Sept., 2010 Journal of Resources and Ecology Vol.1, No.3 J. Resour. Ecol. 2010 1(3) 231-237 DOI:10.3969/j.issn.1674-764x.2010.03.006 www.jorae.cn Water topic A Distributed Soil Erosion and Sediment Transport Sub-model in Non-point Source Pollution and Its Application in Guishui Watershed XIA Jun 1 and XUE Jinfeng 2 * 1 Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China; 2 Department of Water Quality Engineering, College of Power and Mechanic Engineering, Wuhan University, Wuhan 430072, China Abstract: Soil erosion was very serious in the Guishui area of Guanting reservoir. In order to control the non-point source (NPS) pollution of soil loss there, a distributed soil erosion and sediment transport sub-model with less parameters and more convenient application was built in this paper, which was composed of the USLE model and the sediment transport model. Firstly, USLE was used to calculate soil erosion after suitable calculation formulae of its factors were selected. And then the watershed was generalized into river network, we applied the relation between S-curve and pollutant-collecting area coefficient we had established into the solution of one-dimensional water quality transportation equation gained from Laplace transform and inverse Laplace transform, and derived the distributed sediment transport model. Finally, relied on DEM, this paper made research on the model application in Guishui watershed by picking up geographical information from the soil map and land-use map of Guishui watershed. Application results indicated that this model can not only be used to make research on the sediment pollution resulting from NPS pollution, but also on the spatial distribution of soil erosion, offering scientific foundation for realizing best agricultural management in this watershed. The soil loss in Guishui watershed mainly comes from the mountain and hill with large slope and low vegetation coverage, therefore, the key for controlling the soil loss shall be taken on the mountain and hill in this watershed. Key words: nonpoint source pollution; distributed model; GIS; Guanting Reservoir; Guishui River 1 Introduction At present, even though distinct improvement is shown on the water quality in Guanting Reservoir, it was once retreated from Beijing Drinking Water Supply System in 1997 due to its serious pollution. According to water sample analysis results in a rainfall in late July 2002, the maximum value of suspended sediment concentration in the Guishui River was 1.56 g L 1 during the precipitation, while it was only 0.15 g L 1 before the precipitation, which indicated that sediment pollution resulted from soil erosion in Guishui watershed of Guangting Reservoir was serious (Xue 2003). In addition, the nitrogen and phosphorus pollution was also serious there (Liang 2001). Therefore, research on NPS pollution of Guishui watershed and on its pollution to Guishui river reservoir and Guanting Reservoir was of crying need at that time. Constructing NPS pollution mathematical model is an effective means to do the research. Up to now, NPS pollution models have gone through two stages: lumping model stage and distributed model stage. Compared with lumping models, a distributed model preserves spatial distribution of watershed characteristics and simulated hydrology, sediment and nutrients by dividing the watershed into grids. Therefore, research on the distributed model has become the focal point of this research on the NPS pollution model. Agricultural non-point source pollution model (AGNPS) (Young et al. 1989), water erosion prediction project (WEPP) (Flanagan et al. 1995) and soil and water assessment tools Received: 2010-08-20 Accepted: 2010-09-06 Foundation: National Key Water Project (No.2009ZX07210-006) & The Knowledge Innovation Key Project of the Chinese Academy of Sciences (Kzcx2-yw-126). * Corresponding author: XUE Jinfeng. E-mail: jfxue@163.com.
