Water Resources Research

Development and application of a simple hydrogeomorphic model for headwater catchments

Authors


Abstract

[1] We developed a catchment model based on a hydrogeomorphic concept that simulates discharge from channel-riparian complexes, zero-order basins (ZOB, basins ZB and FA), and hillslopes. Multitank models simulate ZOB and hillslope hydrological response, while kinematic wave models predict saturation overland runoff from riparian zones and route inputs from ZOB and riparian corridors through the channel. The model was parameterized and tested in the Hitachi Ohta Experiment Watershed, Japan. Tank models were parameterized for a 6 month period from May to October 1992, and these models were then tested for the same 6 month period in 1993. In ZB, with relatively shallower soils, total outflow for the 6 month period in 1993 was underpredicted by 25%. Better predictions were obtained for outflow from FA (deeper soils; −17%) and the entire catchment (−5%). Total runoff from the channel and riparian area depends on the ratio of this area to the total catchment area because this corridor is assumed to be saturated at all times. Stormflow response from ZOB was limited during relatively dry conditions and increased substantially during wetter conditions, especially in ZB, which has shallower soils (1.4 m of average); such effects were diminished in FA (deeper soils) and hillslopes. Outflow from ZB had the highest proportion of rapid flow, while slower flow dominates outflow from FA and hillslopes; these different responses appear to be mainly associated with soil depth and topography. Groundwater recharge, estimated by leakage from the lowermost tank in the models, was as high as 61 mm week−1 from ZB, with lesser recharge from other geomorphic components (18–21 mm week−1). These spatially explicit simulations provide a simpler approach to the greater data demands of distributed hydrologic models without compromising process function.

1. Introduction

[2] Although numerous recent studies have outlined the importance of headwater catchments in steep terrain as source areas for runoff [e.g., Gomi et al., 2002; McGlynn and McDonnell, 2003; Haga et al., 2005], unanswered questions remain regarding the spatial and temporal attributes of various hydrologic pathways and source areas [Sidle et al., 2000; Uhlenbrook, 2003; Uchida et al., 2005]. Understanding such a complex hydrological response in headwaters, particularly during storms, and applying these concepts in models are critical for minimizing land use effects, developing sustainable management plans, evaluating the fate and transport of nutrients and contaminants, and assessing sediment disaster potential [Becker and Braun, 1999; Grayson et al., 2002; Sidle, 2006; Tsuboyama, 2006]. In particular, such improved models can assess environmental flows for biota, stormflow generation, and groundwater recharge, as well as delineate hydroclimatic regimes that govern streamflow generation partitioning between different mechanisms and soil layers.

[3] To model stormflow generation in headwaters while considering various hydrologic pathways, catchments need to be discretized into appropriate “hydrological response” units representing dominant flow paths. Earlier studies examined the evidence and characteristics of various flow pathways in specific portions of catchments using direct or indirect techniques [e.g., Whipkey, 1965; Weyman, 1973; Mosley, 1979; Pearce et al., 1986; Tsukamoto and Ohta, 1988; Moore, 1989; Terajima and Moroto, 1990; McDonnell et al., 1991]. On the basis of extensive field data, including hydrometric measurements [Sidle and Tsuboyama, 1992; Sidle et al., 1995; Tsuboyama et al., 2000; Noguchi et al., 2001; Tsuboyama, 2006], tracer experiments [Tsuboyama et al., 1994a], and staining tests [Noguchi et al., 1997, 1999] in the Hitachi Ohta Experimental Watershed, Japan, Sidle et al. [2000] developed a hydrogeomorphic paradigm to describe stormflow generation in steep headwater catchments. The catchment was divided into reasonably definable geomorphic units including zero-order basins, channels, riparian zones, and hillslopes. Each hydrogeomorphic unit has unique characteristics and flow paths associated with stormflow generation [Sidle et al., 1995, 2000; Tsuboyama et al., 2000]. These studies in Japan contributed to the development of the concept of “threshold hydrological response” [e.g., Sidle et al., 1995, 2000], which was the focus of later studies [e.g., Spence and Woo, 2003; James and Roulet, 2007; Weiler and McDonnell, 2007; Nieber and Sidle, 2010]. Many of these investigations and the research in Japan showed that hydrologic response at various scales in steep headwater catchments was strongly affected by antecedent moisture in soils; once soil moisture reached a threshold, outflow from specific hydrologic units occurred [e.g., Sidle et al., 2000].

[4] Kim et al. [2011] modified the tank model to articulate stormflow pathways in the context of threshold hydrological response within zero-order basins and applied this model to such basins in Hitachi Ohta Experimental Watershed. Several flow pathways were considered in their tank model, including overland flow, biomat and preferential flow, subsurface flow, and shallow groundwater flow. On the basis of model simulations, spatial and temporal variations in the contribution of various flow pathways to basin outflow were related to average soil depth, storm size, and antecedent moisture. Because the previous work of Sidle et al. [2000] and the recent modeling study by Kim et al. [2011] both show strong evidence of different flow pathways and threshold responses in various geomorphic components, it appears useful to divide headwater catchments into discrete “hydrogeomorphic response” units to appropriately consider the spatial and temporal variations of each unit to basin outflow under different conditions.

[5] On the basis of this earlier research, the objective of this study is to introduce a process-based, catchment hydrology model that includes tank models for zero-order basins and hillslopes [Kim et al., 2011] together with a kinematic wave model to capture flow dynamics in the riparian corridor and route water in the catchment. The unique feature of this model is the focus on flow pathway dynamics. The model is tested against an independent data set in the Hitachi Ohta Experimental Watershed, a headwater catchment containing several zero-order basins, a perennial channel and riparian zone, and intervening hillslopes. The characteristics and variations of the hydrogeomorphic response units outlined by Sidle et al. [2000] are assessed, and inferences are made relative to flow response and pathways.

