Journal of Hydrology 472–473 (2012) 205–215
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Impact of spatial rainfall variability on hydrology and nonpoint source pollution modeling Shen Zhenyao ⇑, Chen Lei, Liao Qian, Liu Ruimin, Hong Qian State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, PR China
a r t i c l e
i n f o
Article history: Received 2 May 2012 Received in revised form 5 September 2012 Accepted 9 September 2012 Available online 17 September 2012 This manuscript was handled by Konstantine P. Georgakakos, Editor-in-Chief, with the assistance of Emmanouil N. Anagnostou, Associate Editor Keywords: Uncertainty Rainfall Hydrology Nonpoint source pollution Spatial interpolation method SWAT
a b s t r a c t Rainfall is regarded as the most important input for the hydrology and nonpoint source (H/NPS) models and uncertainty related to rainfall is generally recognized as a major challenge in watershed modeling. In this paper, we focus on the impact of spatial rainfall variability on H/NPS modeling of a large watershed. The uncertainty introduced by spatial rainfall variability was determined using a number of commonlyused interpolation methods: (1) the Centroid method; (2) the Thiessen Polygon method; (3) the Inverse Distance Weighted (IDW) method; (4) the Dis-Kriging method; and (5) the Co-Kriging method. The Soil and Water Assessment tool (SWAT) was used to quantify the effect of rainfall spatial variability on watershed H/NPS modeling of the Daning watershed in China. Results indicated that these interpolation methods could contribute significant uncertainty in spatial rainfall variability and the carry-magnify effect caused even larger uncertainty in the H/NPS modeling. This uncertainty was magnified from hydrology modeling (stream flow) into NPS modeling (sediment, TP, organic nitrogen (N) and dissolved N). This study further suggested that H/NPS prediction uncertainty relating to spatial rainfall variability was scale-dependent due to the averaging effect of spatial heterogeneity. From a practical point of view, a global interpolation method, such as IDW and Kriging, as well as elevation data derived from a digital elevation model (DEM), should be included into the H/NPS models for reliable predictions in larger watersheds. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction One of the most important achievements in hydrological science during the recent decades is the development of hydrology and nonpoint source (H/NPS) models (Chaubey et al., 1999; Andréassian et al., 2001). These computational tools have enabled hydrologists and environment scientists to understand the impact of human activities on basin systems (Quilbe and Rousseau, 2007; Van et al., 2008; Sudheer et al., 2011). However, watershed managers often hesitate to draw up related policies due to uncertainty involved in H/NPS modeling (Beck, 1987; Duan et al., 1992). Uncertainty is currently considered as one of the core dilemmas in watershed studies, especially in the field of NPS modeling (Vrugt et al., 2003; Yang et al., 2008; Shen et al., 2012a,b). Rainfall is generally considered as the most important input that drives runoff production and mass transport for the H/NPS models (Syed et al., 2003; Zehe et al., 2005; Kuczera et al., 2006). However, rainfall data often exhibits irregular occurrence, duration and magnitude across a catchment (Bárdossy and Plate, 1992; Das et al., 2008) due to the variation of nature conditions ⇑ Corresponding author. Tel./fax: +86 10 58800398. E-mail addresses:
[email protected] (Z. Shen),
[email protected] (L. Chen). 0022-1694/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhydrol.2012.09.019
(Faurès et al., 1995). A number of studies have investigated the effect of spatial rainfall variability, which is considered as a significant source of uncertainty in H/NPS modeling (O’Connell and Todini, 1996; Woods and Sivapalan, 1999; Kalinga and Gan, 2006; Chang et al., 2007). Traditionally, a rain gauge is the fundamental tool to determine spatial rainfall variability (Berne et al., 2004; Bárdossy and Das, 2008). Designing an accurate rain-gauge network, in terms of the number and location of stations, has been recognized as being particularly important for monitoring rainfall distribution in both large (Dawdy and Bergman, 1969) and small watersheds (Shah et al., 1996; Dawdy and Bergman, 1969). It is reported that rainfall spatial variability plays a dominant role in discharge modeling and its impact varies according to the rainfall–runoff formulation of the H/NPS model (Koren et al., 1999). It is further demonstrated by Troutman (1983, 1985) and Segond et al. (2007) that the response of hydrology models to rainfall input is scale dependent. Fu et al. (2011) find that the effect of rainfall input on discharge modeling is relatively low for catchment sizes above 250 km2, and even negligible for watersheds larger than 1000 km2. In general, a well-located station might be sufficient for watersheds up to about 50 ha (Osborn et al., 1972), while 20 km is demonstrated as the threshold distance between stations for a reliable hydrology modeling (Vischel and Lebel, 2007).
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Fig. 1. The location of the studied watershed.
