Flow paths, rainfall properties, and antecedent soil moisture controlling lags to peak discharge in a granitic unchanneled catchment

Authors


Abstract

[1] The lag time between peak rainfall and peak discharge is an important index reflecting hydrological properties in a catchment. To characterize lag times, we studied the effects of rainfall properties, antecedent moisture conditions, and flow paths on runoff response in a forested unchanneled catchment, using a hydrometric and hydrochemical approach. Soil moisture, soil pore water pressure, and piezometric surface were monitored. Also, dissolved silica and organic carbon concentrations of spring water and subsurface water were observed. Runoff response was characterized by two types of lag times: a short lag time (<2 hours) or a long lag time (>24 hours). During events with short lag times, saturation excess overland flow was dominant, and the source area was limited to the near-spring area. During events with long lag times, saturated subsurface flow above the soil-bedrock interface was dominant, and the source area near the spring was connected to the upslope area via saturated zone above soil-bedrock interface. The spring-hillslope hydrological connection to generate peak discharges with long lag times occurred when the sum of cumulative rainfall and an antecedent soil moisture index, which was derived from initial storage of surface soil layer, was greater than 135 mm. Moreover, the time between the upslope connection of source area and subsequent peak discharge decreased with the average rainfall intensity in the time. We conclude that consideration of antecedent soil moisture conditions as well as rainfall amount and intensity is essential for understanding the regional characteristics of lag times and subsurface water movement.

1. Introduction

[2] Water discharging from and transiently stored within small headwater catchments is one of the most important factors controlling the formation of streamflow, development of water chemistry and also the development of landforms in larger catchments [e.g., Tsukamoto et al., 1982; Pearce et al., 1986; Dietrich and Dunne, 1993; Likens and Bormann, 1995]. In other words, in rainfall-runoff processes, the quantity and quality of water are affected by many catchment properties, including water retention and permeability of the soil, vegetation cover, topography and bedrock features. Therefore rainfall-runoff response, as typified by a lag time between rainfall (input) and runoff (output), is a macroscopic indicator of the hydrological properties in the catchment and provides fundamental information to understand mechanisms of storm flow generation.

[3] Some researchers have reported that the lag time between peak rainfall and peak discharge, or the maximum rise of the groundwater table, reflects the lithologic characteristics [Onda et al., 2001] and relates both to timing of landslide initiation [Montgomery et al., 2002] and to landslide mass and depth [Hattanji, 2003]. In granitic headwater catchments in Japan, peak streamflow discharge was nearly contemporaneous with peak rainfall [e.g., Katsuyama et al., 2001; Onda et al., 2001; Uchida et al., 2003a]. However, in a shale and a serpentinite catchment, lag times to peak streamflow were mainly in the range 5–12 (average 10) and 0–20 h (average 6 h), respectively [Onda et al., 2001]. Dunne [1978] pointed out that lag times were influenced by dominant runoff components. For example, subsurface storm flow hydrographs had lags approximately 40 times longer than those of Horton overland flow for catchments in the range 0.1–1.0 km2 [Dunne, 1978].

[4] Recently, hydrometric, hydrochemical and isotopic approaches have yielded much knowledge about the source, flow path and age of runoff water [e.g., McDonnell, 1990; Rice and Hornberger, 1998; Asano et al., 2002; Uchida et al., 2003a]. For example, saturated overland flow from variable source areas as well as direct rainfall into a channel is dominant only during the early part of the storm hydrograph, and its contribution to storm flow is small in humid, temperate forests [Mosley, 1979; Buttle, 1994]. It was also shown that subsurface water in forested hillslopes contributed mainly to storm runoff via rapid flow along the soil–bedrock interface [McDonnell, 1990; Peters et al., 1995; Buttle et al., 2004], and that preferential flow through a temporarily perched saturated zone in a macroporous soil layer brought a rapid increase in discharge after rainfall [Mulholland, 1993].

[5] In addition, recent studies based on tensiometric, piezometric, chemical and thermal data [e.g., Anderson et al., 1997; Montgomery et al., 1997; Uchida et al., 2003b] have demonstrated the important contribution of water moving through bedrock. Uchida et al. [2003b] showed field evidence that seepage water from bedrock recharged a perennial saturated zone above the bedrock near a spring in a steep unchanneled hollow in the Fudoji catchment, Japan. Anderson et al. [1997] and Montgomery et al. [2002] reported that shallow bedrock groundwater in steep unchanneled catchments (CB1 and/or CB2) in the Oregon Coast Range contributed significantly to both storm runoff and seasonal base flow and also had a strong relationship with landslide initiation and its timing.

