Transit time of discharge is a hydrological characteristic used in water resource management. Previous studies have demonstrated large spatial variation in the mean transit time (MTT) of stream base flow in meso-scale catchments. Various relationships between topography and MTT have been reported. Although it is generally assumed that base flow MTT is controlled by the depth of the hydrologically active layer that recharges a stream, this hypothesis has not been tested in field studies. This study confirmed that the depth of hydrologically active soil and bedrock controls spatial variation in MTT. The study used isotopic and geochemical tracer data gathered in the 4.27 km2 Fudoji catchment, central Japan. The results, together with previously documented relationships between topography and MTT, indicate that the depth of the hydrologically active layer is sometimes, but not always, related to topography. A comprehensive understanding of the factors that control base flow production in mountainous catchments will require further study of the water flow path depths that recharge streams.
 The basic theoretical concept of transit time suggested another possibility about its first-order (main) control. If the base flow draining a catchment is treated as a well-mixed, steady state system (e.g., a linear reservoir), then the MTT of base flow (MTT) is described as,
where Qb, the base flow, is the volumetric flow rate through the system and Vm is the volume of mobile water in the system during base flow [e.g., Zuber, 1986]. Generally, based on the water balance, Qb can be described as,
where R is the rainfall rate, ET is the evapotranspiration rate, qs is specific discharge during storm runoff, D is the deep water percolation rate, and A is the drainage area. The volume of mobile water can be described as,
where θm is the mean mobile water content per unit volume and dm is the mean depth of hydrologically active soil and bedrock. From equations (1)–(3), the MTT for base flow can be expressed as,
If the climate, vegetation, and underground materials that store water (e.g., soil and bedrock) are almost homogeneous throughout catchments, we can assume that the rainfall rate (R), evapotranspiration rate (ET ), and deep water percolation rate (D) are also similar. Furthermore, because the porosity of soil and bedrock commonly changes with depth [e.g., Harr, 1977; Katsura et al., 2008], we can assume that θm is a function of dm. That is, the spatial variability in MTT should be related to qs and dm. Hence, we can propose the hypothesis that spatial variation in the MTT of stream base flow in a meso-scale catchment is related to the mean depth of hydrologically active soil and bedrock (dm). We based this hypothesis on recent studies demonstrating that the depths of water sources contributing to hillslope runoff varied greatly with location within a catchment, even when the catchment had uniform bedrock geology, soil type, and land use [e.g., Uchida et al., 2008; Uchida and Asano, 2010]. Recent process studies and theoretical considerations have also tightly linked storage and flow path lengths to catchment response [Harman and Sivapalan, 2009; Sayama et al., 2011] and MTT [Soulsby et al., 2009; Hrachowitz et al., 2010b]. However, most studies investigating the spatial patterns of stream MTT in headwaters have not focused on the spatial pattern of dm because it is nearly impossible to measure directly [e.g., Soulsby et al., 2006]. The depth of hydrologically active soil and bedrock (dm) should be defined by the internal structure of the catchment, such as the distribution of porosity and mobile water in soil and bedrock; thus, it is not necessarily related to surface topography.
 Therefore, we tested the hypothesis stated above by examining the effect of spatial patterns of MTT on the headwaters of a 4.27-km2 catchment consisting of a nearly homogenous landscape of incised valleys and granitic bedrock covered with forest. To compare relative MTTs among locations, we used the degree of isotopic signal dampening [e.g., Maloszewski et al., 1983; McGuire et al., 2005; Tetzlaff et al., 2009b]. The concentration of dissolved silica (SiO2) was used as a tracer to identify the contributing depth of the flow path to stream discharge because previous studies of this catchment demonstrated that dissolved SiO2 increased with the depth of this flow path whereas contact time of groundwater with soil and bedrock had minimal impact [Asano et al., 2003; Uchida and Asano, 2010]. We also tested the effects of qs and topography on the spatial pattern of MTT.