Although the effect of rainfall input on hydrology modeling is a well-studied field, few studies have been performed to extend this analysis to the impact of spatial rainfall variability on chemical NPS runoff and water quality prediction, especially in large watershed (Chaplot, 2005). Moreover, there has been increasing concern regarding to the NPS modeling in the past decade (Maeda et al., 2010; Zhu et al., 2011). The effect of spatial rainfall variability on NPS prediction still poses a valid question. It is more common to have only a few rainfall gauges distributed over the watershed (Bárdossy and Das, 2008). Even under the ideal condition, the well-distributed gauge network cannot fully capture every point over the watershed. In an actual NPS modeling, the spatial rainfall variability is often estimated by means of the interpolation techniques, such as the Centroid method, the Thiessen Polygon method, the Inverse Distance Weighted (IDW) method, and the Kriging method (Mamillapalli, 1998; Hamed et al., 2009; Cho et al., 2009; Fu et al., 2011). It is therefore logical to take interpolation methods into account to quantify the impact of spatial rainfall variability on both chemical NPS runoff and water quality prediction. In this paper, we focused on the impact of rainfall spatial variability on chemical NPS runoff and water quality prediction in a large watershed. The Three Gorges Reservoir Area (TGRA) is located in the upstream area of the Yangtze River at the boundary of Sichuan and Hubei, covering an area of 59,900 km2 and a population of 16 million. The TGRA is affected greatly by the Three Gorges Project – the largest hydropower project in the world, and suffers significantly from serious NPS pollution problems, especially in
the Daning River watershed (Shen et al., 2010). However, there are few studies related to the H/NPS prediction uncertainty in this important watershed. Due to the varying geographical locations and weather conditions, it is of great importance to study the effect of spatial rainfall variability on the H/NPS modeling. The spatial rainfall variability was firstly estimated by means of a variety of interpolation methods as: (1) the Centroid method; (2) the Thiessen Polygon method; (3) the IDW method; (4) the Disjunctive Kriging (Dis-Kriging) method; and (5) the Co-Kriging method. In the second step, the effect was quantified by the Soil and Water Assessment tool (SWAT) (Arnold et al., 1998) in the Daning River watershed, which was located in the central part of the TGRA.
2. Materials and methods 2.1. Watershed description and available data The Daning River watershed (4426 km2) is located in Wushan and Wuxi County, in the city of Chongqing, China (Fig. 1). This watershed is a mixed land-use area that contains 22.2% cropland, 11.4% grassland, and 65.8% forest. The surface soil textures are 26.5% yellow–brown soil, 16.9% yellow cinnamon soil, 14.5% purplish soil and 11.0% yellow soil. The landscape is dominated by 95% mountain and 5% low hills; the geology of this area consists of pre-Sinian crystalline basement and a Sinian–Jurassic sedimentary cover. The former geological formation is composed of
Z. Shen et al. / Journal of Hydrology 472–473 (2012) 205–215
magmatic and metamorphic rocks, and outcrops only sporadically in the area. The latter is widespread and comprises inter-bedded carbonate, sandstone and shale formations. The altitude of this region is 200–2588 m and decreases from northeast to southwest. The climate is humid subtropical with a long growing season, featuring distinct seasons with adequate illumination (an annual mean temperature of 16.6 °C) and abundant rainfall (with an annual mean rainfall of 1124 mm). In this study, the available database was set up as follows: Rainfall data from 2000 to 2007 were collected at ten rainfall gauges inside the watershed and nine gauges at sites approximately 30 km outside the watershed boundary. Meteorological data (2000–2007) – such as daily maximum and minimum air temperature, relative humidity and solar radiation – were collected at the Wuxi County Weather Station. Digital Elevation Map (DEM), developed by the Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (RESDC), was derived by digitizing the national topographic map, at a scale of 1: 50,000. Land-use data were determined using the LANDSAT TM image, for the year 2000 developed by the Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, available at a scale of 1: 100,000. The soil map and the related soil physical data were obtained from the Institute of Soil Science, Chinese Academy of Sciences, at a scale of 1: 1,000,000. Daily measured stream flow data (2000–2007) of Ningqiao (NQ), Ningchang (NC), and WX hydrological gauges were collected from Changjiang Water Resources Commission. Monthly measured sediment and total phosphorus (TP) data from 2000 to 2007 were also obtained at WX hydrological gauges. The database for local planting, harvest, and tillage operations was based on field investigations. 2.2. Spatial interpolation methods In this study, the expected rainfall spatial variations were generated by the daily recorded rain data collected from these 19 gauges and then interpolated by fitting a corresponding method. 2.2.1. The Centroid method The Centroid method, originally proposed by Wood et al. (1990), has already been incorporated into the SWAT model (Neitsch et al., 2002). The theory of this method is that the unknown values can be extracted by the nearby known points. In this study, the data from the rain gauge closest to the centroid of each sub-watershed were selected as the sole input for that particular sub-watershed. Then the areal rainfall data were inputted directly into SWAT utilizing the GIS interface and assumed to be homogeneous across each sub-watershed. 2.2.2. The Thiessen polygon method The Thiessen polygon method, put forward by Thiessen (1911), is another widely-used interpolation algorithm. In this study, the Thiessen polygons were firstly generated using the spatial analyst tool of ArcGIS and manually overlapped with the delineated subwatershed. In the second step, the unknown points in the polygon were extracted from the nearby gauges by ArcGIS calculator using Eq. (1). The generated data were incorporated into the SWAT simulation by creating a virtual rain gauge within the centroid of each sub-watershed. n P1 F 1 þ P2 F 2 þ . . . þ Pn F n X Fi P¼ Pi ¼ F F i¼1
ð1Þ
207
where Pi represents daily rainfall data at station i; Fi is the area of Thiessen polygon associated with station i; and F is the area of the sub-watershed.
