Chen Huaisheng Shen Tsan-hsin
The Watershed Modelling of Runoff Processes and Sediment Processes in Soil Erosion Region (WMRPSP) systematically considers most of the factors regarding water and sediment processes. It focuses on the physical regularity and numerical relationship among those factors from input to output.
To simulate the runoff and sediment processes practically, the WMRPSP keeps close consideration with the land geographical characteristics.
(1)it considers the distribution of precipitation by using the Precipitation Distributing Model (PDM);
(2)it considers the differences of soil which impact the infiltration rate by distinguishing the soil into classes;
(3)it considers the forest distribution and its covering characters which impact the evaporation, transpiration and rainfall interception, and which also impact the surface runoff and infiltration rate by field investigations;
(4)it considers the difference of land use, such as land used for paddy field, for vegetable field, for reservoirs and for impermeable surface (e.g. cement ground);
(5)it considers the difference of soil layers and classifies them into three different layers in modellings;
(6) it considers the flow convergence from different parts of the watershed by using the Flow Transferring Modelling (FTM);
(7)it considers that runoff is the source factors of sediment movement, so the Sediment Processes Modelling (SPM) is operated on the basis of Runoff Process Modelling (RPM).
As the WMRPSP closely reflects the natural peculiarities of the watershed, it can be easily applied to other watershed by changing the concerning parameters. Thus, it is significant in the prediction of the future situation of a planned watershed, or in the assessment of some watershed projects (e.g. forestation, urbanization) and their feasibilities.
1 Geographical Identities of Soil Erosion Regions
As a product of the combination of human activities and natural actions, soil erosion reveals both naturality and sociality.
On one hand, soil erosion usually locates on the area in which the bed rock is soft, the slope is over 25°，the forest cover is poor and rainfall distribution is obviously unbalance in a year. The weakly soil anti-erosion ability and the heavy rainfall erosion potentiality are the natural force of erosion.
In accordance with the formation and the processes of erosion, soil erosion may include three types:
(1)Surface Erosion- as the initial process of erosion, surface erosion occurs on land surface along with the overland flow, it usually takes place on the land surface which is lack of grass cover (Occasionally with few trees). It frequently locates on upland.
(2)Gully Erosion-as the middle process, it occurs in land gutters along with the flow gathering from around. It is the continuance of surface erosion and frequently locates on the midway of slope with little vegetable cover.
Block Erosion - as the terminal process of erosion, it is the development of gully erosion. It locates on steep slopes and easily collapses by heavy rainfall. If it happened, it would cause heavy damage. So, it is the most dangerous in erosion area in South China.
2 Runoff Processes in Soil Erosion Area
There are some particularities of runoff processes in the soil erosion area due to the particular soil characters and surface condition.
2.1 Runoff process in no-rainfall period
Because of the less vegetable cover and the less organism in surface soil layer, less water is stored in underground soil layer. Thus, lack of runoff from underground is in the no-rainfall period. In some serious cases, river or stream may become dry.
2.2 Runoff process in rainfall period
Because of the same reason above, infiltration in soil erosion area is quite small. On the contrary, surface runoff and overland flow are plentiful. According to the gathering process of runoff in this period, runoff processes include two stages:
2.2.1 No-surface runoff stage in rainfall period
In the initial period of rainfall, raindrops do not create over-land flow. They are partially evaporated to balance the temperature variation between rain water and soil, and partially permeate through the soil to supply the subsurface water.
2.2.2 Runoff-creating stage in rainfall period
In this period, besides small part of the rainfall going up as vapour into atmosphere, most of which is collected along the bare slope as overland flow. As the amount of overland flow increases, it is turning into ditch flow and rapidly running into stream. Because the infiltration rate is small, surface runoff amount in soil erosion area is larger than that in vegetable area.
2.3 River runoff process
River runoff process is affected by the overland flow collecting process. In dry seasons, river runoff is from subsurface flow and the discharge is small. In flood seasons, significant change of river runoff is caused by the rainfall processes.
3 Sediment Processes in Soil Erosion Area
Sediment migration is caused by flow movement. Thus, the sediment process is much the same as runoff process.
3.1 Sediment movement in no-rainfall period
As no overland flow is created, no sediment from surface is generated. Sediment contented in runoff comes from the river bed, as well as from human activities in some places. But comparing with those in rainy season, sediment runoff in this period is a fraction.
