Environmental Engineering Reference
In-Depth Information
as base flow (storage in other reservoirs could
also be considered). Alley (
1984
) and Steenhuis
and van der Molen (
1986
) proposed variations
to this approach that more accurately portray
recharge processes. McCabe and Markstrom
(
2007
) describe an easy-to-use computer pro-
gram that determines the water budget in a
fashion similar to that of Thornthwaite and
Mather (
1955
).
Thornthwaite and Mather (
1955
) applied
the model with average monthly data from
Seabrook, NJ (
Table 2.3
). It was assumed that
moisture surplus was split evenly between
direct runoff and base flow.
S
uz
max was set to
300 mm. Precipitation varied little from month
to month, whereas
PET
and
ET
followed a dis-
tinct seasonal pattern being greatest in sum-
mer months and essentially 0 during winter
months. Moisture surplus and base flow were
greater than 0 only during winter and early
spring months. Total base flow for the year was
189 mm or 17% of precipitation.
Example: Thornthwaite and Mather
method
In the late 1940s and through the 1950s C. W.
Thornthwaite and colleagues at the Laboratory
for Climatology of Drexel University developed
a systematic approach to the study of water-
shed water budgets. The objective of this work
was to identify relations among precipita-
tion, potential evapotranspiration, and actual
evapotranspiration worldwide. The approach
laid the foundation for the development of
watershed models in the following decades.
Groundwater recharge was not an explicit com-
ponent in these water budgets, but with some
simple assumptions, recharge estimates can be
obtained.
The procedure of Thornthwaite and Mather
(
1955
) requires only measurements of air tem-
perature and precipitation, although data on
soil texture and the thickness of the soil zone
could also be used. The following equation was
solved for a watershed on a monthly basis:
(2.40)
Example: West Maui, Hawaii
A water-budget approach was used to estimate
historic rates of diffuse drainage to the uncon-
fined aquifers underlying western Maui, the
second largest of the Hawaiian Islands (Engott
and Vana,
2007
). Of concern were falling
groundwater levels and increasing chloride con-
centrations in groundwater. Rising to a height
of 1760 m, West Maui Mountain is the domin-
ant topographic feature in the approximately
1000-km
2
study area. The climate is tropical, and
precipitation varies with elevation and orienta-
tion. Average rainfall is about 8900 mm/yr at
the highest elevations but less than 250 mm/yr
along the southwestern coast of the island. Fresh
groundwater occurs in lens systems and in dike-
impoundment systems. Irrigation water is pri-
marily obtained by surface-water diversion.
A variation of the Thornthwaite-Mather
approach was applied in conjunction with a
Geographical Information System (GIS). The
water-budget equation for a column of soil
extending from land surface to the bottom of
the root zone was written as:
P
=+ +
ET
∆
S
uz
Q
sw
offi
where Δ
S
uz
is the change in soil-water storage
and
Q
sw
offi
is the sum of runoff,
R
offi
, and base
flow,
Q
bf
. If evapotranspiration from ground-
water and change in groundwater storage are
negligible, recharge is often equated with base
flow (a more detailed discussion of base flow
is given in
Section 4.1.2
).
PET
was estimated
by Equation (
2.30
), and a bookkeeping proced-
ure was used for determining actual
ET
, Δ
S
uz
,
and
Q
sw
offi
. Soil-water storage,
S
uz
, was assumed
to have a maximum value of
S
uz
max (100 mm
was originally suggested, but this can be esti-
mated from soil texture and thickness). If
P
was greater than
PET
, then
ET
was set to
PET
and the excess amount of precipitation was
added to
S
uz
. If
S
uz
exceeded
S
uz
max, then
S
uz
was set equal to
S
uz
max and the remaining
excess was added to the moisture surplus,
MS
. The user decides what percentage of the
moisture surplus constitutes direct runoff.
Thornthwaite and Mather (
1955
) suggested
50% for large basins as a general rule, so as a
simple first approximation, the remaining 50%
of the
MS
for each month can be designated
S
temp
=+ + − − +
P
I
FD
R
ET
S
i -1
(2.41)
uz
uz
i
rri
i
offi
i
