Chance-constrained overland flow modeling for improving conceptual distributed hydrologic simulations based on scaling representation of sub-daily rainfall variability

Science of the Total Environment 524–525 (2015) 8–22

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Science of the Total Environment journal homepage: www.elsevier.com/locate/scitotenv

Chance-constrained overland flow modeling for improving conceptual distributed hydrologic simulations based on scaling representation of sub-daily rainfall variability Jing-Cheng Han a, Guohe Huang b,⁎, Yuefei Huang a, Hua Zhang c, Zhong Li b, Qiuwen Chen d a

State Key Laboratory of Hydroscience & Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China Institute for Energy, Environment and Sustainable Communities, University of Regina, Regina, Saskatchewan S4S 0A2, Canada c College of Science and Engineering, Texas A&M University — Corpus Christi, Corpus Christi, TX 78412-5797, USA d Center for Eco-Environmental Research, Nanjing Hydraulics Research Institute, Nanjing 210029, China b

H I G H L I G H T S • • • • •

We develop an improved hydrologic model considering the scaling effect of rainfall. A chance-constrained Hortonion overland modeling approach is proposed. The model improves the simulation of integral runoff volume as well as peak flows. A real world case study presents the applicability and adaptability of the model. Rainfall thresholds are crucial for representing the overland flow generation.

a r t i c l e

i n f o

Article history: Received 3 January 2015 Received in revised form 27 February 2015 Accepted 27 February 2015 Available online xxxx Editor: F. Riget Keywords: Rainfall intensity Surface runoff Scale Modeling efficiency Uncertainty Three Gorges Reservoir

a b s t r a c t Lack of hydrologic process representation at the short time-scale would lead to inadequate simulations in distributed hydrological modeling. Especially for complex mountainous watersheds, surface runoff simulations are significantly affected by the overland flow generation, which is closely related to the rainfall characteristics at a sub-time step. In this paper, the sub-daily variability of rainfall intensity was considered using a probability distribution, and a chance-constrained overland flow modeling approach was proposed to capture the generation of overland flow within conceptual distributed hydrologic simulations. The integrated modeling procedures were further demonstrated through a watershed of China Three Gorges Reservoir area, leading to an improved SLURPTGR hydrologic model based on SLURP. Combined with rainfall thresholds determined to distinguish various magnitudes of daily rainfall totals, three levels of significance were simultaneously employed to examine the hydrologic-response simulation. Results showed that SLURP-TGR could enhance the model performance, and the deviation of runoff simulations was effectively controlled. However, rainfall thresholds were so crucial for reflecting the scaling effect of rainfall intensity that optimal levels of significance and rainfall threshold were 0.05 and 10 mm, respectively. As for the Xiangxi River watershed, the main runoff contribution came from interflow of the fast store. Although slight differences of overland flow simulations between SLURP and SLURP-TGR were derived, SLURP-TGR was found to help improve the simulation of peak flows, and would improve the overall modeling efficiency through adjusting runoff component simulations. Consequently, the developed modeling approach favors efficient representation of hydrological processes and would be expected to have a potential for wide applications. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Under changing environmental conditions, hydrological models have been important tools to describe the hydrological response of climatic and landscape changes on the watersheds (Ferguson and Maxwell, 2010; ⁎ Corresponding author. E-mail address: [email protected] (G. Huang).

http://dx.doi.org/10.1016/j.scitotenv.2015.02.107 0048-9697/© 2015 Elsevier B.V. All rights reserved.

Shen and Phanikumar, 2010; Tong et al., 2012). However, there are too many models confronting us, and hence, how to choose an appropriate one and to determine reasonable model configurations would be a big problem since almost all the models were established with a certain context or based on a specific watershed (Borah and Bera, 2004; Wu et al., 2007). Hydrological process representation is always formulated according to many simplifications and assumptions, and application of these models might be subject to some arguments on the rationality

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

and adaptation (Beven, 2009). Besides, calibration came to be inevitable to ensure that “effective” parameter values were adopted in model application, and parameter identifiability and equifinality would be the major concerns in this regard (Zhang and Savenije, 2005). Although satisfactory simulations might be obtained through modeling operation, water balance simulations over the watershed could not be well verified as a result of a lack of detailed information on hydrologic cycle. According to Beven (1997, 2001), thus, these models should be used with care, and modifications would be necessary to suit particular circumstances. Take the Xin'anjiang model for example, it was initially applied for inflow forecasting of the Xin'anjiang reservoir and mainly proposed for use in humid and semi-humid regions of China (Ren and Yuan, 2006; Zhao, 1992). In this model, the tension water capacity curve was employed to take the spatial heterogeneity of watershed characteristics into consideration, and runoff would only occur in areas where the soil moisture content reaches the field capacity (Ye et al., 2014). Similarly, the saturation excess overland generation was also well demonstrated by TOPMODEL (a TOPography based hydrological MODEL), which introduced a concept of hydrological similarity based on the topographic index to account for the distributed implications of hydrologic variables through indicating the spatial distribution of soil moisture deficit (Beven, 2012; Beven and Kirkby, 1979). In contrast with them, Hortonian overland flow (infiltration excess flow) was found to dominate the hydrograph of many watersheds with (semi-)arid to sub-humid climate (Stomph et al., 2002). As a matter of fact, however, the infiltration and saturation excess mechanisms are not mutually exclusive on a watershed, even at a point on a watershed (Smith and Goodrich, 2005). Johnson et al. (2003) performed hydrological simulations of a watershed in the upper part of the Irondequoit Creek basin using the Hydrological Simulation Program-FORTRAN (HSPF) and the Soil Moisture Routing (SMR) models simultaneously, surface runoff generation of which was simulated as infiltration excess and saturation excess overland flow, respectively. Although overall modeling efficiency values were comparable, simulation accuracy on a seasonal basis was highly related to the runoff-generating mechanism. In addition, the difference in the ability to predict spatial distribution of soil moisture was also significant. Therefore, a potential way to address such dilemma would combine these two kinds of overland flow generation mechanism and make full use of their roles in regulating surface runoff generation associated with specific watershed conditions. Generally, rainfall is the most important input to hydrologic models as its resolution and quality would impose critical influence on hydrologic model's performance (Chu et al., 2012; Neary et al., 2004), and rainfall information proved to be closely related to the usefulness of watershed models. Especially for distributed hydrologic models, rainfall data are required both in the spatially and temporally distributed form. Traditionally, discrete rain gauges are able to provide accurate rainfall measurements at certain points, but interpolation or disaggregation is further needed to satisfy the required data by hydrologic models. Radar-rainfall products have demonstrated great potential for their use in hydrologic applications, while uncertainty of radar-rainfall estimates should be carefully considered, and monitoring and in situ measurement of precipitation might still be indispensable (Krajewski and Smith, 2002). Although spatial distribution of rainfall across the watershed could be better reflected through increasing rain gauges, variations in rainfall characteristics within monitoring intervals could not be explicitly indicated only based on the observations. Besides, deterministic hydrologic models are always driven with an exact rainfall input at each time step, i.e. an average used rather than varying rainfall intensities (Kavetski et al., 2011). As a result, a problem would be arisen as to how the hydrologic processes would actually respond with consideration of varying rainfall intensities instead of averaging them? Meanwhile, it further leads us to look at the simulation uncertainty due to neglecting the roles of variations in model inputs within the computation time step in mimicking runoff response (Beven, 1997, 2001, 2009).

