Transmission Losses

Many semiarid and arid watersheds have ephemeral channels that abstract large quantities of streamflow (Lane, 1982). The abstractions, or transmission losses, reduce runoff volume as the flood wave travels downstream. Chapter 19 of the SCS Hydrology Handbook (Lane, 1983) describes a procedure for estimating transmission losses for ephemeral streams which has been incorporated into SWAT+. This method was developed to estimate transmission losses in the absence of observed inflow-outflow data and assumes no lateral inflow or out-of-bank flow contributions to runoff.

The prediction equation for runoff volume after transmission losses is

$vol_{Qsurf,f}=\begin {cases} 0 & vol{Qsurf,i} \le vol_{thr} \\ a_x+b_x*vol_{Qsurf,i} & vol_{Qsurf,i} > vol_{thr} \end{cases}$ 2:1.5.1

where $vol_{Qsurf,f}$ is the volume of runoff after transmission losses ($m^3$), $a_x$ is the regression intercept for a channel of length $L$ and width $W$ ($m^3$), $b_x$ is the regression slope for a channel of length $L$ and width $W$, $vol_{Qsurf,i}$,$i$ is the volume of runoff prior to transmission losses ($m^3$), and $vol_{thr}$ is the threshold volume for a channel of length $L$ and width $W$ ($m^3$). The threshold volume is

$vol_{thr}=-\frac{a_x}{b_x}$ 2:1.5.2

The corresponding equation for peak runoff rate is

$q_{peak,f}=\frac{1}{(3600*dur_{flw})}*[a_x-(1-b_x)*vol_{Qsurf,i}]+b_x*q_{peak,i}$ 2:1.5.3

where $q_{peak,f}$ is the peak rate after transmission losses ($m^3$/s), $dur_{flw}$ is the duration of flow (hr), $a_x$ is the regression intercept for a channel of length $L$ and width $W$ ($m^3$), $b_x$ is the regression slope for a channel of length $L$ and width $W$, $vol_{Qsurf,i}$ is the volume of runoff prior to transmission losses ($m^3$), $q_{peak,i}$ is the peak rate before accounting for transmission losses ($m^3$/s). The duration of flow is calculated with the equation:

$dur_{flw}=\frac{Q_{surf}*Area}{3.6*q_{peak}}$ 2:1.5.4

where $dur_{flw}$ is the duration of runoff flow (hr),$Q_{surf}$ is the surface runoff (mm H$_2$O), $Area$ is the area of the subbasin (km$^2$), $q_{peak}$ is the peak runoff rate (m$^3$/s), and 3.6 is a conversion factor.

In order to calculate the regression parameters for channels of differing lengths and widths, the parameters of a unit channel are needed. A unit channel is defined as a channel of length $L$= 1 km and width $W$= 1 m. The unit channel parameters are calculated with the equations:

$k_r=-2.22*ln[1-2.6466*\frac{K_{ch}*dur_{flw}}{vol_{Qsurf,i}}]$ 2:1.5.5

$a_r=-0.2258*K_{ch}*dur_{flw}$ 2:1.5.6

$b_r=exp[-0.4905*k_r]$ 2:1.5.7

where $k_r$ is the decay factor ($m^{-1}$ k$m^{-1}$), $a_r$ is the unit channel regression intercept ($m^3$), $b_r$ is the unit channel regression slope, $K_{ch}$ is the effective hydraulic conductivity of the channel alluvium (mm/hr), $dur_{flw}$ is the duration of runoff flow (hr), and $vol_{Qsurf,i}$ is the initial volume of runoff ($m^3$). The regression parameters are

$b_x=exp[-k_r*L*W]$ 2:1.5.8

$a_x=\frac{a_r}{(1-b_r)}*(1-b_x)$ 2:1.5.9

where $a_x$ is the regression intercept for a channel of length $L$ and width $W$ ($m^3$), $b_x$ is the regression slope for a channel of length $L$ and width$W$,$k_r$ is the decay factor ($m^{-1}$ k$m^{-1}$), $L$ is the channel length from the most distant point to the subbasin outlet (km), $W$ is the average width of flow, i.e. channel width (m) $a_r$ is the unit channel regression intercept ($m^3$), and $b_r$ is the unit channel regression slope.

Transmission losses from surface runoff are assumed to percolate into the shallow aquifer.

Table 2:1-7: SWAT+ input variables that pertain to transmission loss calculations.

Variable Name	Definition	Input File
SUB_KM	Area of the subbasin (km$^2$)	.sub
HRU_FR	Fraction of total subbasin area contained in HRU	.hru
CH_K(1)	$K_{ch}$: effective hydraulic conductivity (mm/hr)	.sub
CH_W(1)	$W$: average width of tributary channel (m)	.sub
CH_L(1)	$L$: Longest tributary channel length in subbasin (km)	.sub