4.2 Models
4.2.2 HYMOD
HYMOD is a simple conceptual model. This model has two main components, namely the rainfall excess (two parameters) and two series of linear reservoirs (three parameters, three identical quick and single for the slow response) in parallel as routing components.
The model is based on the characteristics of the runoff production process at a point in a catchment and then a probability distribution which describes the spatial variation in the catchments is derived by algebraic expression (Moore,1985). This model makes an assumption that the soil structure and texture, water storage capacity vary across the catchment, therefore, the distribution function of different storage capacity is described as
F(C) = 1−(C/Cmax)β0≤C ≤Cmax (4.11) The model structure is shown in Figure 4.10. The five parameters of this model are:
the maximum storage capacity in the catchment (Cmax), the degree of spatial variability of the soil moisture capacity within the catchment (β), the factor distributing the flow between the two series of reservoirs (α), and the residence times of the linear reservoirs (Rq) and (Rs). Additional information about the HYMOD model in general can be found inMoore(1985), Boyle et al.(2001) and Wagener et al. (2001). In this research, the HYMOD model was modified by adding snow routing. The degree day method was used to calculate snow accumulation and snow melt. The range of parameters is given in Table4.7.
Excess
α
Storage
Model Discharge
β Rs
P ET
Cmax
Rq
Rs
Rq Rq
SOIL MOISTURE ACCOUNTING ROUTING
Figure 4.10: Schematic representation of the HYMOD model
4.2 Models
Parameter Description Max Min
Cmax Maximum storage capacity 600.000 150.000 Beta Degree of spatial variability of the soil
moisture capacity
8.000 3.000
Alpha Flow distributing factor 0.800 0.200
RS Residence times of the slow reservoirs 0.200 0.010 RQ Residence times of the quick reservoirs 0.700 0.300 Th Threshold temperature for snow melt
initiation
1.500 -1.000
DD Degree-day factor 3.000 1.000
Dew Precipitation/degree-day relation 2.000 0.000
Table 4.7: Model parameters range for the HYMOD
4.2.3 Three reservoirs model
The conceptual three reservoirs model was developed by Jain (1993). The concept of the model described byJain(1993) andSingh et al.(2009), is given here. In this model, rainfall-runoff process is conceptualized by three reservoirs. The catchment is represented with the help of three storages. The first storage, termed as surface storage, represents the water stored in the surface and top few centimeters of soil of the catchment. It has a maximum storage capacity given by Smax. The second storage represents the catchment soil moisture storage and has a maximum water holding capacity given by Cmax. The third storage represents the ground water storage. The possible range of model parameters is given in Table 4.8.
Parameters Description Maximum Minimum Unit
Smax Maximum storage capacity 500 5 mm
Cmax Maximum water holding capacity 1500 15 mm
F(C) Threshold 0.90 0.1
-Finf Factor 0.99 0.001
-Cint Coefficient 0.99 0.001
-Table 4.8: The possible range of the three reservoirs model parameters
The rainfall is input to the surface storage. The water leaves this storage through evaporation, infiltration or overland flow. The moisture content of this storage at any time is denoted by SURF. So as long as SU RF > Ep∗dt (Ep is potential evaporation in mm/hr), the actual evapotranspiration (ET) is at the potential rate, else ET takes place at the lower storage at some lesser rate. If SURF = 0, the ET commences from the soil storage at a rate of Ea (mm/hr) given by
Ea= Csoil
Cmax
∗Ep (4.12)
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Csoil=Csoil−Ep∗dt
IfSU RF < Ep∗dt, the actual ET isSU RF +Ea∗dt where Ea is calculated using Eq.
4.12and dt is length of computation interval in hour. The maximum value ofEa isEp. Infiltration of water from the surface storage to the soil storage takes place at the rate Infil:
Inf il= (1− Csoil Cmax
)∗Finf if SU RF >0 (4.13)
= 0 otherwise
Csoil=Csoil+Inf il∗dt
whereFinf is a factor (mm/hr) controlling the infiltration rate. If SU RF > Smax, the excess water overSmax flows as overland flow (OF). The OF is routed through a linear reservoir LR1 with time constantK1. Water infiltrating from the surface storage enters the soil storage from which outflow this storage can take place through evapotranspira-tion losses, interflow or recharge to the ground water zone.
If the contents of soil storage are greater than a threshold denoted by FC, moisture flows out of it as interflow and recharge to groundwater. The excess moisture available for these two is:
Exw= (Csoil
Cmax
−F C)∗Ewf if Csoil
Cmax
> F C (4.14)
Csoil =Csoil−Exw∗dt
where Ewf is a factor (mm/hr) controlling the volume of excess water. The interflow rate is given as :
IntF =Exw∗Cint (4.15)
and the rate of recharge to groundwater is
RR=Exw∗(1−Cint) (4.16)
whereCintis a dimensionless coefficient which controls how much of the excess moisture goes as recharge and how much as interflow. The interflow is routed through a linear reservoir LR2 with time constantK2. The ground water zone behaves as a linear reservoir whose time constant is KG. The moisture comes out of it as the baseflow (BF).
The flow coming out of the reservoirs LR1, LR2 and LR3 is combined and then routed through a linear reservoir, LR4, to yield the discharge from the catchment, denoted by Qt. The systematic representation of the model structure is given in Figure4.11.
4.2 Models
1 Surface storage SURF
Smax
Cmax Soil storage Csoil
Ground water storage (LR3)
LR 1
LR 2 LR 4
OF
IntF BF
Qt
Precipitation Ep
E
Figure 4.11: Structure of the three reservoirs model (Jain,1993)
4.2.4 Water Flow Balance Simulation Model-WaSiM-ETH
WaSiM-ETH is a physically grid-based and spatially distributed model. Spatial and temporal variability of hydrological process in a complex watershed can be represented by this model (Schulla and Jasper, 2007). This is kind of a physically-based model, where data requirement is low. It consists of several modules: For example, a mod-ule for correction and interpolation of meteorological data, evapotranspiration model, snow model, interception model, infiltration model, soil model, discharge routing model, groundwater model, irrigation model and transport model. To conceptualize some mod-ules, several alternative are available. For instance, inverse-distance-weighting method or altitude dependent regression method can be chosen for interpolation of meteorological data. Similarly, for the calculation of potential evapotranspiration, Penman-Monteith approach, Wendling approach and Hamon approach can be chosen. WaSiM-ETH has two versions, namely TOPMODEL approach after Beven and Kirkby (1979) in the soil model, and secondly the RICHARDS equation for describing the water flow within the unsaturated soil. In this research the TOPMODEL approach is used. The model struc-ture is shown in figure4.12.
The basic input required in WaSiM-ETH is given in table4.9, which includes both spatial and temporal data. Some of the input data needed to be preprocessed. There are several tools available e.g. TANALYS (Terrain Analysis). For more details about WaSim-ETH, refer to Thapa (2009);Liang (2010) and Schulla and Jasper (2007).
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Figure 4.12: Structure of WaSiM-ETH using TOPMODEL approach (Liang,2010)
Categories Subcategories
Spatial
DEM Slope, watershed, flowtime, routing parameters, exposition . . . Land use Albedo, leaf area index,
vegetation, root depth Soil properties
Field capacity, saturated hydraulic conductivity, drainable porosity, soil
topographic index, suction head Temporal Meteorological data
Precipitation, temperature, global radiation, relative sunshine duration,
wind speed, humidity Hydrological data Subcatchments runoff
Table 4.9: Input data for WaSiM-ETH model