Journal of Hydrology (2006) 329, 140– 153
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/jhydrol
Stream–air temperature relations to classify
stream–ground water interactions in a karst
setting, central Pennsylvania, USA
Michael A. O’Driscoll
a,*
, David R. DeWalle
b
a
Geology Department, East Carolina University, 204 Graham Building, Greenville, NC 27858, United States
School of Forest Resources, The Pennsylvania State University, 107 Land & Water Research Building,
University Park, PA 16802, United States
b
Received 3 January 2005; received in revised form 23 January 2006; accepted 6 February 2006
KEYWORDS
Summary Stream–ground water interactions in karst vary from complete losses through swallow
holes, to reemergences from springs. Our study objective was to compare stream–air temperature
and energy exchange relationships across various stream–ground water relationships in a carbonate watershed. It was hypothesized that ground water-fed stream segments could be distinguished
from perched/losing segments using stream–air temperature relationships. Two types of computations were conducted: (1) comparisons of stream–air temperature relationships for the period of
October 1999–September 2002 at 12 sites in the Spring Creek drainage and (2) detailed energy
budget computations for the same period for ground water-dominated Thompson Run and Lower
Buffalo Run, a stream with negligible ground water inputs. Weekly average air temperatures and
stream temperatures were highly correlated, but slopes and intercepts of the relationship varied
for the 12 sites. Slopes ranged from 0.19 to 0.67 and intercepts ranged from 3.23 to 9.07 C. A twocomponent mixing model with end members of ground water and actual stream temperatures
indicated that the slope and intercept of the stream–air temperature relationship was controlled
by ground water inputs. Streams with large ground water inputs had greater intercepts and lesser
slopes than streams that were seasonally losing, perched, and/or distant from ground water
inputs. Energy fluxes across the air–water interface were greatest for the ground water-fed stream
due to increased longwave, latent, and sensible heat losses from the stream in winter when large
temperature and vapor pressure differences existed between the stream and air. Advection of
ground water was an important source and sink for heat in the ground water-fed stream, depending
on season. In contrast, along the seasonally losing stream reach, advection was of minimal
importance and stream temperatures were dominated by energy exchange across the air- water
Water–air temperature
relationships;
Stream temperature;
Stream–ground water
interactions;
Karst hydrology;
Air–water interface;
Energy exchange
* Corresponding author. Tel.: +1 252 328 5578; fax: +1 252 328 4391.
E-mail address: [email protected] (M.A. O’Driscoll).
0022-1694/$ - see front matter c 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2006.02.010
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
141
interface. Overall, results showed that stream temperatures and energy exchange in this carbonate watershed were strongly related to stream–ground water interactions.
c 2006 Elsevier B.V. All rights reserved.
Introduction
The degree to which a stream interacts with the underlying
ground water system is important for a variety of scientific,
practical, and legal reasons, such as wellhead protection
(Nnadi and Sharek, 1999), bank filtration (Sheets et al.,
2002), stream ecology (Brunke and Gonser, 1997), and
non-point source pollution from adjacent lands (Hill et al.,
1998). Stream temperature fluctuations are related to the
nature of stream–ground water interactions and have been
used as signals to trace exchanges between surface and
ground waters (Stonestrom and Constantz, 2004).
In karstic terrains, surface water drainage basins often
differ from ground water basins and it may be difficult to
clearly distinguish between surface water and ground water
(White, 1988). Streams in carbonate settings exhibit a wide
variety of relations with respect to the underlying ground
water system ranging from complete losses due to swallow
holes, to reemergences from discrete springs (Brahana and
Hollyday, 1988; Brown and Patton, 1996).
Carbonate aquifers have been characterized based on annual temperature fluctuations from spring discharges. Seasonal water temperature patterns were found to be good
indicators of the carbonate aquifer type, with conduit-fed
springs showing large seasonal temperature variations and
diffuse-fed springs showing little to no seasonal variation
in water temperature (Shuster and White, 1971). This approach characterizes springs based on the rate of movement
of recharge waters through the underlying carbonate aquifer based on spring water temperatures. Spatial variations
in ground water inputs to streams may also be detected
using in-stream water temperatures (O’Driscoll, 2004).