2.2.3. The IDW method The IDW method is a geometric method based on the assumption that those sites closer to one another are more alike than those farther apart (Philip and Watson, 1986). In this study, the stations were weighted by the inverse distance to the unknown point, which was described in Eq. (2). As there were as much as 2922 daily data points, a program was developed using the ArcGIS Engine to deal with the batch process of data interpolation. This program could be downloaded from http://iwm.bnu.edu.cn. n X ki zðxi Þ
zðx0 Þ ¼
ð2Þ
i¼1
where Z(x0) is the rain data of the unknown point; Z(xi) is the rain data of the rain gauge i; ki represents the weights, which are calculated as:
ki ¼ ½dðxi ; x0 Þp
n X ½dðxi ; x0 Þp
ð3Þ
i¼1
where d(xi, x0) is the distance from unknown point to the rainfall station i; the index p is the power of distance. In general, p values are 1, 2 or 3. In this paper, the value of p was fixed as 2, and the method was called the inverse square method (Hartkamp et al., 1999).
2.2.4. The Dis-Kriging method The Dis-Kriging is a spatial nonlinear interpolation method (Cressie, 1993) on the basis of an optimal, unbiased estimation (Krige, 1951). In this study, the spatial correlation between each pair of points was applied to describe the variance over distance (Isaaks and Srivastava, 1989). Then the weights were calculated by the distances between points as well as the covariation reflected as semicariogram. More information about Dis-Krigin can be found in Schuurmans and Bierkens (2007). The Eq. (4) for Dis-kriging was developed by Matheron (1970) as:
( Pn
Pi¼1 n
ki ðuÞcðua ui Þ þ l ¼ cðua uÞ
i¼1 ki ðuÞ
¼1
ð4Þ
where l is the Lagrange parameter, cðua ui Þ; cðua uÞ is the semivariogram value of the vector represented as ua ui ; ua u.
2.2.5. The Co-Kriging method The Co-Kriging method, a multivariate extension of Kriging (Goovaerts, 1997), was used for merging other geostatistical data (Raspa et al., 1997). In this study, the elevation data, extracted from the digital elevation model (DEM), were integrated as a correction factor. The correlations between variables were described by the crossover-mutation function as:
zðxÞ ¼
n X ki zui þ k½yðxÞ my þ mz
ð5Þ
i¼1
where Z(x) and Zui is the rain data for the unknown point and the rain gauge i; y(x) is the elevation data; n is the number of rain gauges; my and mz is the mean elevation and rainfall value, respectively; and ki and k are the weights calculated as:
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ki rZZ ðxi xj Þ þ kr ZY ðxj xÞ þ lðxÞ ¼ r ZZ ðxj xÞ ðj ¼ 1; 2; . . . ; nÞ
Nsurf ¼ 0:001 C orgN
i¼1 n X
NO3surf ¼ bNO3 C NO3;mobile Q surf
ki rYZ ðx xi Þ þ kr YY ð0Þ þ lðxÞ ¼ r ZY ð0Þ
i¼1 n X
ki þ k ¼ 1
i¼1
ð6Þ where l(x), l(y) are Lagrange parameters considering the constraint of the weight, and rYZ(x xi) is the crossover-mutation function. 2.3. The H/NPS model In this study, the SWAT model, developed by the Agriculture Research Service of the United States Department of Agriculture (USDA-ARS), was used to quantify the effect of spatial rainfall variability on chemical NPS runoff and water quality prediction. The SWAT model is a physically-based model that simulates surface runoff, sediment, and nutrient and pesticide transport primarily from the watershed (Gassman et al., 2007; Douglas-Mankin et al., 2010). The basic components of the SWAT model include hydrology, soil erosion, nutrient and pesticide leaching, crop growth, agricultural management and the generation of weather data (Neitsch et al., 2002). 2.3.1. Model description The hydrology processes of SWAT can be divided into two phases: the land phase and the channel phase. For estimating surface runoff, daily rainfall data are chosen for the curve number (CN) method (USDA-SCS, 1972) and sub-daily data are chosen for the Green-Ampt infiltration method (Green and Ampt, 1911). The SCS curve number equation is:
Q surf ¼
ðRday Ia Þ2 ðRday Ia þ SÞ
ð7Þ
where Qsurf is the accumulated runoff or rainfall excess (mm H2O); Rday is the rainfall depth for the day (mm H2O); Ia is the initial abstractions, which includes surface storage, interception, and infiltration prior to runoff (mm H2O); and S is the retention parameter (mm H2O). The Modified Universal Soil Loss Equation (MUSLE) (Williams, 1969) is used to estimate sediment yield at Hydrologic Research Unit (HRUs) level.
