POTENTIAL WATER STORAGE CAPACITY OF MOUNTAINOUS CATCHMENTS BASED ON CATCHMENT CHARACTERISTICS

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1 Annual Journal of Hydraulic Engineering, JSCE, Vol.59, 215, February POTENTIAL WATER STORAGE CAPACITY OF MOUNTAINOUS CATCHMENTS BASED ON CATCHMENT CHARACTERISTICS Intan SUPRABA 1, Tomohito J. YAMADA 2 1 Member of JSCE, M.Sc., Doctoral Student, Graduate School of Engineering, Hokkaido University (Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido, , Japan) 2 Member of JSCE, Ph.D., Associate Professor, Faculty of Engineering, Hokkaido University (Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido, , Japan) The majority of water catchments in Japan are located in mountainous areas that can produce large quantities of runoff, which may lead to flooding, erosion, and landslides. Thus, it is important to know the minimum total rainfall required to generate surface runoff by estimating the water storage capacity of each catchment. The threshold of minimum total rainfall required to generate surface runoff occurs when at least 95% of total rainfall becomes total loss rainfall such as infiltrates into the ground. The variation in this value is dependent on the catchment characteristics. Based on the relationship between total rainfall and total loss rainfall, the average values of minimum total rainfall required to generate surface runoff and total loss of saturated rainfall were 51.3 mm and 18.5 mm, respectively. Catchments consisting of a smaller area of sedimentary rock and higher values of drainage density, elongation ratio, and catchment width tended to have smaller values of minimum total rainfall required to generate surface runoff. Key Words: Water Storage, Threshold of Minimum Total Rainfall Required to Generate Surface Runoff, Total Rainfall-Total Loss Rainfall, Catchment Characteristics 1. INTRODUCTION When the rainfall rate is larger than the infiltration capacity, the excess rainfall flows over the surface causing flooding and erosion 1). Excess water causes build-up of pore-water pressure, which weakens the materials supporting the slope, thereby causing landslides and flows (e.g., creep, debris flow, and debris avalanche) 2). Thus, estimating the potential water storage capacity in a catchment is necessary to elucidate the fraction of rainwater that can be stored in the catchment, and to determine the fraction that will become surface runoff. One method to estimate threshold runoff by using Geographic Information Systems (GIS) and digital terrain elevation databases has been proposed to improve the US National Weather Service (NWS) flash flood warning program 3). Threshold runoff is defined as the amount of excess rainfall (effective rainfall) that accumulates during a given time period in a catchment area, that is just enough to cause flooding at the outlet of the draining stream 3). Previous studies have investigated the nonlinearity of runoff phenomena in mountain catchments based on the distribution of water holding capacity, which can be used to estimate the effective rainfall intensity for simulating surface runoff. This distribution is calculated using the runoff parameters in equations linking total rainfall with total loss rainfall that is well fitted using the tanh function fitting curve 4),5),6). Analysis of water holding capacity for catchment areas ranging from 1 km 2 to 1 km 2 in size based on rock types classification has been conducted. The rock types are classified into three groups; namely, Quaternary volcanic rocks, Tertiary granitic rocks, and Paleozoic rocks types 7),8). Catchments consisting of Quaternary volcanic rocks have the largest water holding capacity 7),8). Another analysis of water holding capacity and catchment storage of 52 catchments in Japan with catchment areas ranging from.1 to 1 km 2 has been performed to determine the function of the forest in headwater conservation 9). The catchment storage capacity was estimated by rainfall amounts