A variety of approaches have been used to predict stream
water temperatures. Investigators have found that air temperature is a good index of stream temperature at timescales of greater than one week (Mohseni and Stefan,
1999; Ozaki et al., 2003). A common approach to stream
temperature predictive modeling is to use the equilibrium
temperature concept (Edinger et al., 1968). Equilibrium
temperature is the hypothetical temperature that water
reaches under constant atmospheric heating/cooling where
no more heat is transferred at the air/water interface. The
net energy exchange across the air–water interface can be
estimated from the following equation (modified from Mohseni and Stefan, 1999):
Q n ¼ Hns þ Hla Hls Hle Hc
where Qn is the net heat flux across the air–water interface,
Hns is the net solar radiation at the stream surface, Hla is the
longwave radiation downwelling to the surface water body,
Hls is the longwave radiation emitted from the surface water
body, Hle is the latent heat loss due to evaporation, and Hc is
the sensible heat or convective heat exchange. Equilibrium
temperature is the temperature at which the net heat flux
across the air–water interface (Qn) is equal to zero.
Mohseni and Stefan (1999) found that the equilibrium
temperature–air temperature relationship is similar to the
stream temperature–air temperature relationship over the
range of 0–20 C for streams that do not have significant
ground water inputs. If all heat input to a stream is from
the atmosphere, weekly stream temperature should be
close to weekly equilibrium temperature. In stream reaches
with significant ground water inputs, the stream temperature–air temperature relationship should have a smaller
slope and larger intercept than that of the equilibrium temperature–air temperature relationship.
Bogan et al. (2003) found that for 596 streams in the central and eastern United States, a median stream temperature-equilibrium temperature linear relationship existed
with a slope of 0.82 and intercept of 2.8 C when comparing
stream temperature to equilibrium temperature on a weekly
basis. Streams with ground water inputs had slopes less than
the median and intercepts greater than the median. Since
the stream temperature–equilibrium temperature relationship is linearly related to the stream temperature–air temperature relationship, these results indicate that the
stream–air temperature relationship should provide a good
indicator of ground water inputs along streams.
Stream temperature ranges from an upstream temperature to equilibrium temperature over a distance from the
upstream location. The difference between actual stream
temperature and equilibrium temperature is related to the
temperature difference between the source (i.e., ground
water spring or seep) and the air temperature at the source.
Stream temperature will become closer to air temperature
with distance from the source. Flow rate influences the upstream temperatures and affects the stream response to
equilibrium temperature. The greater the flow rates the farther downstream the influence of upstream temperatures
will be present (Mohseni and Stefan, 1999). In a recent study
in the Exe basin, Devon, UK, Webb et al. (2003) found that
stream water temperatures were more sensitive to air temperatures during low flows (below median levels) and water
temperature was inversely related to discharge, indicating
the importance of ground water inputs to stream temperatures. The inverse relationship between water temperature
and discharge is also related to meteorological conditions
and the relationship between discharge and thermal mass.
In a study of losing and gaining stream reaches along alpine
streams in the western US, it was found that diurnal variations in stream temperature and discharge were greater in
losing streams when compared to gaining streams, indicating that stream–ground water relations have a strong influence on stream temperatures (Constantz, 1998).
Study objectives
The goal of this study was to compare stream–air temperature and energy exchange relations across a variety of
catchment areas and stream–ground water relations in a
142
karst basin. It was hypothesized that ground water-fed
stream segments could be distinguished from perched or
losing streams using the surface water temperature versus
air temperature relationship. Spring and seep ground water
inputs are typically close to the regional average annual air
temperature year-round and ground water temperatures are
only slightly affected by meteorological conditions (particularly from diffuse-fed aquifers). Waters from spring-fed
streams will have temperatures that are more influenced
by the advection of ground water than the energy exchange
across the air–water interface.
In this study, two types of computations were conducted
to characterize stream temperature regimes: (1) comparisons of stream–air temperature relations for 12 sites in
the Spring Creek drainage and (2) detailed energy budget
computations for two streams: ground water-dominated
Thompson Run and Lower Buffalo Run, with negligible
ground water influence.
The objectives of this study were:
1. To analyze the differences in energy exchange processes
occurring between a stream dominated by ground water
inputs and one with minimal ground water inputs.
2. To illustrate how the stream versus air temperature relations are affected by ground water inputs at 12 stations
within the Spring Creek drainage basin.
M.A. O’Driscoll, D.R. DeWalle
Study site and hydrology
The Spring Creek watershed
The study sites were located in the Spring Creek watershed,
Centre County, Pennsylvania (see Fig. 1). The watershed is
present in a complex hydrogeological setting of the karstunderdrained, Nittany Valley in the Valley and Ridge Province of the Appalachian region of central Pennsylvania. The
drainage basin consists of a broad carbonate valley containing a variety of solutional features associated with karst
development. Ridges underlain by shale, sandstone, and
quartzite bound the valley (Parizek and White, 1985). The
geologic factors that control the occurrence and movement
of ground water in the bedrock and indirectly in the soil mantle are: topography, joints, fracture concentrations, bedding
planes, variations in rock type, rock texture, primary porosity, permeability, and solutional features (Krothe, 1976).