2. Methodology

2.1. Study Area

[6] To develop a hydrologic response model for a headwater catchment, we focused on the 2.48 ha first-order catchment within the Hitachi Ohta Experimental Watershed (forest basin B, FB), located in the eastern portion of the main island of Honshu, Japan (36°34′N latitude, 140°35′E longitude; Figure 1). The area is covered by a mature second-growth stand of Japanese cedar (Cryptomeria Japonica) and cypress (Chamaecyparis Obtusa) forest with various hardwood and woody understory species occupying small gaps. The drainage is deeply incised with metamorphic bedrock (schist and amphibolites) exposed in the perennial channel; steep hillslopes abut the narrow riparian zone. Average annual precipitation is 1460 mm and includes two major wet periods: a rainy season (Baiu season) in early summer and an autumn typhoon season. Soils are derived from volcanic ash and classified as Inceptisols. Soils consist of a relatively thin (<10 cm) organic horizon overlying clay loam mineral soil that varies in depth from 0.44 to 4.15 m throughout the catchment [Tsuboyama et al., 1994b]. The elevation of the channel bottom and slope of various channel segments is shown in Figure 2; hillslope gradients range from 8.5° to 50.6° (mean gradient of 32.4°). Because of the deeply incised channels, riparian corridors throughout the basin are very narrow (2–3 m including the channel). Detailed descriptions of this site are given by Sidle et al. [1995] and Tsuboyama [2006].

Figure 1.

Topographic maps of the Hitachi Ohta Experimental Watershed, Japan, showing (a) the general location in Japan, (b) the locations of the meteorological station (MS) and catchment FB, and (c) a detailed topographic map of forest basin FB with the two monitored zero-order basins (FA with deeper soils and ZB with shallower soils).

Figure 2.

Elevation of the channel bottom and gradient of various channel intervals.

[7] Within basin FB, there are two gauged subcatchments, both composed of zero-order basins. Basin ZB (0.25 ha) is a deeply incised, unchannelled hollow with steep (mean gradient of 33°) side slopes. Average soil depth in ZB is 1.4 m, ranging from 0.4 m in some locations near the hollow axis to 4.2 m near the topographic divide. Basin FA is larger (0.84 ha) and contains a very short incipient perennial stream. More than 90% of the area of basin FA consists of two zero-order basins with gentler slopes (mean gradient of 27°) and deeper soils (mean depth of 2.1 m; range of 0.4–4.7 m) than in ZB. In our model, FA is treated as one larger zero-order basin. In these zero-order basins, soil depth tends to be shallower along the longitudinal axis of the hollows and deeper near the topographic divides. Two other zero-order basins are apparent in the north portion of FB (Figure 1); neither of these was gauged, and the outlets of these basins, including their connectivity to the channel, are unclear and buffered by other hillslope segments on the basis of field inspections. Thus, these slope segments were treated as a lumped part of the “remaining hillslopes of FB” for modeling purposes. A detailed explanation about the remaining hillslopes of FB is found in section 3.2.3.

2.2. Field Methods and Data Compilation

[8] Precipitation, wind speed, air temperature, relative humidity, solar radiation, and atmospheric pressure were measured in an open area along the ridgetop 250 m north of the outlet of ZB (Figure 1b). Tsuboyama [2006] correlated rainfall records at this station with short-term data collected at a canopy interception plot adjacent to ZB and concluded that rainfall was uniform over the 2.48 ha watershed. Rainfall data were collected every 10 min and were aggregated into 30 min intervals from May to October in 1992 and from March to October in 1993 for use in our modeling study (Figure 3).

Figure 3.

Rainfall and runoff data in 30 min intervals at the two zero-order basins ZB and FA and for the entire 2.48 ha forest basin B (FB) for the 6 month study period in 1992 and 1993.

[9] Daily evapotranspiration (ET) was estimated by the Priestly and Taylor [1972] method, which has been successfully applied to vegetated areas with very small water deficits. While some caution needs to be used in applying this method to forested catchments [Shuttleworth and Calder, 1979], it requires only solar radiation, air temperature, relative humidity, and atmospheric pressure data and assumes the air mass moving across a vegetation layer becomes saturated at equilibrium conditions [Priestly and Taylor, 1972]. Thus, equilibrium ET (Eeq) is given by

equation image

where equation image is latent heat of vaporization (J kg−1), equation image is empirical dimensionless coefficient, equation image is slope of vapor pressure versus temperature relationship (kPa °C−1), equation image is psychrometric coefficient (kPa °C−1), Rn is net radiation (MJ m−2), and G is soil heat flux (MJ m−2). Previous data collected from various surfaces with unlimited water supplies yielded an average equation image value of 1.26 [Priestley and Taylor, 1972]. An approximation of actual ET using Eeq from different land surfaces in Japan, including seasonally varying forest cover, found that equation image ranged from 0.5 to 1.26 [Kondo, 1989]. Therefore, in our humid forest at Hitachi Ohta, we assumed equation image and G = 0. Using this method, total annual ET in 1993 at Hitachi Ohta was about 552 mm.

[10] Outflows from FA, ZB, and FB were continuously monitored at 60° V notch gauging weirs during the study period, 1 May to 31 October 1992 and 1 March to 31 October 1993, with a few short periods of interruption when no rainfall occurred. Because there was no perennial stream in ZB, only intermittent outflow emanated from this basin during selected storms. Discharge data were collected and aggregated for the same time intervals as rainfall data for use in our modeling study (Figure 3). Here we optimize model parameters with data for the 6 month period in 1992 and use data for an 8 month period in 1993 to test the model and conduct further analysis.