3.2 Sediment movement in rainy period
No sooner had a rain begun, then the sediment on the slope surfaces would be delivered. Corresponding to the runoff processes, sediment processes in this period can also be classified into two stages:
3.2.1 Non-overland flow stage
At the beginning of rainfall, soil surfaces is impacted initially by the raindrop, or the so-called rain impact erosion. Raindrop erosion would not cause significant movement of sediment, but it brings about the free sediment accumulation on the soil surface, which would be transported later by the overland flow.
3.2.2 Overland flow stage
Usually, when rainfall rate is larger than soil infiltration rate, overland flow occurs and rain water moves in both horizontal and vertical directions in stead of in only vertical one. The cover of rain water on the land surface declines the raindrop erosion stress. The overland flow will carry the former accumulated sediment particles of the surface and erodes the surface soil with the shearing stress of its turbulent flow.
Besides the above reason of sediment creation, the interchanging of air between soil and atmosphere in rainy period may break the soil surface structure and release loosen particles.
3.3 Sediment transportation within rivers
River sediment including bed load and suspended load is created by the integrated action of raindrop erosion, overland flow erosion and runoff transportation. Before the sediment runoff runs into streams, due to the alleviation of slope and decrease of flow velocity, large amount of sediment is deposited to the bed along with its process. Therefore, the measured sediment concentration is actually the suspended sediment which does not include the deposited one from regional soil surface.
4 The Watershed Modelling of Runoff Processes and
Sediment Processes in Soil Erosion Area
Comparing with other kinds of lands, soil erosion lands are the main composition of erosion watershed. Different kinds of lands play different parts in watershed runoff and sediment processes. Consequently, different combination of lands in different location results in different characters of runoff and sediment processes. So, it is not scientific to treat erosion watershed as one homogeneous region. By considering of the physical landscapes in watershed, the WMRPSP classifies a watershed into numbers of unique regions that are homogeneous with respect to the process character. Each unique region is described by its relevant sub-model.
4.1 The Makeup of WMRPSP
Fig.1 shows the makeup process of WMRPSP.
4.2 The Composition of WMRPSP
Fig.2 shows the composition of WMRPSP.
4.3 Description of the sub-models of the WMRPSP
4.3.1 Precipitation Distribution Model (PDM)
Since the franctionization of the watershed, different unique regions are located in different places of the watershed. So the limited number of precipitation stations
cannot represent the real rainfall of different unique regions. The PDM is established to simulate this space distribution of rainfall by using space linear interpolation method. The function is:
4.3.2 The Runoff and Sediment Processes Model (RSPM)
The PSPM includes four sub-models:
（1） PSPM sub-model in soil erosion region
The simplized structure of the Runoff Processes sub-model is shown at Fig.3, which omits the surface cover action of the eroded soil surface.
This sub-model use the following equation:
Where,
TF(t) is the total output runoff of the erosion unique region at time “t”;
R1(t) is the surface flow at time “t”;
R3(t) is the subsurface flow at time “t”;
J is the average slope of this region;
H(t) is the average surface water cover depth at “t”;
B is the outlet width of the region;
SK is the infiltration constant from surface to soil;
UGA is the cross area of underground flow outlet;
DH(t) is the underground water head at “t”;
L is the length of the region;
UGK is the infiltration constant of underground soil;
E(t) is the evaporation rate at “t”;
UF(t) is the capillary up-going water at “t”;
E0(t) is the observed evaporation rate by instruments;
EC is the constant of evaporation rate;
BK is the constant of capillary up-going water;
A is the area of the unique region;
UGW(t) is the average water content of soil at “t”;
UGWMAX is the maximum underground water content of the region;
DFMIN is the minimum infiltration rate of the region;
DFMAX is the maximum infiltration rate of the region;
CDF is the infiltration exponent of surface;
P(t) is the precipitation volume at time “t”;
The simplized structure of the Sediment Processes sub-model is shown at Fig.4.
This sub-model uses the following equations:
Where,
SPA(t) is the soil particles accumulated on surface at time “t” (kg);
CSPA is the constant of the function;
F(t) is the raindrop splashing force on unit area at “t” (kg);
CF0 is the constant;
CF1, CF2 are indices which represent the reduction of raindrop splashing force by the accumulation of surface rain water cover.