In the valley, stream reaches are underlain predominantly
by carbonate rocks and both surface and subsurface drainage
exist. Perched and losing streams are common in carbonate
uplands for most of the year. Streams in the watershed are
fed by mountain runoff or ground water seeps or springs.
Springs are connected to a diffuse and extensive underground
conduit system that carries ground water flow for up to 23 km
(Giddings, 1974). Water table elevations and ground water
Figure 1 Water table map and surface water monitoring stations (white boxes) for the Spring Creek Watershed (modified from
Wood, 1980). Ground water head contour interval is 30 m. Locations of water temperature and streamflow monitoring sites are
described in Table 1.
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
143
Figure 2 Geological map depicting major aquifer types and fault zones underlying the Spring Creek Watershed (modified from
Fulton et al., 2005). Major springs are indicated by gray circles. Water monitoring sites as labeled in Fig. 1 are indicated by white
boxes.
flowpaths are significantly influenced by the nature of the
underlying carbonate geology (Wood, 1980). The underlying
formations can be classified into four main aquifer types:
diffuse-flow dominated carbonates, fracture-dominated carbonates, conduit-dominated carbonates, and fracture dominated siliclastics (see Fig. 2 – modified from Fulton et al.,
2005).
An extensive ground water trough is located in the valley
center, which indicates that a large amount of drainage
bypasses streams in the upper sections of the watershed
and later emerges possibly along stream channel segments
and at springs in the Bellefonte area (see Fig. 1 – modified
from Wood, 1980). Numerous large springs are present within the Spring Creek watershed (see Fig. 2), a detailed listing
of major springs is provided by Wood (1980) and more recently by Fulton et al. (2005). Springs are frequently found
at bedrock contacts. The largest of the springs, Big Spring,
located along Spring Creek in Bellefonte, discharges approximately 0.5 m3/s.
The most extensive soil association within the carbonate
valley is the Hagerstown (Typic Hapludalf)–Opequon (Lithic
Hapludalf)–Hublersburg (Typic Hapludalf) association
formed as residuum from limestone and dolomite bedrock
(Ciolkosz and Dobos, 1992). The surface water drainage
basin is approximately 378 km2, whereas the ground water
drainage basin drains a considerably larger area, approximately 453 km2 (Giddings, 1974). At the mouth of the Spring
Creek watershed average discharge, as measured at the US
Geological Survey gage at Milesburg, is 7.2 m3/s for the record of 1968–2002. The Spring Creek surface watershed is
comprised of 36% agricultural, 37% forested, 17% urban/suburban, and 10% other land-uses (Sengle, 2002). Typically
land-use associated with the carbonate valley consists of
agricultural and urban land, whereas the siliclastic ridges
are usually forested.
Meteorological and hydrological conditions
Central Pennsylvania has a humid northeastern continental
type climate. Mean annual precipitation in the Spring Creek
watershed is approximately 99 cm based on 76 years of data
(1926–2002) measured at State College. Evapotranspiration
is approximately 43 cm/year or 43% of precipitation based
on precipitation minus long-term discharge data from 1968
to 2002. Mild to extreme drought conditions were present
in central Pennsylvania beginning in the fall of 1998 and
continuing until the spring of 2003 (Pennsylvania State Climatologist, 2003).
144
M.A. O’Driscoll, D.R. DeWalle
two wastewater treatment plants along Spring Creek, and
a fish hatchery, a metal products factory, and mining operations along Logan Branch. Water temperatures were not
logged at these sites during this study. In addition, ground
water withdrawals at the State College Water Authority well
fields remove approximately 3800 million liters per year
(Walsh, 2002) of ground water from the subsurface. The well
fields are located within floodplain sediments adjacent to
Upper Slab Cabin Run and may induce streambed infiltration
along segments of Slab Cabin Run for portions of the year.
Linear regressions were performed between weekly moving average stream temperatures versus weekly moving average air temperatures for all 12 study locations for the period
of October 1, 1999 through September 30, 2002 (see Table
2). The weekly moving average was calculated daily for the
three-year period and each daily value represents the weekly
average preceding that date. Stream temperature–air temperature relations were compared for the 12 stream locations using linear regressions between weekly average
stream temperatures versus weekly average air temperatures. Hourly air and stream temperature were summarized
as weekly moving average data for regression analyses.