3. Modeling Concept and Methods

3.1. Modeling Justification and Framework

[11] The concept that guided the development of our stormflow model for the Hitachi Ohta Experimental Watershed was the hydrogeomorphic paradigm introduced by Sidle et al. [2000]. The model basically consists of two types of algorithms, a modified tank model and a kinematic wave model, which are employed in a spatially explicit manner to emulate dominant pathways in the three hydrogeomorphic units that contribute to storm runoff, i.e., zero-order basins, other (more linear) hillslope segments, and the channel-riparian zone [Sidle et al., 2000]. Tank models have been used for years as simple, accurate representations of lumped hydrological response [e.g., Sugawara, 1961; Yokoo et al., 2001]. In this research, we used a modified tank model developed by Kim et al. [2011] to simulate dominant stormflow mechanisms or pathways from the two major zero-order basins (zero-order basins ZB and FA within catchment FB) and other hillslope segments in the Hitachi Ohta catchment. To simulate routing of storm runoff from the channel-riparian complex, a kinematic wave model was employed.

[12] The tank model concept, developed in Japan [Sugawara, 1961], is a lumped depiction of runoff process that has gained popularity because of its simple structure, ease of calculations, and superior performance compared to other models [e.g., Yokoo et al., 2001]. The tank model consists of a combination of linear or nonlinear tanks. The model assumes that runoff and infiltration occur from the side and bottom outlets of the tank, respectively, and a storage component exists in the tank [Yoon, 2007]. Several conceptual tank models can be combined to simulate various scales of drainage basins. Tank models have been applied for storm runoff modeling, including overland flow, subsurface flow, and groundwater flow [Yue and Hashino, 2000; Yokoo et al., 2001; Chen and Adams, 2006; Park and Cho, 2006]. As such, multitank models can be used to represent stormflow pathways where each path is depicted as a side outlet of a particular tank. Each outlet (pathway) has unique characteristics associated with runoff coefficients, storage components, and lag times for the occurrence of outflow.

[13] Kinematic wave theory has been applied to flood routing for more than 50 years [e.g., Lighthill and Whitham, 1955; Cundy and Tento, 1985]. The theory can be used for estimating solutions to unsteady flow dominated by gravity and friction assuming that the inertial and pressure force terms in the momentum equation can be ignored [Yoon, 2007]. The kinematic wave model for overland flow and channel routing has been modified over the years [e.g., MacArthur and DeVries, 1993] and has become widely respected as an accurate and efficient method to simulate storm runoff from small basins for both overland flow and channel routing [Overton and Meadows, 1976]. Here we use a kinematic wave model to route saturation overland stormflow from the riparian area to the nearby channel and to route water within the channel system to the outlet of the catchment.

3.2. Model Descriptions for Each Hydrogeomorphic Component

[14] To model storm runoff processes in the 2.5 ha Hitachi Ohta catchment (FB), the basin was divided into three types of hydrological response units on the basis of geomorphic considerations: (1) zero-order basins (FA and ZB, the western and southern parts of the entire basin in Figure 1), (2) the channel and riparian zone (the blue line in Figure 1), and (3) the remaining hillslope areas in FB excluding units 1 and 2. The zero-order basins were defined by topographic surveys, while the riparian corridor was delineated by field measurements; these comprised important modeling units. Storm outflow from FA and ZB at each time contributes to streamflow as inflow to the channel at corresponding channel junctions, and the outflow from the remaining hillslopes of FB at each time is added to channel discharge at the outlet of FB (Figure 4a). The outflows from two zero-order basins and the remaining hillslopes in FB are estimated by tank models, and flow through the channel and riparian zone is calculated by a kinematic wave model.

Figure 4.

(a) Diagram of flow calculations and inputs from various hydrogeomorphic segments of the catchment and (b) kinematic wave model for channel and riparian zones.

3.2.1. Zero-Order Basins FA and ZB

[15] To simulate storm outflow from the larger zero-order basin with deeper soils (FA), a modified tank model with three tanks in a series was used. In ZB (smaller zero-order basin with shallower soils), a simpler two-tank model was sufficient [Kim et al., 2011]. For FA, tank 1 of the three-tank model represents rapid runoff in the shallow subsurface regime. Saturation overland flow, which typically occurs in the lower concave portion of the hollow during large storms or storms with very wet antecedent conditions [Tsuboyama et al., 2000], is generated only when the water depth in tank 1 exceeds the specified depth threshold (d1A) in this tank (see lower side outlet of tank 1, O1A, in Figure 5). Additionally, in the rare case when the rate of increase of water depth exceeds the specified threshold (It), this pathway may also represent infiltration excess overland flow. Since infiltration excess overland flow is a function of rainfall intensity and the infiltration capacity of the soil and thus can occur for any depth of water in tank 1, the outlet for overland flow is located on the bottom of the tank. The upper side outlet of tank 1 (O1B) represents rapid stormflow through near-surface flow paths such as biomat flow [Sidle et al., 2007] and other preferential flow paths. A separate outlet seems necessary for these preferential flow paths because they emit shallow subsurface water much more rapidly than storm runoff through the soil matrix and more slowly than overland flow [Tsuboyama et al., 1994a; Sidle et al., 1995, 2007; Noguchi et al., 2001]. Biomat and preferential flow occurs only after the water depth in tank 1 exceeds the specified threshold of the upper outlet (d1B). Infiltration into deeper subsurface soil layers occurs through the bottom outlet of tank 1 (Ov1 in Figure 5).

Figure 5.

Structure of the tank model with three serial tanks showing various flow paths. Side outlets represent flow paths that contribute to streamflow; bottom outlets route either infiltration to deeper tanks (soil or regolith reservoirs) or groundwater recharge and evapotranspiration.

[16] Saturated subsurface flow through the soil matrix is represented as outflow from the side of tank 2 (O2 in Figure 5). This discharge is fed by drainage from tank 1 (Ov1) and is much slower than either overland flow (O1A) or biomat and preferential flow (O1B). Subsurface flow is not produced unless the water depth in tank 2 exceeds the specified threshold of the side outlet (d2). As a result of this threshold, there is a lag time associated with subsurface flow. Deeper infiltration of water from the soil into weathered bedrock or shallow groundwater occurs from the bottom outlet of tank 2 (Ov2 in Figure 5). Consequently, the side outlet of tank 3 (O3) represents shallow groundwater flow (generated once the threshold d3 is exceeded), which is considerably slower and more delayed during storms compared to subsurface flow. For larger zero-order basins with deeper soils, this slow, shallow groundwater discharge may emit for many days after storms or may even be continuous during relatively wet periods. Drainage from the bottom outlet of tank 3 (Ov3) represents a combination of (1) catchment “leakage” via deep percolation and subsequent recharge to deeper groundwater or rerouting of this leakage downstream (bypassing the outlet of FB) and (2) losses by evapotranspiration.

