The hydrologic cycle
can be represented in quantitative terms by a water balance equation. A
water balance equation is a closed equation representing the principle of
conservation of mass. It is simply an estimate of the water entering and
leaving a basinplus or minus changes in
the storage of water for a given time period. Water enters as precipitation
and may leave as stream flow, ground water flow, and evaporation from soil,
surface water, and plants (evapotranspiration).
Water is stored as soil moisture, in surface water bodies, and in the ground
water reservoir.
Precipitation is the
source of ground water and surface water in the Tunkhannock Creek
watershed. Long-term precipitation data are available from the Montrose
station located approximately 2.5 miles northwest of the northern boundary
of the watershed. Annual precipitation at Montrose for the years 1990 to
2000 ranged from 32.0 to 58.0 inches and averaged 45.4 inches (Figure
1). Precipitation for the period 1990 to 2000 was 2.9 inches below
the long-term (1931-2000) average for the station.
Spatial variability in
precipitation amounts must be considered when estimating the total
precipitation within an area as large as the Tunkhannock Creek watershed.
Figure 2 shows contours of annual
precipitation amounts based on average annual precipitation for the period
1951 to 1980 from rain gages throughout northeastern Pennsylvania. The
contours suggest that long-term average precipitation amounts varied by
approximately ten inches across the watershed. Area-weighted average annual
precipitation within the watershed during the period 1951-1980 was 39.1
inches, approximately 8% less than the average for the same period at the
Montrose station. Average annual precipitation within the watershed for the
period 1990 to 2000 was estimated at 41.8 inches by reducing Montrose
station data by 8% (Figure 1).
Evapotranspirationis the sum of
evaporation plus water vapor given off through plant leaves in a process
referred to as transpiration. The evapotranspiration process is a major
component of the water cycle in the Tunkhannock Creek watershed. If enough
water is available to supply the needs of plants and maintain
soil moisture
at saturation, evaporation
from the soil and transpiration from plants proceed at a maximum rate called
potential evapotranspiration. At times of no precipitation,
evapotranspiration depletes soil moisture and actual evapotranspiration may
be less than potential evapotranspiration. Precipitation in excess of
actual evapotranspiration replenishes soil moisture.
Potential
evapotranspiration was estimated using Malmstrom’s (1969) empirical formula based on mean monthly air
temperature and saturation vapor pressure (see text box). Calculations were
based on temperature data from the Montrose, Pennsylvania weatherstation.
Mean monthly potential evapotranspiration and precipitation are compared in
Figure 3. Evapotranspiration varies
seasonally with the highest potential amounts during June, July and August,
and lowest amounts during December, January, and February. Potential
evaporation rates in excess of precipitation (red regions on
Figure 3) were most common during the summer
months, but occurred during the period May through October. Precipitation
surpluses, when precipitation exceeds potential evapotranspiration, are
common during the winter and spring months. Mean annual evapotranspiration
for the period 1990 to 2000 was 17.8 inches.
Figure 3
also shows the depth to ground water in a well located approximately 0.9
miles north of the watershed near New Milford, Pennsylvania. The water
level is unchanged or increases when water draining from the ground water
reservoir is replenished by recharge during times of water surplus. Ground
water levels fall when potential evapotranspiration exceeds precipitation.
Malmstrom (1969) suggested an empirical equation for estimating mean
monthly evapotranspiration.
Where:
ETM is monthly potential evapotranspiration in
cm/month
esat(Ta) is saturation vapor
pressure in mb at average monthly temperature (Ta) in
oC
Saturation vapor pressure is the maximum vapor pressure that is
thermodynamically stable. Its value can be calculated as:
Recharge occurs when
infiltrating precipitation arrives at the water table where it becomes part
of the ground water reservoir. The amount of recharge depends on three
factors: (1) the amount of precipitation that is not lost to
evapotranspiration and runoff; (2) the verticalhydraulic conductivity of surficial deposits; and (3) the
transmissivity of the
aquiferand potentiometric gradient, which determine how much water can move away
from the recharge area. If more water is transmitted downward to the water
table than is moved laterally away, the water table rises. Small
differences in local conditions (e.g. soil, vegetation, slope, prior
precipitation events) can cause large differences in recharge. Thus,
recharge is spatially and temporally highly variable in a given basin.
Ground water
flows from recharge
areas to discharge areas where it flows toward the surface and may
escape as a spring,
baseflow, or by evapotranspiration.