9

According to the Horton's overland flow theory (Beven, 2004), infiltration excess flow is affected greatly by the rainfall intensity, and hence, consideration of varying rainfall intensity at short time-scale might lead to a distinct surface runoff response due to smaller hydrologic process representation. Kandel et al. (2003, 2005) proposed a scaling approach to capture the sub-time-step rainfall variability in rainfallrunoff and erosion modeling. A cumulative probability (CDF) distribution of rainfall intensities was introduced by them to represent the effect of temporal variability of rainfall intensities at a smaller time scale on hydrological processes, and significant improvements in the simulation of surface runoff were achieved. Note that the infiltration excess flow was the main form of surface runoff at their study site, and saturation excess flow was considered only through incorporating a simple bucket-storage capacity concept. Thereupon, surface runoff generation should further be reflected through carefully mediating infiltration excess and saturation excess flow occurring on the watershed. As far as the probabilistic form of rainfall intensity is concerned, one effective and convenient approach to deal with random uncertainty would be the chance-constrained stochastic programing approach (Jiang and Guan, 2013). In this approach, chance constraints emerge naturally as a modeling tool under various decision making circumstances (Arellano-Garcia, 2006; Li et al., 2008; Miller and Wagner, 1965), and cumulative probability level could be applied to control risk in decision making under uncertainty. Consider that infiltration excess flow is simulated based on the chance constraints between the infiltration capacity and the stochastic rainfall intensity, and overland flow generation under two kinds of mechanism would then be regulated through the rain water infiltration into soil which could be manipulated according to “the risk level” in chance constraints. Thus, a chance-constrained overland flow modeling approach would be developed to realize the simulation of surface runoff generation while taking the effect of varying sub-time-step rainfall intensities into consideration in case of no detailed rainfall data being available. Therefore, this paper aims to develop an adaptive hydrologic modeling approach for representing adequately the process of overland flow generation and achieving improved modeling efficiency. The structure is organized as follows. The modeling framework is first formulated, including the hydrologic model and the chance-constrained overland flow modeling procedures. Then, a case study is introduced to present the study area and data, followed by the field experiments carried out to investigate the variability of the rainfall intensity. Thereafter, hydrologic simulations with various modeling schemes are performed, and the obtained results are further analyzed and discussed to illustrate the usefulness of the proposed approach. Finally, conclusions are given as well as the acknowledgements. 2. Model formulation 2.1. Hydrologic model The applied Semi-Distributed Land-use Runoff Process (SLURP) hydrological model is a continuous and daily time step based model that requires division of a target watershed into subareas known as Aggregated Simulated Areas (ASAs), which is consistent with a subwatershed in terms of watershed subdivision (Han et al., 2013b; Kite and Kouwen, 1992; Santos et al., 2015). These subareas are further divided by ToPographic PArameteriZation (TOPAZ) into a number of units with different types of land cover based on vegetation, soil and land use conditions (Lacroix et al., 2002; Valle Junior et al., 2015). Topographic characteristics and aggregation statistics for each land cover within each ASA are also derived using the TOPAZ package, such as elevation, distance to the nearest stream and distance to downstream. In addition, each land cover is characterized by a distinct set of model parameters. With particular hydrologic response to rainfall, each land cover class within each ASA in fact functions as a Hydrological Response Unit (HRU) in the hydrologic model (Arnold et al., 1998). Hence, the

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J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

SLURP model can be well adopted for assessing climate change and land use impact on streamflow. Besides, it fits between lumped watershed models and fully distributed physically based models, and thus, it has been well tested in many watersheds at different scales (Kite, 1990, 1993; Su et al., 2000; Woo and Thorne, 2006). Conceptually, SLURP simulates the vertical water balance for each HRU each day using four nonlinear reservoirs, i.e. canopy storage, snow storage, fast storage and slow storage. As shown in Fig. 1, such hydrologic processes as precipitation, canopy interception, evapotranspiration, snowmelt, infiltration, overland flow, subsurface and groundwater flow are represented and carried out accordingly (Armstrong and Martz, 2008). The total runoff in hydrograph (Qtotal) can be simply described using following expression: Q total ¼ Q 1 þ Q 2 þ Q 3 þ Q 4

ð1Þ

where Q1 represents infiltration excess flow; Q2 is saturation excess flow; Q3 indicates interflow and Q4 stands for groundwater flow. Modeling procedures may be further found from details described by Kite (2001). Note that two kinds of overland flow are considered as infiltration excess flow and saturation excess flow separately in the model. Overland flow appears when the rainfall rate exceeds the infiltration capacity of soil or water remaining in the aerated soil layers after infiltration exceeds the fast storage capacity. As such, it allows the flexibility of SLURP to account for surface runoff generation processes across a complex watershed. Subsurface flow (interflow and groundwater flow) is calculated at a rate depending on the water content of the fast and slow storage reservoirs as well as the water transfer coefficient (Jing and Chen, 2011a). Manning's equation in conjunction with a timecontributing area relationship is applied to route surface and subsurface flow from each HRU to the nearest channel within an ASA. Then, the combined runoff is converted to streamflow and routed sequentially between ASAs based on the hydrological storage techniques or the Muskingum–Cunge channel routing method. 2.2. Chance-constrained Hortonian overland flow modeling SLURP runs at a daily time step, and model inputs such as rainfall are aggregated at each day during modeling operation. As stated above, it would ignore the effects of the sub-daily variability of rainfall intensity on hydrological processes as simulations are performed based on daily average water flux. Without proper consideration of varying rainfall intensity within one day, it may lead to inaccurate simulation of overland flow for SLURP, especially in the mountainous watersheds with

complex rainfall patterns. Hence, SLURP lacks power in modeling surface runoff generation when portraying daily water flux exchanges throughout the hydrologic cycle in a watershed system. Therefore, such a scaling approach as probability distribution is incorporated within the SLURP model to account for the sub-time-step characteristics of daily rainfall in this study, aiming to reflect the actual overland flow process occurring during each rainy day. Fig. 2 illustrates the probabilistic representation of rainfall intensity, where a probabilistic distribution is used instead of a deterministic daily rainfall amount. According to the Hortonian overland flow (Beven, 2004), no infiltration excess flow would occur as a result of the infiltration capacity greater than the average daily rainfall intensity with a value of “c” as depicted in Fig. 2. If stochastic rainfall intensity is considered, by contrast, there would always be overland flow generation as part of sub-daily rainfall rate would necessarily exceed the infiltration capacity. Thus, the schematic shadow area would directly contribute to the infiltration excess flow generation. However, it makes no sense that any daily rainfall events would cause direct surface runoff for all the rainy days in view of the varying rainfall intensity. To address such a paradox, a chance-constrained control approach to deal with uncertainty is proposed to determine whether overland flow would be produced in a rainy day (Charnes and Cooper, 1959), and an assigned criterion is defined to initiate the Hortonian overland flow modeling. To be specific, Hortonian overland flow simulation is performed only if the infiltration capacity is less than the criterion rainfall intensity corresponding to a cumulative probability of 0.99 for example. That is, the shadow area in Fig. 2 would not be integrated as part of overland flow contribution if the infiltration capacity exceeds the chosen criterion. In order to make above expression formulated, we have to assume that the state of canopy store (occurrence of throughfall) is independent of the rainfall intensity as stated by Kandel et al. (2005). With negligible snowfall available, the assumption also works for this study. Consider that the probability density function (pdf) and cumulative distribution functions (cdf) of rainfall intensity within the time step are f(RI) and ρ(RI), respectively, where RI refers to the rainfall intensity. Thus, the cdf of throughfall can be given as follows. and cdf:
RIt ðρÞ ¼