[17] A more simplified two-tank model was developed for the smaller zero-order basin with shallow soils (ZB) to reduce the number of parameters [Kim et al., 2011]. For ZB, the function of the two tanks is the same as for the first two tanks in the three-tank model used in FA, except that the side outlet of tank 2 now represents combined subsurface and shallow groundwater flow. This simplification seems justified because of the difficulty in separating these two flows in the shallow soil mantle of ZB. Additionally, the concept of deeper groundwater flow (i.e., drainage from O3 that was simulated in FA) contributing to storm discharge from ZB is not relevant because no base flow occurs from this smaller zero-order basin with shallow soils. In this two-tank model for ZB, the bottom outlet of tank 2 has the same function as the bottom outlet of tank 3 in basin FA (simulated by the three-tank model); that is, it represents leakage and evapotranspiration. In reality, evaporation of intercepted rainfall occurs above the soil surface (i.e., in the canopy), and transpiration occurs within soil down to bedrock. At Hitachi Ohta, ET usually varies from 0.02 to 0.12 mm h−1; the maximum value for the entire 8 month period in 1993 was 0.17 mm h−1. During this period, the combined leakage-ET estimate from the lowermost tank would likely affect the proportion of surface-subsurface flow versus base flow, but the magnitude of this effect would not be great because of the high rainfall inputs.

[18] To preserve the nature of this model, we tried to minimize the number of parameters. The three-tank model used in FA has five threshold parameters that trigger runoff (d1A, d1B, d2, d3, and It), while the simpler two-tank model used in ZB has four threshold parameters (d1A, d1B, d2, and It). These thresholds exemplify the concept of hydrological threshold response emphasized in earlier field and conceptual research in this catchment [e.g., Sidle et al., 1995, 2000, 2001; Tsuboyama et al., 2000] and later employed by numerous researchers related to hillslope and small catchment hydrological response [e.g., Spence and Woo, 2003; Tromp-van Meerveld and McDonnell, 2006; James and Roulet, 2007; Zehe and Sivapalan, 2009; Nieber and Sidle, 2010]. Each tank outlet (both side and bottom outlets) has a coefficient used for regulating outflow based on the following linear proportionality:

equation image

for side outlet, and

equation image

for bottom outlet, where Om(t) and Ov,n(t) are the outflows from the mth side and nth bottom outlets at time t, respectively; km and fn are the coefficients of the mth side and nth bottom outlets, respectively; Dm(t) is the depth from the water surface to the mth outlet at time t; and Dt,n(t) is total water depth in the nth tank at time t. Outflow from the mth outlet only occurs when the water level is above the outlet. The coefficients km and fn for each outlet have unique values from 0 to 1. Om(t) is calculated by equation (2) for each time step, and thus runoff from the zero-order basin and water depth of each tank at time t are

equation image

where I(t) is inflow to the tank from the upper tank or rainfall amount at time t in case of tank 1. Thus, in addition to the five threshold parameters needed for triggering runoff in FA (four parameters in ZB), parameters are needed for (1) each side outlet (k1, k2, and k3) and (2) each bottom outlet (f1, f2, and f3).

3.2.2. Channel and Riparian Zone

[19] Generally, the saturated zone of the riparian area adjacent to perennial channels expands during storms, particularly in larger and gently sloping catchments with wide riparian corridors [Dunne and Black, 1970]. However, on the basis of the field observations and the hydrogeomorphic conceptual model developed at Hitachi Ohta, it is assumed that all rainfall on the channel and narrow riparian zone converts to streamflow because of the shallow soil depth, incised channel, steep side slopes, and the extent of saturation in the riparian zone [Sidle et al., 1995, 2000]. Thus, a kinematic wave model was employed to route saturation overland flow across the riparian zone and within the channel.

[20] The channel cross section was simplified as a trapezoid with maximum (upper) and minimum (lower, streambed) widths of 1.0 and 0.5 m, respectively; the combined width of the channel and riparian zone is 2.5 m [Sidle et al., 1995] (Figure 4b). Runoff generated on the riparian zone was assumed to flow perpendicular to the channel. Discharge per unit width of overland flow on the riparian zone can be expressed as a function of flow depth and Manning's equation:

equation image

where, yo is average depth of overland flow (m) and n is Manning's roughness coefficient. The value of n for overland flow is usually greater than for channel flow [MacArthur and DeVries, 1993]. So is the average gradient (m m−1) of the overland flow element, equation image, and mo = 5/3. The following equation was used to calculate continuous overland flow per unit width:

equation image

where i is rainfall intensity (m s−1), f is infiltration rate (m s−1), t is time (s), and x is flow distance (m) perpendicular to the channel. Equations (4) and (5) represent the momentum and continuity equations for kinematic wave routing of overland flow, respectively. Substituting equation (4) into equation (5) yields

equation image

where yo and qo can be calculated from equations (6) and (4), respectively.

[21] The basic form of the equations for kinematic wave routing of stormflow in the channel is similar to those for saturated overland flow in the riparian zone (equations (4) and (5)).

equation image
equation image

where Qc and Ac are discharge (m3 s−1) and cross-sectional area of flow (m2), respectively. The parameter qo is inflow per unit length contributed by lateral inflow from the riparian zone, rainfall on the stream, and outflows from FA and ZB at the junctions (Figure 4a). Kinematic wave parameters equation image and mc denote effects of channel cross-sectional shape, slope, and roughness. The values for a trapezoidal cross section are

equation image
equation image

where Sc is average slope of channel element (m m−1), w and yc are the bottom width and flow depth (m), respectively, and z is side slope of channel (m m−1). Values of equation image and mc are obtained by numerical fitting to measured data. Partial differential equations of the kinematic wave model for both overland and channel flow were solved using a finite difference method with an explicit scheme [Mitchell and Griffiths, 1980].

