Localized bedrock aquifer distribution explains discharge from a headwater catchment

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1 WATER RESOURCES RESEARCH, VOL. 47, W07530, doi: /2010wr009884, 2011 Localized bedrock aquifer distribution explains discharge from a headwater catchment Ken ichirou Kosugi, 1 Masamitsu Fujimoto, 1 Shin ya Katsura, 2 Hiroyuki Kato, 1 Yoshiki Sando, 1 and Takahisa Mizuyama 1 Received 13 August 2010; revised 7 March 2011; accepted 8 April 2011; published 16 July [1] Understanding a discharge hydrograph is one of the leading interests in catchment hydrology. Recent research has provided credible information on the importance of bedrock groundwater on discharge hydrographs from headwater catchments. However, intensive monitoring of bedrock groundwater is rare in mountains with steep topography. Hence, how bedrock groundwater controls discharge from a steep headwater catchment is in dispute. In this study, we conducted long-term hydrological observations using densely located bedrock wells in a headwater catchment underlain by granitic bedrock. The catchment has steep topography affected by diastrophic activities. Results showed a fairly regionalized distribution of bedrock aquifers within a scale of tens of meters, consisting of upper, middle, and lower aquifers, instead of a gradual and continuous decline in water level from ridge to valley bottom. This was presumably attributable to the unique bedrock structure; fault lines developed in the watershed worked to form divides between the bedrock aquifers. Spatial expanse of each aquifer and the interaction among aquifers were key factors to explain gentle and considerable variations in the base flow discharge and triplepeak discharge responses of the observed hydrograph. A simple model was developed to simulate the discharge hydrograph, which computed each of the contributions from the soil mantle groundwater, from the lower aquifer, and from the middle aquifer to the discharge. The modeling results generally succeeded in reproducing the observed hydrograph. Thus, this study demonstrated that understanding regionalized bedrock aquifer distribution is pivotal for explaining discharge hydrograph from headwater catchments that have been affected by diastrophic activities. Citation: Kosugi, K., M. Fujimoto, S. Katsura, H. Kato, Y. Sando, and T. Mizuyama (2011), Localized bedrock aquifer distribution explains discharge from a headwater catchment, Water Resour. Res., 47, W07530, doi: /2010wr Introduction [2] Understanding a discharge hydrograph is one of the most important areas in catchment hydrology because it is essential for flood prediction, water resources management, and chemical and ecological material transport. Various processes such as saturated and unsaturated water flow in the soil layer [e.g., Tani, 2008], preferential flow [e.g., Tsuboyama et al., 1994], and spatial and temporal variation of the source area [e.g., Vivoni et al., 2008] have been examined as dominant processes in controlling discharge. [3] Recently, the importance of bedrock groundwater has been emphasized worldwide in watersheds with various climates and geological features [e.g., Hattanji and Onda, 2004; Tromp-van Meerveld et al., 2007]. In order to determine runoff processes of bedrock groundwater, piezometric 1 Laboratory of Erosion Control, Department of Forest Science, Graduate School of Agriculture, Kyoto University, Kyoto, Japan. 2 Erosion and Sediment Control Division, Research Center for Disaster Risk Management, National Institute for Land and Infrastructure Management, Tsukuba, Japan. Copyright 2011 by the American Geophysical Union /11/2010WR and tensiometric responses have been measured [Wilson and Dietrich, 1987;Haria and Shand, 2004;Kosugi et al., 2006; Katsura et al., 2008a], sprinkler and tracer experiments have been performed [Anderson et al., 1997;Montgomery et al., 1997], and hydrogeochemical studies have been conducted [Uchida et al., 2003; Soulsby et al., 2007]. While these previous studies have advanced the understanding of the contributions of bedrock groundwater to the discharge hydrograph, the results derived from these studies are based on observations within the soil mantle and shallow bedrock. To elucidate the effects of bedrock groundwater on the form of the discharge hydrograph, the dynamics of bedrock groundwater should be measured directly. [4] Some recent studies have monitored bedrock groundwater in nested wells excavated in mountainous terrains. In a 0.85 km 2 basin including Mirror Lake in the White Mountains of New Hampshire, 31 wells were drilled into bedrock to analyze the interaction of bedrock groundwater with surface water [Tiedeman et al., 1998; Winter et al., 2008]. The results suggested that Mirror Lake and its inlet streams drain a groundwater recharge area that is about 1.5 times the area of the surface water basin. By monitoring a network of 15 bedrock wells instrumented in a 10 km 2 basin, Gleeson et al. [2009] examined factors that govern recharge W of16

2 to fractured bedrock aquifers. They found that soil thickness and hydraulic conductivity are critical parameters that control rapid and localized recharge. However, no previous study has analyzed interactions between bedrock groundwater and surface hydrological processes by employing a bedrock well network instrumented in mountains with steep topography. [5] The objective of this study is to clarify how complex flow systems within bedrock groundwater control discharge from a steep headwater catchment. In particular, we focus on the generation processes of multipeak discharge responses. Double-peak discharge responses have been observed in several watersheds; namely, flashy first peaks were recorded just after rainfall peaks, while second peaks lagged behind rainfall peaks by several tens of hours to a few days [Agata and Tanaka, 1997; Birkinshaw, 2008]. To understand doublepeak discharge responses, hydrologists have conducted detailed monitoring [e.g., Anderson and Burt, 1978; Haga et al., 2005] and numerical simulations [e.g., Birkinshaw, 2008; Sonoda et al., 2009; Harman and Sivapalan, 2009]. Whereas some studies have suggested that a possible source of the second peak could be groundwater in a thick deposition surrounding a valley bottom [Burt and Butcher, 1985; Masiyandima et al., 2003] or a saturated zone in an upslope region that exhibits delayed connection to the stream because of