[6] Thus it is important for understanding the mechanisms controlling lag times to study the recharge and lateral flow processes of subsurface water through the soil matrix, soil pipe or bedrock fractures, and to illustrate the effects of rainfall properties and initial moisture conditions on streamflow generation. The previous studies on the lag time have considered several factors controlling flow paths and water velocity; the delay of the subsurface water response to the rainfall [Anderson and Burt, 1977, 1978], the propagation of the groundwater rise from the upper part of the valley floor to the outlet of the catchment [Hihara and Suzuki, 1988], the initial loss of the early part of the rainfall due to initial soil water deficit [Mulholland, 1993], the topographic slope, which is proportional to subsurface water velocity in Darcy's law [Montgomery and Dietrich, 2002], the spatial and temporal variation of piezometric response of the bedrock groundwater [Montgomery et al., 2002], and the lithologic character affecting the bedrock groundwater flow [Onda et al., 2001].

[7] However, very few studies have tried to characterize lag times based on subsurface water dynamics, rainfall properties and water chemistry. Therefore the objective of this study is to clarify the effects of flow paths, rainfall characteristics and antecedent moisture conditions on the lag time in a granitic unchanneled catchment using hydrometric and hydrochemical observations.

2. Study Site

[8] The study was conducted in a 0.65 ha forested, unchanneled catchment, the L1 catchment, in the Mizugaki Research Watershed, located in the northern part of Yamanashi Prefecture, central Japan (Figure 1a). This catchment is underlain by granitic rock. The elevation ranges from 1495 to 1555 m. The slope of the catchment is steep: the average slope is 26.7° and the relief ratio is 0.46. The slope along the concavity (line SP–A in Figure 1a) is steep in the upper part (line P4–A, 28.8°) but relatively moderate in the lower part (line SP–P4, 13.3°).

Figure 1.

(a) Location of study site, the L1 catchment in the Mizugaki Research Watershed, and detailed map of topography and measurement points. (b) Longitudinal profile along line SP–P4 shown in Figure 1a and instrumentation.

[9] The spring, where water seeps from the soil to the ground surface, is at the lowest part of the catchment (SP in Figure 1a). The saturated area around the spring varies from about 4 m2 at low-flow periods to 20 m2 at high-flow periods, and accounts for only 0.06–0.37% of the total catchment area.

[10] The soil is brown forest soil and is predominantly made up of three distinct layers (A, B, and C horizons). We defined bedrock as the layer that cannot be penetrated with the hand auger (0.07 m in diameter). The depth of soil to bedrock was investigated at five sites around each measurement point (SP–P4 in Figure 1b) and additionally at 2 m intervals from P1 to P2.5 using the hand auger. The depth of soil to bedrock near the spring (SP) and at the lower part of the concavity (P1–P4) ranges from 0.3 to 0.8 m and 1 to 3 m, respectively. Although the soil depth in the upper part of the catchment was not investigated in detail, the depth is more than 1 m because a small auger (1 m in length and 0.02 m in diameter) can easily penetrate fully. The depth of the A horizon at the spring and the hillslope ranges from 0.3 to 0.4 m and 0.05 to 0.4 m, respectively, and the B horizon (sand/clay soil) ranges from 0.1 to 0.2 m and 0.5 to 0.7 m, respectively. Most tree roots are concentrated in the A horizon.

[11] The averaged saturated hydraulic conductivities estimated using three 100 cm3 cores from the shallow (0–0.3 m), middle (0.3–1.0 m) and deep part (1.0 m ~) of the soil are 103, 102 and 101 mm h−1, respectively (Figure 2). The soil is rich in pores and the averaged porosities at the same depths (shallow, middle and deep) are 0.75, 0.71 and 0.64, respectively.

Figure 2.

Saturated hydraulic conductivity (Ksat) in soil profile and typical soil horizon in the hillslope. Line plot shows mean of logKsat at each sampling depth.

[12] The mean annual air temperature at the catchment is 7.1°C and ranges from −15.0 to 27.4°C. January is the coldest and August is the warmest month. Annual precipitation is about 1150 mm, mostly as frontal rain and typhoon-derived rain in summer. From late December to early April, the study site is covered with snow. The approximate water equivalent of the snow cover varies between 10 and 100 mm.

[13] The forest overstory is occupied by Japanese larch (Larix kaempferi), which is a summer green needleleaf tree and has been planted at this study site since the 1960s, while the understory is composed of deciduous broadleaf trees (Quercus mongolica, Ostrya japonica, and Weigela japonica).

3. Methods

3.1. Definition of Lag Time and Analysis of Storm Events

[14] Storm events, defined as having a total rainfall of more than 10 mm, were analyzed in this study. Rain days were defined as those where the 24 hour rainfall was greater than 0.2 mm. Lag time was defined as the time between peak rainfall and peak discharge, according to Mosley [1979] and Onda et al. [2001] (Figure 3). The peak rainfall intensity (Rpk) was determined based on the maximum 30 min rainfall intensity. The initial discharge (Qi) of the event was defined as the discharge just before the first pulse of rainfall. The runoff coefficient from rising (TQup) to peak (TQpk) was estimated by dividing the total amount of direct runoff by the rainfall amount from TQup to TQpk. The direct runoff was estimated by subtracting base flow, which was assumed equal to Qi, from total runoff.

Figure 3.

Definition sketch for analysis of storm event. Abbreviations are related to Figure 7 and Table 1.