3.2.3. Planar Hillslopes

[22] The remaining hillslopes within the headwater catchment that were outside the two major zero-order basins and the riparian-channel complex constitute about 56% of the area of FB. On the basis of field observations and experiments, these hillslopes contributed runoff to the channel during storms via subsurface flow from the soil matrix, preferential flow paths (particularly when soils were very wet), and shallow groundwater discharge. No overland flow was observed on these slopes during storms [Sidle et al., 1995]. As noted, two other poorly connected zero-order basins exist within FB, and these were included in the remaining hillslopes. Conceptually, this should not introduce a large error because the tank model used to simulate the remaining hillslopes has the same structure as the model used in FA (containing two zero-order basins with deeper soils).

[23] A modified tank model with three tanks in series was used to simulate stormflow contribution from the remaining hillslopes in the headwater catchment. The appropriateness of this model for simulating flow in the remaining hillslopes was evident because the major observed storm runoff pathways corresponded with the tank outlets. Outlet O1B represents biomat and preferential flow that was common during the peak and recession limbs of storm hydrographs when antecedent moisture was high [Sidle et al., 1995]. Subsurface and shallow groundwater discharge, represented by outlets O2 and O3, occurred during most storms and increased as catchment wetness increased. Total outflow generated from the remaining hillslopes was added to stream discharge at the outlet of FB (Figure 4). In larger catchments, this hillslope discharge may need to be distributed proportionally throughout the channel and routed downstream as kinematic wave elements.

3.3. Parameter Optimization of the Models

3.3.1. Kinematic Wave Model

[24] Because our observations are for discharge at the outlet of the entire catchment (FB), to optimally parameterize the kinematic wave model for the channel and riparian zone, we need to select a period when only this narrow corridor contributed to catchment discharge. Sidle et al. [2000] showed that the direct outflow from FB during the first storm of the 1992 typhoon season (19 September 1992) could be totally accounted for by saturation overland flow from the riparian zone and direct channel interception; thus, this storm is ideal for model optimization. As such, kinematic wave parameters were manually optimized for this storm by trial and error using R2 criteria.

equation image

where Qobs and equation image are the observed outflows and their mean values, respectively, Qsim is the simulated runoff, and R2 is the coefficient of determination. Kinematic wave parameter optimization was conducted prior to calibration of the tank model parameters for the remaining hillslopes of FB. Base flow was separated from the runoff hydrographs to identify the overland flow portion of the hydrograph by projecting a linear separation of slope 2 m3 h−2 km−2 (the same method used by Sidle et al. [2000]) from the onset of storm runoff [Hewlett and Hibbert, 1967], and slope of the overland flow element (riparian zone) was assumed to be 2 × 10−5 m m−1.

[25] The values of Manning's coefficient (n) used in the kinematic wave model for the riparian zone and channel were 0.38 and 0.036, respectively. The values of these optimized parameters were within reasonable ranges of surface materials; n = 0.17–0.8 for bare surfaces [MacArthur and DeVries, 1993] and n = 0.02–0.07 for natural stream channels [Arcement and Schneider, 1989]. Simulated combined outflow from the channel and riparian zone for the 19 September 1992 storm closely agrees with observations (Figure 6). During the first runoff peak, the overestimation of flow appears to be mainly due to the assumption that the riparian zone was continuously saturated. Such discrepancies could easily be corrected by introducing an initial abstraction based on antecedent moisture, although this may not be necessary for most of the major storms at Hitachi Ohta during wet periods.

Figure 6.

Simulated outflow from the channel and riparian zone for a typhoon storm in 1992 as optimized by the kinematic wave model.

3.3.2. Tank Model

[26] Parameters of the tank models applied to the two zero-order basins (FA and ZB) as well as the remaining hillslopes of FB were optimized for the 6 month period from 1 May to 31 October 1992 (Figure 3) when detailed flow records were available for both basins. Intermittent discharge from a soil pit in a small hillslope segment (not the entire hillslope or zero-order basin) was also available to qualitatively assess flow path response during storms [Sidle et al., 1995, 2000]. The parameters of the tank models for FA and ZB were referred from Kim et al. [2011].

[27] The parameters used in the tank model were optimized using a genetic algorithm (GA) [Holland, 1975] as the objective function in equation (11). This algorithm has been widely and effectively applied as a robust method of parameter optimization in water resources [e.g., Liong et al., 1995; Guan and Aral, 2005; Mohan, 1997; Cheng et al., 2005; Wu and Chau, 2006]. The GA process basically consists of selection, crossover, and mutation, where the initial population of parameters is randomly generated as a parent generation. Next, a new generation that is more evolved than its parent develops through the processes of selection, crossover, and mutation. These processes are then reiterated until the most evolved generation (optimal solution) emerges.

[28] Numerous trial simulations were performed to determine the parameters of GA. First, ranges of the critical parameters for GA were established: 50–200 for the number of populations, 500–3000 for the number of generations (iterations), 50%–100% for the probability of crossover, and 1%–15% for the probability of mutation. On the basis of these simulation trials, the following optimal GA parameters were selected: 100 for the number of populations, 1000 for the number of generations, 90% for the probability of crossover, and 10% for the probability of mutation. Simulation results based on optimized parameters are shown in Figure 7. Simulations generally compare well with observations through the entire period. Total predicted outflow from zero-order basins and hillslopes for the 6 month period was ±5% of observed. Stormflow response from zero-order basins was limited during dry conditions and increased substantially during wetter conditions, especially in ZB with shallow soils.

Figure 7.

Observed and simulated runoff from entire catchment FB for the 1992 season.

