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The version of SMARG implemented in Source comes from the CRC for Catchment Hydrology Rainfall-Runoff Library (RRL), where it is referred to as SMAR.
Scientific Provenance
SMARG is the soil moisture and accounting model (SMAR) (O’Connell O’Connell et al., 1970; Kachroo, 1992)
Scientific Provenance
SMARG is SMAR with modification to route surface runoff and the groundwater contribution to the stream separately (Kachroo and Liang, 1992). This modified model is also often referred to in the literature as SMAR rather than SMARG (e.g. Podger, 2004; Tuteja and Cunnane, 1999; Vaze et al., 2004).
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SMARG consists of two components in sequence, a water balance component and a routing component. A schematic diagram of the SMAR SMARG model is shown in Figure 1. The model utilises input time series of daily rainfall and pan evaporation data to simulate stream flow at the catchment outlet. The model is calibrated against observed daily stream flow.
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The surface run-off generated from the landscape is routed (attenuation and lag) to the catchment outlet using the linear cascade model of Nash (1960). The model was obtained as a general solution relating a given input of unit volume to a given output as in equation 1.
| Equation 1 |
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where:
t = simulation time-step (d);
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The generated surface runoff (rs mm·d-1) and the routed runoff (QrT mm·d-1) can be time averaged, as in equations (2) and (3), to represent the daily values.
| Equation 2 |
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| Equation 3 |
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The linear model described by equation 4 (below) is the simplest representation of a causal, time invariant, relationship between an input function of time (generated runoff) and the corresponding output function (routed runoff). It is used in conceptual modelling, as a component, representing the routing or diffusion, effects of the catchment on those components of the rainfall hyetograph contributing to the outflow.
| Equation 4 |
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where:
m = memory of the pulse response function (d).
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The mass balance equation for the groundwater system can be written as in equation 5:
| Equation 5 |
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where:
QTrech = recharge to the groundwater system (mm.s-1).
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The pulse-response function for the groundwater component can be obtained in a manner analogous to equation 1, as in equation 6 (i.e. equation 1 with n and Γ(n) equal to 1; Vaze et al., 2004).
| Equation 6 |
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The recharge QTrech and the discharge QTg can be time averaged to mm·d-1 in an analogous manner to the generated surface runoff (rs) and the routed runoff (QrT), as in equations 2 and 3.
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Table 1. Parameters in SMARG and their default values
| Parameter | Description | Units | Default | Range |
|---|---|---|---|---|
| C | Evaporation coefficient | none | 0 | 0-1 |
| G | used to estimate the proportion of moisture in excess of soil moisture storage capacity recharging groundwater (and also discharged to the stream) | none | 0 | 0-1 |
| H | used to estimate the proportion of rainfall excess contributing to the generated runoff as saturation excess runoff or the Dunne runoff | none | 0 | 0-1 |
| Kg | Time lag parameter for groundwater routing | none | 0.01 | 0.01-200 |
| n | Surface runoff hydrograph ‘shape’ parameter (i.e. number of linear reservoirs) | none | 1 | 1-10 |
| nK | Surface runoff hydrograph ‘scale’ parameter (i.e. time lag parameter in Nash cascade model) | none | 1 | 1-10 |
| T | Ratio of potential evapotranspiration to pan evaporation | none | 0 | 0-1 |
| Y | Infiltration capacity of the soil | mm.d-1 | 0 | 0-100 |
| Z | Effective moisture storage capacity of the soil contributing to the runoff generation mechanisms | mm |
| 200 | 0-125 |
| Info | ||
|---|---|---|
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| Note: the number of soil layers is determined from "Z" (Soil Moisture Storage Capacity) and a constant in the code which is 25 mm (the depth of each of the "groundwater"/soil layers in mm of water). |
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Table 2. Recorded variables
| Variable | Parameter | Frequency | Notes |
|---|---|---|---|
| PET | Potential evapotranspiration | time-step |
| x | Excess rainfall | time-step | see Figure 1 |
| INF | Infiltration | time-step | Estimated from (1-H’)x (see Figure 1) |
| r1 | Direct runoff | time-step | see Figure 1 |
| r2 | Rainfall in excess of infiltration capacity (Hortonian runoff) | time-step | see Figure 1 |
| r3 | Moisture in excess of soil moisture capacity discharged to stream | time-step | see Figure 1 |
| r9 | Moisture in excess of soil moisture capacity recharging (percolating to) groundwater | time-step | see Figure 1 |
| rs | Generated surface runoff | time-step | see Figure 1 |
| QOUTsurf | Routed surface runoff (from gamma function) | time-step | see Figure 1 |
| QOUTgw | Routed groundwater runoff | time-step | see Figure 1 |
| SMStot | Soil moisture store contents (total of all layers) | time-step | see Figure 1 |
Reference list
Kachroo, R.K. (1992). River flow forecasting. Part 5. Applications of a conceptual model, Journal of Hydrology, 133: 141–178.
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Vaze, J., Barnett, P., Beale, G., Dawes, W., Evans, R., Tuteja, N.K., Murphy, B., Geeves, G., and Miller, M. (2004). Modelling the effects of land-use change on water and salt delivery from a catchment affected by dryland salinity in south-east Australia, Hydrological Processes, 18: 1613–1637.