3.2. Hydrometric and Hydrochemical Observations

[15] We monitored rainfall, discharge from the spring, soil moisture content, soil pore water pressure and piezometric head from the start of the rainy season to just before snowfall (mid-June 2003 to mid-December 2003). In addition, we observed the dissolved silica and dissolved organic carbon (DOC) concentrations of the spring water, soil water and bedrock groundwater.

[16] A 0.2 mm tipping bucket gauge (Davis rain collector) recorded rainfall at 10 minute intervals in an open site 250 m north of the study site. Spring discharge was gauged using a 60° V notch weir equipped with a pressure transducer (HI-NET HM-500) and recorded using a data logger (HI-NET HIT-AL1) at 5 minute intervals.

[17] Soil moisture content in the surface soil layer (0–0.3 m deep) along the concavity was measured by water content reflectometers with rods 0.3 m in length (Campbell CS615) installed vertically from the soil surface at positions P1, P2, P2.5, P3, and P4 (Figure 1b). The CS615 probes, calibrated in the laboratory, were monitored each minute, and the 5 minute means were stored on a data logger (Campbell CR10X). Soil pore water pressure just above the soil-bedrock interface was measured automatically using tensiometers with pressure transducers (Daiki DIK-3021) at P1 and P2.

[18] Piezometric surface was determined by stainless steel pipes as piezometers at SP, P1, P2 and P3. Each pipe (50 mm in diameter, 2 m in length) had nine 8 mm diameter perforations in the lowest 0.1 m and was equipped with a cone head. We cannot penetrate the bedrock with the hand auger but can stick the cone head pipes into the bedrock by hitting with a 4 kg hammer. The screens of pipes at SP, P1, and P2 were located within the bedrock, but at P3 they were above the soil-bedrock interface because the pipe length was nearly equal to the soil depth at P3. At SP, P1 and P2, the piezometer was equipped with a pressure transducer (HI-NET HM-500) and a data logger. In addition, the vertical hydraulic gradients between the soil and the bedrock at P1 and P2 were calculated using the data from both tensiometer above the soil-bedrock interface and the piezometer in the bedrock at each measurement point. At P3, the depth to water in the piezometer below the ground surface was measured manually with an electronic indicator at 1- to 2-week intervals and additionally during several storm events. Data obtained automatically were adjusted to 10 minute data for analysis.

[19] Soil water was sampled by tension lysimeters at depths of 0.2, 0.3, 0.5 and 1.0 m. The lysimeters were installed vertically from the soil surface adjacent to P2. Suction to the lysimeters was regulated by a hand-held vacuum pump to −70 kPa. Sufficient sample could be obtained from most lysimeters in 4–24 hours. Soil water samples were taken between 2 and 13 times a month. Water in the piezometer at P2 as bedrock groundwater was sampled twice; i.e., before and after the observation period of piezometric head (30 May 2003 and 16 December 2003). Spring water samples were taken 5 to 14 times a month.

[20] Water samples were filtered through 0.2 µm filters and analyzed for dissolved silica and DOC. Dissolved silica concentrations, as mg SiO2 per liter, were estimated by the molybdenum yellow method [American Public Health Association, 1992]. Dissolved inorganic carbon was removed by air bubbling at pH 3.0, and then DOC concentrations were determined using a total organic carbon analyzer (Shimazu TOC-5000A).

3.3. Antecedent Soil Moisture Condition

[21] We used an antecedent soil moisture index (ASI) to quantify the effects of initial soil moisture conditions on the subsurface water dynamics. This index can more explicitly represent the antecedent soil moisture condition than a rainfall-derived index such as the antecedent precipitation index. We calculated ASI for each storm event as the initial storage of the surface soil layer in the catchment based on the volumetric water content at the measurement points (P1, P2, P2.5, P3, and P4). To simplify, the measurement points were regarded as the representative points of the area with equivalent altitude and the catchment was divided into five subareas (Figure 4). In addition, the surface soil layer was regarded as the 0–0.3 m deep, where the CS615 probes were inserted. Then, ASI is

equation image

where VWCi is the volumetric water content of the surface soil at the measurement point in the subarea i, D is the thickness of the surface soil (300 mm), Ai is the area of the subarea i, and Aw is the whole catchment area (Figure 4).

Figure 4.

Subareas divided on the basis of the altitude of the measurement points for calculating the antecedent soil moisture index.

4. Results

4.1. Rainfall, Spring Discharge, and Subsurface Water

[22] The total amounts of rainfall and runoff at the spring during the study period (12 June 2003 to 20 December 2003) were 776 mm and 321 mm, respectively. The L1 catchment received a lot of rainfall from July through August, and so the spring discharge and the soil moisture content were relatively high (Figures 5a–5c). The spring discharge and the soil moisture content quickly responded to rainfall events.

Figure 5.