CH is the hardness exponential which represents the relation between soil wetness and soil hardness;
SSR(t) is the sediment delivered by slope flow at “t” (kg);
CSSR is the constant;
CSV is the sand unit weight, in average, CSV=2.65×10 kg/m3;
SN is the roughness of soil surface;
（2） RSPM sub-models in vegetable covered region
Fig.5 The Structure of Runoff Processes Model in Vegetable covered region.
This sub-model uses the following equations:
WIA(t)=(WIAMAX-WIA(t-1))(1-EXP(-P(t)) (17)
WIG(t)=(WIGMAX-WIG(t-1))(1-EXP(-P(t))) (18)
WIAMAX=CIA×LIA×CWIA×A (19)
WIGMAX=CIG×LIG×CWIG×A (20)
EA(t)=EIA(t)+ ELA(t) (21)
EIA(t)= E0(t)×CIA×LIA×WIA(t)/WIAMAX×A (22)
ELA(t)= E(t)×CIA×LIACEA (23)
EG(t)= EIG(t)×ELG(t) (24)
EIG(t)= E0(t)×CIG×WIG(t)/WIGMAX×A (25)
ES(t)= E(t)×1-CIG (26)
E(t)= E0(t)×EC×BK×SSW(t-1)/SSWMAX (27)
UF(t)= ES(t)+EG(t) (28)
UFF(t)=UF(t)(UGW(t-1)/UGWMAX-SSW(t-1)/SSWMAX) (29)
DF(t)=DFMIN+(DFMAX-DFMIN)×(1-SSW(t-1)/SSWMAX) (30)
DFF(t)=DFFMIN+(DFFMAX-DFFMIN)×(1-UGW(t-1)/UGWMAX) (31)
R1(t)=J×H(t)×B/SK (32)
SKV=SK+CSK×(CIA-CIG) (33)
R2(t)=SSA×SSK×DH(t)/L (34)
R3(t)=UGA×UGK×DH(t)/L (35)
TF(t)=R=1(t)+ R2(t)+ R3(t) (36)
Where,
t is the time (sec.);
WIA(t) is the intercepted water volume by arbor and shrub (m3);
WIG(t) is the intercepted water volume by grass (m3);
WIAMAX is the maximum of WIA (m3);
WIGMAX is the maximum of WIG (m3);
CIA is the arbor and shrub cover percentage (%);
CIG is the grass cover percentage (%);
LIA is the average leafs area of arbor and shrub in unit area (m2/m2);
CEG is the evapotranspiration rate of leaves;
CWIA is the water interception capacity of arbor leaves (m3);
CWIG is the water interception capacity of grass leaves (m3);
EA(t) is the evapotranspiration from arbor and shrub (m3);
EG(t) is the evapotranspiration from grass (m3);
EIG(t) is the evapotranspiration from grass leaves (m3);
ES(t) is the evapotranspiration from soil (m3);
DFMIN is the saturated infiltration rate of soil (mm);
DFMAX is the maximum infiltration rate of soil (mm);
SSW(t) is the water content in soil layer (m3);
SSWMAX is the saturated water content in soil layer (m3);
SKV is the roughness of the vegetable covered region;
CSK is a constant;
SSA is the cross area of the soil flow outlet in the specified region (m2);
SSK is the infiltration constant of subsurface soil layer.
The Sediment Processes sub-model in the vegetable-covered regions is similar to Fig.4. But base on assuming that no soil erosion on the grass-covered surface is occurred while raining, a simple relation may be established as following:
SSR(t)=CSSR×CSV×(H(t)×J) ×A× (1-CIG)/SN (37)
Where, SSR(t) is the sediment delivered by slope overland flow (kg); Other parameters were described above.
（3） RSPM sub-models in paddy field
Paddy fields are managed by mankind. They serve as the reservoirs in planting season and the water in them is operated by the farmers. In unplanting season or in some particular period of the planting season, paddy fields need dry condition and the water drains off if any supply to the fields. Fig.6 shows the structure of RPSM sub-model in paddy fields.