232 (SWAT) (Arnold et al. 1998; Neitsch et al. 2001) are typical distributed NPS pollution models. However, there exist some problems in the application of these models to China. For example, AGNPS is an event-based model that does not reflect temporal variation. Although WEPP and SWAT are continuous time and distributed parameter models, the intensive, site-specific parameter requirements are so numerous that it is very difficult to transfer these models to other watersheds (Heng et al. 1998). If we can reduce the number of parameters to be calibrated in such models, its application will become very easy and simple. The objective of our research is to construct a new continuous time and distributed parameter NPS pollution model based on hydrodynamics, so as to simulate the transfer and transport of pollutants. This will enable the management and control of NPS pollution. In this paper, the sediment-sub-model, and its application of the new distributed time-variant NPS pollution model, is introduced. 2 Methods The sediment-sub-model is composed of USLE model and suspended sediment transport model. The former is used to simulate the process of soil loss from hillslope to stream or river under the impact of precipitation and streamflow. The latter is used to simulate sediment delivery process in the stream or river. 2.1 USLE model USLE is the most universal equation to estimate soil loss by water erosion. It was put forward by USDA-ARS after observation for more than 40 years in experimental plots. USLE established by Wischmeier and Smith is (Novotony et al. 1981): LA = (R) (K) (LS) (C) (P) (1) where LA is soil loss amount caused by rainstorm (t ha-1); R is rainfall energy factor; K is soil erosion factor; LS is length-slope factor; C is vegetation coverage factor; P is controlling erosion measures factor. Factor R was firstly determined in eastern United States, and later was developed over the world. With temporal and spatial variation, its formula put forward by people had different changes. The formula (Soil Conservation Society of America 1976) adopted by this paper is: R = (0.0158 P I30 ) -1.2 (2) where P is rain depth, I30 is maximum 30 min rainfall intensity. Factor LS is calculated by use of the following equation (Soil Conservation Society of America 1976) Journal of Resources and Ecology Vol.1 No.3, 2010 where L is slope length, S is the slope. (3) Factor K is the measure of soil potential erosion, and is the function of five soil parameters including the percentage of mucky and fine sandy soil (0.05 to 0.1mm), the percentage of sand (>0.1mm), the percentage of organic matter, soil texture classification and permeability. Factor C is concerned with vegetation cover, soil and management measures affecting erosion speed, and factor P is concerned with soil and water conservation measures. Their value is given by Novotony et al. (1981). 2.2 Research on suspended sediment transport model 2.2.1 Sediment delivery ratio During the sediment is transported to watershed outlet, some of them will deposit, others will be transport, and transport proportion in its yield is called sediment delivery ratio, expressed by Dr, which is mainly the function of transport distance and is defined as: (4) where Dr,j is sediment delivery ratio of DEM grid j; Lj is the distance from grid j to watershed outlet section; b is a constant. 2.2.2 Suspended sediment transport model If molecular and turbulent diffusion coefficients are omitted, one dimension water quality transfer and transform basic equation can be derived (Luo et al. 1997): (5) For no lateral inflow and settling of suspended sediment, SiA=0; in Eq. (5), CQ represents transport rate of suspended sediment, here expressed by Qs ; for uniform river, suppose that the average flow velocity is v then A=Q/v, bring them into Eq. (5), the result is: that is: (6) where Qs is transport rate of suspended sediment; t is
XIA Jun, et al.: A Distributed Soil Erosion and Sediment Transport Sub-model in Non-point Source Pollution and Its Application in Guishui Watershed time; L is flow distance; v is average flow velocity E is longitudinal dispersion coefficient. If E and v are constant, equation (6) belongs to constant coefficient differential equation or linear diffusion wave equation. When inflow is instantaneous unit impulse function, outflow can be drawn from the following mathematical equations: (7) where Eq. (7b) is initial condition, Eq. (7c) and (7d) are upper and down boundary conditions, respectively. Through Laplace transform and inverse Laplace transform, the expression for instantaneous concentration curve of suspended sediment can be derived (The Yangtze River Water Resources Commission 1993; Li et al. 1996): (8) The outflow hydrograph named as S curve can be derived: (9) where is Gause error func- 233 (11) where (Qs)j is transport rate of suspended sediment in runoff at the