Temporal fluctuation of (a) rainfall, (b) spring discharge, (c) soil water content, (d) soil pore water pressure head, (e) piezometric surface, and (f) vertical hydraulic head gradient (positive means downward flow). SP, P1, P2, P2.5, P3, and P4 show the measurement points on Figure 1. NOC shown on vertical axis in Figure 5e means the nonoccurrence of water table in the piezometer. Dashed lines shown on the right side of Figure 5e indicate the location of soil-bedrock interface.

[23] The soil pore water pressure head at P1 was temporarily positive, that is, the saturated zone above the soil-bedrock interface appeared transiently at P1 (Figure 5d). On the other hand, the positive pore water pressure at P2 existed throughout the study period. In contrast, the water table above soil-bedrock interface at P3 never occurred, even during the largest rain event in the middle of August (Figure 5e). Therefore the saturated zone above the soil-bedrock interface showed two types of setting: connection and disconnection between SP and P2.

[24] The fluctuation patterns of piezometric surfaces of bedrock groundwater were very different by location (Figure 5e). The piezometric surface at SP was almost constant, whereas at P1 and P2 varied widely. Especially, at P2, the fluctuation was remarkable and the piezometric surface was mainly above the soil-bedrock interface.

[25] The vertical hydraulic head gradient between the soil and the bedrock at P1 and P2 tended to be positive, indicating the vertical flux from the soil to the bedrock (downward flow), but infrequently became negative (upward flow) at P1 when the time between storm events was long, or at P2 when several days passed after the large storms (Figure 5f).

4.2. Features of Storm Events and Lag Times

[26] Thirteen storm events with features shown in Table 1 were analyzed. Total rainfall amounts in all events were less than 100 mm and the majority (ten events) was less than 50 mm. Rainfall durations ranged from 2 to 46 hours. Peak rainfall intensities ranged from 4 to 24 mm h−1 but most were less than 10 mm h−1. ASI ranged widely from 61 to 105 mm. Initial losses were less than 3 mm in many cases and were 6 mm at most.

Table 1. Features of Eventsa
EventTotal Rainfall, mmRpk,b mm h−1Rainfall Duration, hoursInitial Loss,c mmQpk,d mm h−1Qi,e mm h−1Runoff CoefficientfASI,g mmLag Time, hours
  • a

    Events with total rainfall more than 10 mm are analyzed.

  • b

    Peak 30 min rainfall intensity.

  • c

    Rainfall amount from TRst to TQup.

  • d

    Peak discharge.

  • e

    Initial discharge of the event.

  • f

    Period for the calculation of runoff coefficient is from rise in hydrograph to peak discharge.

  • g

    Antecedent soil moisture index derived from the initial storage of surface soil (0–0.3 m deep). See equation (1).

25 Jun20.610.4130.00.1140.0200.0040.3
1 Jul10.63.6160.20.0220.0090.00191.30.7
3 Jul10.64.4100.00.0190.0060.00196.80.3
12 Jul20.420.026.20.3300.0050.00899.50.5
25 Jul44.224.0141.00.2830.0290.151105.446.5
5 Aug33.220.0121.60.2010.0600.00587.80.5
8 Aug96.023.2370.01.4600.0580.22499.230.2
14 Aug75.86.0460.21.1730.3460.152100.727.0
20 Sep71.65.6512.00.1290.0040.01260.81.5
24 Sep33.65.2460.00.1480.0070.02485.21.3
13 Oct10.68.830.40.1110.0240.00573.90.5
21 Oct22.06.8143.40.1110.0070.01084.00.5
29 Nov36.04.4253.20.2990.0290.21099.239.5

[27] Lag times ranged from 0.3 to 46.5 hours but were grouped at both ends: less than 2 hours and more than 24 hours. The events with short lag times (<2 hours) accounted for 69% (nine events) of the total, and in particular, events of less than 0.5 hours made up 46% (six events). Events with long lag times (>24 hours) accounted for 31% (four events) of all. There was a large spread (about 20 hours) among the long lag times.

[28] In comparison with events with short lag times, the events with long lag times had considerably larger runoff coefficients. The events with long lag times had relatively large amounts of rainfall compared to the events with short lag times. The lag times, however, were not simply related to the rainfall characteristics. For example, the 14 August event and the 20 September event differed greatly in lag times, though the rainfall characteristics of their events were similar (about 70 mm total amount and 6 mm h−1 intensity). These storms had very different antecedent conditions (Table 1).

4.3. Response of Subsurface Water to Rainfall

[29] The responses of subsurface waters to rainfall differed according to the hydrograph type. Concrete examples are shown in Figure 6. The hydrographs of spring discharge were classified into two types: single-peaked type (Figure 6a) and double-peaked type (Figure 6b). On the double-peaked hydrograph, the peak discharge (maximum discharge) appeared as the second peak, and so the lag time tended to be long.

Figure 6.

Examples of responses of spring discharge and subsurface water to rainfall: (a) event with a short lag time and (b) event with a long lag time.