Methods
Streamflow and water temperature
Twelve sites were used for water temperature and streamflow data collection. Data were collected on an hourly basis
by the Water Resources Monitoring Committee of the Spring
Creek Watershed Community, administered by the ClearWater Conservancy, a local watershed conservation group
(State College, Pennsylvania) from October 1, 1999 until
September 30, 2002 (sites noted in Fig. 1) (ClearWater Conservancy, 2003). Hourly air temperatures were obtained
from the Pennsylvania State Climatologist Station at the
University Park Campus (Pennsylvania State Climatologist,
2003). A summary of the sites, catchment areas, average
streamflows for the period of October 1999–September
2002, and average hydrological yields (streamflow/catchment area) for that period are presented in Table 1 (modified from Sengle, 2002).
In addition to ground water discharge as springs and
seeps, several point source discharges are present along
streams within the basin, including two fish hatcheries and
Table 1 Summary of monitoring station locations, basin areas, average streamflow and hydrologic yield (average streamflow/
catchment area) for the three-year study period
Monitoring Station
Station
ID
Latitude
Longitude
Basin
area (ha)
Streamflow
(m3/s)
Hydrologic yield
(m3/s/ha)
Spring Creek Upper – Linden Hall Road Bridge
Cedar Run – Brush Valley Road Bridge
Slab Cabin Run – Millbrook Marsh
Thompson Run – Millbrook Marsh
Spring Creek Houserville – Trout Road Bridge
Spring Creek Axemann – Spring Creek Road Bridge
Logan Branch Lower – State Route-150 Bridge
Buffalo Run Lower – Lower Coleville Road Bridge
Spring Creek Milesburg – McCoy Dam
Logan Branch Upper – Odd Fellows-SR 144
Buffalo Run Upper – SR550 at Filmore
Slab Cabin Run Upper – South Atherton Street
SPU
CEL
SLL
TR
SPH
SPA
LOL
BUL
SPM
LOU
BUU
SLU
40/47/34
40/47/40
40/48/44
40/48/47
40/50/02
40/53/24
40/54/27
40/54/35
40/55/54
40/52/30
40/51/30
40/47/05
77/47/54
77/47/50
77/49/54
77/50/09
77/49/38
77/47/39
77/46/54
77/47/38
77/47/11
77/45/45
77/53/00
77/50/15
3403
4526
4328
1021
15,058
22,236
5832
6941
45,300
3324
3262
3795
0.40
0.30
0.20
0.27
1.29
1.27
1.76
0.30
4.91
0.67
0.16
0.12
1.19E 04
6.63E 05
4.69E 05
2.69E 04
8.57E 05
5.71E 05
3.02E 04
4.33E 05
1.08E 04
2.04E 04
4.80E 05
3.29E 05
Table 2 Summary of the linear regression equations for weekly average stream–air temperature relationships for all 12
locations for the three-year study period
Location
Slope (B0)
Intercept (B1)
R2
S
B0se (±)
B1se (±)
N
Lower Logan Branch
Upper Logan Branch
Lower Cedar Run
Lower Slab Cabin Run
Upper Slab Cabin Run
Spring Creek at Axemann
Spring Creek at Houserville
Spring Creek at Milesburg
Upper Spring Creek
Upper Buffalo Run
Lower Buffalo Run
Lower Thompson Run
Average slope and intercept
0.185
0.428
0.487
0.615
0.625
0.585
0.528
0.426
0.207
0.640
0.672
0.272
0.47
9.07
7.66
5.58
5.04
4.58
5.94
5.32
7.08
8.18
3.23
3.61
8.44
6.14
96.0
92.4
95.2
92.2
88.4
97.7
97.6
98.0
86.5
96.3
95.3
97.1
0.3478
1.102
0.9833
1.183
1.566
0.8079
0.7569
0.5447
0.7379
1.120
1.346
0.4239
0.0013
0.0037
0.0033
0.0076
0.0101
0.0027
0.0027
0.0018
0.0024
0.0044
0.0045
0.0014
0.0195
0.0532
0.0457
0.1244
0.1663
0.0376
0.0359
0.0254
0.0345
0.0759
0.0627
0.0197
843
605
1096
557
502
1096
1096
1096
1096
787
1079
1096
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
Energy fluxes at the air–water interface from
meteorological and radiation data
Energy fluxes at the air–water interface for Thompson Run
(TR) and Lower Buffalo Run (BUL) were calculated using
site-specific hourly stream temperature data for the period
of October 1, 1999 through September 30, 2002. These
streams were chosen because they had the most complete
records and had similar flow rates but differed in their relationship with the ground water system (Thompson Run,
spring-fed/Buffalo Run, seasonally losing). Meteorological
and radiation data were obtained from the Rock Springs
Agricultural Research Station (Latitude: 40.72 North, Longitude: 77.93 West, Elevation: 376 m, approximately 4.5
miles west of Slab Cabin Run) as part of the SURFRAD network (SURFRAD, 2004). Short-wave and long-wave radiation,
relative humidity, wind speed, barometric pressure and air
temperature data were collected at the Rock Springs site
and used in this study in the form of weekly moving averages. These data were paired with site-specific stream temperature data collected at each site.