end of time interval number j (kg s-1); (qs)j-i + 1 is transport rate of suspended sediment in the time interval number j-i+1 (kg s 1). According to the relation between S-curve and water (pollutant)-collecting area coefficient we have established and the relation between area A and number of DEM grids (Xue et al. 2007), Equation (10) can be written in the form: In addition, the relation between transport rate (qs)j-i + 1 in equation (11) and average transport rate in unit DEM grid is: (13) in which (qs)j-i + 1,cell is average transport rate of suspended sediment in unit DEM grid in the time interval number j-i+1. From equation (11), (12) and (13), it can be derived If (qs)j-i + 1,i stands for total transport rate of suspended sediment in (ni-ni-1) DEM grids in time interval number j-i+1, then is equal to (qs)j-i+1,i. In this case, the transport rate of suspended sediment in runoff at the outlet of watershed can be written as: (15) tion. Its expression is Transform S curve into time interval concentration curve or confluence coefficient as follows: which can be also written as: (10) where Pi is confluence coefficient in the time interval number i, Si is S curve at the end of time interval number i, Si-1 is S curve at the end of time interval number i-1. The outflow curve of suspended sediment can be drawn: For spatial-variant transport rate of suspended sediment, where (qs)j-i + 1,k is transport rate of suspended sediment in certain grid k among ni-1 +1 to ni grid in time interval number j-i+1. The concentration of suspended sediment at the outlet of watershed is: (17)
234 where Q j is the flow at watershed outlet (or downstream section) on day j resulting from rainfall, (Q 0) j is dry weather flow at watershed outlet on day j, (C S0) j is the dry weather concentration of suspended sediment at watershed outlet on day j, (Q S) j is transport rate of suspended sediment at watershed outlet on day j resulting from rainfall. 3 Application research in Guishui watershed 3.1 The study area As a branch of Yongdinghe river system, the primary river crossing this watershed, Guishui River traverses the Yanqing Basin into Guangting Reservoir, its catchment area is closed in essence. Xue (2007) has introduced hydrological survey of this watershed, where the mountainous region accounts for 25%, hill accounts for 20%, and plain field accounts for 55%. At present, the nature vegetation coverage in mountain area is high, while in the flat and hilly region, due to large area of cultivation, its vegetation condition is poor, and even in some area, nearly all are the bald hills with serious soil erosion. 3.2 Information extraction The variables K, C and P in USLE have close relationship with soil type and land use. For gaining exact soil type and land use information, based on the geographical coding information contained in DEM, we primarily made picture superimposition on the soil and land use image of Guishui watershed with Mapinfo, extracted the soil and land use information from soil map and land use map to build property database and created 1000m 1000m soil map and land use map with ArcView (Ma et al. 2006). Water flow direction and flow length are two important hydrological information, water flow direction is the basis of splitting watershed, and water flow length is not only the basis of ranking and coding grid according to the distance to watershed outlet, but also an important factor affecting the transport of sediment, nitrogen and phosphorus. Based on DEM, we extracted the water flow direction and flow length of each grid with the hydrological analysis module of ArcView GIS. According to water flow length, ranked and coded the 1000m 1000m grid, and stored the data of water flow direction and flow length into the watershed resource database (Xue et al. 2007). Slope data are extracted from DEM (1000m 1000m) directly, and are stored into the watershed resource database. Journal of Resources and Ecology Vol.1 No.3, 2010 3.3 Model Calibration and validation 3.3.1 Calibration and validation As described by Xue et al. (2007), due to no data of Guishui watershed after 1960, we use 1950s data to calibrate and validate the model. In view of relatively great sediment concentration in 1956, it is selected to calibrate parameters of sediment sub-model. At first, the sediment yield is calculated by USLE, and then sediment concentration at the watershed outlet Laojuntang is calculated by sediment transport model, wherein the values of parameters b,α and β are initially calculated by moment method and are adjusted by step acceleration method. During parameter adjustment, the following equation is selected as the target function: where, C m and C sm are the observed concentration and simulated concentration of peak i respectively, T m and T sm are the observed peak time and simulated peak time of peak i separately, K is the constant