2 ranging from 5 to 25 mm, and mainly depended upon the surface geology and soil type. The largest catchment storage was identified in catchments covered by granite and volcanic ash 9). A recent study to estimate catchment storage based on the relationship between total rainfall and total loss rainfall for 47 catchments in Japan showed that runoff parameters in the tanh function can be utilized to estimate the potential water storage (actual water holding capacity) for catchments with stable (constant) tanh curves, of which the majority are located on Honshu Island 1). The objective of our study was to estimate the minimum total rainfall required to generate surface runoff, which is almost zero when there is a rainfall event. The variation in the minimum total rainfall required to generate surface runoff was analyzed based on catchment characteristics. 2. METHODOLOGY (1) Data Hourly rainfall and hourly runoff data of 16 catchments in Japan were obtained from the Water Information System of the Ministry of Land, Infrastructure, Transportation, and Tourism of Japan (MLIT) database 11). The geographical distribution of all catchments is shown in Fig. 1. The target period for the study was summer and autumn (i.e., June- October for a minimum of 1 years [22 211]). Among the 16 catchments, some were excluded from the analysis; namely, those catchments that lacked data for the full target period, such as those with data from only June 25 or June 28; those with runoff data, but no rainfall data; and those with unrealistic rainfall values. In addition, the shapes of the hydrographs varied among the catchments due to snow melt, and snowmelt periods were also excluded from the analysis. Fig.1 Geographic distribution of 16 catchments. Diamonds denote catchments with constant tanh curves, the colored bar indicates the value of a (see Fig. 2a) as total loss of saturated rainfall (mm), triangles denote catchments with non-constant tanh curves, and circles denote other catchments that lacked complete datasets. After carefully checking the quality of the data, only 36 catchments located in 14 prefectures in Japan had the full dataset for the summer and autumn seasons from June October for a minimum of 1 years (22 211). Among these 36 catchments, longer datasets existed for 1 catchments located in Hokkaido Prefecture, which is the second largest and northernmost island in Japan (14 years, ). For the Kusaki Dam catchment in Gunma Prefecture, older datasets was added manually (3 years, ). (2) Relationship between total rainfall and total loss rainfall A streamflow hydrograph was separated into base flow and surface runoff components using the streamflow hydrograph separation technique (HYSEP) introduced by the U.S. Geological Survey (USGS) 1),12). Surface runoff in HYSEP refers to direct runoff (quickflow) that is the sum of overland flow and interflow (sub-surface flow). After separating a hydrograph into base flow and surface runoff components, total rainfall and total loss rainfall can be obtained. Total rainfall is defined as the total amount of rainfall within one rainfall event, whereas total loss rainfall is defined as the total amount of rainfall that does not contribute to surface runoff such as infiltrates into the ground 1). Total loss rainfall, F(R), can be expressed by the linear Volterra-type integral equation of the first kind 5),6) : R F(R) = R (R h) S(h)dh (1) where R is total rainfall (mm), F(R) is total loss rainfall (mm), and h is water ponding depth in the surface soil layer (mm). The solution of Eq.(1) can be obtained by Laplace transformation 5),6) : S(R) = d2 F df dr2 + [1 ] δ(r) (2) dr R= where δ(r) is Dirac s delta function (the fraction of the non-permeation area in the catchment). The total rainfall-total loss rainfall relationship is expressed using the well-fitted tanh function fitting curve 5),6),1) : F(R) = a tanh(b R) (3) where a and b are the runoff parameters. By substituting Eq.(3) into Eq.(2), and solving the derivative equation, the water holding distribution profile is expressed as follows 5),6) : S(R) = (1 ab)δ(r) + 2ab 2 sinh(br) (4) cosh 3 (br) where S (R) is the water holding capacity distribution (1/mm). (3) Constant and non-constant catchments classification Relationship between total rainfall and total loss rainfall for each catchment is plotted by using Eq.(3).

