Hydrology Studio employs the Modified Att-Kin (Attenuation Kinematic) and the Muskingum-Cunge methodologies for channel reach routing.

Both theories are based on a discharge-flow area relationship where:

The equations and formulas used to compute x and m are further described in Technical Release 20 (TR-20). Hydrology Studio allows you to optionally directly enter these variables when using the Modified Att-Kin method.

## Modified Att-Kin

The Modified Att-Kin method’s procedures are as follows:

Where:

Ot + dt = outflow at time t+dt

Ot = outflow at time t

It = inflow at time t

C = routing coefficient

The routing coefficient is computed as:

Where:

dt = time interval in seconds or hours

K = L/(mV)

Where:

L = channel reach length (ft)

m = factor relating average velocity and wave velocity (celerity)

V = average velocity (ft/s)

## Muskingum-Cunge

The Muskingum-Cunge routing procedure has been incorporated into the NRCS TR20 hydrologic model. It will typically give higher peak flows than the Modified Att-Kin method. Both methods are more appropriate for modeling long channels.

Muskingum-Cunge computes outflows using four primary coefficients as shown in the following equation:

Where:

O2 = Outflow discharge at time 2

O1 = Outflow discharge at time 1

Where:

dt = time interval in seconds

K & X are constants determined from:

Where:

L = length of the channel reach

m = factor relating average velocity and wave velocity (celerity)

V0 = average velocity

Where:

Q = peak inflow

T0 = top width at Q

S0 = longitudinal slope