i.e., the layer consists of canopy), respectively. f v is transmissivity to radiation of vegetation cover, R is the downward net radiation (W/m 2 ), Q M is heat flux expended to melt snow (W/m 2 ), Q B is heat flux supplied to the ground (W/m 2 ), Q R is heat flux supplied to the ground surface by rainfall (W/m 2 ), H g and H v are sensible heat flux from the ground surface and vegetation cover (W/m 2 ), le g and le v are latent heat flux from the ground surface and vegetation cover (W/m 2 ), li is latent heat flux associated with interception evaporation from the vegetation cover (W/m 2 ), T g and T v are the representative temperatures at the ground surface and vegetation cover (K), ε is emissivity (ground surface = 1.00, ground snow surface = 0.97), and σ is the Stefan-Boltzmann's constant ( W/m 2 /K 4 ). From these equations, representative temperatures ( T g andt v ) and the heat flux expended to melt snow Q M are obtained. Then, sensible and latent heat fluxes are calculated by means of the bulk Equations (3) and (4). ( ), ρ ( ) { ( ) }, ρβ { ( ) } H = C ρc U T T H = C C U T T (3) g p Hg g v p Hv v leg = lρβ gchgu esat Tg e lev = l vchvu esat Tv e (4) p p where C p is specific heat at constant pressure (1,004 J/K/Kg), ρ is density of air (kg/m 3 ), U is wind speed (m/s) at the specific elevation above ground, T is air temperature ( C) at the specific elevation above ground, C Hg and C Hv are bulk transfer coefficient at ground surface and in the vegetation layer respectively, β g and β v are evaporation effectiveness factor at the ground surface and in the vegetation layer respectively, e sat is saturate water vapor pressure (hpa), e is water vapor pressure (hpa) at the specific elevation above ground, and p is pressure on ground (hpa). Then, the values for bulk transfer coefficient and evaporation efficiency are decided for each mesh according to the ground cover per 1-km mesh. The bulk transfer coefficient and evaporation efficiency for each ground cover are chosen by referring to values in the literature (Kuchizawa, 2002: Kondo, 1994), and adjustments for both values are repeated to achieve best agreement with the water budget of the entire basin. Table 2 shows the estimated evapotranspiration for the reference points on the Ishikari River (Ishikari-ohashi Bridge) and its major tributaries (four gauging stations) in the basin. In the Table 2, the evapotranspiration (two-layer model) was calculated by averaging all the mesh values in each basin during The evapotranspiration (water budge method) is the difference between total precipitation (rainfall and water equivalent of snowfall) and the runoff depth -48-

5 measured at the gauging station. From table 2, it was found that these evapotranspiration values are almost equal. Evapotranspiration according to the region can be compared using Table 2. The values for the Chitose River are less than those for other basins. This characteristic is observed in values obtained using the water budget method, and in those obtained using two-layer model. The Chitose River basin is characterized by low elevation, high temperature, and small ratio of forest (Table 2). Higher temperatures tend to increase evapotranspiration. It is thought that the small ratio of forest along the Chitose River contributed to the basin s small evapotranspiration. Therefore, it became clear that with this method, the estimation of evapotranspiration, which reflects the conditions in the basin, is possible. Estimation of density of snow cover, depth of snow cover The density of snow cover increases with its dead weight. In this analysis, the density of snow cover was calculated by the following equation based on the viscous compression theory of Kojima (1957). 