RIt RI

  RI ðρÞ

in which, RIt is the intensity of throughfall.

Precipitation, P

Evapotranpiration, E

Interception, Throughfall C

Canopy Storage Snowfall, P-C

Rainfall, P-C Infiltration, I

Snow Storage

Fast Storage

Snowmelt, M

Overland flow, Q1+Q2 Q1: Infiltration excess flow Q2: Saturation excess flow

Percolation, RP

Slow Storage

Interflow, Q3

Groundwater flow, Q4

Fig. 1. Vertical water balance of the SLURP hydrologic model for each land cover.

ð2Þ

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

Cumulative probability

0.99 0.95 0.90

and generalized Pareto distributions are commonly used theoretical distributions. Disagreements still exist among researchers as to which distribution would be preferred to represent the temporal variability of rainfall intensities. However, Kandel et al. (2005) concluded that none of the rainfall distribution models appears clearly superior, and the best fitted twoparameter lognormal distribution to represent the observed data was finally recommended (Kandel et al., 2004). Similar with them, the lognormal distribution is also employed to represent the sub-daily variation in the rainfall intensity in this study. Specific pdf and cdf of the lognormal distribution are given by:

(a)

0.50

0

Probability density

(b) Average daily rainfall intensity Infiltration capacity

f ðRIÞ ¼

Fig. 2. Probabilistic representation of sub-daily rainfall variability: (a) cumulative probability distribution and (b) probability density.

In SLURP, the daily infiltration excess overland flow is calculated using: ð3Þ

where P is the daily rainfall amount (throughfall) and Inf denotes infiltration capacity at each day, depending on the maximum infiltration capacity of soil and current soil moisture according to: In f ¼

1−

C1 C 1; max

 Inf max

Q1 ¼

1

:

0

ðRIt −Inf Þdρ;

ð4Þ

0

In f ≤RI t;1−s

ð5Þ

others

where s stands for the level of significance (i.e. “risk” in chanceconstrained programming), while RIt, 1-s is the criterion, corresponding to the rainfall intensity with cumulative probability 1-s. As for the rainfall intensity less than infiltration capacity, no Hortonian overland flow is generated. Thus, the actual amount of Hortonian overland flow should be further calculated based on the integral computing part of Eq. (5). Z

1

ðRIt −In f Þdρ Z 1 Z ρðIn f Þ 0dρ þ ðRI t −Inf Þdρ ¼ ρðIn f Þ Z 0þ∞ RIt  f ðRIt ÞdRI t −Inf  ½1−ρðInf Þ; Inf ≤RI t;1−s ¼

ð7Þ

ð8Þ

where μ is the expectancy, and σ is the standard variance. The “erf” is the error function and expressed using following equation. 2 er f ðxÞ ¼ pffiffiffi π

Z

x

−t

e

2

ð9Þ

dt

0

To determine the two parameters of the lognormal distribution, following constraints will be further provided. Z

þ∞ 0

RIt  f ðRIt ÞdRIt ¼ P

!

where C1 and C1,max are current soil moisture and the maximum capacity of fast store, respectively and Infmax is the maximum infiltration capacity. It is worth mentioning that rainfall intensity RIt here is deterministic, and represents the average daily rainfall intensity. Consider that the rainfall intensity is expressed with a probability function, and the following integral equation would then be employed to calculate the resulting Hortonian overland flow: 8Z <

1 −ð ln RI−μ Þ2 =ð2σ 2 Þ pffiffiffiffiffiffi e σ  2π  RI


 lnRI−μ pffiffiffi ρðRIÞ ¼ 0:5  1 þ er f σ 2

c d Rainfall intensity (mm/day)

Q 1 ¼ P−Inf ; RIt ≥Inf

11

μ ¼ ln ðP t Þ−

ð10Þ t

σ2 2

ð11Þ

Generally, standard variance σ is obtained through fitting the observed data in the particular location. In this study, we used a log linear regression model to estimate the standard variance of the rainfall intensity for each rainy day. Thus, the standard variance can be calculated using: σ ¼ a  ln ðP Þ þ b

ð12Þ

where a and b are the regression coefficients. As a result, an improved hydrologic model based on SLURP is formulated through coupling a chance-constrained Hortonian overland flow modeling approach. With a case study demonstrated in the Three Gorges Reservoir (TGR) region, the resulting hydrologic model is regarded as SLURP-TGR(1-s), where s represents the level of significance in the chance-constrained control. 2.3. Model calibration and validation The data was split into two separate samples for calibration and validation. Eight parameters for each land cover were determined to be first calibrated with the calibration sample by both manually and Shuffle Complex Evolution algorithm developed at the University of

0

ð6Þ

In f

where ρ(Inf) is the cumulative probability of rainfall intensity when it takes values less than infiltration capacity Inf for each time step. Consequently, a chance-constrained Hortonian overland flow modeling method is successfully developed. Statistical distributions are often used to characterize the rainfall intensity variation, including theoretical and empirical probability distributions. For instance, the exponential, gamma, beta, lognormal,

Table 1 Parameters for each land cover in model calibration. Parameter

Lower bound

Upper bound

Sensitivity

Initial contents of slow store (%) Maximum infiltration rate (mm/day) Manning roughness, n Retention constant for fast store (day) Maximum capacity for fast store (mm) Retention constant for slow store (day) Maximum capacity for slow store (mm) Precipitation factor

0 10.0 0.0001 1.0 10.0 10.0 100.0 0.8

100 200 0.1 50 1000 1000 5000 1.5

Low Low Low High High High Medium High

12

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

Fig. 3. Location of the Xiangxi River watershed in the Three Gorges Reservoir area.