4. Results and Discussion

[29] Storm runoff simulation was conducted on the basis of data from March to October 1993 by using the parameters optimized with the 1992 data. This simulation provides an independent test of the model and the basis for further assessment. Water depths in tanks 1 and 2 were initialized as 0 for each of the three tank models (ZB, FA, and remaining hillslopes of FB). In tank 3 of the models for FA and the hillslopes of FB, the initial water depth was set at 19.3 and 178.4 mm, respectively; these represent the optimized thresholds for generating shallow groundwater flow (d3) in these catchment components with perennial channels. Rainfall data for March through April 1993 were used to initialize the water depth in each tank; the actual analysis was performed on the results for the 6 month period from May to October 1993.

4.1. Hydrological Response

4.1.1. Comparison of Simulated Versus Observed Response

[30] Simulated outflow from FB corresponds well to observations in 1993 even though peak runoff during certain moderate and large storms is underpredicted (Figure 8a). In general, the model underpredicted storm runoff peaks when there was abundant antecedent rainfall and slightly overpredicted runoff peaks during storms preceded by little rainfall. Because there was greater total and more continuous rainfall during the entire 6 month period in 1993 compared to 1992 (30 day and 60 day antecedent rainfalls are 53.7–327.2 and 95.8–477.3 mm, respectively, at the beginning of individual storms during the 6 month period in 1993), the tank model parameters estimated for the period in 1992 were calibrated on the basis of relatively less flow compared with the flow in 1993. Thus, the underpredicted storm runoff peaks in 1993 seem reasonable. Total simulated outflow (Osim) from the two zero-order basins and the remaining hillslopes in headwater catchment FB agrees well with observed outflow (Table 1). The tank model in ZB had the poorest performance (outflow underpredicted by ≈25%), while other parts of the catchment with deeper soils (FA and FB, which contained generally deeper soils) underpredicted outflow by only ≈17% and 5%, respectively (Table 1).

Figure 8.

(a) Observed and simulated runoff from entire catchment FB for the 1993 season. (b) Discharge from various flow paths in the remaining hillslopes of FB and discharge from the channel-riparian complex, including the contributions from FA and ZB. (c) Water depth changes in the three tanks of the model for the remaining hillslopes of FB as an indicator of antecedent moisture conditions.

Table 1. Outflow From Each Flow Pathway of the Two Zero-Order Basins and the Remaining Hillslopes of FB for the 6 Month Simulation Period
BasinTotal Outflowa (mm)
O1AO1BO2O3ChannelbOsimOobsOsim/Oobs
  • a

    Values in parentheses are the percentage of outflow compared to total outflow.

  • b

    The outflow from the channel and riparian zone was calculated directly from rainfall on the area and converted into mm according to the area of FB.

  • c

    The outflow from each pathway is not for the entire catchment but for the remaining hillslopes of FB.

ZB25.88 (13.1)107.25 (54.3)64.54 (32.6)--197.68266.870.741
FA13.55 (3.6)30.54 (8.2)63.44 (17.0)265.15 (71.1)0.40 (0.1)372.66447.230.833
FBc0.96 (0.3)13.37 (4.0)38.55 (11.5)269.89 (80.1)13.89 (4.1)481.63506.100.952

4.1.2. Response From Various Hydrogeomorphic Units

[31] Observed responses from each hydrogeomorphic unit within catchment FB are shown for a series of storms in 1993 ranging from relatively dry to very wet antecedent conditions (Table 2 and Figure 9). Direct runoff was estimated by separating base flow using same method used by Sidle et al. [2000], i.e., the method of Hewlett and Hibbert [1967].

Figure 9.

(top) Rainfall hyetographs and (middle) associated observed and simulated outflows from the entire forest basin B (FB). (bottom) Discharge from the two zero-order basins (ZB and FA) and the entire catchment FB.

Table 2. Rainfall Characteristics of Selected Storms in 1993 and Associated Hydrologic Contributions From Various Hydrogeomorphic Units and Entire Catchment FB
Storm DateStart TimeStorm Length (h)Total Rainfall (mm)API30a (mm)Direct Runoffb (mm)
FBFAZB
  • a

    The 30 day antecedent precipitation index.

  • b

    Values in parentheses are the percentage of runoff compared to total rainfall.

13 Jun18:0019.04.9109.80.0283 (0.58)0.0009 (0.02)0.0000 (0.00)
28 Jun14:305.09.5151.80.1435 (1.51)0.0005 (0.01)0.0000 (0.00)
7 Oct17:0031.049.5172.39.4027 (19.00)7.9648 (16.09)14.8395 (29.98)

[32] Contributions from zero-order basins FA and ZB to discharge from catchment FB varied considerably with changing antecedent moisture estimated using the 30 day antecedent precipitation index (API30; Figure 9 and Table 2). Additionally, the percentage of rainfall that appears as discharge increases most dramatically with increasing antecedent moisture in ZB, followed by catchment FB; smaller discharge increases occurred from FA because of deeper soils (Table 2). During the 13 June storm with relatively little antecedent rainfall, the two zero-order basins contributed <2% of the total rainfall to discharge from FB (Figure 9a). As antecedent moisture increased (Figure 9b), the zero-order basin with shallow soils (ZB) began to augment outflow from FB, and by mid-October, almost 30% of the total storm rainfall appeared as runoff from ZB (Figure 9c and Table 2). These latter outflows from ZB tended to be short term and focused around the peak rainfall intensity (Figure 9c). Simulated discharge per unit area of ZB was almost twice that from the overall catchment (FB) near the peak of the 7 October storm when API30 was very high (172.3 mm; Figure 9c and Table 2). The simulated threshold behavior noted in ZB (earlier stormflow response due to shallower soils) and FA (later response due to deep soils) was also observed in our 1992 simulations and the earlier field observations by Sidle et al. [2000].