Q sed ¼ 11:8ðQ surf qpeak Ahru Þ0:56 K usle C usle Pusle Lusle F CFRG
ð8Þ
where Qsed is the sediment yield on a given day (metric tons); Qsurf is the surface runoff volume (mm H2O/ha); qpeak is the peak runoff rate (m3/s); Ahru is the area of the HRU (Hydrological response units) (ha); Kusle, Cusle, Pusle and Lusle is the USLE soil erodibility factor, cover and management factor, topographic factor; and coarse fragment factor, respectively. The mass production and transport processes of SWAT are calculated at the HRU level (Eq. (9)–(11)) and combined at the outlet of each sub-watershed. Then the nutrients were routed through the channels, ponds, reservoirs, and wetlands to the watershed outlet, using the QUAL2E model (Brown and Barnwell, 1987). More information about the SWAT model is referred to Neitsch et al. (2002).
Psurf ¼ 0:001 C orgP
Q sed eP:sed Ahru
Q sed eN:sed Ahru
ð9Þ
ð10Þ ð11Þ
where Psurf, Nsurf and NO3surf is the amount of organic P, organic N and nitrate in surface runoff (kg/ha); CorgP, CorgN and CNO3,mobile is the concentration of organic P, organic N (g P/metric ton soil) and nitrate (kg N/mm H2O) in the top 10 mm of soil; eP:sed and eN:sed is the P and N enrichment ratio; bNO3 is the nitrate percolation coefficient. 2.3.2. Model preparation and evaluation criteria The drainage area controlled by the Wuxi hydrological gauge (WX) was chosen as the study catchment, covering approximately 2027 km2 (Fig. 1). The parameter calibration and validation was performed using the Sequential Uncertainty Fitting Version-2 (Abbaspour et al., 2007), which had been incorporated into the SWAT-CUP software (Abbaspour, 2009). For the runoff, the ENS during calibration and validation period was both 0.86. For the sediment, the ENS was 0.73 and 0.61, respectively. For TP yield, the ENS in calibration and validation period was 0.76 and 0.51. More details about model calibration are available in Shen et al. (2008, 2010, 2012a,b) and Gong et al. (2011). There were many studies showing that SWAT simulations carried out in monthly time step generally provides better prediction outputs than those in daily step (Van et al., 2008). It was thus considered to be more meaningful to analyze uncertainty and accuracy on the basis of monthly modeling. The modeling outputs considered were simulated flow, sediment, and total phosphorus (TP), organic nitrogen (N) and dissolved N at the watershed outlet. The prediction uncertainty was quantified by analyzing the SWAT outputs, by means of the mean value, standard deviation (SD), the coefficient of variation (CV) and the relative error (RE), which were defined as:
Pn ðQ sim;i Q mea;i Þ2 ENS ¼ 1 Pi¼1 n 2 i¼1 ðQ mea;i Q mea Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðxi XÞ SD ¼ n1 CV ¼
RE ¼
SD X xi xbaseline xbaseline
ð12Þ
ð13Þ
ð14Þ
ð15Þ
where xi and xbaseline is the model output for i and baseline scenario, Qmea,i is the observed data, Qsim,i is the simulated data, and Q mea is the mean value of the observed data. 3. Results 3.1. Effect on rainfall spatial variability The interpolated density and distribution of rainfall were described in Fig. 2, indicating that the spatial rainfall variability attributed to these five interpolation techniques was significant. As represented in Fig. 2a, the Centroid method derived data from eight stations across the watershed. This inefficient use of rainfall gauge stations resulted in a notable increase of areal rainfall input from east to west over the watershed. As seen in Fig. 2a, several areal rainfall inputs were defined by improper gauges. For example, there were Cha and Xjb stations located in sub-watershed 7.
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(a) Centroid method
209
(b) Thiessen polygon method
(c) IDW method
(d) Disjunctive Kriging method
(e) Co-Kriging method Fig. 2. The interpolated density and distribution of rainfall relating to the uncertainty of spatial rainfall variability.
However, as Xn station, which is located in sub-watershed 5, was closer to the centroid of sub-watershed 7, and the recorded rainfall data from Xn were assumed to represent the areal rainfall input of sub-watershed 7. As a result, although the recorded rainfall of subwatershed 7 was 1142 mm (Xjb) and 1478 mm (Cha) in 2000, a lower value – 1193 mm (Xn) – was obtained. As illustrated in Fig. 2b, the Thiessen polygon method made use of the recorded data from all of the 10 stations within the watershed and another three gauges (Shy, Dch and Lm) outside the watershed. The areal rainfall input of sub-watershed 7 was calculated by involving both Cha and Xjb stations inside as well
as Xn station in the vicinity of sub-watershed 7. A better description of spatial rainfall distribution was obtained by weighting the nearby stations. However, as shown in Fig. 2b, several unrealistic jump values existed when crossing the boundaries between the Thiessen polygons. Fig. 2c–e described the spatial rainfall variability using the IDW, Dis-Kriging and Co-Kriging, respectively. Instead of the single areal input, the rainfall spatial variability was obtained by dense isolines with a gradient of 50 mm. These three methods made full use of 19 stations. It could be observed from Fig. 2c–e that the rainfall was relatively homogeneously distributed from north to south,
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Table 1 The uncertainty of spatial rainfall variability and the areal rainfall input for each sub-watershed. No
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Method Centroid
Thiessen
IDW
Dis-Kriging
Co-Kring
1648.0 1401.0 1648.0 1938.0 1193.0 1193.0 1193.0 1055.0 1055.0 1624.0 1416.0 1938.0 1055.0 1416.0 1055.0 1055.0 1079.0 1079.0 1055.0 1079.0 1416.0 1079.0
1549.3 1231.0 1552.7 1454.9 1276.3 1390.2 1118.3 1055.0 1118.2 1638.1 1300.0 1729.8 1055.0 1402.9 1102.1 1055.0 1100.5 1055.0 1055.0 1055.0 1347.9 1070.2