[30] During the 5 August event, with a short lag time (Figure 6a), spring discharge quickly responded to rainfall and reached a peak 0.5 hours after peak rainfall. Subsequently, the discharge decreased quickly to the preevent level within a day. Soil moisture contents at all measurement points and soil pore water pressure at P2 were also sensitive to rainfall and reached a peak immediately after peak rainfall. In contrast, soil pore water pressure at P1 and piezometric surfaces at all measurement points hardly responded to rainfall.

[31] During the 25 July event, with a long lag time (Figure 6b), the spring discharge quickly increased according to peak rainfall and then slightly decreased. The time between the peak rainfall and this first peak discharge was 0.5 h, i.e., the same as the lag time during the 5 August event shown in Figure 6a. After that, the discharge further increased and reached a peak 46.5 hours after peak rainfall. The many measurement points responded remarkably to the further increase of the discharge. Soil moisture contents at P2 and P2.5, soil pore water pressures at P1 and P2, and piezometric surface at P2 increased after the small initial peak directly following rainfall.

[32] These features of subsurface water responses to rainfall were almost the same for the other events. Responses of soil water content, soil pore water pressure and piezometric surface during all events are shown, based on the values at times when rain started (TRst), peak rainfall occurred (TRpk) and peak discharge occurred (TQpk), in Figure 7. During events with short lag times, soil moisture content tended to continue to increase from TRst to TQpk, but responses of soil pore water pressures and piezometric surfaces hardly or slightly responded regardless of rainfall amounts (Figure 7a). Especially, the soil pore water pressures at P1 remained below 0 m, indicating unsaturated conditions above the soil-bedrock interface at P1. During events with long lag times (Figure 7b), although soil moisture contents at all measurement points tended to increase from TRst to TRpk, the pattern after TRpk to TQpk was different. Soil moisture content increased at TQpk at P2, but decreased at P3 and P4. At P1 and P2.5, the pattern was the same as P2 under the larger rainfall amounts (8 August and 14 August). Soil pore water pressures at P1 and P2 and piezometric surface at P2 increased remarkably after TRpk to TQpk. Especially, the soil pore water pressure at P1 changed drastically after TRst to TQpk, i.e., from unsaturated to saturated conditions above the soil–bedrock interface at P1. For example, during the 8 August event, the soil pore water pressures at P1 remarkably increased from −0.2 to 0.9 m (Figure 7b).

Figure 7.

Response diagram of subsurface water based on the values at TRst, TRpk and TQpk (see Figure 3): (a) events with short lag times and (b) events with long lag times. Events in Figure 7a (top) are less than 30 mm in total rainfall, and those in Figure 7a (bottom) are more than 30 mm.

4.4. Silica and DOC Concentration of Subsurface Water and Spring Water

[33] Dissolved silica and DOC concentrations of subsurface water ranged from 1.3 to 20.9 mg L−1 and 0.2 to 10.1 mg L−1, respectively (Figure 8a). On soil waters at depths of 0.2–1.0 m, silica and DOC concentrations during nonstorm events were not very different from those during storm events in terms of average and range (Table 2). Silica concentrations in the shallow soil layer (depth: 0.2 and 0.3 m) tended to be lower than those from deeper soil layers (0.5 and 1.0 m) and bedrock (2.0 m), but the DOC concentrations were higher (Figure 8a).

Figure 8.

Bivariate plot for silica and DOC concentrations of (a) subsurface water and (b) spring water. The boxes in Figure 8b, whose sides consist of maximum and minimum concentrations of silica and DOC in subsurface water, indicate the approximate domains of the various types of subsurface water.

Table 2. Dissolved Silica and DOC Concentrations of Soil Water During Nonstorm and Storm Events
DepthAverage During Nonstorm (Minimum–Maximum), mg L−1During Nonstorm Sample SizeAverage During Storm (Minimum–Maximum), mg L−1During Storm Sample Size
Silica
0.2 m8.0 (5.0–12.5)187.2 (4.3–8.4)14
0.3 m7.0 (1.3–9.0)166.6 (1.5–8.2)10
0.5 m9.8 (4.3–12.5)249.2 (3.8–11.3)13
1.0 m11.5 (5.9–14.3)2311.3 (7.9–14.2)17
DOC
0.2 m5.1 (2.5–10.1)184.1 (1.3–7.5)14
0.3 m2.6 (0.4–5.0)162.1 (0.7–3.2)10
0.5 m0.8 (0.3–1.6)240.6 (0.3–1.3)13
1.0 m0.5 (0.2–2.0)230.5 (0.2–1.6)17

[34] Dissolved silica and DOC concentrations of spring water ranged from 9.6 to 15.4 mg L−1 and 0.4 to 8.3 mg L−1, respectively (Figure 8b). Spring waters had a narrow range of silica concentrations compared with soil waters, and fall between those of shallow soil (0.2 and 0.3 m) and bedrock (2.0 m) in silica concentration. Relative to spring waters during nonstorm events, silica concentrations of spring waters during storm events with short lag times were somewhat lower, and those during storm events with long lag times were clearly lower. DOC concentrations of spring waters during events with short lag times were quite different from those during events with long lag times; the DOC of spring waters during events with short lag times varied widely and tended to be higher than during nonstorm events, but DOC during events with long lag times were lower than during short lag time events.