Above parameters can be estimated by following equations:
1） In planting season, surface of paddy field needs water cover:
SW(t)=SW(t-1)+P(t)+IR(t)-E1(t)-R1(t)-DF(t) (38)
PLW(t)=PLW(t-1)+DF(t)+UFF(t)-E2(t)-R2(t)-DFF(t) (39)
UGW(t)=UGW(t-1)+DFF(t)-R2(t)-UFF(t) (40)
E1(t)=EW(t)+EP(t) (41)
EW(t)= E0×EC×A (42)
EP(t)= EW(t)×BK×CIGCEP (43)
E2(t)=0 (44)
DF(t)= R2(t)+DFF(t) (45)
DFF(t)= DFMAX×(1-UGW(t)/UGWMAX)CDEF/GWK (46)
UFF(t)=0 (47)
① Surface flow
If no rainfall occurs, surface flow should be as follow:
R1(t)=SW(t)-SWLIM+E1(t)+DF(t) (48)
Where, SWLIM is the season-limited need of water in field surface (mm);
When R1(t)>0, the paddy field is just in draining, then IR(t)=0; otherwise, when R1(t)>0, the surface water is not enough for crop growth and the irrigation should be taken as IR(t)= -R1(t) if assuming that water is taken from the watershed itself. In this case, the real surface flow is not created.
In rainfall period, surface flow may have two cases:
a. if SW(t)>SWLIM, then R1(t)> SW(t)-SWLIM
b. else, R1(t)=0
② Subsurface flow (occurred in the plough layer of soil)
As the result of field construction, water in the paddy field soil is held by field bank and the plough layer (which is hard and density). The infiltration rate and the difference of water head of it is very small. Its movement can be described by Darcy function (see equation 34).
③Ground water flow
Ground water flow can be illustrated as the same as eqt. 35.
2） n non-planting season, surface of paddy fields needs sunshine:
In this period, surface flow is determined by the surface water storage. Equations which had been applied above in soil erosion region can simulate the processes.
In paddy field, the high content of organism, the well-managed soil surface, the soften slope and the water-covering layer make the soil particles hard to be eroded. But their erosion process modeling can be described as those of erosion region. (eqt. 14-16)
(4) RSPM in reservoir system
Reservoir system includes reservoir land basin and reservoir water area. As managed water body, runoff and sediment process from reservoir outlet are wholly controlled by reservoir operators, who is followed the running rule of the reservoir or according to rainfall. Water level and sediment process in reservoir system is really that of running regulation (see Fig.7):
In above figure, RPM and SPM of land are models of the former described which are determined by the basin land surface character. Total Flow is the input flow from reservoirs watershed to reservoir itself. It includes surface flow, subsurface flow and underground flow. “Water Storage in reservoir” may be simulated by using water equation:
RSV(t)=RSV(t-1)+R(t)+P(t)-RR(t)-E(t)-DFR(t) (49)
Where, RSV(t) is the reservoir stored water volume at time “t” (m3);
RR(t) is the outlet flow of reservoir at time “t” (m3);
E(t) is the evaporation at time “t” (m3);
DFR(t) is the seepage water reservoir bank at time “t” (m3);
The reservoir outlet flow is determined according to the reservoir running rule:
1)When RSV(t) is less than reservoir death storage (RSVMIN), RR(t)=0;
2) When RSV(t) is greater than RSVMIN and less than RSVAVA, which is called the anti-flood water storage of reservoir, RR(t) is equal to reservoir average outlet flow (RAVA).
3) When RSV(t) is greater than RSVAVA and less than reservoir designation maximum capacity (RSVMAX), the operator of the reservoir had to decrease the stored water, so the outlet flow is increased:
RR(t)=(RSV(t)-RSVAVA)×QK +RAVA (50)
Where, QK is the draining rate of the reservoir.
4) When RSV(t) is grater than RSVMAX, then
RR(t)=(RSV(t)-RSVMAX)×QQK(RSV(t)-RSVAVA)×QK+RAVA (51)
Where, QQK is the floor draining rate of the reservoir.
5) Flow Transferring Model (FTM)
After surface, subsurface and underground runoff is created from basin area, it will gather into streams and rivers. The Flow Transferring Modes is designed to simulate this process.
As regions in watershed are partially characterized with their distances from the watershed outlet, the measured data of river flow are the reflect of flow from different places of the basin in different time. Thus, according to the gathering way of water from the watershed, we can divide the watershed into several zones, in which the same interval time will be taken when flow runs to the watershed outlet. The mathematical description is as follow:
Where,
RC(t) is the outlet discharge at time “t” (m3);
R1(t-dt ) is the flow created from region “i” at time “t-dti”;
dt is the time interval of flow transferring from region “i” to the watershed outlet.
n is the total number of region.