Arizona (SCE-UA) (Duan et al., 1992). Table 1 provides the parameters used in the calibration operation and their assigned ranges as well as corresponding sensitivity. Comparison of calibration and validation simulations against observations was then carried out, respectively. Moreover, model performance was evaluated both visually using the hydrographs/regressive chart and statistically for its general “goodness of fit” in terms of Nash–Sutcliffe Efficiency (NSE) (Nash and Sutcliffe, 1970), ratio of the root mean square error to the standard deviation of measured data (RSR), determination coefficient (R2) and percent bias (PBIAS), which are outlined as follows (Moriasi et al., 2007): n X

NSE ¼

n X 2 2 ðqi −qÞ − ðqi −ci Þ

i¼1

n X

n

n X

2

R ¼" n

qi  ci −

i¼1 n X

2

qi −

i¼1

n X

PBIASð%Þ ¼ 100 

i¼1

qi 

i¼1

!2 #"

n

qi

i¼1

n X

n X

n X

!2 ci

i¼1 n X i¼1

2

ci −

n X

!!2 #

ð15Þ

ci

i¼1

n X qi − ci n X

i¼1

ð16Þ

qi

i¼1

i¼1

ð13Þ 2

ðqi −qÞ

i¼1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n X 2 ðqi −ci Þ

where qi is the observed flow on day i; ci is the simulated flow on day i; n is the number of simulated time steps; and q is the average measured flow. 3. The study area and data

i¼1 RSR ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n X 2 ðqi −qÞ

ð14Þ

i¼1

The study area is the Xiangxi River watershed, which is located in Hubei part of China TGR region, draining an area of about 3200 km2 (Fig. 3). The Xiangxi River originates in the Forest Nature Reserve of Shennongjia with a mainstream length of 94 km, and joins the Yangtze

Table 2 Description of the weather and hydrometric stations. Station

Monitoring type

Location

Elevation

Average annual rainfall/runoff (1960–2010)

ZHJ ZGD ZJP SYS Xingshan

Weather station Weather station Weather station Weather station Hydrometric station

31°15′20″N, 110°43′30″E 31°25′26″N, 110°56′55″E 31°25′10″N, 110°42′20″E 31°12′22″N, 110°57′40″E 31°14′18″N, 110°44′05″E

406 m 1300 m 680 m 930 m 183 m

994.6 mm/year 1054.4 mm/year 932.6 mm/year 1055.1 mm/year 37.0 m3/s

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22 Table 3 Types of land cover with corresponding area proportions in the Xiangxi River watershed. Land class

Land use–soil complexes

Area proportion (%)

1 2 3 4 5 6

Forest-Argosols Forest-Primosols/Ferralosols Grass/Orchard/farmland-Argosols Grass/Orchard/farmland-Primosols/Ferralosols Urban and rural lands/residence/mining Water

29.3 47.7 11.0 8.5 0.8 2.7

River as a first class tributary some 30 km northwest of the China Three Gorges Dam. Typically, the whole watershed experiences a northern subtropical climate with annual precipitation ranging from 670 mm to 1700 mm, and exhibits significant spatial variability in topography and land cover types. According to Han et al. (2014b), no significant trends in precipitation were detected for the last 50 years, but annual average streamflow was found to decrease as a result of the increasing watershed management activities. The land use in this area is mainly dominated by forest and could be categorized into five classes: forest, grass, urban, farmland and water body. It should be pointed out that the topography of this watershed is so scattered and mountainous, not allowing massive land cultivation and settlement in large parts. Hence, human activities are mainly restricted to level areas and smoother slopes (Seeber et al., 2010). Nonetheless, the Xiangxi River watershed

13

is still one of the most representative watersheds in TGR region in terms of runoff volume, topographic features and economic conditions. To perform watershed hydrologic simulation requires a series of model inputs. A 30-m-resolution digital elevation model for the TGR area was obtained from the Chinese Academy of Sciences (CAS). Land use and soil data with a scale of 1:100,000 were prepared by the Data Centre for Resource and Environmental Sciences of CAS to identify the land cover distribution over the Xiangxi River watershed in 2000. As shown in Fig. 3, there are four official weather stations, i.e. Shuiyuesi (SYS), Zhengjiaping (ZJP), Zhangguandian (ZGD) and Zhaojun (ZHJ), and one controlled hydrometric station of Xingshan (Table 2). Regarding the weather stations, daily meteorological observations of 1991–1998 were purchased from the Meteorological Bureau of Xingshan County, including air temperature, dew point, precipitation, sunshine duration, wind speed, and relative humidity. Daily streamflow records with a fixed format for eight years were prepared by the Hydrological Bureau of Xingshan County. Both wet and dry periods were covered by the 8-year data available, and furthermore, no drastic changes in climate and land use took place in the watershed. In this study area, the temperature inputs for elevation differences were derived with a lapse rate of 0.75 °C per 100 m and precipitation was increased by 1% per 100 m relative to the monitoring stations (Jing and Chen, 2011b). According to data availability, point ‘actual’ evapotranspiration was computed by multiplying a coefficient of 0.8 with potential evapotranspiration obtained based on a modification of

Fig. 4. Distribution of land covers and the installed rainfall monitoring stations across the Xiangxi River watershed.

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

Table 4 Newly installed weather stations for rainfall monitoring. Station

Location

Elevation

ZJS NDH YDH PSS XHS

N31°14′15″, E110°44′36″ N31°11′28″, E110°57′54″ N31°12′19″, E110°51′29″ N31°29′5″, E110°47′52″ N31°31′19″, E110°52′43″

180 m 533 m 307 m 404 m 713 m

the Penman equation (Morton, 1983; Sun et al., 2007). Distribution of land use and soil types across the watershed has been stable over decades (Han et al., 2013a, 2014b). However, soil distribution is not totally consistent with land use, and therefore, land use and soil were combined to characterize the land covers as soil properties determine many key processes of surface and subsurface flow. As a result, six types of land cover were formed with the representation of land use– soil complexes as shown in Table 3 and Fig. 4. Based on the resulting distribution of land covers, the land use development is still controlled at a satisfying level, but the entire watershed has recently undergone potential environmental problems due to local pyrite mining, sand mining, new land reclamation for agriculture and other human activities. Besides, it is always the main concern of the local government to achieve efficient flood protection and agricultural irrigation.

over the watershed. After that, we chose five small sub-watersheds to set weather stations for real-time monitoring as illustrated in Fig. 4, and Table 4 presents locations of the chosen sub-watersheds. The newly established weather stations were mainly configured with the wireless Vantage Pro2 (Davis Instruments), which has a versatile sensor suite combining the rain collector, temperature and humidity sensors and an anemometer into one package. Besides, a solar radiation sensor and a ultra-violet (UV) radiation sensor were also mounted next to the rain collector cone. The monitoring parameters include rainfall, rainfall rate, air temperature, barometric pressure, dew point, evapotranspiration, humidity, wind, heat index, solar radiation and UV. Both sensors and console are powered using the included power adapter in association with additional C batteries. In order to sustain long working hours and to avoid overwriting of the memory card, all the monitoring was sampled and recorded every 30 min. Note that only the rainfall and rainfall rate data were used in this study. After successful setting and test, the installed weather stations began to record the meteorological indices, and monitoring still proceeds now. Equipment items are maintained every three months, and the recorded data are accordingly collected. Herein, the observed rainfall amount and rainfall rate for two years from Oct, 2010 to Oct, 2012 were used to analyze the variation of sub-daily rainfall intensity. According to Vantage Pro2 sampling, the expectancy and the standard variance of rainfall intensity for a rainy day were calculated based on duration timeweighted statistics as follows: n X

