Threshold behavior in a fissured granitic catchment in southern China: 2. Modeling and uncertainty analysis

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1 WATER RESOURCES RESEARCH, VOL. 49, , doi: /wrcr.20193, 2013 Threshold behavior in a fissured granitic catchment in southern China: 2. Modeling and uncertainty analysis Congsheng Fu, 1,2 Jianyao Chen, 1 Huabo Jiang, 1 and Linyao Dong 1 Received 6 July 2012; revised 4 March 2013; accepted 7 March 2013; published 28 May [1] In general, preferential flow occurring in forest catchments cannot be reasonably described using classical partial differential equations. As a result, linear or nonlinear reservoir models are widely used in hillslope and catchment hydrology. Currently, few studies have simulated the hydrological threshold behavior that has been observed in many experimental catchments. In this study, five models with different structures were constructed using linear reservoir method to explore the inherent mechanisms of threshold behavior and to analyze the uncertainty of model structure in threshold simulations. According to the model results, the average bedrock depression storage over the study catchment (0.99 km 2 ), which can be represented using the height of the lowest lateral outlet from the reservoir bottom (h 1 ), was mm. Substantial movable water percolated into the fissure bedrock and was discharged into the streamflow as base flow after storm events, illustrating why the slope of the linear relationships between the total event precipitation plus the antecedent soil moisture index (P þ ASI) and the event quick flow depth above the rising threshold was less than one. Streamflow was simulated effectively by all five models with (h 1 > 0) or without (h 1 ¼ 0) bedrock depression storage; however, different ratios of annual infiltration into bedrock to annual interflow discharged to the stream were obtained by models with h 1 > 0 ( ) and h 1 ¼ 0 ( ). Namely, the calculated infiltration into bedrock was larger by models with h 1 > 0 than that by models with h 1 ¼ 0. At the storm event scale, the simulated total bedrock flow was larger than the interflow for models with h 1 > 0 by a ratio of 1:0.7, whereas for models with h 1 ¼ 0 the ratio was 1:1.5. Citation: Fu, C., J. Chen, H. Jiang, and L. Dong (2013), Threshold behavior in a fissured granitic catchment in southern China: 2. Modeling and uncertainty analysis, Water Resour. Res., 49, , doi: /wrcr Introduction Companion to Fu et al. [2013] doi: /wrcr School of Geography and Planning, Sun Yat-sen University, Guangzhou, China. 2 Department of Geography, Nipissing University, Ontario, Canada. Corresponding author: J. Chen, School of Geography and Planning, Sun Yat-sen University, Guangzhou , China. (chenjyao@mail.sysu.edu.cn) American Geophysical Union. All Rights Reserved /13/ /wrcr [2] In the hydrological system, threshold behavior is a sudden, extremely nonlinear, and qualitative change in hydrological metrics (dependent variables), e.g., hillslope interflow, event stormflow depth, and event quick flow depth, when the driving hydrological inputs (independent variables), e.g., total event precipitation (P), antecedent soil moisture index (ASI), P þ ASI, reach specific values [Buttle et al., 2004; Tromp-van Meerveld and McDonnell, 2006a; Detty and McGuire, 2010; Penna et al., 2011]. The dependent variables are usually very small when the independent variables are below the corresponding thresholds; otherwise, these dependent variables are either much larger or begin with or increase to very large values. Threshold behavior is one of the representative characteristics of nonlinearity in the hydrological system [McDonnell et al., 2007]. [3] Although several field studies with respect to the hydrological threshold phenomenon have been implemented at hillslope [Tromp-van Meerveld and McDonnell, 2006a] and catchment [Detty and McGuire, 2010; Penna et al., 2011] scales, modeling studies are also needed in threshold analysis, for example, to quantitatively explore bedrock depression storage at catchment scale, which could not be easily investigated by field observations. On the basis of experimental observations for hillslopes, several modeling studies have examined the reasons for, and functions of, threshold behavior. Lehmann et al. [2007] modeled the rainfall threshold behavior for subsurface flow based on percolation theory on a hillslope in the Panola Mountain Research Watershed (PMRW) in Georgia, USA. They found that the threshold value was a combination of the connectivity of the subsurface flow delivery system, the storage capacity of each site (termed lattice in their study), and the percolation rate of subsurface flow into the bedrock. According to threshold behavior observations for a hillslope at the Maimai site in New Zealand, Graham and McDonnell [2010] constructed a hillslope model characterized by water delivery at the soil-bedrock interface through preferential flow paths, the existence of bedrock depressions, and the occurrence of bedrock leakage. They found that the 2536