0 () t ( K ) 1 d ρ Ws = ρ dt η exp ρ s Table 2: Water budget estimation for each river basin (mean values from ) Basin Ishikari River Uryu River Sorachi River Yubari River Chitose River Reference point s Ishikari-ohashi Bridge where s Ws t is weight of snow pack. According to Kojima (1995), the value for K in Equation (5) is m 3 /kg, and for the coefficient of viscosityη 0, values such as kg-day/m 2 were reported to have been measured. In this analysis, parameter K and η 0 were set at m 3 /kg and 10 kg-day/m 2. The water equivalent of snow cover, and snow cover depth at a point in time (t ) are obtained from the following: ρ is density of snow pack, ( ) ( t) ρsf 3 Sw() t = Sw( t 1) { m() t + e() t } + Sf () t 10 (6) ρ w Uryu Bridge Akabira Kiyohoro Bridge Uranosawa Area of basin (km 2 ) 12,697 1,661 2,531 1,116 1,142 Mean elevation (m) Ratio of forest (%) Mean LAI Mean temperature ( C) Rainfall (mm/yr) 1, ,031 1,058 1,000 Water equivalent of snowfall (mm/yr) Runoff depth (mm/yr) 1,289 1,471 1,278 1, Evapotranspiration (water budget method) (mm/yr) Evapotranspiration (two-layer model) (mm/yr) (5) -49-

6 S d () t () t ρ () t 3 Sw 10 = ρ (7) s where S w is water equivalent of snow cover (mm), S d is depth of snow cover (m), m is the snowmelt (mm), e is the evapotranspiration (mm), and ρ w is the density of water (=1,000 kg/m 3 ). The estimated snow depth was shown Figure 2. In this figure, the snow depths measured by the Sapporo District Meteorological Observatory was compared to the calculated snow cover depth. The calculated values in the figure are obtained from the mesh where this observation station is located. In the figure, then the snow accumulation begins, the snow cover reaches its greatest depth, and the last snow melts, are well reproduced. Next, Figure 3 compares the images of calculated snow-covered areas with the satellite images (NOAA/AVHRR, Band1). The figure shows the snow cover at two days: April 28, 2001, and May 13, White parts indicate snow-covered areas, and gray parts indicate snow-free areas. In the figure, although the calculated results tend to overestimate the snow-covered area, they are general agreement with the snow-covered areas interpreted from w Snow cover depth (cm) April 28, 2001 Satellite image May 13, 2001 Satellite image Calculated Calculated Figure 3: Estimated distribution of snow cover (White portions show areas with snow cover; gray portions show areas without snow) satellite images. The pattern of decline in the snow-covered area is also well reproduced. From these results, it is thought that the method proposed in this paper enables accurate reproduction of snow cover depths at observation stations and will help to provide an understanding of the distribution of snow cover over a wide area /10 99/02 Sapporo District Meteorological 99/06 99/10 00/02 00/06 Year/Month 00/10 Measured Calculated Figure 2: Estimated depth of snow cover: Sapporo District Meteorological Observatory 01/02 01/06 RUNOFF ESTIMATION Runoff model Next, calculation of runoff is performed for each mesh in accordance with the input values for the amounts of rainfall, snowmelt, and evapotranspiration. For each mesh, the discharge from the upstream mesh is calculated by channel routing (channel routing model), as well as the runoff that occurs within the mesh (slope runoff model). These rates of flow at the tail end of the mesh are added, and that sum is the runoff toward the downstream mesh. Channel routing is calculated from the following equation, which is a modified kinematic wave equation (Shinagawa, 1992): -50-

7 Discharge (m 3 /s) 8,000 6,000 4,000 2,000 River: Isikari River Location: Isiakri-ohashi Bridge Area of basin: 12,697 km 2 Measured Calculated / / / / / / /01 Year/Month Q 5 i Q Q + = t 3 n B x Figure 5: Reproduced and measured runoff (at Ishikari-ohashi) where Q is discharge (m 3 /s), i is the gradient, n is the roughness coefficient, and B is the river width (m). The gradient i is determined by extracting the lowest elevation in the mesh to be calculated and that of the mesh downstream, and obtaining the difference between the two elevations. The roughness coefficient n is set at The river width B was estimated by means of the method using the catchments