[33] The proportion of storm runoff from the channel-riparian complex to that from the outlet of FB declined rapidly with increasing antecedent moisture. For example, in 1992, the riparian complex contributed >60% of the total outflow from FB during a storm preceded by relatively dry conditions; this contribution declined to 12% during a later storm in the wettest period. In the 1993 simulations, even larger magnitudes of decline were observed. Similar decreases in the contribution of storm runoff from the channel-riparian complex were noted in the field [Sidle et al., 2000]. Because saturation overland flow (plus direct channel interception) is assumed to occur uniformly across the entire riparian-channel complex, the total amount of simulated flow from this area depends on the ratio of the riparian-channel area to the constituent catchment area, and as such, the 6 month discharge from the riparian complex in FB is much larger than that from FA (Table 1).

4.1.3. Response From Various Flow Pathways

[34] The hydrologic response from various flow pathways in the two zero-order basins and the remaining hillslopes was inferred by discharge from the side outlets of respective tanks in the multitank model. Response from the channel-riparian complex was considered to be direct channel interception of rainfall or saturation overland flow and is presented as the sum of these values in Table 1. Simulated outflows from the various flow paths are shown in Table 1 (O1A, O1B, O2, O3, and channel); for outlet O3 (shallow groundwater), this includes base flow for both FA and the remaining hillslopes in FB.

[35] The proportion of total simulated outflow from each flow pathway varied during the 6 month period on the basis of the soil depth and topography of each subarea. Outflow from ZB, a deeply incised hollow with shallower soils, had the highest proportion of rapid flow, such as overland flow (O1A) and biomat and preferential flow (O1B), while slower flow dominates outflow from FA and the remaining hillslopes of FB (Table 1). Comparing outflows from hillslopes of FB with FA, the proportions of surface flow, biomat and preferential flow, and shallow subsurface flow from hillslopes of FB are much less than those from FA; thus, these differences contribute to an increased proportion of shallow groundwater flow from hillslopes of FB (Table 1). These variations in proportions of various outflow components appear to be mainly due to soil depth and topography. Deeper soils hold more water and slowly release this stored water via base flow. Much of the rainfall on the deeply incised hollow follows rapid pathways (overland or biomat and preferential flow) and quickly converges in the channel, whereas rainfall on hillslopes of FB usually flows via slower pathways and may reinfiltrate and contribute to base flow.

4.2. Basin Water Storage and Leakage

[36] Kim et al. [2011] noted that shallow groundwater storage in FA is analogous to the water depth in tank 3 because of the controls on the dynamics of this reservoir related to both storage and the slow release of water via base flow; in contrast, tanks 1 and 2 are analogous to flow pathways in the soil. The water depth in tank 3 of zero-order basin FA is highly influenced by API30 [Kim et al., 2011]. The dynamics of water depths in tanks 1, 2, and 3 of the tank model for the remaining hillslopes of FB are similar to those of FA (Figure 8c). For the remaining hillslopes of FB, the water depth in tank 3 at the beginning of each of the 56 storms occurring during the 6 month period (Table 3) is plotted against API values ranging from 10 to 90 days (Figure 10). The very weak relationship (R2 = 0.26) between API10 and water depth in tank 3 markedly improved for longer antecedent rainfall indices, with the best regression relationship obtained for API50 (Figure 10e; R2 = 0.88).

Figure 10.

The water depth in tank 3 of the remaining hillslopes in FB plotted against various antecedent rainfall indices.

Table 3. Characteristics of Storms That Occurred From May Through October 1993, Hitachi Ohta Experimental Watershed, Japan
Storm DateStart TimeStorm Length (h)Total Precipitation (mm)
2 May13:0016.017.9
9 May20:3035.028.8
14 May04:3016.015.1
18 May02:308.02.8
20 May15:305.07.8
22 May17:3012.515.1
2 Jun23:0046.055.4
5 Jun15:3023.09.5
9 Jun03:3011.52.7
10 Jun18:003.014.2
13 Jun18:0019.04.9
19 Jun08:3027.527.8
20 Jun22:306.53.4
21 Jun18:302.021.3
23 Jun04:0020.56.6
26 Jun11:0016.05.7
28 Jun15:005.09.5
29 Jun11:3043.514.4
2 Jul18:3019.026.4
5 Jul04:0014.547.9
10 Jul04:3019.07.8
12 Jul09:304.01.1
13 Jul00:005.50.6
13 Jul18:3064.015.5
17 Jul15:3015.03.2
19 Jul00:3025.011.3
24 Jul12:0046.039.4
30 Jul16:3016.05.5
31 Jul19:002.02.3
3 Aug08:0026.010.3
6 Aug03:0023.517.3
8 Aug08:0026.514.3
14 Aug05:008.57.8
16 Aug00:009.57.0
17 Aug02:305.51.6
18 Aug06:001.53.2
18 Aug19:3015.05.5
21 Aug18:004.01.2
24 Aug00:001.06.1
26 Aug15:3029.5174.4
30 Aug01:305.51.8
3 Sept05:004.00.6
4 Sept01:3012.532.5
6 Sept17:3080.032.7
10 Sept18:009.553.0
14 Sept09:3011.518.6
17 Sept16:006.51.1
22 Sept11:3037.050.9
30 Sept21:0013.56.2
3 Oct18:0014.022.7
7 Oct17:0031.049.5
14 Oct00:0013.03.9
17 Oct00:0018.511.1
21 Oct03:3015.017.4
23 Oct18:002.08.5
30 Oct03:3024.513.3

[37] It has been established that hydrographs from the bottom outlet of the lowest tank are potentially useful for estimating relative groundwater recharge from specific areas (ZB, FA, and the remaining hillslopes of FB) of the catchment [Kim et al., 2011]. Thus, net leakage from the lowermost tank of each hydrogeomorphic component (i.e., recharge) was calculated by subtracting daily evapotranspiration (ET) from estimated tank leakage (see values in Figure 11a). When ET is larger than leakage, net leakage is assumed to be zero. Thus, with this correction, net leakage provides a reasonable estimate of groundwater recharge plus deep subsurface recharge that may contribute to channel flow further downstream (below the outlet of FB). While average weekly values of recharge (i.e., net leakage) roughly correspond to rainfall inputs (Figure 11b), accumulated recharge from the three geomorphic units (FA, ZB, and the remaining hillslopes of FB) varied greatly over the 6 month period (Figure 11c). Total recharge from ZB is more than 2 times higher than recharge from FA and the remaining hillslopes of FB (per unit area). This difference appears to be related to intermittent leakage from the lowermost tank of ZB during storms (Figure 11a). During events, recharge may be an order of magnitude higher in ZB compared to FA (deeper soils) and the remaining hillslopes of FB (Figure 11b). This more sporadic response is likely associated with the small basin area, shallow soils, and lack of perennial channel in ZB.