2. Study Sites
2.1. General Description
 The Fudoji catchment is located in the Tanakami Mountains (35°N, 136°E) in Shiga Prefecture, central Japan (Figure 1). The catchment area covers 4.27 km2 at an elevation ranging from 289 to 600 m above sea level. Mean annual atmospheric temperature is 10.9°C, and mean annual precipitation is 1712 mm (1981–1998), most of which is rainfall. The study area is underlain by Cretaceous Tanakami granite. The bedrock is weathered and fractured, and we observed several cracks in bedrock outcrops. Forest covers the entire catchment. Most streams are incised and confined by side slopes. The soil depth of the hillslopes ranges from 15 to 130 cm. Additional details of the bedrock seep and zero-order hollow discharge (Figure 1) are presented in the works of Asano et al.  and Uchida et al. .
2.2. Spatial Patterning of Flow Paths
 In our catchment, previous studies have indicated that dissolved SiO2 concentration is a useful tracer to identify the contributing depth of the flow path to discharge [Asano et al., 2003; Uchida et al., 2003, 2008]. The mean SiO2 concentrations in water were similar in the soil layer of the hillslope, regardless of sampling depth, although the mean residence time of water increased with depth [Asano et al., 2003]. These results indicated that the dissolved SiO2 concentrations in groundwater were independent of contact time with minerals. Furthermore, dissolved SiO2 concentrations were much higher in bedrock seeps than in water in the soil layer. These results suggested that SiO2 concentrations increased with the increasing depth of runoff sources of discharged water, and that they varied only minimally during lateral transport [Asano et al., 2003; Uchida et al., 2003]. The negative relationship between mean SiO2 concentration and the amplitude of seasonal temperature variation documented at 12 seeps from bedrock fractures in other granite mountain demonstrated that mean SiO2 concentration increased with the depth of water sources [Uchida et al., 2008]. This finding also confirmed the applicability of SiO2 as an indicator of flow path depth at granite mountains.
 The SiO2 concentrations of streams showed a convergent spatial pattern with drainage areas, i.e., the concentrations of zero-order hollow discharges largely varied in space and became similar among sampling locations in higher-order streams via simple mixing processes (Figure 2, all plots) [Asano et al., 2009; Asano and Uchida, 2010]. Depending on the longitudinal profile, starting from different zero-order hollows, SiO2 concentrations in streams showed increasing (Figure 2, open circles), decreasing (Figure 2, open squares), or constant (Figure 2, circles with crosses) asymptotic patterns. These results suggest that the depth of the contributing hydrologically active soil and bedrock of low-order streams largely varies in space, whereas that of higher-order streams reflects the integration of the contributing upstream depths. Both types of subcatchments, where the depth of contributing hydrologically active soil and bedrock increases or decreases with total catchment area, are present in the study area.
 Samples were collected from a small perennial seep from a bedrock fracture (bedrock seep) and a flow from a zero-order hollow (zero-order hollow discharge) just 2 m downstream from the bedrock seep (Figure 1). At these sampling locations, MTT was previously estimated [Asano et al., 2002]. Samples were also collected from six streams downstream from the zero-order hollow at the locations shown in Figure 1. This longitudinal profile of stream sampling locations corresponds with the decreasing asymptotic profile shown in Figure 2, where squares indicate that the depth of the contributing hydrologically active soil and bedrock became progressively shallower in sampling locations that were further downstream. At locations close to the zero-order hollow discharge sampling sites, composite throughfall samples were obtained by three individual collectors with bottles fitted to 21-cm-diameter funnels.