heterogeneity in soil hydraulic properties [Sonoda et al., 2009], many other studies have regarded bedrock groundwater as a source of the second peak. For example, Mulholland [1993], Lakey and Krothe [1996], and Onda et al. [2001] suggested that bedrock groundwater made large contributions to delayed peaks in discharge from watersheds underlain by limestone, dolomite, and sedimentary rock, respectively. However, direct monitoring of groundwater using densely located bedrock wells has not been conducted to reveal the causes of these double-peak discharge responses. [6] In this study, we conducted measurements in eight bedrock wells installed in a steep, 2.10 ha headwater catchment. Our previous studies in this catchment [Kosugi et al., 2008; Katsura et al., 2008b] analyzed the dynamics of soil mantle groundwater along the main hollow in relation to the dynamics of bedrock groundwater monitored in two bedrock wells excavated in middle and upstream regions of the catchment. The present study involved monitoring catchment discharge, soil mantle groundwater at three points, and bedrock groundwater in the eight bedrock wells. On the basis of these long-term observations and numerical modeling, we discuss how bedrock groundwater controls multipeak discharge responses of the steep headwater catchment. 2. Method 2.1. Study Site [7] Field observations were conducted for two hydrological years (14 February 2008 to 12 February 2010) in an unchanneled headwater catchment of the Nishi otafuku-yama Experimental Watershed (2.10 ha; N, E; Figure 1), located in the Rokko mountain range of southern Hyogo Prefecture, central Japan. The Rokko mountain range consists of granite and peaks at 932 m above sea level (asl). The area around the main crests is an uplifted peneplain. The whole mountain range has been greatly affected by diastrophic activities, producing many active and inactive fault lines. The climate is warm temperate, with rainfall peaking in summer and little snowfall in winter. The region has a mean annual temperature of 12 C, precipitation of 1800 mm, maximum snow depth of 10 cm, and 10 snow cover days. [8] The entire Nishi otafuku-yama Watershed is covered by secondary forest with dense undergrowth of bamboo grass and is underlain by granitic bedrock called the Rokko Granite. The watershed is 741 m asl at its lowest point and 875 m asl at its highest point, the latter being one of the main crests of the Rokko mountain range (Figure 1). The area around the crest belongs to the uplifted peneplain and has relatively gentle topography. The rest of the watershed exhibits very steep topography. The mean slope gradient of the watershed is 34. The distribution of soil mantle thickness in the watershed was measured at a horizontal grid size of 10 m 10 m using a cone penetrometer, giving an average soil thickness of 1.45 m with a standard deviation of 0.63 m. We found heads of old landslides at a point midway up the main hollow (i.e., point A in Figure 1) and at a point approximately 25 m downstream of point A. The main hollow downstream of point A was steep and narrow, and the soil mantle in this region consisted of coarse colluvium that included gravels. For more information on the experimental watershed, see Kosugi et al. [2008] and Katsura et al. [2008b] Hydrological Observations [9] Three wells were installed in the soil mantle along the main hollow (Figure 1, points A, B, and C). They consisted of PVC pipes with a 5.5 cm inner diameter and 5 mm diameter holes perforated entirely around the periphery. These wells were manually drilled to the bedrock surface. The depths of wells A C (equivalent to the soil depth at each point) were 2.27, 1.15, and 1.30 m, respectively. [10] Bedrock wells with depths of m were drilled at eight locations (Figure 1 and Table 1), using a hydraulic feed type boring machine. Because of the steep topography and lack of an access road, we used a monorail system, which was originally developed for orcharding on steep terrain (up to 45 ), to transport all materials and equipment. Unscreened portions of the bedrock wells were about one fourth to two thirds of total depth (Table 1). In the screened portions of the wells, the space between the casing and the surrounding rocks was completely filled with bentonite with a low saturated hydraulic conductivity (<10 10 cm s 1 ) in order to prevent preferential flow along the casing. [11] Water levels in the soil mantle and bedrock wells were measured automatically using pressure gauges with accuracies of 0.2 and 3 cm, respectively (STS Sensor Technik Sirnach AG, DL/N70). At the outlet of the watershed, the discharge was measured at a V notch weir with an angle of 90 by using a pressure transducer with an accuracy of 0.1 cm (STS Sensor Technik Sirnach AG, DL/N70). Precipitation was measured using a tipping bucket rain gauge at an open space near the ridge. The recording interval for all data was 5 min. A heavy storm event on 2 August 2009 caused excessive sediment deposition in the V notch weir. As a result, discharge data contained errors for 2 5 August of16

3 Figure 1. Topography of the Nishi otafuku-yama Experimental Watershed showing the locations of wells. The vertical line for each bedrock well indicates well depth, weathering class distribution, and maximum water level. Well b (35 m deep) and well c (70 m deep) are located at about the same point Bedrock Characteristics and Electric Resistivity Distribution [12] Rock samples collected from well e indicated the existence of a thick, strongly weathered (D class) layer at the depths of m (Figure 2). Below the strongly weathered layer, a moderately weathered (C L class) layer was present until a depth of 17.5 m, which was underlain by a weakly weathered (C M class) layer. Similar thick, strongly weathered (D class) and moderately weathered (C L class) layers were also found at wells a, b, c, and f (Figures 1 and 3). In contrast, rocks collected from well g Table 1. Depths of Bottom, Boundary Between Unscreened and Screened Portions, and the Shallowest and Deepest Groundwater Levels of Bedrock Wells a Well Bottom Boundary Shallowest WL b Deepest WL b a b c c d c e c f g h a All values indicate depths (in meters) from ground surface. b The shallowest and deepest water levels (WL) for the observation period (14 February 2008 to 12 February 2010). c Groundwater level decreased below the bottom of well. (Figure 2) were less weathered (C L C M classes) at all