3 a) b) TOTAL LOSS RAINFALL (mm) TOTAL LOSS RAINFALL (mm) FUTASE DAM, SAITAMA PREFECTURE Location = (lat); (lon) Catchment Area = km 2 R 2 =.8988 a = ± b =.994 ± TOTAL RAINFALL (mm) 5 FUJIWARA DAM, GUNMA PREFECTURE 45 Location = 36.8 (lat); (lon) Catchment Area = 4.2 km 2 4 R 2 = a = ± b =.117 ± TOTAL RAINFALL (mm) Fig.2 Relationship between total rainfall and total loss rainfall for a) Futase Dam catchment in Saitama Prefecture, b) Fujiwara Dam catchment in Gunma Prefecture. Graphs of total rainfall and total loss rainfall showed that those 36 catchments could be classified into two groups, 23 catchments with constant tanh curves (see Fig. 2a), and 13 catchments with nonconstant tanh curves (see Fig. 2b) 1). A catchment with a constant tanh curve is characterized by a constant stage following the linear stage (see Fig. 2a), which is produced by heavy rainfall events with a small loss of total rainfall. The localized gradient is the curve gradient at a certain point (total rainfall that causes a saturated condition), which is obtained by taking the derivative of Eq.(3). By determining localized gradient at the constant stage as.5 for 23 catchments with constant tanh curves, total rainfall causing saturated condition was 2 mm. Based on rainfall events with a total rainfall > 2 mm, a catchment is classified as having a constant tanh curve if more than 6% of the rainfall amount in one rainfall event become surface runoff. For 23 catchments with constant tanh curves, the average ratio of total surface runoff to total rainfall is 6.7%, and the average ratio of total loss rainfall to total rainfall is 39.3%. As for 13 catchments with nonconstant tanh curves, the average ratio of total surface runoff to total rainfall is 38.9%, and the average ratio of total loss rainfall to total rainfall is 61.1%. a A recent study found that parameter a in the total rainfall-total loss rainfall relationship equals to the height of the tanh curve (see Fig. 2a), and can represent the average maximum water storage for catchments with constant tanh curves 1). The parameter a is named total loss of saturated rainfall because it can be obtained only when the catchment previously ever experienced saturated condition due to some heavy rainfall events with small total loss rainfall. The saturation condition is indicated by constant stage in the tanh curve (see Fig. 2a) 1). (4) Threshold of minimum total rainfall required to generate surface runoff The threshold of minimum total rainfall required to generate surface runoff is defined as the amount of rainfall that almost does not contribute to surface runoff at all, or nearly zero surface runoff, when it rains. The threshold is determined as at least 95% of total rainfall becomes total loss rainfall such as infiltrates into the ground, and a maximum of 5% of total rainfall becomes total surface runoff. Opposite from parameter a that is obtained at the constant stage of a tanh curve, the threshold of minimum total rainfall required to generate surface runoff is found at the linear stage of a tanh curve, and indeed, it is plotted close to the 1 to 1 plot between total rainfall and total loss rainfall. (5) Rock classification The raw data of rock types were obtained from the MLIT database 13). The method for classifying rock type and class can be described as follows: (a) Obtain the area of rock type for each catchment. There are 36 rock types in Japan, including andesitic, basaltic, black schist, conglomerate, gabbro, granitic, gravel, sand, clay, and rhyolitic. (b) Classify those 36 rock types into three rock classes; namely, igneous, metamorphic, and sedimentary 2),14),15). (6) Catchment morphometry Catchment morphometry analysis is used to measure the configuration of the earth s surface, and the shape and dimension of its landforms 16). The morphometric parameters are classified into three aspects; namely, linear (stream length, stream order, bifurcation ratio), areal (drainage density, elongation ratio, catchment width, overland flow length), and relief (average slope, relative relief) 16),17),18). The prominent morphometric parameters for analysis of flash flood severity are those related to basin shape and topography 19). Thus, we selected drainage density, catchment width, longest drainage length, and elongation ratio as parameters for our analysis.