2 threshold value was influenced by evapotranspiration (antecedent drainage days and potential evapotranspiration) and bedrock leakage. At the catchment scale, Kusumastuti et al. [2007] analyzed the influences of two thresholds, the field capacity threshold and the saturated storage capacity threshold, on flood frequency curves using one rainfall model and four runoff generation models with or without the inclusion of the field capacity threshold or the saturated storage capacity threshold. According to their study, the excesses of both the field capacity threshold and the saturated storage capacity threshold could be reflected in low (< 5 years) and large (> 40 years) return periods, as indicated by breaks in the slope of flood frequency curves. To date, however, only a few modeling studies have focused on hydrological threshold behavior, including the three studies discussed above. Even fewer threshold modeling studies at the catchment scale have been conducted, particularly studies based on field monitoring results. [4] According to previous studies, the existence of non- Darcian flow, e.g., macropore flow and pipe flow, is a common phenomenon in experimental forest catchments [Sidle et al., 2000; Weiler et al., 2003; Weiler and McDonnell et al., 2007]. However, non-darcian flow cannot be properly described using classic partial differential equations based on Darcy s law, e.g., Richard equations. Researchers often use linear or nonlinear reservoir models to describe the subsurface flow in forest catchments [Seibert and McDonnell, 2002] because no better method has been developed. The well-known HBV model and the model built by Seibert and McDonnell [2002] for the Maimai site (catchment scale), along with models for threshold behavior constructed by Lehmann et al. [2007], Graham and McDonnell [2010], and Kusumastuti et al. [2007], were all based on linear or nonlinear reservoirs. However, few studies have examined the structural uncertainty of such models [Kusumastuti et al., 2007; Samuel et al., 2011]. In addition, the influence of model structure on the determination of the threshold behavior has rarely been analyzed. For instance, infiltration into bedrock was found to be a nonnegligible phenomenon in several catchments and accounted for threshold behavior [Lehmann et al., 2007; Graham and McDonnell, 2010], but analysis regarding the influence of model structure on the predicted percolation into bedrock, along with its relationship to threshold behavior, have not yet been undertaken. This study aimed to (a) quantitatively analyze the threshold of bedrock depression storage at the catchment scale, which has yet to be adequately analyzed using modeling methods; (b) explore why the slope of the linear relationship (between P þ ASI and the event quick flow depth above the threshold) is less than one; and c) analyze the uncertainty of the model structure and its influence on the determination of the threshold behavior and hydrological processes. southern China. According to observations at the field site [Fu et al., 2012a, 2012b], the runoff generation of the study catchment (0.99 km 2 ) was characterized as follows: [6] (a) The infiltration rate, vertically through macropores and pipes in soil layers, was very high (10 4 m/s), as was the discharge of subsurface flow (interflow). [7] (b) Infiltrated water was divided into two fractions: the supply to soil moisture deficit and the recharge to saturated water storage. The soil moisture was gradually recharged to field capacity if P þ ASI was large enough. [8] (c) Subsurface flow could be generated even if soil moisture was still below field capacity, and was mainly generated at the soil-bedrock interface, e.g., plot B of Fu et al. [2012a], or around comparative aquitards within thick soil layers, e.g., plot A of Fu et al. [2012a]. [9] (d) Bedrock depression storage influenced the generation of interflow. [10] (e) Percolation into bedrock was not negligible Model Description [11] On the basis of the runoff generation characteristics of the study site, five numerical models with different structures were constructed to determine the controls on threshold behavior. For all five models, the studied catchment, which has no obvious riparian zone as defined by Hill [2000], was separated into hillslope grids and stream grids (Figure 1). Both were 60 m 60 m, and the stream grid was composed of stream segments (length: 60 m; width: stream width) and hillslope segments (length: 60 m; width: 60 m stream width). As shown in Figure 2, soil water storages of hillslope grids and the hillslope segments of stream grids were divided into unsaturated soil water storage (below field capacity) and saturated soil water storage. When rainfall occurred, one fraction of precipitation recharged the unsaturated soil water storage (vertical left side of Figure 2), and the other fraction of precipitation infiltrated to saturate soil water storage (lateral right side of Figure 2) as preferential flow. Evaporation occurred only through unsaturated soil water storage, and evaporations from saturated soil water storage and bedrock storage were omitted. Subsurface flow that was generated from saturated soil water storage (from the lateral outlets in Figure 2) moved downslope from the catchment divide to the stream and eventually entered the stream segments. Bedrock storage was supplied by the percolation of saturated soil water 2. Study Site and Model Development 2.1. Runoff Generation Characteristics of the Study Site [5] The models constructed in this study are mainly based on the observations at the Coastal Experimental Research Base (CERB) located at the Zhuhai campus of Sun Yat-sen University near Tangjiawan town, Zhuhai, Figure 1. grids. Schematic diagram of hillslope and stream 2537

3 Figure 2. Schematic diagram of soil water storage of models 1 (a), 2 (b), 3 (c), 4 (d) and 5 (e). (D soil, soil depth; SU, unsaturated soil water storage; SS, saturated soil water storage; FC, WP, SM sat, and SM represent field capacity, wilting point, saturated soil water content, and practical soil water content, respectively; ZS, depth of saturated soil water storage; P, precipitation; AE, actual evapotranspiration; h 1 and h 2 are the heights of the lower and the upper lateral outlets, respectively; Q S1, Q S2, and Q S0 represent the lower, upper lateral interflow and vertical infiltration into the bedrock, respectively; Q S0,with limitation is the limitation of vertical infiltration rate into the bedrock). storage. The bedrock of the whole catchment was processed as one storage unit. [12] (a) Precipitation [13] The precipitation (P) inputs for the five models were obtained from a rain gauge that was located within the study catchment. [14] (b) Evaporation [15] Potential evaporation (PET) for each computational time interval was calculated using a sine equation (equation (1)), from the observed daily pan (E 601) evaporation, PET daily, based on the assumption that PET reached a maximum at 14:00 and a minimum at 02:00, corresponding to the highest and lowest temperatures during a day, as shown in equation (1): iþ39 sin PET i ¼ PET daily abs 30: ; (1) where i is the time step index, and 48 is the number of computational time intervals (0.5 hr) within one day. The values of 39 and 2 in this equation were set to ensure that PET reached a maximum at 14:00 and a minimum at 02:

4 The divisor of was set to make the sum of the sine function, with i changing from 1 to 48, equal to 1. [16] Actual evapotranspiration (AE) was calculated using two equations that are used in the HBV model [Sælthun, 1995; Seibert, 1997]: SM-WP FC-WP < Par 1; AE ¼ PET SM-WP ðfc-wpþpar1 ; (2) SM-WP FC-WP Par 1; AE ¼ PET; (3) where SM is practical soil water content (%), FC is field capacity (%), WP is wilting point (%), and Par1 is a parameter controlling AE (0.5< Par1<1). [17] (c) Infiltration [18] The fractions of infiltrated rainwater (P) that were assumed to supply unsaturated soil water storage (RU) and saturated soil water storage (RS) are shown in equations (4) and (5), respectively. Infiltration equations (4) and (5) are similar to those used in the HBV model [Sælthun, 1995]. The division of soil water storage into unsaturated soil water storage and saturated soil water storage (Figure 2) is similar to the model constructed by Seibert and McDonnell [2002]. RU ¼ P 1 SM WP FC WP ; (4) SM WP RS ¼ P FC WP : (5) [19] If the saturated soil water storage rises to the soil surface, saturation-excess overland flow is generated. [20] (d) Interflow [21] A linear reservoir with one or two lateral outlets was employed to calculate interflow in the five models in this study. One vertical outlet at the bottom of the reservoir was used to describe the percolation of saturated soil water storage into the bedrock, as shown in Figure 2. The calculation algorithm is shown below. If 0 < SS h 1, or if SS > h 1 and SS < h 1 þ h 2 or if SS h 1 þ h 2 End of options Q S1 ¼ 0; (6) Q S2 ¼ 0; (7) Q S1 ¼ ðss h 1 ÞK S1 Sl 0:5 ; (8) Q S2 ¼ 0; (9) Q S1 ¼ h 2 K S1 Sl 0:5 ; (10) Q S2 ¼ ðss h 1 h 2 ÞK S2 Sl 0:5 : (11) [22] For model 1, h 1 ¼ h 2 ¼ 0, and K S1 ¼ K S2 ; for model 2, h 2 ¼ 0 and K S1 ¼ K S2 ; and for model 3, h 1 ¼ 0. [23] For models 1 4, [24] For model 5, Q S0 ¼ SS K S0 : (12) Q S0 ¼ min SS K S0 ; Q S0; with limitation : (13) [25] In equations (6) (13), SS is saturated soil water storage (m), and Q S1, Q S2, and Q S0 represent the lower, upper lateral interflow, and vertical infiltration into the bedrock (m/s), respectively. The variables h 1 and h 2 are the heights of the lower and the upper lateral outlets (m), respectively, K S1 and K S2 are the outflow coefficients of the two lateral outlets (1/0.5 h), and K S0 is a parameter controlling the percolation of saturated soil water storage into bedrock (1/0.5 h). Sl represents the grid gradient, and Q S0,with limitation is the limitation of vertical infiltration rate into the bedrock within a specific time interval (m/s). [26] (e) Bedrock flow [27] The bedrock water storage of the entire catchment was processed as a linear reservoir, and its outflow was added to the total runoff at the catchment outlet as follows: h rock ¼ h rock þ Q S0 t; (14) Q rock ¼ h rock K rock : (15) where Q rock is bedrock groundwater flow (m/s), h rock is storage depth (m), t is the calculation time interval (0.5 h), and K rock is a parameter controlling the bedrock groundwater flow (1/0.5 h). It is worth mentioning that the nonlinear reservoir method had also been employed to delineate bedrock groundwater flow in a model [Fu et al., 2012a] similar to model 1 in this study; however, the improvement in model performance compared to the linear reservoir method was limited and negligible, even though two more parameters were added in the nonlinear reservoir method. Subsequently, the linear reservoir method was selected for all five models in this study. Note that the groundwater dynamics are usually very complicated at the catchment scale; for example, Seibert et al. [2003] reported that the groundwater levels close to a stream were in phase with the runoff in a Sweden catchment, whereas the changes in groundwater levels in upland areas lagged behind the streamflow. Similar to the case for many other experimental catchments, we do not have groundwater level data in upslope areas, and that is the reason why the simple linear reservoir model was used, although it may not reflect the complicated groundwater dynamics at the catchment scale. [28] (f) Routing of interflow [29] The routing of interflow in hillslope grids was achieved by the steepest-descent method (D8 method). Interflow accumulated in the hillslope segments of stream grids was discharged to the adjacent stream segments (Figure 1). [30] Routing of saturation-excess overland flow and river routing [31] The study site is a steep catchment with an average gradient in all grids (60 m 60 m) of 0.44 and an average 2539