 Sampling was conducted between June 2002 and June 2003 at about 2–3-week intervals on days with no rain. The discharge rate was monitored using V notch weir at the zero-order hollow discharge sampling locations (Figure 1). The hydrogen and oxygen isotopic compositions of samples were determined using a dual-inlet isotope ratio mass spectrometer that contained CO2/H2O and H2/H2O equilibration devices. The analysis was performed using a Finnigan Delta Plus mass spectrometer at Nagoya University. Repeated analyses of working standard water showed reproducibility within 0.05‰ and 0.5‰ for oxygen and hydrogen isotopic composition, respectively. Values were expressed as conventional delta notations with respect to standard mean ocean water [Craig, 1961a]. The concentration of dissolved reactive SiO2 was determined using the molybdenum yellow method. Analyses of dissolved SiO2 were reproducible, with a mean standard deviation of 3 μmol L−1 (1.6% coefficient of variation).
3.2. Estimation of MTT and the Depth of Hydrologically Active Soil and Bedrock
 We calculated the deuterium excess (d-excess), which is the surplus of deuterium relative to the relationship between δ18O and δD [Dansgaard, 1964], assuming an equilibrium condition with a slope of 8, which is the slope of global meteoric water line and average of river, lake, rainfall, and snow in many parts of the world [Craig, 1961b]. The d-excess in precipitation showed a clear sinusoidal seasonal pattern around the study area [Taniguchi et al., 2000], and this seasonal pattern has been useful in evaluating MTT in this region [e.g., Kabeya et al., 2007].
 We calculated the standard deviation of d-excess for each sampling location as a surrogate or proxy for the relative difference in MTTs among locations. Data from observation days with <7 mm of daily discharge were used to exclude the effect of high flow. We took 14–15 samples from each sampling location for analysis. McGuire et al.  evaluated spatial variation in MTT within 0.085–62.4-km2 catchments in Oregon and identified a strong relationship between MTT estimated by lumped parameter convolution models with an exponential transit time distribution and the ratio of the standard deviation of stable isotopes in streamflow samples to that of precipitation (r2 = 0.81). A similarly strong relationship was also found in Scotland within catchments ranging from 1 to 293 km2 (r2 = 0.84) [Soulsby and Tetzlaff, 2008]. These findings suggest that this simple measure of tracer damping is useful for the comparison of relative MTTs among locations within a catchment. Because our eight sampling locations were located within 2.7 km of each other at elevations ranging from 289 to 505 m, we assumed that isotopic variation in precipitation was similar at all sites and simply compared the standard deviation of d-excess in stream base flow. A higher standard deviation of d-excess equated to less damping of isotopic signals and a lower MTT [McGuire et al., 2005; Tetzlaff et al., 2009b]. We estimated uncertainty in standard deviations derived from the degree of reproducibility of isotope analysis using the following simulation. First, we randomly generated errors within 0.05‰ and 0.5‰ for oxygen and hydrogen isotopic compositions, respectively, added these to observed data, and generated d-excess data. We then calculated the standard deviation of d-excess for each sampling site using these generated data. We then repeated this generation and calculation 200 times and defined 95% confidence intervals for each sampling site.
 Previous studies demonstrated that the SiO2 concentration is a useful measure for the evaluation of the contributing depths of flow paths; higher SiO2 concentrations should be associated with greater contributing depths [e.g., Asano et al., 2003; Uchida and Asano, 2010]. Thus, we calculated the mean concentration of SiO2 at each sampling location and compared these concentrations to evaluate the relative depths of hydrologically active soil and bedrock at each location.
3.3. Evaluation of the Effect of Storm Runoff qs
 According to equation (4), the MTT of base flow should also be related to the stormflow volume (qs). Here, we provide a method for the examination of the effect of qs on spatial variation in MTT.