coefficient, which shall be confirmed as required. The reliability of calibration results is evaluated with the deterministic coefficient d, where, S is the mean square deviation of simulated concentration,,σ is the mean square deviation of observed concentration,, c i,s is the simulated sediment concentration of number i, c i,o is the observed sediment concentration of number i, c - is the average of observed concentration. As a result, when the model parameters b, α and β are -0.42, 145.84 and 31.58 respectively, the fitting effects of simulation and observation at the watershed outlet are optimal, the targeted function S is 4.32 (K=0.5). Sediment simulation results and peak statistic analysis results of 1956 are given in Fig. 1 and Table 1, respectively. Afterward, simulated sediment concentrations of 1957, 1958 and 1960 were calculated by the model with calibrated parameters and were validated by use of observed sediment concentrations in the hydrologic yearbook. Simulation results are shown in Figs.2 4, and the statistic analysis on their peak value is presented in Table 1. 3.3.2 Results and discussions Though calculating formulas of factors in USLE have great effect on simulation accuracy, there are no universal
XIA Jun, et al.: A Distributed Soil Erosion and Sediment Transport Sub-model in Non-point Source Pollution and Its Application in Guishui Watershed expressions like USLE. Therefore, it is necessary to strengthen the research on expressions of factors so as to Fig. 1 The curve of sediment concentration (1956). Fig. 2 The curve of sediment concentration (1957). Fig. 3 The curve of sediment concentration (1958). Fig. 4 The curve of sediment concentration (1960). 235 improve simulation accuracy. In addition, many studies show that the effect of slope on sediment yield is very
236 Journal of Resources and Ecology Vol.1 No.3, 2010 Table 1 Statistical results of main peak of sediment concentration. Data Observed Simulated Peak error Sediment concentration (g L 1 ) Sediment concentration (g L 1 ) Peak time Relative error of sediment concentration (%) Peak time error (day) 1956-07-08 8.24 9.00 1956-07-08 9.2 0 1956-07-17 3.72 10.4 1956-07-17 179.6 0 1956-07-29 12.2 21.2 1956-07-29 73.8 0 1956-08-03 7.34 1.83 1956-08-03 75.1 0 1956-09-04 4.38 6.33 1956-09-03 44.5 1 1957-07-13 12.9 9.19 1957-07-12 28.8 1 1957-07-15 14.8 41.1 1957-07-16 177.7 1 1957-07-26 7.78 7.16 1957-07-25 8.0 1 1958-07-10 30.9 24.22 1958-07-10 21.6 0 1958-07-15 9.17 1.5 1958-07-15 83.6 0 1958-08-08 9.28 5.9 1958-08-08 36.4 0 1958-09-14 2.4 2.66 1958-09-13 10.8 1 1960-07-06 6.06 8.34 1960-07-07 37.6 1 1960-07-16 10.1 34.55 1960-07-15 242 1 Certainty coefficient d 1956=9.5%,d 1958=50.5% great. Accordingly, it is proposed to using grids as small as possible in calculation, so as to reduce the error resulting from the average of slope. From Table 1, it can be seen that most of small peaks have relatively little errors, while some of big peaks have much larger errors. In addition, certainty coefficients of simulation are not too high, such as the highest is in 1958, only 50.5%, and secondly in 1956, 9.5% only. The factors that lead to these results are complicated, wherein the quantity and quality of water from Baihebao reservoir is a major factor. For example, the observed suspended sediment concentration is 24.3 g L 1 at Baihexiabao station on July 29, 1956, and is 13.1 g L 1 at Laojuntang station on July 31, 1956, while the simulated sediment concentration at Laojuntang station is only 4.02 g L 1, these results show that the influence of Baihebao reservoir is very great. However, it can not be considered due to lack of data. From the curves of sediment concentration, it can be seen that simulation results are basically consistent with the change rule of observation, though there are certain errors. In addition, relatively strong precipitation happened in 1956 and in 1958, and when the calibrated sediment sub-model with observed data of 1956 is applied to the sediment simulation of 1958, good results are acquired. Thus, the sediment sub-model presented in this paper has practical value. 3.4 Spatial distribution of soil loss After calibration and validation, the spatial distribution of soil loss in Guishui watershed is researched. In view of low precipitation and big simulation errors of 1957 and 1960, and quite the opposite of 1956 and 1958, we mainly study the monthly mean distribution of soil loss of the latter, and map out their spatial distribution (Figs.5 and 6). The results indicate: (i) the soil loss becomes more easily under great rainfall intensity and long-lasting rainfall. For example, the maximum 30min rainfall intensity of 1958 was less than that of 1956, and monthly mean rainfall was also so, which result in the calculated soil losses of 1958 mostly less than 137 t month -1 km -2 and in those Fig. 5 Spatial distribution of soil loss (1956).