4. Field experiment of rainfall monitoring In the mountainous Three Gorges Reservoir area, occurrence of rainfall changes frequently and widely across a watershed. Hence, the daily precipitation data in the TGR region might be invalid when applied as inputs in hydrologic modeling (Shen et al., 2012), especially for those models without adequate consideration of spatiotemporal rainfall variability. Li et al. (2014) demonstrated that the rainfall variations in TGR are time-scale and location dependent, and the short-duration storms are widespread. Thus, field survey and monitoring experiment would be of great importance to better understand the variations of sub-daily rainfall. An extensive field survey was carried out in 2010, attempting to get basic and preliminary knowledge of the precipitation and runoff patterns

1.0

Standard variance of ln(RI) Linear fitting

y=0.170x+0.017 2 0.6 Adjusted R =0.86 0.4 0.2

(a)

0.0

0.5 1.0 2.7 7.4 20.1 54.6 Daily rainfall amount (mm)

Standard variance

1.0 0.8

0.8

n X j¼1

DT j ¼

Pj

.

ð19Þ

RI j

1.0

Standard variance of ln(RI) Linear fitting

y=0.186x+0.0023 2 0.6 Adjusted R =0.88 0.4 0.2

(b) 0.0 0.5 1.0 2.7 7.4 20.1 54.6 Daily rainfall amount (mm)

YDH

1.0

Standard variance of ln(RI) Linear fitting

0.4 0.2

(d) 0.0 0.5 1.0 2.7 7.4 20.1 Daily rainfall amount

54.6

ð18Þ

j¼1

ZJS

y=0.123x+0.0815 0.6 Adjusted R2=0.80

ð17Þ DT j

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n h i2 uX u RI j −EðRIÞ  DT j , u u σ ðRI Þ ¼ u j¼1 n X u t DT j

Standard variance

0.8

XHS Standard variance

Standard variance

1.0

EðRIÞ ¼

RI j DT j ,

j¼1

0.8

Standard variance

14

0.8

NDH Standard variance of ln(RI) Linear fitting

y=0.170x+0.0095 2 0.6 Adjusted R =0.82 0.4 0.2

(c) 0.0 0.5 1.0 2.7 7.4 20.1 54.6 Daily rainfall amount (mm)

PSS Standard variance of ln(RI) Linear fitting

y=0.163x+0.0324 2 0.6 Adjusted R =0.86 0.4 0.2

(e) 0.0 0.5 1.0 2.7 7.4 20.1 54.6 Daily rainfall amount (mm)

Fig. 5. Relationship between the standard variance of rainfall intensity and daily rainfall amount: (a) XHS station; (b) ZJS station; (c) NDH station; (d) YDH station; and (e) PSS station.

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

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Table 5 Evaluation of modeling performance for both calibration and validation. Model

NSE

SLURP SLURP-TGR(0.90) SLURP-TGR(0.95) SLURP-TGR(0.99) SLURP-TGR(0.90_10) SLURP-TGR(0.95_10) SLURP-TGR(0.99_10) SLURP-TGR(0.90_20) SLURP-TGR(0.95_20) SLURP-TGR(0.99_20) SLURP-TGR(0.90_30) SLURP-TGR(0.95_30) SLURP-TGR(0.99_30) a b

R2

RSR

PBIAS (%)

Ca

Vb

C

V

C

V

C

V

0.635 0.625 0.623 0.569 0.661 0.665 0.659 0.657 0.659 0.652 0.649 0.654 0.654

0.600 0.543 0.545 0.587 0.605 0.624 0.613 0.602 0.630 0.603 0.592 0.629 0.607

0.603 0.612 0.614 0.657 0.583 0.579 0.584 0.585 0.584 0.590 0.592 0.588 0.588

0.632 0.676 0.675 0.643 0.628 0.613 0.622 0.631 0.608 0.630 0.639 0.609 0.627

0.650 0.634 0.636 0.589 0.664 0.666 0.665 0.662 0.663 0.656 0.658 0.658 0.657

0.605 0.549 0.551 0.643 0.605 0.624 0.614 0.602 0.632 0.604 0.594 0.629 0.608

−16.36 −10.22 −12.64 −0.65 −8.33 −3.62 −10.71 −7.33 −5.35 −7.73 −13.31 −8.72 −8.73

−12.42 −13.05 −8.56 0.56 −3.38 −0.09 −6.64 −2.54 −1.95 −2.76 −8.21 −4.92 −3.82

Calibration. Validation.

where E(RI) is the rainfall intensity expectancy for one rainy day, taking the same value with the daily rainfall amount; RIj is the jth recorded rainfall intensity; DTj is the time duration for the jth recorded rainfall; σ(RIj) is the standard variance of the rainfall intensity for the rainy day; and Pj is the amount of the jth recorded rainfall. A log-linear regression model was employed to build the relationship between the variability of the rainfall intensity (i.e. standard variance of the lognormal distribution of the rainfall intensity) and daily rainfall amount. Thus, five regression models were developed to estimate the variability of the rainfall intensity over the watershed as demonstrated in Fig. 5. Note that the established linear relationship is actually between the standard variance of ln(RI) and ln(P), and the standard variance of ln(RI) can be obtained using the following equation. " σ ¼ ln 1 þ

σ ðRIÞ2 EðRIÞ2

# ð20Þ

Consequently, a probability distribution function was yielded based on estimated σ and μ for the rainfall intensity in a rainy day. Then, the proposed overland flow modeling approach could be integrated to perform hydrologic modeling simulation. 5. Results and discussion 5.1. Model performance evaluation Taking into account the negligible effects of small rainfall events on the observed overland flow generation, rainfall thresholds would be necessary to identify effective daily rainfall ranges contributing to the occurrence of Hortonian overland flow (Sivakumar, 2005). Therefore, three rainfall thresholds were assigned herein to examine the resulting simulations through the SLURP-TGR(1-s) model. Thus, a combination of rainfall threshold and s in SLURP-TGR(1-s) would lead to a series of the SLURP-TGR models. For example, SLURP-TGR(0.90_10) denotes a SLURP-TGR model with the critical rainfall threshold and s of 10 mm and 0.10, respectively. As indicated in Table 5, there are totally thirteen hydrologic models implemented in this study. These models were first calibrated using 1826 continuous daily streamflow records from January 1, 1991 to December 31, 1995, and validation was then performed against 1096 subsequent daily streamflow observations (1996–1998). Table 5 gives the results of model performance evaluation based on NSE, RSR, R2 and PBIAS. Values in bold and italic show that no better simulations for SLURP-TGR were obtained than SLURP in terms of the corresponding criteria. Nonetheless, the “worse” results still revealed comparable goodness of fit between SLURP-TGR and SLURP.

