Watershed Scale Physically Based Water Flow, Sediment and Nutrient Dynamic Modeling System - Landscape Ecology for Sustainable Environment and Culture - page 142

Table 8.1 Processes and approximation techniques in the GSSHA model

Process Approximation

Precipitation distribution Thiessen polygons (nearest neighbor) Inverse

distance-squared weighting

Snowfall accumulation and melting Energy balance

Precipitation interception Empirical two parameter

Overland water retention Specified depth

Infiltration Green and Ampt (GA) Multi-layered GA Green and

Ampt with Redistribution (GAR) Richard's
equation (RE)

Overland flow routing 2-D diffusive wave

Channel routing 1-D diffusive wave, 1-D dynamic wave

Evapo-transpiration Deardorff Penman-Monteith with seasonal canopy

resistance

Soil moisture in the vadose zone Bucket model RE

Lateral groundwater flow 2-D vertically averaged

Stream/groundwater interaction Darcy's law

Exfiltration Darcy's law

to improve stability, and allow interaction between the surface and subsurface
components of the model. The combination of improvements in the stability of the
overland and channel routing schemes has allowed significant increases in model
computational time steps over previous versions.

8.2.1.1 Overland Flow Routing

Water flow across the land surface is shallow, unsteady, and non-uniform. This
flow regime can be described by the Saint-Venant equations which are derived
from physical laws regarding the conservation of mass and momentum. Overland
flow routing in GSSHA employs the 2D diffusive wave equation, which allows for
backwater and reverse flow conditions. The 2D (vertically integrated) continuity
equation for gradually-varied flow over a plane in rectangular (x, y) coordinates is
(Julien et al. 1995 ):

@ h

@ t þ @ q x @ x þ @ q y @ y ¼ i e

ð 8 : 1 Þ

where h = surface water depth [L], q x , q y = unit discharge in the x- or y-direc-
tion = Q x /B x ,Q y /B y [L 2 /T], Q x , Q y = flow in the x- or y-direction [L 3 /T], B x ,
B y = flow width in the x- or y-direction [L], i e = excess net precipitation rate [L/T].
The diffusive wave momentum equations for the x- and y-directions are written

as:

S fx ¼ S 0x @ h
@ x

ð 8 : 2a Þ