XIA Jun, et al.: A Distributed Soil Erosion and Sediment Transport Sub-model in Non-point Source Pollution and Its Application in Guishui Watershed 237 References Fig. 6 Spatial distribution of soil loss (1958). of 1956 mostly more than 502 t month -1 km -2 ; (ii) the hill and mountainous regions with large slope and poor vegetation coverage, have higher soil loss. This change rule of soil loss of 1956 is more clear than that of 1958, which shows that the more soil loss, the clearer change rule; and (iii) in Guishui watershed, the soil losses are mostly from the low mountain and hill, and mainly distribute in the sub-watershed of Xilongwan and Xinhuaying. The soil loss in sub-watershed of Gucheng is rather low, because the vegetation coverage there is high even with many steep mountains. Therefore, the control of soil loss should put emphasis on low mountain and hill area in Guishui watershed. Arnold J G, R Srinivasan, R S Muttiah, J R Williams. 1998. Large area hydrologic modeling and assessment. Part I: Model development. Journal of the American Water Resources Association, 34(1):73 89. Flanagan D C and M A Nearing. 1995. USDA-Water Erosion Prediction Project (WEPP). NSERL Report No.10, USDA-ARS National Soil Erosion Research Laboratory, West Lafayette, Indiana. Heng H H and N P Nikolaidis. 1998. Modeling of nonpoint source pollution of nitrogen at the watershed scale. Journal of the American Water Resources Association, 34(2): 359. Li H E, Shen J. 1996. Nonpoint source pollution mathematical model. Xi an: Northwestern Polytechnical University Press. (in Chinese) Liang T, Zhang X M, Zhang S. 2001. The study of distribution of N, P and heavy metals in Guanting Reservoir and Yongdinghe River. Progress in Geography, 20(4):341 346. Luo W S, Song X Y. 1997. Water environmental analysis and forecast. Wuhan: Wuhan University of Water Conservancy and Hydro- Electric Power. (in Chinese). Ma Y T, Xue J F, Liang T, Xia J, et al. 2006. Research on dissolved nitrogen and phosphorus loading model based on GIS. Environmental Science, 27 (9):1765 1769. Neitsch S L, J G Arnold, J R Kiniry, J R Williams. 2001. Soil and water assessment tool theoretical documentation (2000). Texas: Grassland, Soil and Water Research, Agricultural Research Service. Novotony V, G Chesters G. 1981. Handbook of nonpoint pollution: Sources and management. Van Nostrand Reinhold Company. Soil Conservation Society of America. 1976. Soil erosion: Prediction and control. The Proceedings of A National Conference on Soil Erosion. West Lafayette, Indiana: Purdue University. The Yangtze River Water Resources Commission. 1993. Hydrologic forecast method. Beijing: Water Conservancy and Hydropower Press. (in Chinese) Xue J F. 2003. Research on watershed distributed nonpoint source pollution hydrodynamics model. Doctoral Dissertation, Wuhan University. Xue J F and Xia J. 2007. Research on runoff sub-model of non-point source pollution model. Water International, 32(3), 428 438. Young R A, C A Onstad, D D Bosch and W P Anderson. 1989. AGNPS: A nonpoint source pollution model for evaluating agricultural watersheds. J. Soil and Water Conservation, 44(2):168 172. 分布式土壤侵蚀和泥沙输移非点源污染子模型及其应用研究 夏军 1 2, 薛金凤 1 中国科学院地理科学与资源研究所陆地水循环及地表过程重点实验室, 北京 100101; 2 武汉大学动力与机械学院水质科学与技术系, 武汉 430072 摘要 : 官厅水库妫水地区土壤侵蚀较为严重 为控制妫水地区的土壤流失非点源污染, 本文建立了一个参数较少 便于应用的分布式土壤侵蚀和泥沙输移子模型 该模型由 USLE 模型和泥沙输移模型组成 首先, 本研究确定了 USLE 中各因子的计算公式, 用该模型计算土壤流失 然后, 将流域概化为河网, 利用曾提出的应用于经 Laplace 变换和逆变换求得的一维水质迁移转化方程的解中的面积汇污系数和 S 曲线之间的关系, 推导得到了分布式泥沙输移模型 最后, 从妫水河流域土壤图 土地利用图中提取地理信息, 以 DEM 为依据, 研究了该模型在妫水河流域的应用 结果表明, 该模型不仅可用于研究非点源泥沙污染, 而且可用于研究流域内土壤侵蚀的空间分布, 为实现农业最佳管理提供科学依据 妫水流域土壤流失主要来自坡度较大 地表植被覆盖差的丘陵和山地, 控制土壤流失应该将重点放在该流域内的丘陵和山地上 关键词 : 非点源污染 ; 分布式模型 ;GIS; 官厅水库 ; 妫水河