4 3. RESULTS (1) Values of total loss of saturated rainfall and its standard deviation, and minimum total rainfall required to generate surface runoff The value of the total loss of saturated rainfall (a) of the 23 catchments with constant tanh curves varied from 81.8 mm to 17.9 mm, with an average value of 18.5 mm. A higher value of a indicates a greater capacity of catchment storage. The majority of catchments with a higher a are located on Honshu Island. The maximum value of a, 17.9 mm (average), was found in the Matsubara Dam catchment in Ooita Prefecture (33.19 N, E), whereas the minimum value, 81.8 mm, was found in the Nomura Dam catchment in Ehime Prefecture (33.36 N, E) (see Fig. 1). The value of a may vary for a similar value of total rainfall, because a is highly influenced by the initial soil moisture conditions. The variation of standard deviation in a which mainly due to the soil moisture initialization is shown in Fig. 3. Fig.3 Geographic distribution of 23 catchments with the standard deviation of total loss of saturated rainfall for catchments with constant tanh curves. Fig.4 Geographic distribution of 47 catchments. Diamonds denote catchments with constant tanh curves, the colored bar indicates the value of the minimum total rainfall required to generate surface runoff (mm), triangles denote catchments with non-constant tanh curves, and circles denote other catchments that lacked complete datasets. The minimum total rainfall required to generate surface runoff varied from 7.9 mm to mm, with an average value of 51.3 mm. The higher minimum value indicates a higher capacity of catchment storage. The highest and lowest values of the minimum total rainfall required to generate surface runoff were found in the Satsunaigawa Dam catchment in Hokkaido Prefecture (42.59 N, E), and the Kyuuragi Dam catchment in Saga Prefecture (33.33 N, 13.1 E), respectively (see Fig. 4). (2) Scatter diagram between catchment area and minimum total rainfall required to generate surface runoff Fraction of the minimum total rainfall required to generate surface runoff (mm) LEGEND: Scatter diagram of igneous rock class Scatter diagram of metamorphic rock class Scatter diagram of sedimentary rock class Igneous rock class Metamorphic rock class Sedimentary rock class Fraction of catchment area (km 2 ) Fig.5 Scatter diagram between fraction of catchment area (km 2 ) and fraction of the minimum total rainfall required to generate surface runoff (mm) for catchments with constant tanh curves. Red denotes igneous rocks, green denotes metamorphic rocks, and purple denotes sedimentary rocks. It can be seen from Fig. 5 that catchments with a larger catchment area covered by sedimentary rock tended to have a higher value of minimum total rainfall required to generate surface runoff, followed by catchments covered by igneous rock and catchments covered by metamorphic rock, which both produced similar results. (3) Catchment morphometric and runoff parameters relationship The relationships between catchment morphometric parameters and the runoff parameters (i.e., total loss of saturated rainfall and minimum total rainfall required to generate surface runoff) for 23 catchments with constant tanh curves are analyzed based on correlation coefficient analysis. The area of those catchments varied from 13.6 km 2 to km 2. The catchments were classified by their areas using a cluster analysis that represented the approximate groupings of the catchment areas based on distance or dissimilarity function. Identical catchment areas had zero distance or dissimilarity, and all of the others had positive distance or dissimilarity. Based on the cluster analysis, the 23

5 a) b) c) catchments could be classified into three groups; namely, catchments with an area of 1 2 km 2, catchments covering an area of 2 45 km 2, and catchment with an area of km 2. The correlation coefficients between the catchment morphometric parameters and runoff parameters for different groups of catchment areas are presented in Table 1a and Table 1b. Results showed that the runoff parameters are closely correlated with the drainage density, elongation ratio, and catchment width for catchments with larger areas (45 65 km 2 ). In catchments with smaller areas (1 45 km 2 ), all of the morphometric parameters are poorly correlated with those runoff parameters. Total loss of saturated rainfall and minimum total rainfall required to generate surface runoff were closely related to the permeable areas of the catchment. Dirac s delta function in Eq.(2) represents the fraction of impermeable areas in the catchment 5),6). The correlation coefficients between the morphometric parameters of the catchment and Dirac s delta function are presented in Table 1c. Table 1 Correlation coefficient between catchment morphometric parameters and a) total loss of saturated rainfall, b) minimum total rainfall required to generate surface runoff, and c) Dirac s delta function. Catchment morphometric parameters 4. DISCUSSION Correlation coefficient for catchment area 1-2 km km km 2 Drainage density (m/km 2 ) Longest drainage length (km) Elongation ratio Catchment width (km) Catchment morphometric parameters Correlation coefficient for catchment area 1-2 km km km 2 Drainage density (m/km 2 ) Longest drainage length (km) Elongation ratio Catchment width (km) Catchment morphometric parameters Correlation coefficient for