4.5. Fluctuations in Silica and DOC Concentrations of Spring Water During Storm Events

[35] Three examples of silica and DOC concentration in spring water during storm events are shown in Figures 9 and 10. One is an event with a short lag time, and the other two are events with long lag times. In the case of the former (Figure 9), silica decreased from the beginning of rainfall to peak discharge and then recovered to the initial level (strong negative correlation with discharge; r2 = 0.90, p < 0.01), but DOC increased rapidly, as in a flushing, and then decreased to the initial level (clockwise hysteretic relation with discharge).

Figure 9.

Time series of rainfall, spring discharge, soil water content, soil pore water pressure, piezometric surface, vertical hydraulic gradient, and silica and DOC concentration in spring water through the 20 September event (a short lag time event). Vertical dashed line shows the time of peak discharge.

Figure 10.

Time series of rainfall, spring discharge, soil water content, soil pore water pressure, piezometric surface, vertical hydraulic gradient, and silica and DOC concentration in spring water through an event with a long lag time: (a) the 8 August event and (b) the 14 August event. Vertical dashed lines show the time of peak discharge.

[36] In one of the two events with a long lag time (Figure 10a), a portion of data was missing, unfortunately, but the fluctuation pattern of the event could be deduced approximately. DOC was very low both before the event (1.1 mg L−1) and about 2 days after the end of rainfall (0.7 mg L−1). Silica was high before the event (14.8 mg L−1) but was low about 2 days after the rainfall (10.6 mg L−1). This pattern was distinct from that of the event with a short lag time shown in Figure 9, which presented the recovery of silica after the rainfall.

[37] Another example of an event with a long lag time is shown in Figure 10b. Silica was very low at beginning of the event (9.6 mg L−1) but gradually increased as spring water discharge increased during the rainfall. DOC was very low at the beginning of the event (1.6 mg L−1) and low DOC continued throughout the event.

5. Discussion

5.1. Lag Time and Flow Path

5.1.1. Storm Events With Short Lag Times

[38] A number of studies on the subsurface hydrological conditions, which influence storm runoff, have focused on water sources and storm runoff flow paths [e.g., Pearce et al., 1986; Sidle et al., 2000; Carey and Woo, 2001]. Hortonian overland flow, which rarely emerges in forested catchments, and saturated overland flow were considered to be components contributing only to the early part of the hydrograph rising limb [Mosley, 1979; Buttle, 1994]. When this saturated overland flow, whose source areas vary seasonally and dynamically during storm events [e.g., Dunne and Black, 1970], is the dominant component, the storm events usually have short lag times. In this study, the events with short lag times resulted in an increase in soil moisture content during the hydrograph rising limb, whereas the soil pore water pressure above the soil-bedrock interface at P1 and the piezometric surfaces of bedrock groundwater at all measurement points showed only a very small or zero increase (Figures 6a, 7a, and 9). In addition, DOC at 0.2 m deep ranged from 1 to 10 mg L−1; at 0.3 m deep ranged from 0.5 to 5 mg L−1 (Figure 8) and DOC in spring water during the event shown in Figure 9 was around 2 to 8 mg L−1 before and after the event. DOC in deeper soil was clearly lower than DOC in spring water during the event. Therefore DOC in spring water should originate from the shallow soil layers, with the assumption that the silica and DOC concentrations near the spring are the same as those measured near P2. These results suggest that the shallow soil water was the main contributor to storm runoff during events with short lag times.

[39] If the source area of saturated overland flow effectively expanded as the spring discharge increased, the fraction of water moving through the DOC-rich shallow soil layer would increase and DOC concentrations of spring water would increase with discharge. The increase in DOC of spring water, however, seemed to be transient and the DOC concentration of spring water was not correlated to the discharge (Figure 9). Therefore we inferred that, during the events with short lag times, the shallow soil layer in almost all areas of the catchment acted as a sink for the rainwater and the major source area of storm runoff was restricted to the saturated area near the spring. This is consistent with what the runoff ratio (runoff coefficient <0.01, shown in Table 1) during most events with short lag times was the same order as the saturated area ratio (<1% of the catchment area). The decrease in silica concentrations is consistent with flow over the saturated area. These results suggest that the factor causing short lag times was the saturated overland flow through the shallow soil layers near the spring.

5.1.2. Storm Events With Long Lag Times

[40] The subsurface hydrological setting of the events with long lag times differed substantially from that of the events with short lag times in the upslope expansion of saturated zone above the soil–bedrock interface, which was shown by the positive pore water pressure at P1 (Figures 6b and 10). The groundwater flow through bedrock fractures was not a dominant flow path during the events with long lag times, judging from the positive gradient of vertical hydraulic head, i.e., the infiltration from soil mantle into bedrock (Figure 10). These suggest that the subsurface flow through the soil mantle was an important flow path during the events with long lag times.