 We can estimate the relationship between the ratio of stormflow to total runoff (stormflow ratio) and the ratio of the MTT of each sampling site to the MTT of the zero-order hollow discharge. The stormflow ratio [qs/(R – ET – D)] of this zero-order hollow discharge in Fudoji was known [Uchida et al., 2003]. Uchida et al.  calculated the mean annual stormflow volume (qsA) and the mean annual total discharge volume [(R – ET – D)A] based on 3 years of observational data. Stormflow was calculated by simple hydrograph separation using a straight line connecting the point of initial runoff to the inflection point on the recession limb on a semilogarithmic graph scale [Uchida et al., 2003]. These previous observations determined that the mean annual stormflow ratio [qs/(R – ET – D)] was 0.07 [Uchida et al., 2003]. Using this value and equation (4), we conducted a simulation.
 We estimated the relative ranges of MTT at our study sites based on the isotopic variation that we observed. Assuming that the system response function is expressed as an exponential flow model [e.g., Asano et al., 2002] and that the time series data of input and output can be described as sinusoidal curves [e.g., Asano et al., 2002], MTT can be described as,
where k is a constant, SD represents the standard deviation of d-excess, and in and bs indicate input (i.e., throughfall) and base flow, respectively. The amplitudes of sinusoidal input and output are usually used for the estimation of MTT [e.g., Maloszewski et al., 1983; Kubota, 2000]. Given the reported linear relationship between the amplitude of sinusoidal curves and the standard deviation of the entire time series (r2 = 0.81) [McGuire et al., 2005], we can derive equation (5) from the traditional equation [e.g., Maloszewski et al., 1983; Kubota, 2000]. We calculated the relationship between the standard deviation of d-excess and relative MTT using equation (5) and observed data.
3.4. Topographic Analysis
 Drainage areas for each sampling location were obtained from 1:2500 and 1:25,000 topographic maps. A 10-m digital elevation model (DEM) was used to compute topographic characteristics that have been reported in previous studies [McGuire et al., 2005; Tetzlaff et al., 2009a]. Stream networks were determined using a channel-threshold area method. Using previous analyses of the area-slope relationship [e.g., Montgomery, 2001], we found that this relationship showed breaks at ∼1300 m2. We conducted a field survey to confirm the results of the area-slope relationship analysis. We measured the drainage areas of 32 stream initiation points ranging from 183 to 9339 m2 (median: 846 m2, mean: 1420 m2). This region lacks an obvious dry season, and we confirmed that most stream starting points did not move except during the heaviest rainfall periods. Thus, the channel-threshold area was set at 1300 m2. A comparison of determined stream networks with the location of stream heads in the field indicated that the modeled stream network generally agreed well with the real stream network in this geomorphic region, although this threshold area is smaller than previously reported threshold areas of other sites (5000 and 50,000 m2 [McGlynn et al., 2003; McGuire et al., 2005; Tetzlaff et al., 2009a]).
 Each pixel was linked to the stream pixel to which it drained by assuming that the flow path followed the surface topography. Here, we used a single-direction flow algorithm to determine flow paths. Based on these flow paths, we computed three indices for each hillslope pixel for upstream areas of each sampling location, excepting the bedrock seep and zero-order hollow discharge sampling sites. These indices are the hillslope length (L), which represented the distance from the stream, the mean hillslope gradient (G) along each flow path to its entrance into the stream, and the ratio of hillslope length and mean hillslope gradient (L/G), which has been related to MTT in previous studies [e.g., McGuire et al., 2005; Tetzlaff et al., 2009a]. The mean hillslope gradient was computed by dividing the elevation above a stream by the distance from a stream for each flow line. At the bedrock seep and zero-order hollow discharge, we counted the distance and mean gradient along each flow line to the sampling location as hillslope length and gradient, as the drainage areas of the bedrock seep and zero-order hollow discharge were less than the threshold area. Then, we calculated arithmetic mean values to characterize each sampling location. We also computed the commonly used topographic wetness index [ln (a/tanβ)], where a is the upslope accumulated area and β is the local slope angle [Beven and Kirkby, 1979].