(5) Sediment Transferring Model (STM)
When sediment is carried to the stream, sediment movement is changed. On the one hand, stream flow is different from overland flow, it is larger in discharge and relatively steady in flow velocity. On the other hand, solid materials not only move along the stream, but also exchange between stream water and stream bed. Thus, two statuses of sediment movement exist in this process: (1) suspended load and (2) bed load.
As measured the sediment concentration is only response the suspended load, we consider the bed load and the deposit sediment are the loss of water sediment content. In contrary, the sediment floated from bed by flow is the addition of water sediment content. Therefore, the sediment transferring model can be descried as follows:
Where, SA(t) is the calculated suspended load in monitoring section at time “t” (kg);
TRS(t-dt ) is the sediment amount created from range “i” at time “t” (kg);
CS is the sediment depositing rate;
RC(t) is the calculated flow discharge at time “t” on the monitoring section (m );
SRC is the flow carrying parameter.
5 Case Study
In the WMRPSP, we particularly attend to the weight of erosion region in selected basin. Thus, the author selects a typical soil erosion watershed -Wuhua River Basin as the research watershed (see fig.8).
Wuhua basin, located about 115°14′42″E——115°36′30″E and 23°51′00″N ——24°26′40″N, is a famous soil erosion area in Guangdong province, south China. It has an area of 1031 km , in which soil erosion area occupies 232.3 km (27.4% of the basin), the vegetable-covered area covers 565.9 km2(54.92%), paddy field covers 117.2 km2(11.37%) and the reservoir basin accounts for 65.2 km2(6.33%).
Wuhua basin is located in south sub-topical monsoon climatically region with an average annual rainfall of 1475 mm including the maximum rainfall intensity reaching 184 mm/day. The bedrock of the basin is mainly granite which is deeply weathered.
Wuhua basin is also a historical agriculture and population condensed area. Fuel of the basin is totally wood and grass. So the long term overload deforestation has changed the watershed into the most heavy erosion area.
(1) Data
According to the characteristics of physics, geomorphology, topography, geoponics and geology, the Wuhua basin was divided into 52 homogeneous regions. Data concerning these regions were collected from map and field investigations.
Runoff data were measured by Hezikou stream gagging station from 1981 to 1983. Also, data from 8 rainfall monitoring stations were used in modellings verification and simulation.
(2) Parameters
Totally 33 parameters were used in the WMRPSP. They include evapotranspiration rate, interception rate of vegetable, surface roughness, infiltration rate, indices of raindrop splashing force reduction, initial or imitational parameters (e.g. maximum infiltration rate, initial soil water content etc.) and equation constants. All of them have been explained above.
(3) Optimization of Parameters
To rationally obtain the models parameters, the authors select the following equation as the target function to optimizing parameters:
Where, ERR is the target function value of related error between observed value and calculated one. As demand of the model, ERR should be less than 0.2 to represent the optimized parameters are rational;
VO(t) is the observed value at time “t”, which is watershed outlet discharge when optimizing in Runoff Process Model or sub-model, or which is the watershed outlet sediment value when optimizing in the Sediment Process Model;
VC(t) is the calculated a value at time “t”, which has the same means as VO(t) in different model;
tm is the terminal time.
In this case study, we selected 24 floods (1981-1982) by selecting 6 hours as the time interval of calculation to verify the WMRPSP parameters. The simulated results are shown in Fig.9 (a)-(b).
(4) Modelling
Using the verified parameters, we calculated totally 17floods in 1983. As considering ERR<0.2 is passed for error, 1 of 17 floods for runoff and 3 for sediment are out of this limit. So the passed rate is 94.1% in runoff process modeling and 82.4% in sediment process modeling.
6 Conclusion
The WMRPSP is designed to strongly describe the natural processes. And it does prove itself from case study as it has following advantages:
(1)It fully considers the differences in land types in a basin.
(2)It uses real time (continuous) modeling, so it can illustrate the physical process.
(3) It considers the mankind effects on paddy fields and reservoirs.
(4)It also considers rainfall distribution.
(5) Models parameters are relatively steady by analyzing the simulated results. It proves this model is valuable for future prediction (if the land use were changed, the simulated results would be different).
(6)It not only can be used in flood simulating, but also can in dry-seasons flow.simulating (with no rainfall input to be given).
（原载：中泰学会会议论文集（国际会议），1989。）
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