Ground water recharge
in the Tunkhannock Creek watershed was estimated using the RORA program
(Rutledge, 1998). The RORA program is
an inverse method that estimates recharge from stream flow data based on
Rorabaugh’s (1964) recharge model and superposition (i.e.
recharge events are additive) (see text box). Stream flow data from the
U.S. Geological Survey stream gage on Tunkhannock Creek, near Tunkhannock,
Pennsylvania were used for estimation of recharge. Rutledge’s method also
requires the estimation of a recession constant (K) for the basin. The
recession constant describes the rate of draining off of ground water from
the basin following a recharge event and is largely a function of basin
geology. A mean K value of 40.7 days was estimated from stream flow data
using the computer program RECESS (Rutledge, 1998) and manual methods. The
estimated mean annual ground water recharge for the period 1990 to 2000 was
15.3 inches (110 million gallons per year). Mean monthly recharge is shown
on Figure 5. Recharge rates are slowest
(~0.4 inches per month) during June, July, August, and September and reach a
maximum of about 3.5 inches/month during March.
Rutledge (1998, 2000) developed
an equation for estimating ground water recharge from stream flow data
based on Rorabaugh’s (1964) model of an
ideal aquifer flow system. Rutledge’s equation can be approximated
as:
where:
R is recharge in units of length
Q is total ground water discharge at critical time tc
K
is the recession index in units of time. The recession index is a
measure of the time required for the ground water discharge to recede
by one log cycle when the recession becomes nearly
linear (Figure 4).
The mean annual stream
discharge from the Tunkhannock Creek watershed was estimated using daily
flow records from the Tunkhannock Creek gauging station. During the
period 1990 to 2000, mean annual discharge was 20.1 inches (range 13.0 to
31.8 inches). Total stream discharge is a sum of direct surface runoff
and ground water discharge to streams (i.e. baseflow).
Baseflow is that part
of stream discharge derived from ground water seeping into the stream and is typically the main component of ground water discharge within a basin.
Ground water discharging as baseflow within the Tunkhannock Creek Watershed
was estimated from daily stream flow records from the Tunkhannock Creek
gauging station using the computer program PART
(Rutledge, 1998). Figure 4illustrates the separation of a stream flow hydrograph into runoff
and baseflow components. The mean baseflow for the period 1990 to 2000
at the Tunkhannock Creek gauging station was about 12.7 inches.
Surface runoff was estimated as the difference of total stream discharge and
baseflow. Mean annual surface runoff for the period 1990 to 2000 was
7.4 inches. Ground water discharge on average sustains approximately 63% of
total surface water flow from the basin.
The mean rate of
ground water recharge is 2.6 inches greater than the mean rate of ground
water discharge from the basin. If ground water withdrawals are
negligible, the difference based on long-term mean values is due to model
and data errors, riparian evapotranspiration and deep ground water seepage
(ground water outflow)
(Rutledge, 2000).
Rutledge
(1998) examined the relation of recharge and discharge estimates
from a large number of basins and estimated riparian evapotranspiration in
the range of 1 to 2 inches (25th and 75th
percentiles). Because the gage used to estimate baseflow in the
Tunkhannock Creek is located approximately 4 miles upstream from the mouth
of the stream, it is likely that some part of the observed difference
between recharge and discharge is due to ground water outflow in addition to
riparian evapotranspiration.
A water budget for a
basin such as the Tunkhannock Creek watershed can be expressed as an
equation whose terms reflect the purpose of the computation.
In its general form,
the water balance equation may be represented by:
P + QSI + QGI – ET – QSO – QGO
– Ds
– n = 0
where:
P = precipitation
QSI , QGI
= surface and groundwater inflow into the boundary from outside
ET= evapotranspiration
QSO , QGO=
surface and groundwater outflow from the boundary
Ds
= change of storage volume within the boundary (groundwater storage, soil
moisture, moisture in vegetation, water in streams and lakes)
n= discrepancy term
(since all water balance components are subject to errors of measurement and
estimation, the discrepancy term is added (see
Text Box))
All terms are in
consistent units of volume or volume/time.