5 stream gradient of According to a previous research [Li, 2007], the kinematic wave approximation of onedimensional Saint Venant equations can be used to simulate the movements of both saturation-excess overland flow and streamflow. The control equations are ¼ r; q ¼ S1=2 0 n h5=3 ; (17) where h is the water depth in saturation-excess grids or stream grids (m), q is the discharge per width (m 2 /s), r represents the saturation-excess water (S excess, units were changed to m/s, by dividing by the time step) on saturationexcess grids or stream precipitation (m/s), S 0 is the grid gradient, and n is roughness from Manning s equation. qði; tþ X q up ðj; tþ j Discrete ð16þ : x hði; tþ hði; t tþ þ ¼ rði; tþ: t [32] Incorporating (17) into (18): qði; tþ X q up ðj; tþ j þ qði; tþ qði; t tþ x t ¼ rði; tþ; (18) (19) where ¼ðnS 1=2 0 Þ 3=5 and ¼ 3 5. [33] Equation (19) can be solved using the Newton iterative method. The connections of different flow systems or components are shown in Figure Model Parameters [34] As shown in Figure 2 and Table 1, models 1, 2, 3, 4, and 5 have four, five, six, seven, and eight parameters to be calibrated, respectively. For example, in model 5 the parameters K S1, K S2, K S0, K rock, Par1, h 1, h 2, and Q S0,with limitation need to be calibrated. Experimental or empirical values are used for other parameters such as FC, WP, and n. 3. Results [35] According to a previous soil survey at the CERB site [Fu et al., 2012b], the soil depth of the catchment was set to an average value of 0.9 m for all five models. On the basis of an oven drying experiment for determination of soil water content at plot A [Fu et al., 2012a], and considering that the soil type was comparatively uniform (loamy sand or sandy loam) in the catchment [Fu et al., 2012b], FC, WP, and SM sat were set equal 0.23, 0.10, and 0.40, respectively, for the entire catchment for all five models. Manning s roughness coefficient n was set to 0.25 for the hillslope grids (saturation-excess overland flow) and 0.01 for stream segments. The calculation time interval in all five models was 0.5 h. [36] The scopes of the parameters (Table 1) were set after the initial calibration work (results are not shown). The common parameters were set with the same scope for all five models for comparative purposes, as shown in Table 1. For each of the five models, 2000 parameter sets were sampled using the Monte Carlo method. The objective calibration functions were the Nash Sutcliffe efficiency (NSE) (equation (20), as proposed by Nash and Sutcliffe [1970]) and the volume efficiency (VE) (equation (21)): 2 NSE ¼ X N VE ¼ 1 abs 6 4 i¼1 X N 2 i¼1 X N i¼1 3 ðq obs Q mod Þ ; (20) Q obs Q obs Q mod XN Q obs i¼1 X N Q obs i¼ : (21) [37] In equations (20) and (21), Q abs and Q mod are the observed and simulated streamflow, respectively, and Q obs is the mean value of the observed streamflow Calibration and Validation [38] The study period was from 20 November 2006 to 31 March One example of simulated streamflow (NSE¼ 0.87; VE¼ 0.96) using model 1 versus observed values is shown in Figure 4a, which shows that the simulated streamflow fits the observations very well. If 1 January 2007 to 30 June 2007 was defined as a calibration period (3 dry months: January March; 3 wet months: April June), and 1 July 2007 to 31 March 2008 was defined as a validation period (3 wet months: July 2007 September 2007; 6 dry months: October 2007 March 2008), the NSE values for Figure 3. Sketch map of the model structure. Evap represents evapotranspiration, and Precip represents precipitation. 2540

6 Table 1. Ranges of the Model Parameters a ID K S1 (1/0.5 h) K S2 (1/0.5 h) K S0 (1/0.5 h) K rock (1/0.5 h) h 1 (m) h 2 (m) Par1 Q S0,with limitation (m/s) Model Model Model Model Model a K S1 and K S2 are the outflow coefficients of the lower and the upper lateral outlets, respectively; K S0 is a parameter controlling the percolation of saturated soil water storage into bedrock; K rock is a parameter controlling the bedrock groundwater flow; h 1 and h 2 are the heights of the lower and the upper lateral outlets, respectively; Par1 is a parameter controlling actual evapotranspiration; Q S0,with limitation is the limitation of vertical infiltration rate into the bedrock. these two periods are 0.88 and 0.85, and the VE values are 0.85 and 0.88, respectively. For a complete hydrological year from 1 April 2007 to 31 March 2008 (wet season: April September; dry season: October March), the NSE and VE values are 0.87 and 0.96, respectively. The performance of the model for the complete hydrological year can represent the model s efficiency for both the calibration and validation periods because the complete hydrological year covers most of the calibration and validation periods. Hence, no further calibration and validation results are presented for the five models in the remainder of this paper. The simulated streamflow between 1 April 2007 and 31 March 2008 was used to calculate NSE and VE, and data from 20 November 2006 to 31 March 2007 were used to initialize the model. The NSE plots for model parameters from the Monte Carlo simulations are shown in Figure 5. [39] In addition, the streamflow on 1 April 2007 and 31 March 2008 was small and close to zero (Figure 4a), illustrating that both the saturated soil water storage and bedrock storage were also close to zero at both the beginning and end of the statistical period. Because of this, the influences of such storage changes on runoff generation are not discussed further Parameter Identification Analysis [40] In Figure 5b, 5d, and 5e, h 1 is shown to be the most easily identifiable parameter for models 2, 4, and 5 with h 1 > 0. For models 2, 4, and 5, the calibrated h 1 with the largest NSE values were 2.0, 2.4, and 1.5 mm, respectively. The range of h 1 values with NSE values larger than 0.87 were (two parameter sets), (two parameter sets), and (three parameter sets) mm, respectively, and the NSE values decreased rapidly when h 1 was out of these ranges. In addition, K S1 and K S0 were also identifiable parameters for all five models, but they were not as sensitive as h 1. The next easily identifiable parameter was K rock. The other four parameters, K S2, Par1, h 2, and Q S0,with limitation, were not identifiable. [41] The average bedrock depression storage of the study catchment can be represented using h 1 in models 2, 4, and 5. The above results illustrate that the identified high-nse h 1 was mm, indicating that the average bedrock depression storage of the study catchment is mm. Bedrock depression storage is not included in models 1 and 3 with h 1 ¼ Model Efficiency Analysis [42] As shown in Figure 2, and considering that h 1 is the most easily identifiable parameter, models 1 and 3 can be classified into one group with h 1 ¼ 0, and models 2, 4, and 5 can be classified into another group with h 1 > 0. For models 1 and 3, 174 and 196 of the 2000 parameter sets resulted in NSE 0.85 and VE 0.90, respectively. The numbers of parameter sets for models 2, 4, and 5 with NSE 0.82 and VE 0.90 were 77, 82, and 71, respectively (Table 2). Therefore, models 1 and 3 are more efficient in terms of high-nse parameter sets than models 2, 4, and 5, or to summarize, models with h 1 ¼ 0 are more efficient than models with h 1 > 0. It is also worth noting that within the model group with h 1 ¼ 0, model 3 (196 parameter sets with NSE 0.85 and VE 0.90) is more efficient than model 1 (174 parameter sets with NSE 0.85 and VE 0.90). Similarly, model 4 is more efficient than model 2 within the model groups with h 1 > 0. Also, the efficiency of model 2 is close to that of model 5, the efficiency of which has been affected by the limitation on the percolation rate into bedrock. As a result, for both model groups with h 1 ¼ 0 and h 1 > 0, models with two lateral outlets are more efficient than those with only one lateral outlet Influence of Model Structure on Annual Flow Components [43] Table 2 shows that the average annual actual evapotranspiration, annual infiltration into bedrock, and annual interflow discharged to the stream calculated by model 1, using parameter sets with NSE 0.85 and VE 0.90, are similar to those calculated by model 3, as are the corresponding values calculated by models 2, 4, and 5 using parameters with NSE 0.82 and VE For all five models, the modeled annual infiltration into bedrock is larger than the annual interflow discharged to the stream. In addition, the calculated ratios of annual infiltration into bedrock to annual interflow discharged to the stream by models 2, 4, and 5 ( ) are larger than those calculated by models 1 and 3 ( ). In other words, as Table 2 indicates, more saturated soil water storage infiltrated into the bedrock when using models 2, 4, and 5 than predicted by models 1 and Influence of Model Structure on Event Flow Components [44] In order to analyze the influence of model structure on event flow components, hydrographs of 36 storm events from December 2006 to October 2008 were separated, with beginnings and endings determined using the constant slope method [Hewlett and Hibbert, 1967]. For all five models in this study, storm streamflow consisted of four components: (a) direct precipitation on the stream, (b) bedrock flow from pre-event bedrock storage, defined as preevent bedrock flow, (c) bedrock flow from infiltration into 2541