1501.4 1385.5 1501.1 1609.4 1293.9 1178.4 1175.8 1110.6 1150.6 1554.4 1296.9 1645.7 1086.5 1382.6 1147.4 1070.6 1136.7 1076.5 1078.7 1078.9 1345.8 1119.2
1418.9 1222.2 1600.8 1721.2 1322.7 1106.8 1151.0 1079.1 1109.1 1669.7 1280.5 1675.3 1073.2 1379.4 1149.5 1069.4 1130.7 1088.3 1085.3 1089.7 1352.3 1131.5
1457.7 1393.8 1507.2 1582.7 1319.2 1142.8 1189.0 1110.4 1138.2 1552.3 1291.6 1607.5 1107.2 1383.9 1178.4 1102.7 1145.5 1109.2 1104.8 1105.5 1367.6 1136.8
whereas obvious spatial heterogeneity could be observed from east to west over the watershed. However, the local density of isolines related to different interpolation methods appeared to be slightly different. There were more dense isolines around the rain stations when using the IDW method. This could be explained by considering that the interpolated results using IDW were more significantly impacted by the nearby stations, resulting in a phenomenon called ‘data cluster’ (Goovaerts, 2000). As a semi-distributed H/NPS model, the SWAT model used the areal rainfall of each sub-watershed as the forcing input (Neitsch et al., 2002). It was therefore more instructive to check the spatial rainfall variability for each of the sub-watershed. Table 1 indicated that the CV values varied from 0.010 to 0.098 among sub-watersheds, with a range of SD from 14.15 mm to 162.24 mm. The greatest variability in a sub-watershed level input was observed in subwatershed 4, for which the annual averaged rainfall (from high to low) ranged from 1938.0 mm for the Centroid method, 1721.2 mm for the Dis-Kriging method, 1609.4 mm for the IDW method, 1582.7 mm for the Co-Kriging method and 1454.9 mm for the Thiessen Polygon method. As noted previously, the Centroid method and the Thiessen polygons method were two widely-used techniques (Mamillapalli, 1998; Cho et al., 2009). However, there was a great uncertainty in rainfall input with a difference of 33.2% between these two methods. However, even though the smallest variation (CV of 0.010) was considered (sub-watershed 14), there was still a 2.6% difference. This could be explained by reference to Fig. 2, which illustrated high-intensity isolines in sub-watershed 4, indicating a heterogeneous rainfall pattern, and low-intensity isolines in sub-watershed 14 relating to a more homogeneous distribution of rainfall. The averaged SD and CV value for each sub-watershed was 47.75 mm and 0.035, respectively. It could thus be concluded these interpolation methods resulted in considerable uncertainty of the spatial variability of rainfall and, therefore, a doubtful forcing input for the model, particularly at the sub-watershed level. 3.2. Effects on H/NPS Modeling Uncertainty analysis related to the monthly outputs of stream flow was illustrated in Fig. 3a and b that the value of SD ranged from 0.042 m3/s (January in 2002) to 49.255 m3/s (July in 2007), with the CV values ranging from 0.01 (November in 2004) to
Mean
SD
CV
1515.0 1326.7 1561.9 1661.2 1281.0 1202.2 1165.4 1082.0 1114.2 1607.7 1317.0 1719.3 1075.4 1393.0 1126.5 1070.5 1118.5 1081.6 1075.8 1081.6 1365.9 1107.3
79.46 81.94 56.05 162.24 47.18 98.60 27.77 24.86 33.00 46.77 49.95 116.44 19.86 14.15 43.29 17.44 24.88 17.60 19.01 16.48 26.17 27.49
0.052 0.062 0.036 0.098 0.037 0.082 0.024 0.023 0.030 0.029 0.038 0.068 0.018 0.010 0.038 0.016 0.022 0.016 0.018 0.015 0.019 0.025
0.39 (August in 2007). Up to 48% of simulated NPS-flow was found to have CV values higher than 0.1, with an averaged CV value being 0.21. The narrowest interval was 1.839–1.959 m3/s (January in 2002), while the greatest variation was observed as 138.6– 264.8 m3/s (June in 2007). It was not surprising that greater uncertainty (interval and SD) occurred in the relatively wet period since rainfall and flow in the wet season changed frequently and widely in TGRA (Shen et al., 2008, 2012a,b). Results summarized in Fig. 3a further demonstrated large and frequent changes in simulated NPS-flow in the TGRA, as illustrated by the following results using different methods from July, 2007: 115.2 m3/s for the Centroid method, 198.9 m3/s for the Thiessen polygon method, 203.4 m3/s for the IDW method, 204.4 m3/s for the Dis-Kriging method and 211.5 m3/s for the Co-Kriging method. The baseline scenario (the Centroid method) was established and the RE (July in 2007) was as high as 73%, 77%, 77%, and 84% for the Thiessen polygon method, the IDW method, the Dis-Kriging method, and the Co-Kriging method, respectively. It could thus be inferred that rainfall spatial variability relating to interpolation methods had a significant impact on the NPS-flow simulations. Results illustrated in the box diagrams (Fig. 3b) further indicated the simulated NPS-flow was 0.9363 m3/s (January in 2003)–302 (July in 2000) m3/s for the Centroid method. This compared with simulated NPS-flow of 1.442 m3/s (January in 2006)–323.5 m3/s (July in 2000) for the Thiessen polygon method, 1.423 m3/s (January in 2006)–327.3 (July in 2000) m3/s for the IDW method, 1.483 m3/s (January in 2006)–330 (July in 2000) m3/s for the Dis-Kriging method, and 1.449 m3/s–332.9 (July in 2000) m3/s for the Co-Kriging method. The simulated NPS-flows related to other four interpolation methods were slightly higher than that obtained using the Centroid method. It might be explained by the assumptions, made in H/NPS models such as SWAT, that the recorded rainfall affected the entire sub-basin (Neitsch et al., 2002). This might result in an under-prediction of the areal rainfall input due to the neglecting of the real center and the peak values of rainfall. However, this study showed that a well-generated areal rainfall might result in the SWAT model routine higher runoff volume over the watershed. Several studies had reported the SWAT model often underestimated flow in the rainy season (Zhang, 2001; Shen et al., 2008, 2012a). Therefore, it was inferred that those interpolation methods might be a means to solve this problem.
