Background: In assignment #$13$ you determined the CN values for the four subbasins in Happyland Watershed. The next step is to compute TL for each subbasin, compute two mainstem channel inputs, put all values into a model input file, and finally run HEC$-1.$

Field Data: Use map and data for Happyland River watershed on Figure $1$ from assignment #$13.$ You do not need the soils and land cover maps for this assignment.

The time lag $($TL$)$ is the time it takes rain water falling on a subbasin to reach the outlet of that subbasin. It is a function of overland flow and channel flow, using the longest channel path in the subbasin $($not necessarily the mainstem channel$).$ TL may be estimated using an empirical equation derived for a region, such as the one you have been provided with at the bottom of Figure $1.$ Note units!!!

The other part of the assignment is obtaining the two inputs you have to add for the RD line of your model.

Assignment:

$1.$ Calculate TL in hours using the empirical equation I provided with the maps.

a$.$ Use n$=0\mathrm{.}07$ for overland flow roughness, since hillslopes have a lot of frictional vegetation.

b$.$ Variables L and Lca need to be determined for the longest flow path in each subbasin, which is not necessary the same as the longest path along the mainstem river from D to C to B to A$.$ You have to assess each subbasin for yourself.

c$.$ L is the length of the longest stream in each subbasin, so one you find that path, then add up the stream lengths to get the total length for each subbasin.

d$.$ Lca is different. Make a copy of Figure $1$ and cut out each subbasin with scissors. Now gently prop a subbasin on the tip of a pin and try to find the exact spot where the paper is evenly balanced all around so it does not fall off. Push the pin through that point. This is the $$centroid$$ of the subbasin.

e$.$ Once you know the centroid, then draw a line from that point to the longest stream, but go to the point on the stream that yields a perpendicular junction between your line and the stream itself. We do not care about the length of the perpendicular line itself; it is just a tool to find the junction point. This junction point marks one end and the point at the mouth of the subbasin is the other. Lca is the length along the stream between these two points. It is called the stream length to the subbasin centroid. Again, it is not the length of the perpendicular line, but the length along the stream.

f$.$ Calculate the slope along the stream using the elevations at the points in the watershed. Slope is the difference in elevation divided by stream length between those points. Note that S needs to be calculated in units of feet$/$mile$.$

$2.$ Once water is at a subbasin outlet, it must be routed to the outlet of the whole basin through the river network. This relies on the RD line in the input file. To do this you need to know the channel length $($units of feet!!!$),$ slope $($units of feet$/$feet$!!!),$ and bed roughness $($n$)$ of the mainstem river. This is not the same as what you just calculated for TL$,$ because that was an empirical equation I gave you $($not built into HEC$-1)$ for converting rainfall across the subbasin into runoff at the subbasin outlet. Instead, the RD line is seeking to know the roughness of the mainstem channel to move water between points A$,$ B$,$ C$,$ and D$.$ Use the information in Figure $1$ to determine L and S for each segment of the mainstem river $($e$.$g$.$ D to C$,$ C to B$,$ and B to A$),$ but now converting the numbers to units of feet and feet$/$feet$,$ respectively. Use $0\mathrm{.}04$ as the n value for the mainstem river. Put these values onto the RD lines where needed.

$3.$ If you are at all confused at this point about the numbers, their units, where they go$,$ or what they mean, then please open the HEC$1.$PDF file, which is the manual, and go to the end where there is an appendix with an alphabetical listing of all lines by its two$-$letter designator. That appendix explains what each line requires.

$4.$ Open the HEC$-1$ input file named $$wgin$.$dat$.$

a$.$ Comparing to assignment #$12,$ you should recognize the information related to each subbasin in terms of the BA$,$ PB$,$ PI$,$ LS$,$ and UD lines. Those are the lines you should already understand from that assignment, but now we are also adding in another line for you, the RD line. Note that there are more PI lines here, because it is a longer storm with smaller fractions of rain in each $15-$minute interval. Note that each subbasin has its own set of these lines.

b$.$ We have already established that the storm will be $3$ of rain and it will fall uniformly over all subbasins at the same time. That is what the PB and PI lines are tell you.

c$.$ Using the data from assignments #$13$ and #$14$ as well as the information on Figure $1$ from assignment #$13,$ type the values for the BA$,$ PB$,$ PI$,$ LS$,$ and UD lines into the wgin.dat file.

d$.$ Next, the new lines in this file for you to learn about and work with are the RD and HC lines.

e$.$ RD lines control the routing for flow down the mainstem channel. They