7 Figure 4. Schematic of flow components. (calculated using model 1; annual Nash-Sutcliffe efficiency (NSE) ¼ 0.87 and annual volume efficiency (VE) ¼ 0.96; K S1 ¼ 0.256, K S0 ¼ 0.054, K rock ¼ 0.004, Par1¼ 0.758; subfigures (b), (c), and (d) are for a rainfall-runoff event during which very limited event bedrock flow contributed to streamflow; subfigures (c), (f), and (g) are for a rainfall-runoff event during which substantial event bedrock flow contributed to streamflow). the bedrock during a storm event, defined as event bedrock flow, and d) interflow. The water retention capacity of the loamy sand and sandy loam soils in the study catchment was very small, movable water drained quickly and the hillslope interflow ceased within several hours after precipitation [Fu et al., 2012a]. In addition, there is no obvious riparian zone in the study catchment. Consequently, the interflow from hillslope and riparian zone was very limited between storm events, and bedrock flow was assumed to be the dominant component of pre-event streamflow. The preevent bedrock flow, coming from the pre-event bedrock storage, can be calculated using equation (15) during storm 2542

8 Figure 5. Scatter plots of model parameters from the Monte Carlo simulations. (2000 parameter sets for each model). (a) Model 1. (b) Model 2. (c) Model 3. (d) Model 4. (e) Model

9 Figure 5. Continued two storm events in November 2006 and May 2007, are given in Figures 4d and 4g. For both of these events, interflow is the most important component, while event bedrock flow is also substantial for the May 2007 event (Figure 4g). [45] Figure 6 shows that all five models can effectively simulate the event streamflow depth (ESD), and threshold behavior can be identified between P þ ASI and ESD. However, Table 3 and Figure 7 illustrate that the calculated event flow components were different for the different model groups. The fractions of pre-event bedrock flow, event bedrock flow, and interflow to ESD, as calculated by model 1 using parameter sets with NSE 0.85 and VE 0.90, were similar to those calculated by model 3. The corresponding values calculated by models 2, 4, and 5 using parameters with NSE 0.82 and VE 0.90 are also similar. [46] According to models 1 and 3, the ratio of total bedrock flow (pre-event bedrock flow þ event bedrock flow) to interflow was around 0.7 (1:1.5 1:1.4), whereas the corresponding ratio was around 1.4 (1:0.7) when using models 2, 4, and 5. As a result, the dominant components of event streamflow differ between models 1 and 3 (interflow) and models 2, 4, and 5 (bedrock flow). However, event bedrock flow is less than interflow for both models 1 and 3 at ratios of 1:3.6 1:3.4 and for models 2, 4, and 5 at ratios of 1:1.9 1:1.6. [47] Infiltration rate to bedrock versus the ratio of annual infiltration into bedrock to annual interflow [48] According to our analysis, among all the parameters in the five models, only K S0 has a linear relationship with the ratio of annual infiltration into bedrock to annual interflow discharge to stream (Figure 8). Figure 8 also shows that these linear relationships are more significant for model groups with h 1 ¼ 0 (models 1 and 3, Pearson r: ) than for model groups with h 1 > 0 (models 2, 4, and 5, Pearson r: ). The correlation analysis presented in Figure 8 verifies the similar behaviors among the models in the same group. events. The total bedrock flow, coming from the total bedrock storage (pre-event bedrock storage þ percolation into bedrock during storm event), can also be calculated using equation (15). The event bedrock flow is the difference between the total bedrock flow and the pre-event bedrock flow. Examples of flow components, calculated by model 1 using a parameter set with NSE¼ 0.87 and VE¼ 0.96, for 3.6. Factors that Influence the Ratio of Preevent Bedrock Flow to Event Streamflow Depth (ESD) [49] In this study, pre-event streamflow was defined as the initial bedrock flow. Correlations between initial bedrock flow and the ratios of pre-event bedrock flow to ESD for 36 storm events, by all five models, are shown in Figures 9a, 9c, 9e,9 g, and 9i. It is clear from the figure that the Table 2. Model Efficiency and Modeling Results at the Annual Scale a,b ID Nash-Sutcliffe Efficiency (NSE) Range Number of Parameter Sets Additional Criterion: Volume Efficiency 0.90 Actual Evaporation (mm) (Averaged) Infiltration into Bedrock (mm) (Averaged) Interflow Discharged to Stream (mm) (Averaged) Ratio of Infiltration into Bedrock to Interflow Discharged to Stream Model :1 Model :1 Model :1 Model :1 Model : 1 a Statistics in this table cover the period from 1 April 2007 to 31 March b 2000 parameter sets are generated for each of the five models using Monte Carlo method, and statistics in this table are only based on the high-nse ( 0.85 for models 1 and 3; 0.82 for models 2, 4, and 5) and high-ve ( 0.90) parameter sets. 2544