4.1. Roles of Depth of Hydrologically Active Soil and Bedrock
 The standard deviations of d-excess varied from 0.4 to 1.4 at the sampled locations (Table 1). The bedrock seep showed the smallest standard deviation. Sampling locations at small streams (zero-order hollow discharge and St3) showed small standard deviations (0.7–0.8), and these values generally increased in a downstream direction at larger streams (St6–St8; 1.2–1.4).
Table 1. SD of d-excess for Each Location
Total Catchment Area (km2)
Elevation of Sampling Location (m)
SD of Deuterium Excess
Zero-order hollow discharge
 The standard deviation of d-excess significantly decreased with increasing mean dissolved SiO2 concentration (Figure 3). Spearman's rank correlation coefficient (rs) between the standard deviation of d-excess and mean dissolved SiO2 concentration was −0.95 (Table 2), indicating that base flow MTT increased with the contributing depth of hydrologically active soil and bedrock. This finding clearly supported our hypothesis that spatial variation in the MTT of stream base flow is related to the depth of the flow path.
Table 2. Spearman's Rank Correlation Coefficient (rs) Between the SD of d-excess and Mean SiO2 and Topographical Indices
Mean SiO2 and Topographical Indices
Mean hillslope length (L)
Mean of mean hillslope gradient (G)
Topographic wetness index
Total catchment area
 The estimation of relative MTT suggested that the ratio of base flow MTT at the downstream sampling site St7 (standard deviation of d-excess: SDbs = 1.4) to that of the zero-order hollow discharge (SDbs = 0.8) was almost 0.62 (Figure 4a). The simulation showed that the reduction in relative MTT by decreasing stormflow ratio, and the stormflow ratio of the zero-order hollow discharge was 0.07 (Figure 4b). Therefore, the reduction in relative MTT between the zero-order hollow discharge and the larger stream due to the differences in qs could be a maximum of 7% when we assumed that the stormflow ratio was zero (Figure 4b). These results suggest that the decrease in MTT in the downstream direction, which is almost 40% of the MTT of the zero-order hollow discharge, is much greater than the estimated decrease in MTT associated with a decreasing stormflow ratio (<7%). This result showed that the contribution of qs could be <18% of the spatial variation in MTT at our site, and supported our hypothesis that spatial variation in stream base flow MTT was mostly related to the mean depth of hydrologically active soil and bedrock.
4.2. Relationships Between Topography and MTT
 The topography appeared to have various effects on spatial MTT distribution (Figures 5a–5e). The standard deviation of d-excess decreased with both increasing mean hillslope length and mean hillslope gradient, implying that MTT increased with increases in these parameters (Figures 5a and 5b). Similarly, the standard deviation of d-excess was related to the ratio of hillslope length to mean hillslope gradient (L/G) and the topographic wetness index, indicating that base flow MTT decreased with increases in these parameters (Figures 5c and 5d). The absolute value of Spearman's rank correlation coefficient (rs) between the standard deviation of d-excess and the topographic wetness index (rs = 0.77) was smaller than were those between the standard deviation of d-excess and mean hillslope length (rs = −0.93), mean hillslope gradient (rs = −0.93), and mean L/G (rs = 0.93; Table 2).
 The total catchment area and standard deviation of d-excess were positively correlated; however, this relationship might differ in other longitudinal profiles. Given that the spatial variation in mean dissolved SiO2 showed a convergent pattern when we sampled a larger number of profiles (Figure 2) and that a clear relationship exists between SiO2 and the standard deviation of d-excess (Figure 3), we can expect that the relationship between the total drainage area and the standard deviation of d-excess is likely to be highly variable in zero-order hollow discharges and to converge with the drainage area, as shown by Hrachowitz et al. [2010a].