As compared to SLURP, the SLURP-TGR models without rainfall thresholds considered resulted in relatively poor model performance, but we could still perceive the merits of SLURP-TGR in diminishing the deviation of runoff volume against observations according to PBIAS. Hence, increasing surface runoff simulations rendered by Hortonian overland flow generation played a limited part in improving the modeling efficiencies, indicating more constraints are further needed to reproduce accurate discharge response. By contrast, almost all the SLURP-TGR models appeared to be superior to SLURP given other three rainfall thresholds. Moreover, total amounts of runoff volume simulations were significantly improved for both calibration and validation. Therefore, it could be concluded that variations of sub-daily rainfall intensity for small daily rainfall events have insignificant influence on the overland flow generation in the Xiangxi River watershed. It might be attributed to the specific rainfall-runoff pattern of the target watershed. However, incorporation of large daily rainfall amounts within Hortonian overland flow generation modeling would help produce convincing high flow simulations, which lead to better results with regard to PBIAS. Consequently, rainfall thresholds for trigging Hortonian overland flow simulation would be required to reflect the actual role of variation of sub-daily rainfall intensity in producing overland flow. As for various rainfall thresholds, inappreciable improvements were achieved through increasing the threshold level, but “worse” results were found in several cases. Note that different magnitudes of rainfall event for calibration and validation might impose distinct impacts on the results (Han et al., 2014b). In addition, calibration operation would offset the difference between simulations and observations, so model performance evaluation might be subject to parameter uncertainty to a certain extent. Nevertheless, the SLURP-TGR model seems to perform “best” when the rainfall threshold was set as an amount of 10 mm. Table 6 Evaluation of modeling performance for the entire simulation period. Model

NSE

SLURP SLURP-TGR(0.90) SLURP-TGR(0.95) SLURP-TGR(0.99) SLURP-TGR(0.90_10) SLURP-TGR(0.95_10) SLURP-TGR(0.99_10) SLURP-TGR(0.90_20) SLURP-TGR(0.95_20) SLURP-TGR(0.99_20) SLURP-TGR(0.90_30) SLURP-TGR(0.95_30) SLURP-TGR(0.99_30)

0.616 0.578 0.576 0.576 0.627 0.642 0.632 0.624 0.641 0.623 0.614 0.640 0.626

a

Satisfactory.

R2

RSR Sa S S S S S S S S S S S S

0.620 0.650 0.651 0.651 0.610 0.598 0.607 0.613 0.598 0.614 0.621 0.600 0.612

S S S S S Good S S Good S S Good S

0.628 0.584 0.586 0.617 0.631 0.643 0.636 0.628 0.645 0.627 0.623 0.644 0.630

PBIAS (%) S S S S S S S S S S S S S

−17.75 −11.77 −11.67 1.46 −11.19 −5.29 −11.77 −10.31 −6.35 −9.94 −14.60 −10.03 −11.63

S Good Good Very good Good Very good Good Good Very good Very good Good Good Good

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0 50

Runoff (m /s)

800

Rainfall Observations SLURP-TGR(0.90_10) SLURP

3

600

100

Rainfall (mm)

(a) 1000

150 200

400

250 200

300

Runoff (m /s)

Observations SLURP-TGR(0.95_10) SLURP

3

600

150

Rainfall (mm)

0 1 1 1 1 1 1 1 1 /1 -31 /9/ /5/ /1/ /9/ /5/ /1/ /5/ /9/ 6/1 97 97 98 96 96 97 98 9 98 -12 8 19 19 19 19 19 19 19 19 19 9 19 (b) 0 1000 50 800 Rainfall 100

200

400

250 200

300

0

3

Runoff (m /s)

Obervations SLURP-TGR(0.99_10) SLURP

600

150

Rainfall (mm)

1 1 1 1 1 1 1 1 1 -31 /9/ /5/ /1/ /1/ /9/ /5/ /1/ /9/ /5/ 96 96 97 96 97 97 98 98 98 -12 19 19 19 19 19 19 19 19 19 98 9 1 (c) 0 1000 50 800 Rainfall 100

200

400

250 200

300

0 1 1 1 1 1 1 1 1 1 /1 /9/ /5/ /5/ /5/ /1/ /1/ /9/ /9/ 2-3 6/1 96 96 9 97 98 97 97 98 98 8-1 19 19 19 19 19 19 19 19 19 9 19

SLURP-TGR(0.90_10) SLURP-TGR(0.90_20) SLURP-TGR(0.90_30)

40

SLURP-TGR(0.95_10) SLURP-TGR(0.95_20) SLURP-TGR(0.95_30) SLURP

SLURP-TGR(0.99_10) SLURP-TGR(0.99_20) SLURP-TGR(0.99_30)

20

0

-20

Fig. 7. Comparison between SLURP and SLURP-TGR for the monthly runoff simulations.

AUG

APR

Dec 1998

Month

DEC

APR

AUG

DEC

APR

AUG

DEC

APR

AUG

DEC

APR

AUG

DEC

AUG

APR

DEC

APR

AUG

DEC

AUG

-40

Jan 1991 APR

3

Residuals of monthly runoff simulations (m /s)

Fig. 6. Comparison between SLURP and SLURP-TGR for validation results of the daily discharge simulations against observations: (a) SLURP-TGR(0.90_10); (b) SLURP-TGR(0.95_10); and (c) SLURP-TGR(0.99_10).

60

17

Observed monthly runoff SLURP

50 40 30 20 10 0

DEC

NOV

OCT

SLURP-TGR(0.99_10) SLURP-TGR(0.99_20) SLURP-TGR(0.99_30) SEP

AUG

JUL

JUN

SLURP-TGR(0.95_10) SLURP-TGR(0.95_20) SLURP-TGR(0.95_30) MAY

APR

FEB

-20

MAR

SLURP-TGR(0.90_10) SLURP-TGR(0.90_20) SLURP-TGR(0.90_30)

-10

JAN

3

Average simulated residual of monthly runoff(m /s)

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

Month Fig. 8. Comparison between SLURP and SLURP-TGR for the monthly average runoff simulations.

The significance level in chance-constrained modeling determines whether Hortonian overland flow would appear or not. To decrease significance level s is likely to result in more Hortonian overland flow generation. With three levels of significance considered in SLURP-TGR, modeling simulations showed better performance at the significance level of 0.05 than 0.1 when three rainfall thresholds were considered, suggesting that the contribution of infiltration excess flow to runoff is indispensable and cannot be neglected. However, to decrease the significance level to 0.01 would not lead to further improvement on model performance as compared to that of significance level 0.05. Therefore, infiltration excess flow is generated at a certain level and depends on both actual rainfall intensity and underlying surface, and it is further implied that infiltration excess flow account for only a small part of runoff conditions in the Xiangxi River watershed.