10 Figure 6. Comparison between observed and modeled event streamflow depth. A large storm (precipitation ¼ mm) is included in subfigures (a) Model 1, (c) Model 2, (e) Model 3, (g) Model 4, and (i) Model 5, but not in subfigures (b) Model 1, (d) Model 2, (f) Model 3, (h) Model 4, and (j) Model 5. (Model 1: annual NSE ¼ 0.85, annual VE ¼ 0.99; model 2: annual NSE ¼ 0.82, annual VE ¼ 0.98; model 3: annual NSE ¼ 0.85, annual VE ¼ 0.98; model 4: annual NSE ¼ 0.82, annual VE ¼ 0.92; model 5: annual NSE ¼ 0.82, annual VE ¼ 0.97.) correlations are more significant for the model group with h 1 ¼ 0 (models 1 and 3, Pearson r: 0.81) than for the model group with h 1 > 0 (models 2, 4, and 5, Pearson r: ). Considering that the threshold behavior between P þ ASI and ESD (Figure 6) was found in the study catchment, the correlations between initial bedrock flow (P þ ASI) and the ratios of pre-event bedrock flow to ESD were also analyzed (Figures 9b, 9d, 9f, 9h, and 9j). In Figure 9, the linear relationships incorporating P þ ASI (for models 1 and 3, Pearson r: 0.88; for models 2, 4, and 5, Pearson r: ) show higher correlations than those that do not incorporate P þ ASI. This is because there is a linear relationship between P þ ASI and ESD above a specific threshold (Figure 6). 2545

11 Table 3. Modeling Results at the Storm Event Scale a,b,c ID Ratio of Pre-Event Bedrock Flow to Event Streamflow Depth (%) Ratio of Event Bedrock Flow to Event Streamflow Depth (%) Ratio of Interflow to Event Streamflow Depth (%) Ratio of Total Bedrock Flow (Pre-Event þ Event Bedrock Flow) to Interflow Ratio of Event Bedrock Flow to Interflow Model : : 3.4 Model : : 1.8 Model : : 3.6 Model : : 1.6 Model : : 1.9 a The ratios of direct precipitation on the stream to event streamflow depth in the five models are all b Thirty-six storm events were used for these statistics. c Statistics in this table are all average values using parameter sets with the ranges of Nash-Sutcliffe efficiency and volume efficiency shown in Table Discussion 4.1. Model Structural Uncertainty [50] Models 2, 3, and 4 from Kusumastuti et al. [2007] are based on the runoff generation mechanism of saturation excess, specifically that no subsurface flow is generated until the soil moisture reaches field capacity. Model 2 from Kusumastuti et al. [2007] with only one lateral outlet is similar to model 1 in this study. Models 3 and 4 from Kusumastuti et al. [2007] have two lateral outlets and are similar to model 3 in this study. Graham and McDonnell [2010] incorporated only one lateral outlet for the subsurface storage reservoir (corresponding to saturated soil water storage in this study), and the storage below this lateral outlet, to our understanding, represented the bedrock depression storage of the modeled hillslope. The bedrock leakage coefficient in Graham and McDonnell s [2010] model corresponds to the parameter K S0 in models 1, 2, 3, and 4 in this study. Thus, Graham and McDonnell s [2010] model is similar to model 2 in this study. In the well-known HBV model [Sælthun, 1995; Seibert, 1997], the upper zone, which corresponds to the saturated soil water storage in this study, is modeled by a linear reservoir with two lateral outlets. The positions of the two lateral outlets are the Figure 7. Ratios of different flow components to event streamflow depth. (Ave represents event-averaged value). 2546