depths (Figures 1 and 3). The rocks contain many fissures, especially at m depth, where rock samples were crushed during boring operations (Figure 2). Rock samples collected from well h showed similar degrees of weathering to those collected from well g (Figures 1 and 3). At well d, a strongly weathered (D class) layer was located below a thick, weakly weathered (C M class) layer that contained numerous fissures (Figures 1 and 3). [13] To investigate the geological scheme for the bedrock layer, electric resistivity image profiling using a polepole electrode array [Shima et al., 1995] was conducted on 5 6 August Along the main hollow of the watershed, 93 electrodes were installed at 2 m intervals for a horizontal length of 184 m (Figure 3, line I). On line II, which crosses line I at well f and passes through wells h and e, 50 electrodes were installed at 2 m intervals for a horizontal length of 98 m (Figure 3). An observed apparent resistivity pseudosection was corrected by applying an inverse analysis based on the finite element method [Shima et al., 1995] for providing a two-dimensional resistivity distribution. [14] Resistivity was generally high at the surface and low in the depth of bedrock (Figure 3), suggesting a presence of deep bedrock groundwater. Along line I, the thickness of the surface high-resistivity zone (>2000 m) was relatively large in the region between wells b and f, probably representing the thick weathered rock layer because weathered granitic rocks show high resistivity 3of16

4 notably characterized by gentle and significant variations in base flow (Figure 4c). The base flow had broad peaks in August 2008, May 2009, and August 2009 (Figure 4c, striped red arrows). That is, the base flow peaked twice in the second hydrological year. Moreover, the peak in August 2009 was greater than the other two peaks by a factor of approximately 3. Thus, the increased amount of base flow explained the large total discharge observed in the second hydrological year. The comparison between Figures 4a and 4c suggests that the broad peaks in base flow roughly corresponded with peaks in the 2 week averaged rainfall observed 1 3 months before. [16] On a detailed timescale hydrograph, we observed double-peak discharge responses for three storm events (Figure 5c, solid green arrows). That is, whereas the flashy first peaks occurred just after the rainfall peaks, the second peaks lagged behind the rainfall peaks by about 2 3 days. We observed the double-peak discharge responses for eight storm events in total during the whole observation period. An average lag time between the rainfall peak and the first peak in discharge was 3.1 h (with a standard deviation of 1.5 h), while an average lag time between the rainfall peak and the second peak in discharge was 72 h (with a standard deviation of 17 h). [17] After 3 April 2009 (Figures 5c and 4c, dotted yellow arrows), the discharge rate showed a gradual increase, although no major storm events occurred on or around 3 April This increase in base flow continued for about 2 months, resulting in the peak around the end of May 2009 (Figure 4c, one of the striped red arrows), which can be recognized as the third peak in discharge. Similar gradual increases in discharge were observed after the storm events on 15 June 2008 and 2 August 2009 (Figure 4c, dotted yellow arrows), both of which caused third peaks (Figure 4c, striped red arrows). Such triple-peak discharge responses have not been reported in previous studies and are novel findings of this study. Figure 2. Bedrock samples collected from wells e and g. Empty parts represent depths where rock samples were crushed and washed away during boring operations. under unsaturated conditions [Shima et al., 1995]. A similar thick high-resistivity zone was found around well e on line II (Figure 3). Around well h, the surface high-resistivity zone was very thick and displayed extremely high resistivity (>10,000 m). 3. Results 3.1. Discharge [15] In the first and second hydrological years, total precipitation was 1381 and 1679 mm, respectively, and total discharge was 215 and 937 mm, respectively (Figures 4a and 4c). Although the discharge hydrograph showed rapid and flashy responses to major storm events, it was more 3.2. Soil Mantle Groundwater [18] Soil mantle groundwater at point A showed rapid and flashy changes (Figure 6b) in response to major storm events; the groundwater developed under heavy rainfall and disappeared just after the rainfall ceased. [19] At point B, we observed similar flashy changes (Figure 6c). However, the groundwater table generated on 2 August 2009 did not disappear after the rainstorm event and instead lasted for 71 days, showing gradual changes and a broad peak in the middle of August. Such semiperennial groundwater (SPG) occurred eight times over an 8 year observation period (i.e., , ) [Kosugi et al., 2008; Katsura et al., 2008b]. Kosugi et al. [2008] and Katsura et al. [2008b] demonstrated that the source of SPG was bedrock groundwater because the waveform, temperature, and chemistry of the SPG were similar to those of bedrock groundwater observed in well f. [20] At point C, rapid and flashy responses to storm events superimposed on gentle variations in perennial groundwater height (Figure 6d). Katsura et al. [2008b] showed that the perennial groundwater was fed by bedrock groundwater, while the flashy changes were recharged by storm rainwater. 4of16

5 W07530 KOSUGI ET AL.: LOCALIZED BEDROCK AQUIFER DISTRIBUTION AND DISCHARGE W07530 Figure 3. Cross sections along the main hollow of the watershed (line I) and along a line perpendicular to the main hollow (line II) showing locations of soil mantle and bedrock wells, vertical distribution of rock weathering class at each bedrock well, water levels in bedrock wells, and electric resistivity profiles Bedrock Groundwater [21] Figure 7 shows groundwater depth from the soil surface observed in each bedrock well. Figure 7 indicates that groundwater hydrographs are not adequately characterized by their depths. For instance, whereas the depths of groundwater observed in wells c and f differed by more than 30 m, both of these wells produced gentle hydrographs, which were similar to each other. Moreover, the water level of well a showed relatively rapid and large responses to rainfall events, even though it was the deepest among all the bedrock wells. Previous studies also reported rapid and significant