Annual average runoff simulations over the cumulative watershed to Xingshan station (mm)

700

Model performance was further analyzed for the daily discharge simulations from 1991 to 1998 as presented in Table 6. According to the model performance ratings for recommended statistics by Moriasi et al. (2007), modeling simulations could be categorized into “unsatisfactory”, “satisfactory”, “good” and “very good” based on NSE, RSR, R2 and PBIAS criteria. Note that these criteria were recommended for a monthly step, but they were still adopted to assess the daily time step based model at this time. As a matter of fact, performance of both the SLURP and SLURP-TGR models in this study could be regarded as “very good” for simulations at the monthly step (RSR b 0.5, NSE N 0.7 and R2 N 0.8). Nonetheless, significant improvement on daily discharge simulations could be found to be achieved by SLURP-TGR through ameliorating the PBIAS. In addition, the optimal combination of the rainfall threshold and the significance level would be 10 mm and 0.05, respectively.

Groundwater flow Interflow from slow store Interflow from fast store Overland flow Annual average runoff depth at Xingshan station

600

500

400

100

0

P 5) 9) 0) 0) 0) 0) 0) 0) 0) 0) 0) 0) _1 _1 _3 _2 _2 _3 _3 _2 _1 UR 0.9 0.9 0.9 R( R( (0.90 (0.95 (0.99 (0.90 (0.95 (0.99 (0.90 (0.95 (0.99 S L GR( G G T T T PPPGR GR GR GR GR GR GR GR GR UR LUR LUR RP-T RP-T RP-T RP-T RP-T RP-T RP-T RP-T RP-T S SL S U U U U U U U U U SL SL SL SL SL SL SL SL SL

Model Fig. 9. Runoff component simulations over the cumulative watershed to Xingshan station.

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J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

Table 7 Annual average water balance components and runoff contributions (mm) across the whole watershed. Model

APa

EAb

ORc

IFd

GWe

TRf

SLURP SLURP-TGR(0.90_10) SLURP-TGR(0.95_10) SLURP-TGR(0.99_10) SLURP-TGR(0.90_20) SLURP-TGR(0.95_20) SLURP-TGR(0.99_20) SLURP-TGR(0.90_30) SLURP-TGR(0.95_30) SLURP-TGR(0.99_30)

1192.13 1146.25 1084.63 1131.13 1146.25 1085.75 1141.13 1184.63 1120.75 1147.63

359.00 349.13 345.63 351.38 353.50 345.75 355.63 357.88 350.00 351.13

35.19 32.93 34.43 32.16 37.31 35.42 37.06 33.21 32.81 39.17

451.00 428.42 424.16 468.07 401.00 405.03 425.00 423.00 438.00 419.00

215.96 196.15 156.07 158.36 213.12 182.46 187.31 227.75 173.59 199.49

702.00 657.38 614.75 658.25 651.63 622.88 648.88 683.88 644.75 658.13

a b c d e f

Adjusted precipitation (mm). Evapotranspiration. Overland runoff. Interflow. Groundwater flow. Total runoff.

5.2. Hydrograph and monthly runoff simulations Fig. 6 displays the daily discharge simulations for SLURP and SLURPTGR in the validation period. With three significance levels in association with rainfall threshold 10 mm, SLURP-TGR simulations are presented in comparison with SLURP as well as the observations. Notably, the daily discharge regime of the Xiangxi River is too complex to be perfectly mimicked, and similar results were obtained for the three SLURP-TGR models. When compared to SLURP, SLURP-TGR led to improved simulations for

the peak runoff. In addition, SLURP-TGR(0.95_10) seemed to perform better than the other models, which is consistent with the analysis of model performance evaluation above. However, underestimation of some peak runoff still happened in many cases for both SLURP and SLURP-TGR. Such deficiency might be caused by insufficient accounting for the spatial distribution of rainfall over the TGR watersheds, of which the highly varying rainfall distribution might not be well characterized by the monitoring of a few weather stations. In conjunction with complex rainfall flux, a lot of small hydroelectric structures across the watershed would also be responsible for such phenomenon (Han et al., 2014b). According to the model performance on monthly runoff hydrograph, the SLURP-TGR models with rainfall thresholds considered were also found to yield more reliable simulations than SLURP based on the criteria of NSE, RSR, and R2. As depicted in Fig. 7, SLURP-TGR would effectively narrow down the difference between simulations and observations at the first month. In contrast with SLURP-TGR, SLURP resulted in relatively poor simulations at the beginning because parameters related to initial soil moisture were not carefully determined. Besides, SLURP-TGR was found to be able to result in more efficient simulations than SLURP when simulations were overestimated relative to observations. That is, SLURP-TGR could lower the overestimation of monthly runoff to some extent. However, SLURP seemed to produce more accurate predictions when the underestimated simulations happened against observations. In spite of this, SLURP-TGR still lead to better results of total runoff simulations as inferred from Fig. 8. An interesting pattern could be also generalized from the figure that the average values of monthly runoff simulations for almost all the SLURP-TGR models were lower than SLURP. Such decreases in monthly runoff simulation from October

Fig. 10. Comparison of annual runoff simulations with SLURP and SLURP-TGR across the watershed.

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

to April would positively help improve the simulations for SLURP-TGR. Moreover, it could be found that the bigger the decrease is, the resulting model performance would be better. Accordingly, SLURP-TGR(0.95_10) would be an optimal hydrologic model for performing rainfall-runoff simulations in the Xiangxi River watershed. 5.3. Water balance components As described above, simulation results were analyzed only through comparing the single integral runoff output at Xingshan station. To understand the capability of SLURP-TGR to streamflow simulations, four types of stream flow contributing to the runoff at Xingshan station were further analyzed, i.e. overland flow, interflow from fast store, interflow from slow store, and groundwater flow. Fig. 9 shows the annual average runoff component simulations for SLURP-TGR and SLURP. Obviously, there existed considerable differences for the simulations of four types of flows between SLURP and the SLURP-TGR models. Nevertheless, it was agreed that interflow from fast store is the main runoff contribution. Without rainfall thresholds for triggering the Hortonian overland flow simulation, the SLURP-TGR model produced more overland flow simulations. While among the other models, the differences for the overland flow simulations are slight. Interflow from slow store is very small and only happened in SLURP-TGR modeling. However, interflow from fast store and groundwater flow simulations by SLURP differed greatly from SLURP-TGR. Regardless of this, the simulated total runoff drained to Xingshan station by SLURP-TGR is more close to the observation than SLURP. Consequently, SLURP-TGR seems to be capable of generating better overall runoff simulations through adjusting the contributions from various runoff components, and the linkages between

19

surface and subsurface flow could be well represented by SLURP-TGR. Still, the most satisfactory simulations were accomplished by SLURPTGR(0.95_10). Table 7 presents the water balance components across the whole watershed simulated by SLURP and SLURP-TGR. Similar to runoff simulations at Xingshan station, the total runoff simulations at the watershed outlet by SLURP-TGR were lower than SLURP. However, no appreciable changes were obtained by SLURP-TGR for the evapotranspiration and overland flow simulations (Table 7). By contrast, such hydrologic variables as adjusted precipitation, interflow and groundwater flow lead to various simulations. It can be explained by the model parameters obtained through calibration operation. In comparison with SLURP, SLURP-TGR affects the roles of such model parameter in simulating overland flow generation as the maximum infiltration rate, which is directly correlated to the capacity of the fast store. Thus, the resulting interflow and groundwater flow would be regulated accordingly, and runoff simulations could be improved through adjusting actual contributions of runoff components. Moreover, such adjustments would be more likely to take advantage of the calibration operation. 5.4. Spatial distribution of hydrologic fluxes Variations in the spatial distribution of water balance component simulations were further investigated across the watershed. Compared to the SLURP model, slight decreases in precipitation for SLURP-TGR (take a rainfall threshold of 10 mm for example) were observed. Actually, the difference in areal rainfall between SLURP and SLURP-TGR was caused by precipitation factor, which is optionally applied to account for inexact rainfall information and depends on the types of land cover. When it

Fig. 11. Comparison of annual average fast store runoff simulations with SLURP and SLURP-TGR across the watershed.