area (Yamazaki et al., 1999). To obtain the slope runoff within a mesh, the tank model shown in Figure 4 is used. Based on the parameters identified at a dam in the Ishikari River basin (Nakatsugawa, 2003), minor modifications are made to these values, and the obtained values are used as parameters for the model. The parameter values are the same for all meshes. (8) a 1 =0.320 a 2 =0.236 z 1 =42.00 z 2 =4.430 b 1 =0.154 a 3 =0.027 b 2 =0.040 z 3 = a 4 =0.089 (r-e) a 1 q 1 z 1 z 2 b 1 p 1 z 3 b 2 p 2 q 2 a 2 a 3 a 4 q 3 q 4 Figure 4: Slope runoff model (tank model) Results of long-term runoff calculation Figure 5 shows the reproduced hydrograph and the measured hydrograph at Ishikari-oohashi Bridge in the Ishikari River basin. This figure reproduces the floods that accompanied snowmelt in April to June, and runoff that accompanied rainfall. Runoff is the final stage in the hydrologic cycle, and if the sequences of hydrologic variables are not accurately recreated, the amount of runoff cannot be reproduced. These results support the validity of the runoff model and indicate that items composing the hydrologic cycle, such as evapotranspiration and snowmelt, are accurately reproduced. CONCLUSIONS The results are summarized as follows. 1) Evapotranspiration and snow cover depths were reproduced using the method proposed in this paper. The reproduced values were similar to the measured values. 2) Using the evapotranspiration and snow cover depths obtained above, the runoff for a period spanning four years was calculated. The long-term runoff, including runoff during the snowmelt period and the rainfall flood, was reproduced. -51-

8 3) These results demonstrate that the method proposed in this paper can accurately reproduce the hydrologic variables of the cold snowy basin. ACKNOWLEDGEMENTS This research was done in the Civil Engineering Research Institute of Cold Region. This research was commissioned by the Hokkaido Development Bureau of the Ministry of Land, Infrastructure and Transport to whom we wish to express our gratitude. REFERENCES Ishii, T., Nashimoto, M. and Shimogaki, H. (1999), Estimation of leaf area index using remote sensing data J. Japan Soc. Hydrol. & Water Resour., Vol.12, No.3, pp (in Japanese with English summary) Kojima, K (1957), Viscous compression of natural snow layers III, Low Temperature Science, Ser. A, 16, pp (in Japanese with English summary) Kondo, J. ed. (1994), Meteorology for water environment, Asakura Shuppan Co., Lid., Tokyo, Japan. (in Japanese) Kuchizawa, H., and Nakatsugawa, M. (2002), Estimation of snow pack condition and evapotranspiration based on water and heat balances in watershed, Monthly Report of Civil Engineering Research Institute, 588, pp (in Japanese with English summary) Lu, M., Koike, T, and Hayakawa, N. (1998), Development of a distributed snowmelt analysis system using AMeDAS data and digital geographic information, Annual Journal of Hydraulic Engineering, JSCE, Vol.42, pp (in Japanese with English summary) Nakayama, K., Itoh, S., Fujita, M. and Saitoh, D. (2000), Run-off analysis considering snow melt in a mountainous river, J. Hydraulic, Coastal and Environmental Engineering, No.691, II-57, pp (in Japanese with English summary) Nakatsugawa, M.,Hamahara, Y. and Hoshi, K. (2003), Long-term runoff calculation considering change of snow pack condition, Annual Journal of Hydraulic Engineering, JSCE, Vol.47, pp (in Japanese with English summary) Shinagawa, M., Yamada, T. and Toyoda, Y. (1992), Evaluation of the effects of flood prevention on the formation of hydrograph, J. Japan Soc. Hydrol. & Water Resour., Vol.5, No.3, pp (in Japanese with English summary) Foundation of Hokkaido River Disaster Prevention Research Center (1998), Ishikari River Area Landscape Intelligences. (in Japanese) Yamaguchi, M., Shinjo, N., Mitamura, K., Ueno, T. (1999): Simulation of sediment yields on TOYOHIRA River, Proceedings of Hokkaido chapter of the Japan society of civil engineers, No. 55(B), pp