rises in the water table in deep bedrock wells during and after precipitation events [e.g., Gburek and Folmar, 1999 ; Rodhe and Bockgård, 2006]. A possible cause of such large variations was suggested to be quick water flow within rock fractures [e.g., Gleeson et al., 2009]. In well d, flashy responses were combined with gentle responses (Figure 7). Well d was screened from the soil surface to the depth of 26.3 m (Table 1), where the space between the casing and surrounding rocks was completely filled with bentonite with a low saturated hydraulic conductivity (<10 10 cm s 1). Thus, the possibility of a preferential flow along the casing is highly unlikely, and flow within rock fissures [Gleeson et al., 2009] can presumably explain the flashy responses. At well d, the existence of a thick, weakly weathered (CM class) layer with many fissures (Figures 1 and 3) might be related to the occurrences of fissure flow. [22] When observed groundwater levels were plotted against their altitudes (i.e., Figure 4b), they indicated the presences of three different aquifers : upper, middle, and lower aquifers. In the upper aquifer, the water level of well a showed rapid and large responses. Wells c, d, e, and f all produced similar hydrographs showing gentle responses and broad peaks, indicating the large spatial expanse of the aquifer. The broad peak was observed once in the first hydrological year and twice in the second hydrological year (Figure 4b, striped red arrows). We observed large differences in water level between the middle and upper aquifers, while the spatial distribution of water levels was nearly flat within the middle aquifer (Figures 4b and 3). For instance, at a specific time point in the low water level periods (18 January 2009, Figure 3, purple lines), the water level difference between wells a and c was 14.9 m, while the water level variation within the middle aquifer was 0.6 m. At a time point in the high water level periods (21 August 2009, Figure 3, thick blue lines), the difference in level between wells a and c was still 14.9 m, while the level variation within the middle aquifer was 1.3 m. [23] Among the four wells belonging to the middle aquifer, well f produced the lowest level during high water level periods (Figures 4b and 3), indicating that the outlet of the middle aquifer was located around well f. In well d, flashy responses were combined with the gentle hydrograph of the middle aquifer. Furthermore, flashy perched groundwater was formed in the shallow well b, which was located at about the same point as well c (Figures 1 and 3), during high water level periods. These flashy water supplies did not cause any rapid changes in the middle aquifer hydrograph, suggesting a large capacity of the middle aquifer. [24] Wells g and h, which belong to the lower aquifer, produced hydrographs similar to each other (Figure 4b). In their hydrographs, narrow peaks (Figure 4b, solid green arrows) and broad peaks (Figure 4b, striped red arrows) are synthesized. Again, we observed a sharp drop in water level between the lower and middle aquifers (Figures 4b and 3). For instance, at a time point during the low water level periods (18 January 2009), the water levels of wells g and h were lower than that of well f by 4.8 and 5.1 m, respectively (Figure 3, purple lines). At a specific time 5 of 16

6 Figure 4. (a) Hyetograph, (b) bedrock groundwater hydrographs, and (c) discharge hydrograph. Thin lines in the groundwater hydrographs represent that the water level decreased below the bottoms of wells. Numbers in parentheses in Figure 4c represent overscaled peak values. The gray line in Figure 4c represents discharge data containing some errors. The shaded period corresponds to the period shown in Figure 5. point during the high water level periods (21 August 2009), the level differences were 12.1 and 12.8 m for wells g and h, respectively (Figure 3, blue lines). Although well h was dug on the ridge at a point 15 m higher than the point of well f, which was located in the hollow, the water level of well h was always lower than that of well f by 2 13 m (Figures 3 and 4b). Within the lower aquifer, well h showed lower water levels than well g for high water level periods (Figure 4b). Thus, a hollow of the lower aquifer was located at a ridge in the surface topography. Previous studies have found some evidence of groundwater flow across topographic divides by measuring variations in stream inflow [Genereux et al., 1993] or by conducting numerical modeling [Tiedeman et al., 1998]. We confirmed the existence of such a flow on the basis of the intensive observations of bedrock groundwater. 4. Discussion 4.1. Discharge Versus Bedrock Groundwater [25] From our observations of bedrock wells, we found a fairly regionalized distribution of bedrock groundwater; that is, upper, middle, and lower aquifers were present (Figure 4b). Instead of a gradual and continuous decline in water level from ridge to valley bottom, we observed large differences in water level between the upper and middle aquifers and between the middle and lower aquifers, as if waterfalls existed within the bedrock (Figure 3). The regionalized groundwater distribution suggests complex flow systems that should influence the formation of the triple-peak discharge responses shown in Figures 4c and 5c. [26] A comparison between Figures 5b and 5c indicates that, whereas the flashy first peaks in discharge occurred in 6of16

7 Figure 5. (a) Hyetograph, (b) bedrock groundwater hydrographs, and (c) soil mantle groundwater and discharge hydrographs, on a detailed time scale. correspondence with the peaks in soil mantle groundwater at point C, the second peaks in discharge occurred at about the same time as the narrow peaks (defined as the first peaks) in the well h hydrograph (Figure 5b, solid green arrows), which were generated in response to major storm events. We found similar peak-time correspondences for all of the eight storm events that caused the double-peak discharge responses. That is, as indicated in Figure 8, the lag time between the rainfall peak and the second peak in the discharge hydrograph was similar to the lag time between the rainfall peak and the first peak in the well h hydrograph. Figure 8 also shows that the lag time between the rainfall peak and the first peak in the discharge hydrograph was comparable to the lag time between the rainfall peak and the peak in the soil mantle groundwater at