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J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

comes to the calibrated parameters of SLURP-TGR, almost all the values of precipitation factor were found to decline, especially for the forest cover, which occupies the most part of the watershed. However, the decrease is so slight that no significant change was obtained for the rainfall pattern across the watershed (not shown). Fig. 10 demonstrates annual runoff simulations across the watershed. Apparently, the annual runoff exhibits clear spatial variations and presents a different pattern from the rainfall, and its simulations at each subwatershed varied depending on specific locations. Generally, less runoff was generated in the middle and northern parts of the Xiangxi River watershed. It is interesting that both SLURP and SLURPTGR resulted in similar spatial patterns of annual runoff simulations. However, runoff generation at northern subwatersheds seemed to be reduced by SLURP-TGR. Noticeable differences of annual average runoff at other subwatersheds could also be witnessed between SLURP and SLURP-TGR. Nevertheless, total annual runoff drained to Xingshan station simulated by SLURP-TGR was found to be less than SLURP. Fast store runoff and slow store runoff simulations are shown in Figs. 11 and 12. It could be found that the simulated runoff is mainly composed of fast store runoff, which accords well with hydrological processes in most forest areas. According to the fast store runoff simulations, they were largely subject to the subwatershed conditions, such as geographic locations, terrain features and land cover. Note that decreasing fast store runoff simulations by SLURP-TGR at western and northern subwatersheds would help improve simulated discharges drained to Xingshan station relative to observations (Fig. 11). With slight differences existing in overland flow simulations, the interflow simulations would be mainly responsible for such outcomes as a result of changes in model parameters' values (Table 7). Although almost all the annual

slow store runoff simulations at subwatersheds reveal a contribution less than 800 mm, discrepancies of the spatial distribution simulations could not be ignored for SLURP-TGR and SLURP as shown in Fig. 12. Additionally, manifest distinctions were also indicated for different configurations of SLURP-TGR. It might be explained from the parameter calibration, which was found to play a key role in adjusting slow store runoff simulations for SLURP according to Han et al. (2013b). Based on the findings mentioned above, the resulting simulations of the fast and slow store runoff presented complex and varying distribution across the watershed. However, SLURP-TGR still gave rise to a similar pattern of spatial distribution with SLURP irrespective of the differences in total runoff volume. Consequently, the simulations of slow store runoff and fast store runoff act such roles as to compensate each other in guaranteeing optimal overall modeling efficiency. In addition to varying simulations of hydrologic variables, substantial differences existed in the model parameters of SLURP and SLURP-TGR. Thus, uncertainty analysis should be considered to help better understand the obtained simulations through SLURP and SLURP-TGR (Jin et al., 2010). As indicated by the evaluation of modeling performance, the simulation uncertainty with SLURP-TGR might have decreased compared to SLURP (Han et al., 2014a). Although the simulation uncertainty could be reduced through increasing the goodness of fit between simulations and observations, runoff component simulations still rely on the calibrated parameters to such a large extent that highly varying simulations would result, especially for the interflow and ground flow in this study. With negligible difference in evapotranspiration, SLURP-TGR seems to be more capable of adjusting the contribution of various runoff components than SLURP in simulating the total runoff at Xingshan station. In this regard, SLURPTGR would take advantage of reducing the deviation of runoff volume

Fig. 12. Comparison of annual average slow store runoff simulations with SLURP and SLURP-TGR across the watershed.

J.-C. Han et al. / Science of the Total Environment 524–525 (2015) 8–22

simulation, and enhance modeling efficiency through convincing hydrologic process representation. It is further revealed that the flexibility and adaptability of the SLURP-TGR model in parameter calibration should help to improve model performance. 6. Conclusion An improved hydrologic model based on SLURP was developed to reflect the effects of varying rainfall intensity within each daily time step on hydrologic processes. To achieve this, a probability distribution approach coupled with a chance-constrained predictive control was developed. Through demonstrating the SLURP-TGR hydrologic model in the Xiangxi River watershed of the TGR area, several conclusions could be summarized as follows. (1) Contribution of infiltration excess overland flow to runoff generation cannot be neglected in the Xiangxi River watershed, and simulations of hydrological processes could be convinced through considering the impacts of sub-daily rainfall intensity variations on overland flow. Yet, there exist rainfall thresholds, below which such effects would be redundant and inconducive in modeling efforts. Besides, the significance level could be well utilized to represent the Hortonian overland flow. (2) The newly developed SLURP-TGR model was found to result in more satisfactory performance than SLURP, and the deviation of runoff volume could be effectively controlled. Moreover, SLURPTGR was found to produce more reliable overall runoff simulations through adjusting contributions from various runoff components, and improved simulations of the peak flows were also obtained. Thus, SLURP-TGR proved to demonstrate effectively the hydrological processes, and would take advantage of characterizing the linkage between surface and subsurface flow flux for flexibility. (3) Taking into account the sub-daily variability of rainfall intensity, SLURP-TGR could deal with the model input uncertainty at the temporal scale due to averaging the rainfall intensity at each time step, and as such, model performance would be improved through decreasing simulation uncertainty. To better understand the capacity of SLURP-TGR to implement distributed hydrologic simulations, however, uncertainty in hydrological modeling should be further analyzed in the future. (4) Owing to complex terrain and geographic characteristics, the daily rainfall in such watersheds of the TGR area might be invalid. Hence, more rainfall observations would be highly recommended to be employed. In addition to data limitations of the rainfall input, evapotranspiration simulation would also impose nonnegligible impacts on runoff generation. Although the calculated evapotranspiration was similar for SLURP and SLURP-TGR, care should still be required to investigate the impacts of various models of evapotranspiration on runoff simulations. Acknowledgments This study was financially supported by the Major Program of National Natural Science Foundation of China (No. 51190095) and the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2013BAB05B03). Thanks should also be due to those staff and graduate students from North China Electric Power University involved in the field experiment. Moreover, the authors are indebted to the editors and reviewers for their valuable comments and suggestions on the improvement of the manuscript. References Arellano-Garcia, H., 2006. Chance Constrained Optimization of Process Systems under Uncertainty. (Doctor). Technical University of Ilmenau.

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