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(a) Monthly flow
(c) Monthly sediment
(e) Monthly TP
(b) Range of flow
(d) Range of sediment
(f) Range of TP
Fig. 3. The effect of spatial rainfall variability on hydrology and NPS modeling (flow, sediment, TP, org N and solute N).
Results of further analysis of the effect of rainfall input on NPS-sediment and NPS-nutrient modeling were presented in Fig. 3c–j. Analysis of monthly sediment levels indicated that the SD ranged from 0.04 ton (January, 2003) to 626.08 ton (June, 2007), while the value of CV was 0.015 (October, 2003)–1.067 (March, 2003). It could be deduced from Fig. 3c that as much as 73% of simulated NPS-sediment estimates had CV levels higher than 0.1. The biggest variation (SD) could be observed in June, 2007, in which the value of simulated NPS-sediment was 493 ton for the Centroid method, 1867 ton for the Thiessen polygon method, 1901 ton for the IDW method, 1869 ton for the Dis-Kriging method and 1930 ton for the Co-Kriging method. The uncertainty
in hydrology modeling was therefore carried-over and magnified into even larger uncertainty in NPS-sediment modeling due to the mechanism of runoff–sediment formulation in the SWAT model (Cho et al., 2009; Hamed et al., 2009). Further evidence for this could be found in the RE values which were observed as 279%, 286%, 279%, and 291% in June, 2007, respectively. The NPS-TP outputs summarized in Fig. 3e and f indicated the value of SD and CV ranged 0.01–25.13 ton and 0.02–0.88, with the averaged values being 4.50 ton and 0.50, respectively. It was also indicated that as much as 76% of simulated monthly NPS-TP had CV values higher than 0.1. Further evidence for this could be found in the value of simulated NPS-TP and the corresponding RE values in
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(g) Monthly Org N
(h) Range of Org N
(i) Monthly dissovled N
(j) Range of dissovled N Fig. 3. (continued)
Table 2 The prediction uncertainty (flow, sediment, TP, org N, and solute N) relating to spatial rainfall variability. Methods
Flow (m3/s)
Sediment (t)
TP
Org N (t)
Solute N (t)
Centroid Thiessen Value RE IDW Value RE Dis-Kriging Value RE Co-Kriging Value RE Mean value SD CV
46.05
1408.49
78.27
272.24
1355.25
51.5 11.83%
2254.13 60.04%
113.82 45.42%
737.93 171.06%
2856.96 110.81%
52.39 13.77%
2268.74 61.08%
113.01 44.38%
730.12 168.19%
2883.12 112.74%
52.99 15.07%
2299.23 63.24%
111.39 42.32%
728.71 167.67%
2884.6 112.85%
54.01 17.29% 51 3 0.06
2354.96 67.20% 2117 398 0.19
116.48 48.82% 107 16 0.15
733.49 169.43% 640 206 0.32
2939.91 116.93% 2584 688 0.27
February, 2007, which were 7.197 ton, 5.045 ton, 5.251 ton, 7.769 ton and 1182%, 798%, 835%, and 1283% for the Thiessen polygon method, the IDW method, the Dis-Kriging method, and the CoKriging method, respectively. The level of NPS-TP was obviously higher than that of NPS-sediment modeling when using different interpolation methods. The similar result could be obtained via NPS-N simulation (Fig. 3g–j). It could be deduced from Fig. 3g and i that as much as 94% and 89% of simulated monthly organic NPS-N and dissolved NPS-N estimates had CV levels higher than 0.1. Analysis of monthly organic NPS-N levels indicated that the SD varied from 0.01 ton to 323.41 ton, while the value of CV was
0.04–1.17. The averaged SD and CV were 37.21 ton and 0.67, respectively. As to dissolved NPS-N outputs, the SD and CV values were as much as 1.35–626.11 ton and 0.03–0.51, with the averaged values being 110 ton and 0.45. Further evidence for this could be found in the RE values which were calculated as 119%, 119%, 119%, and 123% in July, 2000 and 6%, 5%, 7%, and 7% in August, 2006, respectively. The uncertainty level indicated by averaged CV value ranked as: organic NPS-N (0.67) > NPS-TP (0.50) > dissolved NPS-N (0.45) > NPS-sediment (0.44) > NPS-flow (0.21). Simulated annual H/NPS outputs were also summarized in Table 2. The averaged simulated flow was 51.39 m3/s, with the
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Z. Shen et al. / Journal of Hydrology 472–473 (2012) 205–215 Table 3 The effect of spatial rainfall variability on the accuracy of the SWAT model to simulate flow and NPS pollution. Variable
Centroid
Stream flow Sediment TP
0.83 0.75 0.66
Thiessen
IDW
Dis-Kring
Co-Kriging
Ens
Inc%
Ens
Inc%
Ens
Inc%
Ens
Inc%
0.91 0.82 0.71
10.2 10.1 8.03
0.92 0.81 0.72
11.0 9.20 9.24
0.92 0.80 0.70
11.6 7.20 6.67
0.934 0.775 0.716
12.53 3.33 8.48
