## 2.14.2. Routing Processes[¶](#routing-processes "Permalink to this headline")
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MOSART divides each spatial unit such as a lat/lon grid or watershed into three categories of hydrologic units (as shown in [Figure 2.14.1](#figure-mosart-conceptual-diagram)): hillslopes that convert both surface and subsurface runoff into tributaries, tributaries that discharge into a single main channel, and the main channel that connects the local spatial unit with upstream/downstream units through the river network. MOSART assumes that all the tributaries within a spatial unit can be treated as a single hypothetical sub-network channel with a transport capacity equivalent to all the tributaries combined. Correspondingly, three routing processes are represented in MOSART: 1) hillslope routing: in each spatial unit, surface runoff is routed as overland flow into the sub-network channel, while subsurface runoff generated in the spatial unit directly enters the sub-network channel; 2) sub-network channel routing: the sub-network channel receives water from the hillslopes, routes water through the channel and discharges it into the main channel; 3) main channel routing: the main channel receives water from the sub-network channel and/or inflow, if any, from the upstream spatial units, and discharges the water to its downstream spatial unit or the ocean.

[![Image 1: ../../_images/mosart_diagram.png](https://escomp.github.io/ctsm-docs/versions/master/html/_images/mosart_diagram.png)](https://escomp.github.io/ctsm-docs/versions/master/html/_images/mosart_diagram.png)

MOSART only routes positive runoff, although negative runoff can be generated occasionally by the land model (e.g., \\(q\_{gwl}\\)). Negative runoff in any runoff component including \\(q\_{sur}\\), \\(q\_{sub}\\), \\(q\_{gwl}\\) is not routed through MOSART, but instead is mapped directly from the spatial unit where it is generated at any time step to the coupler.

In MOSART, the travel velocities of water across hillslopes, sub-network and main channel are all estimated using Manning’s equation with different levels of simplifications. Generally the Manning’s equation is in the form of

(2.14.1)[¶](#equation-14-1 "Permalink to this equation")\\\[V = \\frac{R^{\\frac{2}{3}} S\_{f}}{n}\\\]

where \\(V\\) is the travel velocity (m s \-1 ), \\(R\\) is the hydraulic radius (m). \\(S\_{f}\\) is the friction slope that accounts for the effects of gravity, friction, inertia and other forces on the water. If the channel slope is steep enough, the gravity force dominates over the others so one can approximate \\(S\_{f}\\) by the channel bed slope \\(S\\), which is the key assumption underpinning the kinematic wave method. \\(n\\) is the Manning’s roughness coefficient, which is mainly controlled by surface roughness and sinuosity of the flow path.

If the water surface is sufficiently large or the water depth \\(h\\) is sufficiently shallow, the hydraulic radius can be approximated by the water depth. This is the case for both hillslope and sub-network channel routing.

(2.14.2)[¶](#equation-14-2 "Permalink to this equation")\\\[R\_{h} = h\_{h} R\_{t} = h\_{t}\\\]

Here \\(R\_{h}\\) (m) and \\(R\_{t}\\) (m) are hydraulic radius for hillslope and sub-network channel routing respectively, and \\(h\_{h}\\) (m) and \\(h\_{t}\\) (m) are water depth during hillslope and sub-network channel routing respectively.

For the main channel, the hydraulic radius is given by

(2.14.3)[¶](#equation-14-3 "Permalink to this equation")\\\[R\_{r} = \\frac{A\_{r}}{P\_{r}}\\\]

where \\(A\_{r}\\) (m 2 ) is the wetted area defined as the part of the channel cross-section area below the water surface, \\(P\_{r}\\) (m) is the wetted perimeter, the perimeter confined in the wetted area.

For hillslopes, sub-network and main channels, a common continuity equation can be written as

(2.14.4)[¶](#equation-14-4 "Permalink to this equation")\\\[\\frac{dS}{dt} = Q\_{in} - Q\_{out} + R\\\]

where \\(Q\_{in}\\) (m 3 s \-1 ) is the main channel flow from the upstream grid(s) into the main channel of the current grid, which is zero for hillslope and sub-network routing. \\(Q\_{out}\\) (m 3 s \-1 ) is the outflow rate from hillslope into the sub-network, from the sub-network into the main channel, or from the current main channel to the main channel of its downstream grid (if not the outlet grid) or ocean (if the current grid is the basin outlet). \\(R\\) (m 3 s \-1 ) is a source term, which could be the surface runoff generation rate for hillslopes, or lateral inflow (from hillslopes) into sub-network channel or water-atmosphere exchange fluxes such as precipitation and evaporation. It is assumed that surface runoff is generated uniformly across all the hillslopes. Currently, MOSART does not exchange water with the atmosphere or return water to the land model so its function is strictly to transport water from runoff generation through the hillslope, tributaries, and main channels to the basin outlets.