catchment area 1-2 km km km 2 Drainage density (m/km 2 ) Longest drainage length (km) Elongation ratio Catchment width (km) This study investigated the minimum total rainfall required to generate surface runoff, which is of importance because natural disasters such as floods and landslides are caused by excess rainfall. The value of minimum total rainfall required to generate surface runoff varied from 7.9 mm to mm, and its variation could be explained by the catchment characteristics. Catchment morphometry analysis has an important role to understand the geo-hydrological behavior of a catchment. Additionally, rock types that has been discussed in previous studies to analyze water holding capacity and flash flood severity in a catchment 7),8),9),19) is also analyzed in this study. The catchment metamorphic parameters and runoff parameters relationships showed higher correlation coefficients for the larger catchment areas (45 65 km 2 ) with regard to drainage density, elongation ratio, and catchment width (see Table 1a and Table 1b). Higher drainage density, elongation ratio, and catchment width result in less minimum total rainfall required to generate surface runoff, and lower total loss of saturated rainfall. The drainage density can provide a quantitative measure of the average length of stream channels in the entire catchment 17),2) ; a higher drainage density is equivalent to a longer length of stream channels, so more rainwater can be drained out to the outlet. Thus, less rainwater infiltrates into the ground, resulting in smaller values of both, total loss of saturated rainfall and minimum total rainfall required to generate surface runoff. The elongation ratio represents the shape of the catchment, with a higher elongation ratio indicating that the major part of catchment is of high relief 17). A catchment with high relief can quickly drain rainwater to the outlet; thus, a higher elongation ratio causes higher surface runoff and less infiltration. A wider catchment has a higher drainage density; thus, a wider catchment gives rise to higher surface runoff and less infiltration. The relationships between Dirac s delta function and catchment parameters showed that higher values of drainage density, elongation ratio, and catchment width result in a larger value for Dirac s delta function (see Table 1c), which in turn, is equivalent to a larger impermeable area in the catchment, resulting in higher surface runoff. In addition, higher drainage density, elongation ratio, and catchment width result in higher surface runoff as explained previously, and this justifies the linear relationship between those three catchment morphometric parameters and Dirac s delta function. Previous studies have suggested that, for smaller catchment areas, the influence of river channel networks in the catchment can be neglected 21),22). This explains why catchment morphometric parameters are closely correlated with runoff parameters for larger area catchments only. Sedimentary rocks tend to have high primary porosity and very high hydraulic conductivity compared to igneous and metamorphic rocks 14),15). Thus, catchments with a larger area of sedimentary rocks are permeable, and rainwater can easily infiltrate. This explains why catchment areas with a larger fraction of sedimentary rocks tended to require higher minimum total rainfall to generate surface

6 runoff, followed by those areas that were dominated by igneous rocks and metamorphic rocks (see Fig. 5). However, the relationship between the fraction of catchment area of a given rock class and the minimum total rainfall to generate surface runoff was non-linear, that is possibly due to different hydraulic conductivity of each rock type 15), rainfall spatial distribution, and initial conditions of soil moisture 1). Fig. 5 shows that catchments with a larger area of igneous rocks tended to require the next highest minimum total rainfall to generate surface runoff, after those with a larger area of sedimentary rocks. Igneous rocks are an important water source in some regions 15). Igneous rocks such as basalt, andesite, and rhyolite, have a high capacity for water transmission and water storage 15). This is why the majority of catchments, where the minimum total rainfall required to generate surface runoff was > 3 mm, occurred in catchments covered with igneous rocks. 5. CONCLUSIONS The conclusions can be summarized as follows: (a) The minimum total rainfall required to generate surface runoff, and total loss of saturated rainfall are important runoff parameters for assessing the potential water storage capacity of a catchment. (b) The values of minimum total rainfall required to generate surface runoff varied from 7.9 mm to mm, with an average value of 51.3 mm. The values of total loss of saturated rainfall varied from 81.8 mm to 17.9 mm, with an average value of 18.5 mm. A higher value of both parameters indicate a higher capacity of catchment storage. (c) Among 23 catchments with constant tanh curves, a catchment with a higher fraction of sedimentary rocks tend to have higher minimum total rainfall required to generate surface runoff. (d) Variation in minimum total rainfall required to generate surface runoff, and in total loss of saturated rainfall is explained by drainage density, elongation ratio, catchment width, and rock class. 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