[41] Temporal changes in silica concentrations of spring waters could provide some additional information regarding subsurface water flow during storm events. Assuming that the water in the saturated zone closely related to the spring discharge through the rising of the water table caused by infiltration of event rainwater and/or translatory flow of preevent water, the silica concentration of the water in the saturated zone would be diluted during the event and the silica concentration of spring water would decrease as the discharge increased. Figure 11 shows the changes in the silica concentrations when the water tables of the saturated zone at P2 were above the water intake of the 1.0 m tension lysimeter (depth to water table <1.0 m) before and during rainfall. The silica concentrations of the water in the saturated zone after the peak were lower than before the events, indicating the mixing of preevent water in the saturated zone and soil water in unsaturated shallow layers. The silica concentration of spring water seemed to decrease during the 8 August event with increase of the water table (positive pore water pressure) (Figure 10a), indicating that the water after the mixing moved laterally via the saturated subsurface flow along the soil-bedrock interface.

Figure 11.

Changes in silica concentrations when the water tables of the saturated zone at P2 were above the water intake of the tension lysimeter before and during rainfall. The available data under the condition are of the only 1.0 m lysimeter during the 8 August and 29 November events.

[42] In contrast, during the 14 August event (Figure 10b), we could not regard the water contributed to runoff as the water in the saturated zone recharged by shallow soil water, because the silica concentration of spring water continued to increase even when the water table rose during the rainfall. Although the soil water was not sampled during this event, the vertical hydraulic head gradient just before the event indicated the exfiltration from the bedrock into the soil mantle at P2 on August 13 (Figure 10), and the increase in silica concentration of soil water might result from the exfiltration of the bedrock groundwater with high concentration of silica. Then, the silica-rich soil water might have caused the increase in concentration of the spring water during the 14 August event. However, the exfiltration was not quite very common through the study period (Figure 5f).

[43] In either case mentioned above, the spring-hillslope connection of saturated zone should trigger the saturated lateral flow above soil-bedrock interface and the peak discharges with long lag time.

5.2. Hydrological Connection Between Spring and Hillslope

[44] A number of studies have pointed out the importance of hydrological connection between base of hillslope and upslope area for storm flow generation [McDonnell, 1990; Montgomery et al., 1997; Tani, 1997; Sidle et al., 2000; Uchida et al., 2004; Katsuyama et al., 2005]. Tani [1997], Sidle et al. [2000], and Uchida et al. [2004] reported that in high-gradient hillslopes (35–39°), transient saturated area above soil-bedrock interface extended progressively from slope base to upslope area during storm flow periods, and water in the upslope area was rapidly delivered to the slope base via preferential flow paths. Montgomery et al. [1997] showed that a patchy distribution of saturated area above soil-bedrock interface in a steep hillslope and an important contribution of rapid bedrock flow to discharge at slope base during storm flow periods. Montgomery et al. [1997], Tani [1997], and Sidle et al. [2000] also demonstrated that lag times between peak rainfall and peak discharge ranged from about 3 to 9 h and depended on development processes of transient saturated area because the time of peak discharge was approximately consistent with that of peak tensiometric and piezometric response due to rapid drainage by the preferential flow and the rapid bedrock flow. In this study, we observed expansion of saturated zone above soil-bedrock interface from spring area to upslope area during long lag time events. However, the hydrometric observation along the concavity did not indicate preferential flows and rapid bedrock flows. Therefore it is likely that matrix flows through the saturated zone above soil-bedrock interface dominantly contributed to delivery of water from upslope area to spring area and resulted in the long lag times. It is fundamentally difficult to detect local flows such as preferential flows just based on the point measurement we conducted, but the matrix flows as the dominant drainage paths do not contradict the result that peak discharge was much slower than peak tensiometric response during long lag time events (Figures 6b and 10).

5.3. Effects of Antecedent Soil Moisture and Rainfall Characteristics on Lag Times

[45] In this study, we found a unique initial condition in terms of distribution of saturated zone above soil-bedrock interface, i.e., saturated zone existed at SP and P2 but did not exist at P1 just before storm events. Buttle et al. [2004] showed an initial condition that groundwater was held in bedrock depressions in upper hillslope, which affected runoff generation from the hillslope. We did not find such bedrock depressions based on the measurement of bedrock topography along the concavity at 2 m intervals. We also have no information about spatial variability of soil and/or bedrock properties, such as the vertical and lateral hydraulic conductivity and the detailed bedrock topography [e.g., Freer et al., 2002; Montgomery et al., 2002; Brooks et al., 2004]. However, P2 was located in the gentlest part in the study site, where subsurface water might tend to concentrate. In contrast, topography at P1 was slightly steeper than at P2, and then P1 might have higher drainage ability than P2. The difference of slope gradient between at P1 and at P2 might cause the initial distribution of saturated zone above soil–bedrock interface.