point C. Because well h was located near the outlet of the lower aquifer, the double-peak discharge responses of the studied watershed were most likely caused by water supply from bedrock groundwater of the lower aquifer. These results agree with findings by Mulholland [1993], Lakey and Krothe [1996], and Onda et al. [2001], who estimated that bedrock groundwater contributed a large amount to the delayed peaks in discharge from watersheds underlain by limestone, dolomite, and sedimentary rock, respectively. For watersheds underlain by granitic bedrock, Haga et al. [2005] and Sonoda et al. [2009] reported formations of delayed second peaks in discharge. These studies suggested that a possible cause of the second peaks was a delayed connection between the upslope saturated zone and the stream, resulting from spatial heterogeneity in soil hydraulic properties. Conversely, our results indicate that the second peaks in the watershed underlain by granitic bedrock are attributable to bedrock groundwater. [27] After 9 April 2009, the well h hydrograph showed a gradual increase (Figure 5b), which continued for about 2 months, resulting in a broad peak around the end of May 2009 (i.e., the second peak indicated by a striped red arrow in Figure 4b), when the discharge hydrograph showed the third peak (Figure 4c). This gradual increase is likely explained by water supply from the middle aquifer because the middle aquifer showed a continuous increase in water level throughout this period (Figure 5b) and had a peak (Figure 4b, one of the striped red arrows) at about the same time as the second peak in the lower aquifer and the third peak in discharge occurred. The other peaks in the middle aquifer (i.e., the mid-august 2008 and 2009 peaks) also corresponded well with the second peaks in the lower aquifer and the third peaks in discharge. From these results, the triple-peak discharge responses can be explained by three types of water pathways: the first peak was caused by the 7of16

8 Figure 6. (a) Hyetograph and soil mantle groundwater hydrographs at points (b) A, (c) B, and (d) C. Groundwater levels are indicated by heights from soil-bedrock interface (left axis) and altitudes (right axis). peak in soil mantle groundwater around the outlet of the watershed, the second peak was caused by the first peak in the lower aquifer, which was presumably fed by vertical rainwater infiltration, and the third peak was caused by the second peak in the lower aquifer, resulting from an increased lateral water supply from the middle aquifer. [28] The middle aquifer was likely recharged by vertical infiltration through thick strongly or moderately weathered bedrock (Figures 1, 2, and 3) and lateral flow from the upper aquifer. Because of the broad regional expanse and large capacity of the middle aquifer, water supply from the flashy upper aquifer was smoothed in the middle aquifer. As a result, the upper aquifer hydrograph hardly correlated with the discharge hydrograph (Figure 4), while the gentle hydrograph of the middle aquifer controlled the base flow discharge by feeding the lower aquifer. Thus, the spatial expanse of bedrock aquifers and the interaction among aquifers are key factors in explaining the discharge. [29] Many studies conducted in small watersheds in granite mountains showed smooth hydrograph responses with only one peak in each storm event even though substantial bedrock infiltration and exfiltration were observed [e.g., Onda et al., 2001; Uchida et al., 2003; Kosugi et al., 2006]. In the studied watershed, the responses of each of the water pathways were not smoothly connected with one another, forming the anomalous triple-peak discharge responses. Presumably, this response can be attributed to the unique bedrock structure of the studied watershed, which caused the localized bedrock aquifer distribution instead of a gradual and continuous decline in water level from ridge to valley bottom. Figure 3 illustrates sudden changes in electric resistivity profiles between wells a and c, between wells f and g, and between wells f and h. Resistivity profiles have been effectively used to detect bedrock discontinuity caused by fault lines [Matsui, 2009]. Therefore, Figure 3 suggests the existence of faults between the upper and middle aquifers and between the middle and lower aquifers. The hypothesis of a fault dividing the middle and lower aquifers is supported by observations of rock samples collected from wells (Figures 2 and 3), which indicated clear differences in rock physical properties between wells in the middle aquifer (wells c, d, e, and f) and the lower aquifer (wells g and h). Around a fault, rocks are exposed to cataclasis, forming a film of clay minerals with low permeability [Utada, 2003]. As a result, a fault sometimes works as a divide of bedrock aquifers [Shima et al., 1995]. From this information, we presume that fault lines possibly explain the development of the localized bedrock aquifer distribution, preventing smooth connections among different water pathways and resulting in the triple-peak discharge responses. It is expected that localized bedrock aquifer distributions are occasionally developed in watersheds that have been affected by major diastrophic activities, producing many fault lines. For such watersheds, 8of16

9 Figure 7. (a) Hyetograph and (b) bedrock groundwater hydrographs. Thin lines in the groundwater hydrographs represent that the water level decreased below the bottoms of wells. understanding geological properties is essential for explaining discharge hydrographs Water Budget and Spatial Expanse of Bedrock Aquifers [30] In the first and second hydrological years, total precipitation was 1381 and 1679 mm, respectively, and total discharge was 215 and 937 mm, respectively (Figure 4). Consequently, we observed total loss of 1166 and 742 mm for the first and second years, respectively. Suzuki [1980] estimated annual evapotranspiration of mm for a secondary forest in the studied region by conducting water budget calculations using precipitation and discharge data observed for 6 years at a 6 ha watershed ( N, E). Thus, the loss for the first year (1166 mm) was much larger than the expected annual evapotranspiration. The discharge rate and groundwater levels at the end of the first year were similar to those at the beginning of the first year (Figures 4 and 6). For instance, increases in water levels were only 0.92, 0.66, and 0.22 m for