Figure 11.

(a) Estimated evapotranspiration and leakage from the lowest tanks of FA, ZB, and the remaining hillslopes of FB, (b) 2 day moving average of net leakage (recharge) for the same three hydrogeomorphic units (solid line shows weekly averages), and (c) cumulative recharge from each subarea.

[38] Total weekly (26 weeks from 1 May to 29 October) and monthly (from May to October) recharge is compared with respective total rainfall in FA, ZB, and the remaining hillslopes of FB (Figure 12). The relationship between total recharge and total rainfall is strongest in ZB for all time intervals (Figures 12b and 12e). This result is likely due to the smaller residence time of water in the soil layer in basin ZB compared to deeper soils in FA and the more complex topography of the remaining hillslopes of FB. Comparing monthly fluctuations of recharge and rainfall, monthly recharge from FA and the remaining hillslopes of FB reflect fluctuations in monthly rainfall with a 1 month delay, while monthly recharge from ZB directly responds to monthly rainfall; that is, during July, when rainfall decreased, recharge from FA and the remaining hillslopes of FB was still relatively high because of higher rainfall in June. Finally recharge decreased in August despite higher rainfall in August (Figure 11b and Table 4).

Figure 12.

Variations of total net leakage (recharge) versus total rainfall for FA, ZB, and the remaining hillslopes of FB for (a–c) weekly and (d–f) monthly values.

Table 4. Total Rainfall and Estimated Recharge From Each Hydrogeomorphic Unit for Different Periods in 1993
TermsTotal Rainfall (mm)Total Recharge (mm)
FAZBRemaining Hillslopes of FB
May87.75.1348.267.79
June175.122.60103.4921.16
July163.851.74100.7242.38
August249.433.96118.1232.70
September192.984.38119.4369.12
October129.665.3689.7667.31
Entire period998.5263.17579.78240.46

5. Summary and Conclusions

[39] Here we develop and test a simple, process-based hydrologic model for headwater catchments in which the lumped hydrologic response units are based on easily definable geomorphic features (channel-riparian complex, zero-order basins, and remaining hillslopes) associated with the linked hydrogeomorphic paradigm for stormflow generation [Sidle et al., 2000]. The linked hydrological model accurately represents observed discharge from the 2.48 ha headwater catchment, as well as the outflows from the hydrogeomorphic components. For the two zero-order basins and the entire catchment, outflows were −25.9% of measured value in ZB, −16.7% in FA, and −4.8% in the entire catchment of FB.

[40] The increases found in simulated outflow from the headwater catchment, including zero-order basins with increasing wetness, agree well with field observations. Discharge from the small zero-order basin with shallow soils (ZB) responds rapidly to and recedes quickly after rain events once sufficient antecedent moisture accumulates in the basin. In contrast, hydrologic response from the larger zero-order basin with deeper soils (FA) is damped and requires more antecedent rainfall to initiate. The hydrologic response of the remaining hillslopes in the catchment is intermediate to these two zero-order basins, likely because of the complex topography and a few poorly defined (but unmonitored) zero-order basins that do not directly connect to the stream.

[41] Inferences made with respect to flow paths generally correspond with prior field observations. Other than in the riparian area, almost two thirds of overland flow from the catchment was emitted from ZB, and most of the remainder came from FA; this composed only about 8% of the total runoff during the 6 month period in 1993. Simulated increases in preferential flow from all hydrogeomorphic units associated with a threshold response to increases in antecedent moisture lend support to the concept of self-organization of preferential flow paths during such conditions [Sidle et al., 2000]. Because of the deeper soils in FB, lower percentages of preferential flow and higher proportions of subsurface matrix flow were simulated.

[42] This research also provides insights into the nature of spatially and temporally distributed groundwater recharge. By subtracting estimated daily evapotranspiration from the outflow (leakage) of the bottom tanks of zero-order basins and the remaining hillslopes, we found that average weekly values of recharge approximately correspond to trends in rainfall. Weekly recharge estimates from ZB were as high as 61 mm per week, and maximum weekly recharge from FA and the remaining hillslopes of FB was about 21 and 18 mm per week, respectively; these latter maximum recharge rates lag the maximum recharge from ZB by about 3–4 weeks.

[43] The benefits of the lumped modeling approach that we used include the simple structure and computational efficiency along with reduced data requirements compared to distributed hydrological models. As such, the approach outlined here provides an alternative that is able to capture the important physical processes within the catchment, including specific flow pathways and the response of different hydrogeomorphic features.

[44] Although the tank model parameters were calibrated using runoff observations in this study, this simple lumped model could provide better insights into ungauged catchment response by linking the parameters directly with physically based processes or even with parameters estimated by empirical formulas that describe these physical processes. For example, the threshold parameters appear to be related to soil depth, soil porosity, and storage coefficient; the parameters for outlets seem to be related to hydraulic conductivity, runoff coefficient, and infiltration capacity. These relationships between the tank model parameters and parameters that can be physically measured or empirically estimated without runoff observations will improve parameter uncertainty and insights into ungauged catchment behavior.

Acknowledgments

[45] This paper has been reviewed in accordance with the U.S. Environmental Protection Agency's peer and administrative review policies and approved for publication. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. A portion of this research was supported by a postdoctoral award to K. Kim from Appalachian State University.

Ancillary