[46] When the positive pore water pressure above soil-bedrock interface at P1 developed with storm events, the saturated zone drastically expanded from spring area (SP) to upslope area (P2). The occurrence of the positive pore water pressure at P1 can be affected by antecedent moisture conditions of the catchment as well as rainfall characteristics. Figure 12 shows the sum of ASI and cumulative rainfall as a function of time since the start of rainfall for each storm event. The positive pore water pressure at P1 occurred in six events, when the sum of cumulative rainfall and ASI was over about 120 mm. However, two out of six events (20 September and 24 September) had little rainfall after the occurrence of positive pore water pressure at P1 and then the positive pressure was short-lived (e.g., Figure 9). As a result, these two events did not have peak discharges with long lag times. Therefore the value of 135 mm (ASI + cumulative rainfall), beyond which all short lag time events could not reach, was identified as the threshold for the hydrological connection making possible effective water transport from upslope area to spring area via saturated lateral flows during storm events.

Figure 12.

Sum of cumulative rainfall and antecedent soil moisture index (ASI) as a function of time elapsed since start of rainfall event.

[47] Figure 13 shows the effects of average rainfall intensity on the amount of time taken to reach the peak discharge after the occurrence of positive pore water pressure at P1. The time between the occurrence of the positive pressure at P1 and the peak discharge seemed to decrease as the rainfall intensity increased, indicating that the increase of the rainfall intensity accelerated the saturated lateral flow. Therefore the effects of the peak rainfalls on the lag times can differ greatly depending on timing of the peak rainfall, i.e., before or after the upslope expansion of saturated zone above soil–bedrock interface for storms with long lag times. For example, the peak rainfall in the 25 July event and the 8 August event occurred before and after the upslope expansion, respectively, and then the lag time was 46.5 and 30.2 h, respectively.

Figure 13.

Relationship between average rainfall intensity and time to peak discharge after occurrence of the saturation above the soil-bedrock interface at P1. The average rainfall intensity was calculated for the period between the occurrence of the saturation and the peak discharge. Labels show the date of long lag time event.

[48] In this study, to evaluate the antecedent moisture condition in the whole catchment, we arbitrarily divided the catchment into five subareas, and regarded the 0–0.3 m deep as the soil surface layer. Therefore the exact threshold value of the sum of cumulative rainfall and ASI may depend on where to measure soil moisture and how to calculate ASI. However, the shape of the relation shown in this study (Figure 12) remains the same. In addition, the ASI reflects better the effects of evapotranspiration on the antecedent moisture condition compared with the rainfall-derived moisture index such as API [e.g., Mosley, 1979; Fedora and Beschta, 1989], because the ASI is derived from the soil moisture content of the soil layer (0–0.3 m), which roughly corresponded with A horizon, i.e., a main part of root zone. The evapotranspiration in mountainous areas depends on local conditions of meteorology and vegetation [e.g., Band, 1993], and so would be a fundamental factor to evaluate the regional characteristics of rainfall-runoff responses in unchanneled catchments or hillslopes. Thus ASI proposed in this study can be helpful in understanding rainfall-runoff processes closely related to antecedent moisture conditions at the hillslope scale.

6. Conclusions

[49] We focused on the lags to peak discharge and flow paths in a forested unchanneled catchment underlain by granitic bedrock, and analyzed 13 storm events with small to medium magnitude (<100 mm in total rainfall) using a hydrometric and hydrochemical approach. This study led to the following results.

[50] 1. Rainfall-runoff responses in this catchment are characterized by the lag time, and the response patterns are classified into two types. One has a short lag time (<2 hours), another a long lag time (>24 hours).

[51] 2. Lag times are different depending on the dominant flow path during storm event. In the short lag time pattern, the source area of runoff water is limited to the near-spring area and the dominant flow path is the saturated overland flow. In the long lag time pattern, the source area expands upslope by the spring-hillslope connection of saturated zone and the dominant flow path is the saturated lateral flow above the soil-bedrock interface.

[52] 3. Threshold of the spring-hillslope connection to generate peak discharges with long lag times is determined by the sum of cumulative rainfall and ASI, and the threshold value is 135 mm.

[53] 4. Time to peak discharge after upslope expansion of saturated zone decreases as rainfall intensity for the period increases, indicating that effects of the peak rainfall on the lag time differ greatly depending on timing of the peak rainfall, i.e., before or after the upslope expansion.

[54] Therefore we conclude that consideration of antecedent soil moisture conditions in the catchment as well as rainfall amount and intensity is essential for understanding the regional characteristics of lag times and subsurface water movement above soil–bedrock interface.

Acknowledgments

[55] We are grateful to N. Umino, K. Okudaira, A. Ohno, and T. Inuma for help in the field and in conducting the experiments. We thank T. Hirai (University of Yamanashi) for making some useful apparatus for fieldwork. We thank the staff of Mizugaki Mountain Lodge and colleagues at the University of Yamanashi for trouble-shooting support. We also thank six anonymous reviewers for improving earlier versions of this manuscript. The study was supported by a Grant-in-Aid for scientific research from the Japan Ministry of Education and Culture (15001881), Kurita Water and Environment Foundation, and Environment Studies Support Fund of Showa Shell Sekiyu.

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