Water Balance Equation

Soil and Water Assessment Tool
(SWAT)
SWAT is a public domain model actively supported by the USDA Agricultural
Research Service at the Grassland, Soil and Water Research Laboratory in
Temple, Texas, USA.
http://www.brc.tamus.edu/swat/
SWAT is a river basin scale model developed to quantify the impact of land
management practices in large, complex watersheds
Water Balance Equation
SWt = SW + (Rday-Qi-Ea-Pi-QRi)
Where:
SW: soil water content
T: time
Rday: amount of precipitation
Qi: amount of surface runoff
Ea: amount of evapotranspiration
Pi: amount of percolation
QRi: amount of return flow
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SWAT (Soil and Water Assessment Tool) Model
Parameter
Surface Runoff/Initial losses
Recharge
Transmission Losses
Infiltration
Channel Routing
Evapotranspiration
Manning’s Coefficient
Method
SCS Curve Number
Venetis & Sangrey
function of K,TT,P, and L
SCS Curve Number
Muskingum Routing
Penman-Monteith Eq.
Jarret Procedures
Surface Runoff/Initial losses
Initial losses: losses before precipitation
reaches the stream
Two methodologies:
(1) SCS Curve Number Procedure (SCS, 1972)
(2) (2) Green & Ampt Infiltration Method (1911)
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Initial Abstraction
• Surface storage (ponding)
• Interception (by plants)
• Infiltration prior to runoff
Curve Number
• SCS Engineering Division, 1986 tested a
list of soils with varying landuse, soil types
and Antecedent Water Content (AWC).
• Assigned CNs and provided a lookup table
for these numbers all based on daily
conditions.
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SCS Curve Number
SCS Curve Number (CN)
• Function of soil
permeability, land use,
and antecedent soil
water conditions
(losses)
• 4 Hydrologic groups
based on infiltration
capability
Antecedent Soil Moisture Condition
Soil retains a degree of moisture after a rainfall event. This residual
water moisture affects the soil's infiltration capacity. During the next
rainfall event, the infiltration capacity will cause the soil to be
saturated at a different rate. The higher the level of antecedent soil
moisture, the more quickly the soil becomes saturated. Once the soil
is saturated, runoff will occur.
Three types:
• I – dry (wilting point)
• II – average (field capacity)
• III – wet (oversaturated)
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Hydrologic Groups
Groups that share similar runoff/infiltration
potential
• A = High Infiltration/Low Runoff (e.g. alluvial
deposits)
• B = Moderate (e.g. sandstone)
• C = Slow/Low (e.g., massive LS)
• D = Very Low Infiltration/High Runoff (e.g.,
basement)
Distribution of
Soil types (CNs)
Quaternary: 63
Nubian Sandstone: 77
Tertiary LS: 98
Precambrian: 98
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Why not the Green and Ampt Method?
• Too many assumptions that don’t work for
arid areas.
• Predict infiltration assuming excess water
at the surface at all times
• Soil profile is homogenous and AM is
uniformly distributed in the profile.
G & A Schematic
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Losses in the stream
Transmission Losses
tloss = K * TT * P *
ch
ch
L
ch
Kch = Hydraulic Conductivity
TT = Travel Time
Pch = Wetted perimeter of channel
Lch = Length of channel
Evapotranspiration
Evapotranspiration
Evaporation
Transpiration
Vegetation
Open Water Soil Plants
Surfaces
Source: Ward and Trimble 2004
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Controlling Factors
• Energy availability
• Wind speed
• Moisture gradient
1) Temperature
2) Humidity
• Vegetation
• Precipitation
Penman-Monteith Equation
• Comprehensive expression: Combines
components that account for energy needed to
sustain evaporation, strength of the
mechanism required to remove the water and
aerodynamic and surface resistance terms.
• Assume minimal to no transpiration and
canopy interception
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Why not the Priestley-Taylor Method?
• Simplified version of the combination
equation for use when surface areas are
wet.
• Aerodynamic component was removed
and a fudge factor was added to the
energy component.
Why not the Hargreaves Method?
• Least accepted method
• Only accounts for the energy component
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Water Routing
SWAT deals with routing water in volumes
of water
Two Methods:
(1) Variable Storage Method
(2) Muskingum Routing Method
Channel Characteristics
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Muskingum Routing Method
Accounts for flooding by modeling storage
volume in a channel length as a
combination of wedge and prism storages
Manings Equation used throughout
routing
• Calculates open channel
flow
• Introduced by the Irish
Engineer Robert Manning
in 1889.
• The Mannings equation is
an empirical equation that
applies to uniform flow in
open channels and is a
function of the channel
velocity, flow area and
channel slope.
Where:
Q
v
A
n
R
S
Use SWAT default value
Flow Rate, (ft3/s)
Velocity, (ft/s)
Flow Area, (ft2)
Manning’s Roughness Coefficient
Hydraulic Radius, (ft)
Channel Slope, (ft/ft)
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Why not Variable Storage Routing
Method (Williams, 1969)?
• Does not accommodate flooding scenarios
• For a given reach segment, storage is based
on the continuity equation.
V
in
−V
out
=
ΔV
stored
Recharge - Venetis & Sangrey
Exponential decay weighting factor
w rchrg,i = (1-exp[-1/δ gw ])*w seep + exp[-1/ δ gw ]*w rchrg,i-1
Where:
w rchrg,I = amount of recharge entering aquifer of a
given day
δ gw = delay time or drainage time of overlying
aquifer
w seep = total amount of water exiting the bottom of
the soil profile on a given day
w rchrg,i-1
1
= amount of recharge entering aquifer on day i-
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