wells a (the upper aquifer), f (the middle aquifer), and g (the lower aquifer), respectively. The changes in the water levels occurred in the C M class layer for wells a and g and in the C L class layer for well f (Figure 3). By using effective porosity measured by Katsura et al. [2009] for the C M and C L class layers (0.007 and 0.045, respectively), changes in water storage were estimated to be 6.4, 29.6, and 1.5 mm for wells a, f, and g, respectively. That is, the effect of changes in water storage on the annual water balance should be small. Therefore, the large annual water loss of the first year was probably attributable to the groundwater leakage to the depth of bedrock and the groundwater effluxion across the watershed boundary. The existence of the groundwater leakage was supported by cessations in the discharge during winters (Figure 4c) when the groundwater levels were higher than the watershed outlet elevation (741.2 m; Figures 3 and 4b). The existence of the groundwater effluxion was supported by the continual groundwater flow across the topographic divide inferred from the slope of the water table between wells f and h (Figures 3 and 4b). [31] The loss for the second hydrological year (742 mm) was in the range of the reported annual evapotranspiration. However, the hydrographs of wells f and h suggested that the groundwater effluxion across the topographic divide continued for the whole second year (Figures 3 and 4b). Moreover, the discharge rate and groundwater levels at the end of the second year were greater than those at the beginning of the second year (Figures 4 and 6), indicating an increase in the water storage. These results imply a water source other than precipitation. A possible source is an influxion of bedrock groundwater across the topographic divide; the middle and upper aquifers might extend beyond the watershed boundary by collecting water from an area wider than the topographically defined catchment area. [32] Thus, this study suggests that bedrock aquifers extend across topographic divides, producing large effects 9of16

10 Figure 8. Lag times comparing peaks in hyetograph and hydrograph for eight storm events that caused double-peak discharge responses. Crosses represent correlations between lag time comparing the rainfall peak and the peak in the soil mantle groundwater at point C and lag time comparing the rainfall peak and the first peak in the discharge hydrograph. Circles represent correlations between lag time comparing the rainfall peak and the first peak in the well h hydrograph and lag time comparing the rainfall peak and the second peak in the discharge hydrograph. on water balance analyses of topographically defined headwater catchments. For quantifications of the effluxion and influxion of bedrock groundwater, the number of observation wells should be increased, as is planned for future studies in this watershed. In particular, the nature of the spatial expanse of the upper aquifer is unclear since only one well (i.e., well a) was located in this aquifer Soil Mantle Groundwater Versus Bedrock Groundwater [33] By analyzing water chemical and thermal observation results, our previous studies [Kosugi et al., 2008; Katsura et al., 2008b] concluded that sources of the SPG at point B and the perennial groundwater at point C were bedrock groundwater. However, these studies did not discuss which bedrock aquifer fed the soil mantle groundwater. [34] When the lower aquifer water levels were compared with the level of SPG at point B, the latter was always above the former (Figures 3, 4b, and 6c). Consequently, the source of SPG at point B could not be the lower aquifer. Instead, the source of SPG was thought to be the middle aquifer because the peak in SPG occurred at about the same time as the peak in the middle aquifer (i.e., 22 August 2009, Figures 4b and 6c). That is, part of the middle aquifer did not flow into the lower aquifer but directly exfiltrated into the soil mantle. [35] Although the level of soil mantle groundwater at point C was always lower than levels of the lower aquifer (Figures 3, 4b, and 6d), we suspect that the lower aquifer made only a minor contribution to the formation of the perennial groundwater at point C. We propose this because the perennial groundwater at point C did not have clear peaks corresponding to the first peaks in the lower aquifer (Figure 5) and instead showed a waveform similar to that of the middle aquifer (Figures 4b and 6d). [36] From these results, we presume that several exfiltration points of the middle aquifer exist along the main hollow of the catchment, each of which is activated (or inactivated) depending on the middle aquifer water level. These points recharge the SPG at point B, the perennial groundwater at point C, and the base flow discharge Modeling Discharge General Modeling Concept [37] On the basis of the above results and discussion, the discharge of the studied watershed (Figures 4c and 5c), q, can be assumed to be composed of three different components: discharges from the soil mantle groundwater, q 1 ; from the lower bedrock aquifer, q 2 ; and from the middle bedrock aquifer, q 3 (i.e., q ¼ q 1 þ q 2 þ q 3 ). In this study, we developed a simple model to explain the formation of q by assuming that (1) the three discharge components are independent of each other and (2) each discharge component is modeled by a simple storage-discharge relationship Discharge From Soil Mantle Groundwater [38] The discharge from the soil mantle groundwater, q 1 [LT 1 ], was modeled by applying a procedure described by Kirchner [2009]. Here we employed the following power law function [Kirchner, 2009, equation (10)], in which q 1 is related to the recession rate (i.e., the slope of the recession hydrograph): dq 1 dt ¼ aq b 1 ; where t is time and a and b are parameters reflecting hydrological properties of the soil mantle [Brutsaert and Nieber, 1977; Rupp and Woods, 2008]. The parameter b is dimensionless, and the dimension of a varies with b, asl 1 b T b 2. Following the procedure described by equations (11) (14) of Kirchner [2009], a functional relationship between water storage in the soil mantle, S [L], and q 1, is derived from equation (1) 1= 2 b q 1 ¼ ½að2 bþðs S 0 ÞŠ ; S S 0 > 0; q 1 ¼ 0; S S 0 0; where S 0 is the minimal water storage to produce q 1. Time series of S and q 1 can be derived by combining equation (2) with the following finite difference form of the water balance equation: S tþt S 0 ð S t S 0 Þ t ð1þ ð2þ ¼ P t tþt=2 T t tþt=2 q tþt=2 1 ; where P [LT 1 ] is effective precipitation, T [LT 1 ] is transpiration, is the ratio of the contributing area for discharge q 1 to the whole watershed area, t is the distance between the time steps, and t is the time lag accounting ð3þ 10 of 16

