Modified TVGM (Time Variant Gain Model)

Based on the original TVGM, the advanced TVGM is introduced with two separate time variant gain coefficients for two runoff types, i.e., quick flow and baseflow, respectively.

TVGMrunoffquick flowbaseflow

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Quoted fromSong, Jiyun, Jun Xia, Liping Zhang, Zhi-Hua Wang, Hui Wan, and Dunxian She. "Streamflow prediction in ungauged basins by regressive regionalization: a case study in Huai River Basin, China." Hydrology Research 47, no. 5 (2016): 1053-1068. https://doi.org/10.2166/nh.2015.155  

Based on the original TVGM, here we propose an advanced TVGM by introducing two separate time variant gain coefficients for two runoff types, i.e., quick flow and baseflow, respectively. For quick flow:
formula
9
where  is the effective rainfall for generating quick flow, Gs is a time variant gain coefficient for quick flow and can be expressed as:
formula
10
Similarly, baseflow is calculated by:
formula
11
where Rg is the effective rainfall for generating baseflow, Gg is a time variant gain coefficient for baseflow and can be expressed as:
formula
12
In Equations (10) and (12), coefficients g1g2g3, and g4 are constants for a specific watershed.
In addition, unlike the flow routing process by using a single response function for all effective rainfall in the original TVGM as indicated in Equation (3), here we use two separate response functions for routing of quick flow Ys and baseflow Yg, respectively, in correspondence with two time variant gain flow generation mechanisms:
formula
13
formula
14
where us and ug are the response functions for quick flow and baseflow, respectively. These functions are given by:
formula
15
formula
16
Here, n is a numerical parameter indicating the capacity of watershed storage, which is equivalent to the number of linear reservoirs; K is a storage-discharge parameter with the dimension of time (Nash 1957Young & Beven 1991); and Kg is the storage coefficient of ground water with the dimension of time.
Since rainfall data are usually recorded in discrete forms, the analytical forms of instantaneous response functions, i.e., usug, need to be practically discretized for a given duration. The quick flow response function us, viz. the instantaneous unit hydrograph can be discretized using S-curve method (Sherman 1932Cleveland et al. 2008), while the baseflow response ug can be converted into a discrete form through the water balance equation by assuming a linear relationship between ground water storage and discharge (Pedersen et al. 1980Purcell 2006). With commonly adopted unit hydrograph, S-curve and underground linear reservoir, the quick flow Ys and baseflow Yg can be calculated by discrete convolution integrals as:
formula
17
formula
18
where t is the current time step, Tu is the duration of the usc = A/(3.6 × Δt) is a coefficient to transform the unit of runoff volume from m3 s−1 to mm, A is the catchment area in km2, Δt is the time interval in hour, Rs and Rg are effective rainfall in mm, KKG is a coefficient given by KKG = (Kg − 0.5Δt)/(Kg + 0.5Δt).

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Song, Jiyun, Jun Xia and others (2020). Modified TVGM (Time Variant Gain Model), Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/99e5c628-cb77-4d4d-8472-1b7b142d4957
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zhangshuo
Last modify time
2021-01-07
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Initial contribute : 2020-01-05

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zhangshuo
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