12 Figure 8. Correlations between K S0 and the ratio of infiltration into bedrock to interflow for the five models. (a) Model 1. (b) Model 2. (c) Model 3. (d) Model 4. (e) Model 5. same as those in model 3 in this study. Deep percolation into the lower zone, which here corresponds to bedrock storage, is controlled by the percolation rate (mm/d), which corresponds to the Q S0,with limitation parameter in model 5 in this study. The model constructed by Seibert and McDonnell [2002] and calibrated by soft data at the Maimai site also employed a model structure similar to model 3 in this study. [51] The study by Kusumastuti et al. [2007] was based on a hypothetical catchment with assumed model parameters, and thus model calibration and validation were not done. The model constructed by Graham and McDonnell [2010] resulted in (a) the maximum NSE of 0.95 for the 40 day hillslope discharge monitored every 10 min, and (b) correlation coefficients larger than 0.8 between the observed and simulated temporal/spatial tracer breakthrough. Using the HBV model, Seibert [1997] obtained maximum NSEs of 0.81 and 0.86 for the 10 year daily discharges of two catchments (198 and 730 km 2 ) in Sweden. Seibert and McDonnell [2002] reported a maximum NSE of 0.93 for the runoff from the 3.8 ha catchment at the Maimai site during August 1987 December As shown in Table 2, the maximum NSEs for 1 year streamflow monitored every 30 min by the five models in this study are all larger than 0.86, indicating good model performances. In summary, all reservoir models with different structures can effectively simulate streamflow. [52] The results in Tables 2 and 3 show that the height of the lowest lateral outlet (h 1 ) can affect the simulated intermediate hydrologic processes at annual and storm event scales. For example, the simulated ratio of annual infiltration into bedrock to interflow discharged to the stream was larger when using models with h 1 > 0 than that when using models with h 1 ¼ 0. At the storm event scale, the modeled total bedrock flow was larger than the modeled interflow when using models with h 1 > 0, but this result reversed when using models with h 1 ¼ 0. It is reasonable as the bedrock depression in models with h 1 > 0 needs to be filled before the generation of interflow, and the bedrock depression storage will eventually be consumed by percolation into bedrock. As a result, more percolation into bedrock will be generated by models with h 1 > 0 than by models with h 1 ¼ 0, given same percolation rate into bedrock and coefficient of lateral outflow. [53] In summary, although all the five models in this study could simulate the streamflow effectively, the modeled intermediate processes (e.g., percolation into bedrock, interflow discharged to stream) are different. Considering that models without the threshold of bedrock depression storage (h 1 ¼ 0) were more efficient than models with the threshold (h 1 > 0), it can be concluded that significant uncertainty and weak identification of reservoir model structures exist when applied to experimental catchments, especially when streamflow is the only variable for calibration. [54] The above analysis verifies the importance of proper model structures for specific runoff generation characteristics of modeled catchments, e.g., modelers should be careful to implement reservoir models with h 1 ¼ 0 for catchments with flat hillslopes and considerable bedrock depression storage capacities. Multiple kinds of data, including outlet streamflow, intermediate process observations, and both hydrological and hydrochemical data, are necessary for overcoming the uncertainty of model structures Parameter Uncertainty [55] Former studies have reported the equifinality phenomenon in hydrologic models, namely different parameter sets result in identical modeling results [Beven and Freer, 2001]. Seibert [1997] analyzed the parameter identification of HBV model, and reported that only a few parameters were identifiable and most parameters could be found over 2547

13 Figure 9. Correlations between initial bedrock flow, the sum of total event precipitation (P) and the antecedent soil moisture index (ASI), and the ratio of pre-event bedrock flow to event streamflow depth. (a, b) Model 1. (c, d) Model 2. (e, f) Model 3. (g, h) Model 4. (i, j) Model 5. a large range. Seibert [1997] also suggested that model predictions should be given as a range or a distribution of probability. As shown in Figure 5 in this paper, the equifinality phenomenon existed for all five models. For example, many different parameter sets resulted in same NSE of 0.80 for model 1 (Figure 5a), and this phenomenon also existed for the other four models (Figures 5b 5e). In addition, more than 100 high-nse parameter sets were found (Table 2) in all five models, that also illustrated the equifinality phenomenon. [56] According to Figures 5a and 5c, the optimum value of K S1 was most easily found compared to other parameters in models 1 and 3, namely, K S1 is the most easily identifiable parameter in models 1 and 3, which is in accordance with the results of Seibert [1997]. However, the height of the lowest lateral outlet (h 1 ) is the most easily identifiable parameter for models 2, 4, and Bedrock Depression Storage [57] As shown in Figure 8, the relationships between K S0 and the ratio of annual infiltration into bedrock to annual interflow discharged to stream are linear, in models 1 and 3 without bedrock depression, whereas the corresponding linear relationships are not significant in models 2, 4, and 5 with bedrock depression storage. These comparisons illustrate that the bedrock depression storage (h 1 ) acts as a type 2548