11 for travel time delays of the discharge [Beven, 2002]. A variable with the superscript of ðt þ t=2þ represents an average value between t and t þ t. Equation (3) was derived from equation (1) of Kirchner [2009] by introducing the parameter for specifying the contributing area for discharge q 1. For the model application, a, b, t, and were treated as the fitted parameters. The value of S 0 does not need to be specified because q 1 calculations are conducted by using (S S 0 ) as a variable instead of S. [39] During no-rain periods, (S S 0 ) can become negative because of water consumption by transpiration. That is, even after cessations of q 1, the soil mantle loses water by root water uptake. Then, for a subsequent storm event, the negative (S S 0 ) prevents the generation of q 1 until the moisture deficit is fulfilled by precipitation (see equation (2)). However, as transpiration is known to be restrained by soil drought [Tognetti et al., 2009], (S S 0 ) cannot become too small. In order to account for a limitation in the soil moisture deficit, we introduced a minimal value of (S S 0 ), D, as a fitted parameter of the model (D 0). If (S S 0 ) became smaller than D during a solution of equation (3), T was reduced and (S S 0 ) was fixed at D. [40] Values of P and T in equation (3) were estimated by following the methods of a prior study [Kosugi et al., 2002] (Appendix A). Because no discharge was observed and transpiration was estimated to be zero at the simulation starting time point (i.e., 14 February 2008), the initial (S S 0 )value was fixed at zero. The value of t in equation (3) was set as 0.1 h so that the numerical solutions of equation (3) under no-precipitation and no-transpiration conditions could reproduce an analytical recession curve derived from equation (1). Moreover, we conducted q 1 calculations for the entire simulation period (i.e., from 14 February 2008 through 12 February 2010) with t values of 0.05 or 0.01 h and confirmed that the simulation results did not depend on the t values Discharge From Bedrock Groundwater [41] A method similar to the q 1 estimation cannot be applied to estimations of the contributions from the lower aquifer, q 2, and from the middle aquifer, q 3, to discharge. This is because each of the recharge processes in the lower and middle aquifers is not expressed by an independent simple water budget equation (i.e., equation (3)); rather, interactions among all of the aquifers (upper, middle, and lower) should be evaluated. Instead of developing a complicated aquifer network model, this study employed a simple Dupuit-Forchheimer discharge formula [Bear and Cheng, 2010] to compute q 2 and q 3 because storage in aquifers is well represented by the observed groundwater levels. [42] The Dupuit-Forchheimer discharge formula correlates discharge rate from aquifer x, q x [LT 1 ], to height of groundwater table measured from the level of the discharge observation point, h x [L], as where x is defined as q x ¼ x h 2 x ; x ¼ WK s 2LA ; where W [L] is the width of spring, K s [LT 1 ] is the saturated hydraulic conductivity of the aquifer, L [L] is the ð4þ ð5þ horizontal distance between the observation points of discharge and groundwater table, and A [L 2 ] is the watershed area [Bear and Cheng, 2010]. In equation (4), the relationship between q x and h x is expressed by a parabolic line, having a q x value of zero when h x ¼ 0. In the studied watershed, the discharge ceased during winters (Figure 4c), although the groundwater levels of the lower and middle aquifers were higher than the watershed outlet elevation (741.2 m; Figures 3 and 4). That is, q x is equal to zero at a positive h x, which probably is attributable to the groundwater leakage to the depth of bedrock. Consequently, in order to model discharges from the lower aquifer, q 2, and the middle aquifer, q 3, we used the following expanded Dupuit-Forchheimer formula: 2 q 2 ¼ 2 h 2 h c;2 þ qc;2 ; h 2 > ~ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 2 ¼ h c;2 þ q c;2 2 ; q 2 ¼ 0; h 2 ~ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6þ h 2 ¼ h c;2 þ q c;2 2 ; 2 q 3 ¼ 3 h 3 h c;3 þ qc;3 ; h 3 > ~ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 3 ¼ h c;3 þ q c;3 3 ; q 3 ¼ 0; h 3 ~ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð7þ h 3 ¼ h c;3 þ q c;3 3 ; respectively. In equations (6) and (7), the parabolic line obtained by the original Dupuit-Forchheimer formula (i.e., equation (4)) is translated along h x axes by h c,x and along q x axes by q c,x (here, x is equal to 2 and 3 for the lower and middle aquifers, respectively). Values of h c,x and q c,x define magnitude of the translation and control the critical groundwater height for generation and cessation of discharge (i.e., ~h 2 and ~ h 3 in equations (6) and (7), respectively). We performed sensitivity analyses and confirmed that in the expanded Dupuit-Forchheimer formula, all of x, h c,x, and q c,x should be treated as the fitted parameters. [43] For the model application, h 2 in equation (6) was computed as the difference between the groundwater level observed in well h and the watershed outlet elevation (i.e., m), and h 3 was computed as the difference between the groundwater level observed in well f and the watershed outlet elevation. For periods of missing data, the groundwater level in well h was interpolated by translating the groundwater hydrograph observed in well g because wells h and g showed very similar hydrographs (Figures 4b and 7), and the groundwater level in well f was interpolated by translating the groundwater hydrograph observed in well e (Figures 4b and 7) Model Calculation Results [44] A nonlinear optimization procedure [Marquardt, 1963] was used to optimize the parameters by minimizing the residual sum of squares (RSS) comparing the observed discharge rate and the discharge rate computed as the sum of q 1, q 2, and q 3. The derived parameters are summarized in Table 2. The minimized RSS value was 1.46 mm 2 h 2, which produced the Nash-Sutcliffe efficiency factor (NSEF) of [45] Figures 9b and 10b, show that the modeling results generally reproduced the observed hydrographs. Whereas flashy storm hydrographs are composed of the discharge from the soil mantle, q 1, generation of the second peak is explained by the discharge from the lower aquifer, q 2 (Figure 10b). The gentle and considerable variations in the 11 of 16

