Distributed Overland Flow Modeling

ABE 527Rabi H. Mohtar

Associate Professor

Reference: Applied Hydrology, Chow (Maidment/Mays McGraw-Hill, 1988)

Types of Overland Flow (1)

Hortonian Overland Flow“Neglecting interception by

vegetation, surface runoff is that part of the rainfall which is not absorbed by the soil by infiltration”

Horton, 1933It is also called “rainfall excess” = (r-

i)

Types of Overland Flow (2)

Saturation Overland FlowWhen subsurface flow saturates the

soil near the bottom of a slope and overland flow occurs as rain falls onto saturated flow.

Occurs at bottom of hills and near stream banks. Also on vegetated areas in humid regions.

Deterministic Hydrologic Models

A. Lumped Steady: SCS Curve NumberB. Lumped Unsteady: Unit hydrograph

or Linear System TheoryC. Distributed Steady: Channel flow with

no lateral inflowD. Distributed Unsteady: Channel flow

with lateral inflow, Overland flow.

Flow Routing

DefinitionTo determine the time and

magnitude of flow (hydrograph) at a point on a watercourse from known or assumed hydrographs at one or more points upstream. Can be lumped or distributed.

Lumped Flow Routing

Routing through one point such as the outlet. Continuity equation:

S is Storage, I is the inflow and O is the outflow

( ) ( )dS

I t O tdt

Lumped Flow Routing

Level Pool method (flow through reservoir):

S=f(O)Muskingham method:S is linearly related to I and OLinear Reservoir method:S is a linear function of O and its time

derivatives.

Distributed Overland Flow Routingde Saint Venant Equations:Continuity:

Inflow:

Outflow:

Q=flow entering the control volume of the overland flow section

q=lateral inflow entering the control volume

( ) ( )dS

I t O tdt

( )I Q q x

( )Q

O Q xx

Distributed Overland Flow Routing

Continuity:Storage:

Conservation form

S A x

dS Ax

dt tA Q

qt x

Distributed Overland Flow Routing

Continuity:For a unit width:

Q=Vh and A=h

Nonconservation form

( )( )

h Vhq t

t x

Distributed Overland Flow Routing

Momentum:

Forces:Gravitational Force:

Friction Force:

Pressure Force:

( )d m vF

dt

g oF gAS x

f fF gAS x

p

hF gA dx

t

Distributed Overland Flow Routing

Momentum:

( )d m vF

dt

( )= Momentum Outflow - Momentum Inflow + Stored Momentum

d mv

dt

Distributed Overland Flow Routing

Momentum:Momentum Inflow:

Momentum Outflow:

Stored Momentum:

xQV q xv

QQV x

x

X

Qx