 The relationship between various topographic measures and the standard deviation of d-excess (Figure 5) suggested that the depth of hydrologically active soil and bedrock were directly related to topographic measures, such as hillslope length and gradient. However, reported findings on the relationship between the spatial pattern of MTT and topography have varied. Some reported results have illustrated a clear relationship between MTT distribution and topographic measures [e.g., McGlynn et al., 2003; McGuire et al., 2005], whereas others have found less relationship to topography [e.g., Rodgers et al., 2005; Soulsby et al., 2006]. Studies that have found a clear relationship with topography have also reported various contrasting results; some have shown a relationship between MTT and median subcatchment size [McGlynn et al., 2003], whereas others found no relationship with median subcatchment area but a clear relationship with hillslope length and gradient [McGuire et al., 2005]. Furthermore, various studies have demonstrated either a positive or negative relationship between the same topographic indices and MTT. For instance, McGuire et al.  and our study both demonstrated a positive relationship between flow path length and MTT; however, in contrast to our findings (Figure 5, Table 2), McGuire et al.  found that the median flow path gradient was negatively correlated with MTT and that mean L/G was positively correlated with MTT. Some of the sites reported by Tetzlaff et al. [2009b] also showed relationships that opposed those found in the present study.
 A possible explanation for these contrasting relationships between surface topographic measures and MTT is that the depth of hydrologically active soil and bedrock (dm) is often, but not always, related to topography. Furthermore, even in catchments where dm is related to topography, the relationship between dm and topographic measures should differ among sites, as our data and previous studies have demonstrated. If both Qb, and Vm in equation (1) were divided by the mean cross-sectional area of the flow system (a), then the MTT could be described as,
where Lm is the mean flow line length in the contributing flow system for base flow production (equal to Vm/a) and vm is the mean flux of water in the flow system (equal to Qb/a). This equation suggests that if Lm and vm are related to the hillslope length (L) and gradient (G) along each flow pathway estimated by surface topography, then the MTT should be related to L and G. Theoretical studies have also shown the important influence of flow path length on catchment response and MTT [Harman and Sivapalan, 2009; Hrachowitz et al., 2010b]. However, the results of this study and previously observed evidence indicate that we cannot always predict “flow path length” for base flow streams from surface topography. Some field investigations have supported the positive relationship between dm and hillslope length [e.g., Montgomery et al., 1997; Asano et al., 2002] and lack of correlation between dm and the drainage area [e.g., Uchida and Asano, 2010]. However, little available field evidence demonstrates a relationship between dm and topography.
 The spatial patterns of SiO2 concentration suggested the existence of several patterns in the longitudinal profile of dm in our catchment, such as patterns of downstream increase and decrease (Figure 2). However, in this study, we focused only on a single decreasing longitudinal profile of MTT and dm (Figure 3). Therefore, the observed relationship between topographic measures and MTT (Figure 5) can also be an artifact of measuring only a single longitudinal profile. Further field investigations are necessary to clarify the common relationship between base flow MTT and topographic measures.
 Our data confirm the hypothesis that spatial variation in base flow MTT in a meso-scale catchment is related to the depth of hydrologically active soil and bedrock (dm), which is derived from the basic theoretical concept of MTT. Previous studies have demonstrated somewhat contrasting relationships between topographic measures and spatial variation in MTT. Our results and those of previous studies confirm that the depth of hydrologically active soil and bedrock (dm), rather than surface topography, ultimately affects the spatial distribution of water travel time in a catchment. On the basis of our results and previous evidence, we hypothesize that the relationship between the depth of the hydrologically active layer and topography, and thus between MTT and topography, will differ among sites. The relationship between topography and the depth of the porosity distribution of hydrologically active soil and bedrock warrants further study.
 This study was supported by the HyARC Collaborative Research Program, Nagoya University, as well as a grant from the Fund of the Japanese Ministry of Education and Culture for Science Research (20780110). We are grateful to Yumi Mimasu, Nobuhito Ohte, Tetsuya Hiyama, and Susumu Goto for assistance in the field and laboratory and for valuable discussions, and Naoko Fujiwara for helping with the topographical analysis. This manuscript benefited from reviews by Kevin McGuire and two anonymous reviewers.