12 Table 2. Optimized Parameters for Discharge Modeling Parameter Unit Value q 1 Calculation a mm 1 b h b b 1.71 t h D mm q 2 Calculation 2 m 1 h h c,2 m 26.5 q c,2 mm h a ~h 2 m 27.9 q 3 Calculation 3 m 1 h h c,3 m 28.0 q c,3 mm h b ~h 3 m 36.1 a Computed from 2, h c,2, and q c,2 values. b Computed from 3, h c,3, and q c,3 values. base flow discharge as well as the timing and magnitude of the broad third peaks are well fitted by the discharge from the lower aquifer, q 2, and from the middle aquifer, q 3 (Figure 9b). Among the three components of the modeled hydrograph, the discharge of bedrock groundwater (i.e., q 2 plus q 3 ) accounted for 93% of the total discharge. The discharge of soil mantle groundwater, q 1, was small (7%). [46] Among the five parameters related to the q 1 calculations (Table 2), b was optimized to be greater than 1, indicating a nonlinear storage-discharge relationship for soil mantle groundwater [Kirchner, 2009]. While b was in the middle range suggested by previous studies [e.g., Tague and Grant, 2004; Kirchner, 2009], a was relatively large reflecting rapid and flashy responses of storm hydrographs (Figures 9 and 10). The optimized value (Table 2) implied that 4% of the recharge to the soil mantle appeared as discharge at the V notch weir, corresponding to the small contribution of q 1 to the whole discharge (Figure 9). The value of D was optimized to be close to zero (Table 2), indicating that the soil moisture deficit by transpiration was small and q 1 was generated responding to each precipitation event (Figures 9 and 10). The small t value of 1 h (Table 2) corresponded to the quick q 1 responses to precipitation (Figure 10). Validity and sensitivity of the parameters for the q 1 calculations are described in Appendix B. [47] Figure 11 shows plots of equations (6) and (7) with the optimized parameters summarized in Table 2. The value of q 2 was more sensitive to the groundwater height than q 3, indicating that an increase in groundwater level of the lower aquifer has a greater effect on the discharge rate than a similar increase in groundwater level of the middle aquifer. The difference between the lower and middle aquifers is attributable to the difference in 2 and 3 values; that is, 2 was optimized to be greater than 3 by an order of magnitude (Table 2). The lower aquifer is closer to the outlet of the watershed than the middle aquifer, which probably resulted in a smaller L value in equation (5) for the lower aquifer. In addition, the lower aquifer might have a greater hydraulic conductivity, K s, than the middle aquifer because rock samples collected from the lower aquifer contained many fissures (Figure 2). Moreover, it might be that the lower aquifer has greater spring area than the Figure 9. (a) Hyetograph, (b) observed and simulated discharge hydrographs, and (c) difference between the observed and simulated discharge rates. The simulated hydrograph shows each component of discharge from the soil mantle, q 1 ; discharge from the lower aquifer, q 2 ; and discharge from the middle aquifer, q 3. The difference was computed by subtracting computed rate from observed rate. 12 of 16

13 Figure 10. (a) Hyetograph and (b) observed and simulated discharge hydrographs on a detailed time scale. The simulated hydrograph shows each component of discharge from the soil mantle, q 1 ; discharge from the lower aquifer, q 2 ; and discharge from the middle aquifer, q 3. middle aquifer, which resulted in a greater W value in equation (5). All of these characteristics of the lower aquifer likely resulted in the 2 value greater than 3 (see equation (5)), which explains the greater effect of the lower aquifer on the discharge rate (Figure 11). In Figure 11, q 2 and q 3 ceased when h m and h m, respectively. These thresholds (i.e., ~ h 2 and ~ h 3 ) were derived from the optimized parameters summarized in Table 2. Considering the watershed outlet elevation (i.e., m), it was estimated that q 2 and q 3 ceased when groundwater levels observed in wells h and f became smaller than and m, respectively. [48] For detailed analyses on model performances, Figure 9c shows a plot comparing the observed and simulated discharge rates. The absolute value of the difference was smaller than and mm h 1 for 80% and 95% of the whole period, respectively, suggesting that a reasonable match was obtained between the observed and simulated hydrographs. Flashy increases and decreases in the difference occurred for some storm events when the computed q 1 took values greater than 0.01 mm h 1 (Figure 9c, blue circles). When q mm h 1, the absolute difference was small (orange circles). This suggested that most of the simulation error was attributable to misestimation of the discharge from soil mantle groundwater, while estimations of the discharges from bedrock aquifers were reliable. [49] The flashy decreases and increases in the differences tended to occur during the low and high base flow periods, respectively (Figure 9c). That is, the model tended to overestimate and underestimate the discharge from the soil mantle groundwater during the low and high base flow periods, respectively. These modeling results might be explained by the contribution area of the soil mantle groundwater to the discharge hydrograph varying between the low and high base flow periods, affected by changes in exfiltration of the bedrock groundwater into the soil mantle. During the high base flow periods, increased bedrock groundwater exfiltration likely made the soil mantle wetter, which increased the contribution area of soil mantle groundwater to discharge. Such interactions between soil mantle groundwater and bedrock groundwater were not considered in the proposed simple model, which possibly caused the underestimation during the high base flow periods. During the low base flow periods, the simple model could not evaluate the decrease Figure 11. Relationship between discharge rate from bedrock aquifer (q 2 and q 3 ) and height of groundwater tables (h 2 and h 3 ), showing plots of equations (6) and (7) with the parameters summarized in Table 2. Thick lines represent ranges used for model calculations shown in Figure of 16