averaged SD and CV being 3.00 m3/s and 0.06, respectively. The RE values were 11.83%, 13.77%, 15.07% and 17.29%, respectively. For NPS-sediment, the averaged SD and CV was 398 ton and 0.190, while the RE was 60.04% for the Thiessen polygon method, 61.08% for the IDW method, 63.24% for the Dis-Kriging method and 67.20% for the Co-Kriging method. The CV values for NPS-TP, organic NPS-N and dissolved NPS-N was 0.15, 0.32 and 0.27, with the values of RE being 42%, 44%, 42%, 50% for NPS-TP, 138%, 139%, 137%, 140% for organic NPS-N, and 89%, 91%, 94%, 94% for dissolved NPS-N. The uncertainty level indicated by CV value ranked as: organic NPS-N (0.32) > dissolved NPS-N (0.27) > sediment (0.19) > NPS-TP(0.15) > flow (0.06). It could be inferred that spatial rainfall variability relating to spatial interpolation methods introduced greater uncertainty in both annual and monthly NPS modeling. However, SWAT simulation in annual steps generally removed some degree of prediction uncertainty based on monthly steps. Results from further examination of the model performance were given in Table 3. As there was no measured N data available, only NPS-flow, NPS-sediment and NPS-TP modeling were analyzed for the study region. For different interpolation methods, the ENS values were calculated as 0.83–0.93 for NPS-flow, 0.75–0.82 for NPS-sediment, and 0.66–0.72 for NPS-TP. Results clearly indicated that the H/NPS model performance could be improved by advanced spatial rainfall variability (Table 3). For NPS-flow modeling, the ENS value was 0.915, 0.922, 0.927 and 0.934, with the improvement being 10.24%, 11.08%, 11.69% and 12.53% for Thiessen, IDW, Diskriging and Co-Kriging, respectively. The best hydrology modeling was obtained by the Co-Kriging method. For NPS-sediment modeling, the ENS values and corresponding improvement were 0.822 and 10.13% for Thiessen, 0.812 and 9.20% for IDW, 0.801 and 6.67% for Dis-kriging, 0.775 and 8.48% for Co-Kriging. The NPS-TP simulation also benefited from advanced interpolation methods (8.03% for Thiessen, 9.24% for IDW, 6.67% for Dis-kriging and 8.48% for Co-Kriging). Overall, the best results were provided by Thiessen for NPS-sediment and IDW for NPS-TP. This difference could be explained by the fact that the parameters obtained by the Centroid method were fixed in H/NPS modeling related to other interpolation methods. The reason why the measured data were not used was that even with the best possible model calibration, there would be some parameter uncertainty present in the model predictions (Abbaspour et al., 2007; Li et al., 2010). However, Liang et al. (2004) and Hamed et al. (2009) had found that the spatial rainfall variability might have impact on the H/NPS calibration process because this process was based on a comparison of observed and predicted values. It should be noted here that the rainfall input provided by Co-Kriging indicated lower uncertainty (Table 1) and that it was inferred that this method might result in an accurate and precise H/NPS modeling. 4. Discussion A number of previous studies have revealed that the effect of spatial rainfall variability on hydrology modeling is generally quite small in larger watersheds and this effect could even be negligible for watersheds larger than 1000 km2 (Obled et al., 1994; Faurès
et al., 1995; Fu et al., 2011). However, as mentioned above, Table 2 and Fig. 3 show that the uncertainty relating to spatial rainfall variability is propagated through the SWAT model, to some extent, to NPS-sediment modeling and then carried-over and magnified into NPS-N and NPS-P simulation. This greater uncertainty may be due to the fact that NPS production is complex, as it is affected and dominated by both hydrological process and watershed response (Shen et al., 2008; Migliaccio and Chaubey, 2008). As shown in Eq. (8)–(11), the impact of rainfall data on NPS simulation depends not only on the degree of spatial rainfall variability but also on watershed properties such as soils, geology, topographic and management factor (Chaplot, 2005; Shen et al., 2012a). As indicated by the CV value, the uncertainty factors of organic NPS-N, NPS-TP and NPS-sediment are in good consistency because sediment is the main carrier of organic NPS-N and org NPS-P (a part of NPS-TP) (Shen et al., 2008). The higher uncertainty level of organic NPS-N can be explained by the fact that most organic NPS-N was attached to the sediment, whereas there was just a part of NPS-TP (org NPS-P) attached to the sediment (Gong et al., 2011; Shen et al., 2012a). Therefore, the correlation between sediment and organic NPS-N is higher than that between NPS-sediment and NPS-TP. The higher rank of dissolved NPS-N makes sense, as agriculture land is dominant in the Daning watershed, resulting in a soluble form of N and its discharge carried out by means of runoff. Therefore, the control of fertilization was the key in addressing dissolved NPS-N pollution in the Daning River watershed. Based on the results obtained in this study, the uncertainty of hydrology modeling is transformed into larger uncertainty of NPS-sediment modeling