Many forms of this expression are
possible by subdividing, consolidating, or eliminating some of the
terms, depending on the purpose of computation. If changes in
storage are averaged over many years, they tend to cancel out and may be
considered negligible. Also, because watershed boundaries are
commonly
ground
water divides as well as surface water divides, ground water
inflow
Consideration of errors
Numerous assumptions were made in the
parameterization of the water balance equation. To the degree that
these assumptions are unwarranted, they introduce model error
(omission of potentially significant terms in the basic equation). In
addition to model error, uncertainty due to measurement error (in P, T
(temperature used for modeling ET) and Q) is always present. In the
case of precipitation data, additional error is introduced in
computing regional averages from point data and in the case of ET
estimates; model assumptions and a lack of regionalization may be
important sources of error. Efforts to minimize errors are
important. For example, if appropriate to the study, we might choose
to use long-term average values because they always have smaller error
than short-term values. Another way to minimize errors is to measure
or compute all components using independent methods. Otherwise, all of
the errors in the known terms are propagated into the estimated
value. Individual components are commonly found to have uncertainties
of 5 to 25 %.
and outflow terms are negligible.
Thus, a long-term (10 years) annual average water budget for the Tunkhannock
Creek watershed can be formulated as follows:
P – ET - QSO– n = 0
The long-term average
values for these parameters derived in subsequent sections were as follows:
P = 41.8 inches (299,000 million
gallons per year (mgy))
ET = 17.8 inches (127,000 mgy)
QSO = 20.1 inches (144,000 mgy)
QSO = QR + QB
where:
QR = runoff = 7.4
inches
(53,000 mgy)
QB = baseflow = 12.7 inches
(91,000 mgy)
The discrepancy (n) between estimated input and
output values is 3.9 inches. However, as much as 2.6 inches of the
discrepancy may be accounted for by deep seepage of ground water past the
stream monitoring station and riparian evapotranspiration. The water budget
results are summarized in Figure 6.
The water budget for
the Tunkhannock Creek watershed reflects the interaction of regional climate
(prevailing weather patterns) with the geology, topography and land cover
(mostly vegetative and dependent on climate). While geology and topography
are generally stable on time scales of decades to centuries, our climate is
changing at a rate unprecedented since at least 10,000 years ago (IPCC,
2001). During the last century, global mean temperature has risen
1.1±0.4
oF and, according to the Intergovernmental Panel on Climate
Change (IPCC, 2001), “most of the warming
observed over the past 50 years is attributable to human activities." The
northeastern United States has experienced temperature increases of as much
as 4 oF, strong increases in precipitation (up to 20% in some
areas), greater precipitation extremes and shorter periods of snow cover (U.S.
Global Change Research Program, 2001). Global warming is anticipated
to worsen over the next several centuries (O’Neill
and others, 2000), with projected temperature increases of 2.5 to 10.4
oF over the period 1990 to 2100 (IPCC,
2001). Although there is large uncertainty in predictions of the
magnitude of warming over the next few centuries, the magnitude of near-term
warming, over the next 20 to 30 years, is relatively well constrained (Knutti
and others, 2002;
Stott and
Kettleborough, 2002). Stott and
Kettleborough (2002) estimate that the global mean temperature in the decade
2020-30 will be 0.5-2.3 oF greater than in 1990-2000 (5-95%
likelihood range). Attendant changes in precipitation, soil moisture,
evapotranspiration, vegetation types, seasonality, and frequency and
severity of storms and droughts will have important implications for the
hydrologic cycle of the Tunkhannock Creek watershed.
Current models are
unable to simulate and predict near- or long-term climate at the scale of
the Tunkhannock Creek Watershed (413 square miles). However, efforts are
being made to increase the spatial resolution of models to simulate the
effects of climate change at regional rather than global scales. For
example,Lakhtakia and others (1998)simulated the response of the upper west branch of the Susquehanna River Basin (~8700 square miles) to a storm. They found that, while the
meteorological and hydrologic models simulated precipitation and the
resulting hydrologic response of the basin reasonably well for a single
storm, more detailed data on basin physical characteristics and models
capable of longer simulation times were needed for assessing impacts of
climate change. The U.S. Global Change Research
Program (2001) recently examined potential consequences of global
warming on the northeastern United
States using state-of-the science climate models and a range of plausible
scenarios. Key findings that may be pertinent to the Tunkhannock Creek
Watershed were as follows:
The northeast has among the lowest rates of projected future warming in
comparison with the other regions of the U.S.
Winter minimum temperatures
are likely to show the greatest change, with models projecting increases
ranging from 4-5oF to as much as 9oF by 2100. Maximum
winter temperatures will possibly increase much less, but the largest
increases are likely to occur in the winter.
For precipitation, model
scenarios offer a range of potential future changes, from roughly 25%
increases by 2100 on average for the entire region, to little change.
Models provide contrasting scenarios for changes in the frequency and
intensity of winter storms.