14 of threshold and has increased the nonlinearity of the hydrologic system. The influence of bedrock depression storage on subsurface flow generation, and particularly on hydrological threshold behaviors, has been indicated in previous experimental studies [Buttle et al., 2004; Tromp-van Meerveld and McDonnell, 2006b; Graham et al., 2010]. Graham et al. [2010] attributed the difference between the precipitation thresholds of mm at Maimai site and 55 mm at Panola site to differences in the slope and potential storage at the bedrock surface. The respective slopes at the Maimai and Panola sites are 56% (steep) and 14% (flat) and the average slope of the catchment at the CERB site in this study is 44%, which is also very steep. Therefore, the bedrock depression storage of CERB should be close to that of the Maimai site. According to the study by Graham and McDonnell [2010], the calibrated optimum bedrock depression storage at the Maimai site was 1.7 mm, which is within the optimized range of mm at CERB. As a result, the small values of calculated bedrock depression storage ( mm) for the entire catchment using models 2, 4, and 5 are comparatively reasonable Infiltration into Bedrock [58] Recently, the significance of infiltration into bedrock in experimental catchments has attracted the attention of researchers [Uchida et al., 2003; Katsuyama et al., 2004], and the saturated conductivity of bedrock was found to be as high as 10 6 m/s [Katsuyama et al., 2005; Onda et al., 2001; Tromp-van Meerveld et al., 2007; Sanda et al., 2009; Graham et al., 2010]. It is for this reason that the range of the Q S0,with limitation parameter in model 5 of this study was set to be m/s. However, the modeling results obtained from model 5 are similar to those of models 2 and 4. Considering that the parameter Q S0,with limitation is not sensitive, the role of Q S0,with limitation in the limitation of infiltration into bedrock is not significant at CERB. The substantial percolation into bedrock, which models 2, 4, and 5 predicted to be times more than interflow (Table 2), is in accordance with deuterium and 18 O results of Zeng et al. [2009], i.e., groundwater flow contributed 73.3% of streamflow from February 2008 to May 2008 in the study catchment. [59] Among threshold-relevant modeling studies, Lehmann et al. [2007] found that bedrock leakage occupied 65% of the movable water generated at the soil-bedrock surface for a PMRW hillslope at the storm event scale. Graham and McDonnell [2010] reported that percolation into bedrock could make up the largest part (47% of the total precipitation) of the water balance during rainfall-runoff events at the Maimai site, and that the calculated ratio of percolation into bedrock to interflow was 1.3 (1:0.8). In this study, the calculated total bedrock flow was larger than interflow (by a ratio of 1:0.7) at the storm event scale using models 2, 4, and 5, which is similar to the results obtained by Graham and McDonnell [2010]. The optimum K S0 (the proportion of saturated soil water storage percolating into bedrock) from Graham and McDonnell [2010] is /s, and the optimum K S0 in the five models in this study (Figure 5) is for a simulation interval of 30 min, namely /s. Subsequently, the calibrated percolation rate into bedrock in this study is also close to the relevant result by Graham and McDonnell [2010]. [60] Movable water, that generated when P þ ASI was larger than a specific threshold created interflow to the stream and percolation into the bedrock. When above the threshold, the slope between the event quick flow depth and P þ ASI represents the ratio of event quick flow depth to movable water; thus, the slope is equal to the ratio of event quick flow depth to the sum of interflow drained to stream and percolation into bedrock. Percolation into bedrock is equal to the sum of pre-event bedrock flow, event bedrock flow (Figures 4d and 4g), and bedrock flow occurring between storm events. It should be noted that the preevent bedrock flow and bedrock flow occurring between storm events, both of which belong to base flow as defined by Hall [1968], were not included in event quick flow depth. For this reason, the slopes of the linear relationships between P þ ASI and event quick flow depth above the rising threshold were less than one ( , shown in the companion paper). Specifically, as shown in Table 3, the ratio of pre-event bedrock flow to event streamflow ranged from 34.0% to 34.3%. This indicated that the ratio of preevent bedrock flow to event quick flow depth was larger than 34%, meaning that a large proportion of percolation into bedrock was not included in the event quick flow depth. [61] In addition, it is worth noting the important role played by bedrock fissures in high percolation into bedrock. According to Fu et al. [2009, 2012b], the bedrock at the CERB site is strongly weathered and has many fissures. In a recent study, Salve et al. [2012] conducted a field investigation of percolation into bedrock on a m forested hillslope in northern California, which was capped by about 50 cm of stony soil over weathered and fractured argillite. They reported that fracture networks delivered unsaturated flow quickly to the perched groundwater, located 4 18 m below the ground surface, at the interface of weathered bedrock and underlying fresh bedrock, and that all the runoff on the hillslope was generated from this perched groundwater storage. The main assumption in this modeling study, that bedrock fissure flow is the only component of pre-event flow/base flow of the fissured granitic catchment, is in accordance with the filed investigation by Salve et al. [2012]. In contrast, the results in Table 3 illustrate that a certain amount of interflow discharged to streamflow during storm events, and interflow was also observed during field monitoring at two plots [Fu et al., 2012a] at CERB, whereas no interflow was observed by Salve et al. [2012] and all runoff was generated as bedrock fissure flow. [62] In the study catchment at CERB, the groundwater level rarely reached the soil-bedrock interface, and substantial rainwater percolated into the fissured bedrock. Comparatively, the percolation rate into bedrock was very small in some catchments [Buttle et al., 2004], and tight limitations on the bedrock percolation rate (e.g., a decreasing percolating rate with respect to time or storage) should be considered and incorporated into relevant mathematic models. 5. Conclusions [63] Using monitored evaporation, rainfall, and streamflow data at the CERB site, combined with the runoff-generation processes at plot and catchment scales from Fu et al. [2012a, 2012b], five mathematic models were constructed, and the following conclusions were drawn: 2549

15 [64] (a) Reservoir models without the threshold of bedrock depression storage (h 1 ¼ 0) were more efficient than models with such a threshold (h 1 > 0), even though threshold models seem more reasonable. [65] (b) The average bedrock depression storage at the catchment scale, which is equivalent to the height of the lowest lateral outlet from the reservoir bottom (h 1 ), is calculated as mm. [66] (c) Substantial movable water percolated into the fissure bedrock during storm events and later discharged into streamflow as base flow, which explains why the slope of the linear relationships between P þ ASI and the event quick flow depth above the rising threshold, was less than one. [67] (d) Streamflow was well simulated by all five models with (h 1 > 0) or without (h 1 ¼ 0) bedrock depression storage, however, different ratios of annual infiltration into bedrock to annual interflow discharged to the stream were obtained by models with h 1 > 0 ( ) and h 1 ¼ 0( ). [68] At the storm event scale, the calculated total bedrock flow was larger than interflow for models with h 1 > 0 by a ratio of 1:0.7, whereas the opposite result (a ratio of 1:1.5) was obtained for models with h 1 ¼ 0. [69] Although all five models, with different structures, can effectively simulate the streamflow, and different flow components can also be illustrated by different models, modeling accuracy needs to be further studied through field or laboratory experiments to, for example, determine effective measures of bedrock depression storage and infiltration rates into bedrock. Consequently, further monitoring and experimental studies are needed to improve the models constructed in this study and to verify the modeling results obtained. [70] Acknowledgments. This study was jointly supported by the National Natural Sciences Foundation of China (no ), the Natural Science Foundation of Guangdong Province (grant no ), and the Innovation and Application Research Fund of the Water Sciences Department of Guangdong Province ( ). Thanks the editors and reviewers for their kind and valuable comments. Authors also thank April James for early discussions on this topic. References Beven, K., and J. Freer (2001), Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, Buttle, J. M., P. J. Dillon, and G. R. Eerkes (2004), Hydrologic coupling of slopes, riparian zones and streams: an example from the Canadian Shield, J. Hydrol., 287, Detty, J. M., and K. J. McGuire (2010), Threshold changes in storm runoff generation at a till-mantled headwater catchment, Water Resour. Res., 46, W07525, doi: /2009wr Fu, C., J. Chen, and S. 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