and even larger uncertainty of NPS-N and NPS-P prediction due to the mechanism of runoff– NPS formulation in the SWAT model (Cho et al., 2009; Hamed et al., 2009). To better present our study results, the authors define this phenomenon as ‘carry-magnify’ effect. In general, the challenge of H/NPS models lies in the identification, through uncertainty analysis, of which inputs and parameters strongly affect the H/NPS outputs, and the effort trying to define these in the most accurate way (Smith et al., 2004; Vischel and Lebel, 2007; Hamed et al., 2009). It can be expected by examining Table 2 and Fig. 3 that consideration of interpolation methods is very important in NPS modeling, particularly in larger watersheds. In general, these methods can be divided into global techniques and algorithm (Fu et al., 2011). Based on this study, inclusion of the other gauges that are in the vicinity and apart from the studied area can give a more precise description of spatial rainfall variability for H/NPS modeling (seen Fig. 2). This conclusion was similar to those of Goodrich et al. (1995) and Cho et al. (2009). In comparison, local algorithms average the spatial rainfall variability (Faurès et al., 1995; Goodrich et al., 1995). Even though spatial uniformity can be generally assumed in small watersheds (Koren et al., 1999; Fu et al., 2011), this would not be the case for larger watersheds or watershed that experienced great rainfall variability (Bárdossy and Das, 2008; McMillan et al., 2011). This study underlines the importance of using a proper interpolation method that is representative for the scale of interest. From a practical point of view, the current SWAT centroid method can be recommended for the H/NPS modeling in small watersheds or in watersheds with homogeneous rainfall.
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However, global techniques, such as IDW and Kriging, should be also combined into the SWAT modeling of larger watersheds. As shown in Table 3, this study also recommends the incorporation of correction factor be one component for the SWAT model. Taking into account the study needs and data availability cost considerations (Sun et al., 2000; Kavetski et al., 2006; Bárdossy and Das, 2008; Moulin et al., 2009; McMillan et al., 2011), a valuable and available information relevant for H/NPS modeling is elevation data, which can be extracted from the digital elevation model (DEM). 5. Conclusions In this study, the impact of spatial rainfall variability on H/NPS modeling, in terms of prediction accuracy and uncertainty, was evaluated. Based on the results obtained, it was concluded that spatial interpolation resulted in considerable uncertainty of rainfall spatial variability and therefore doubtful H/NPS simulated results, especially for large-scale watersheds. The uncertainty was therefore carried-over and magnified into even larger uncertainty in flow, sediment, TP, organic N and dissolved N modeling due to the mechanism of runoff–NPS formulation in the H/NPS model. The potential impact of uncertainty due to spatial rainfall variability was greatest for organic NPS-N and NPS-TP, followed by dissolved NPS-N and sediment, and least for flow prediction in the Daning Watershed. From a practical point of view, this study suggests that a global interpolation method and the elevation data should be included into the SWAT models to capture spatial rainfall variability. In summary, the conclusion of this study can be extrapolated to other H/NPS models such as AGNPS, ANSWERS and HSPF which also assume a homogeneous rainfall input. However, as detailed measured sediment and TP data were not available for the study region, not all time steps were analyzed in this study. Further studies on a daily or hourly time-step are needed in order to capture chemical flux variability because chemical runoff processes may be also sensitive to event flux. In addition, more studies should also take theoretical analysis and practical steps to examine methods for mitigating prediction uncertainties. Acknowledgements The study was supported by National Science Foundation for Distinguished Young Scholars (No. 51025933), the National Science Foundation for Innovative Research Group (No. 51121003) and the National Basic Research Program of China (973 Project, 2010CB429003). The authors wish to express their gratitude to the Journal of Hydrology, as well as to anonymous reviewers who helped to improve this paper though their thorough review. References Abbaspour, K.C., 2009. SWAT-CUP Programme Version 2.1.5.
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Further reading Bronstert, A., 2003. Uncertainty of runoff modelling at the hillslope scale due to temporal variations of rainfall intensity. Phys. Chem. Earth 28, 283–288.