Meteorological and radiation data processing
A detailed description of net heat flux calculations is provided in O’Driscoll (2004). Net solar (Hns) was calculated
as (1 albedo) · shading factor · measured downwelling
solar. Where albedo was estimated as 0.07 (DeWalle,
1974; Brutsaert, 1982) and shading factors were calculated
from field canopy estimations as 0.93 for Thompson Run and
0.84 for Lower Buffalo Run (DeWalle, 1974) and average
shading factors for direct and diffuse incoming solar fluxes
combined were calculated.
Atmospheric downwelling longwave radiation (Lopen)
was measured at the weather station at Rock Springs.
The open site downwelling longwave radiation was corrected for the effects of shading using view factors developed in DeWalle (1974). For Thompson Run, the fraction of
longwave that would make it to the stream was 0.84, and
for Lower Buffalo Run the factor was 0.76. The longwave
emitted from terrestrial vegetation (Lt) and slopes to the
stream was estimated from the following equation (DeWalle, 1974):
Lt ¼ 2erT 4surface F sv
where e is the emissivity of vegetation and slopes and is estimated at 1, r is the Stefan–Boltzmann constant
(4.899 · 106 kJ/m2 K4), Tsurface is estimated by air temperature in K, and Fsv is the view factor from the streams to terrestrial objects along one bank. View factors were
estimated from those derived by DeWalle (1974). The view
factor to the vegetation cover along each bank for Lower
Buffalo Run was 0.12 and for Thompson Run 0.08. The total
longwave radiation arriving at the stream was calculated
from (DeWalle, 1974):
Hla ¼ Lt þ ð1 2 F sv ÞLopen
Longwave radiation emitted by the streams was calculated
using the following equation (DeWalle, 1974):
Hls ¼ ew rðTwÞ4
145
where ew is the emissivity of the water surface, taken to be
0.97 (Brutsaert, 1982), r is the Stefan–Boltzmann constant
(4.899 · 106 kJ/m2 dK4), and Tw is the water temperature
(K). Net longwave radiation was estimated as open longwave radiation (multiplied by the view factor correction)
plus terrestrial longwave radiation emitted to the stream
minus the longwave radiation emitted by the stream.
Latent heat flux (Hle) was estimated using the method
based on Shulyakovskiy (1969) and modified by Ryan
et al. (1974). This method was chosen because it accounts
for free convection effects. Ground water inputs can cause
stream temperature to deviate significantly from air temperature, when large temperature gradients exist between
the stream and overlying air mass, free convection may affect evaporative losses for these streams (DeWalle, 1976).
The modified Ryan et al. (1974) equation for evaporative
energy losses is:
Hle ¼ 0:00451 U2 þ 0:00379ðT wv T av Þ1=3 ðew ea Þ
where U2 is wind speed at 2 m elevation, Twv is virtual temperature for saturated air at the water temperature in C,
Tav is virtual temperature for air at 2 m height in C, ew is
the saturation vapor pressure at the water temperature,
and ea is the vapor pressure of the air at 2 m height. For this
equation positive values indicate energy losses from the
stream to the atmosphere. For the purposes of stream evaporation calculations, wind speed data were corrected for
elevation to 2-m. Elevation corrections for wind speed were
performed using the power law approximation (Brutsaert,
1982, p. 63), where U2 m = U10 m/(10 m/2 m)1/7 for a wind
speed correction of 80% of the 10 m wind speed. Radiation
and meteorological data collected at the Rock Springs station along with water temperature data measured at the
stream sites were used to estimate energy fluxes to and
from Thompson Run and Lower Buffalo Run.
Wind speed (U) and relative humidity (e) data were measured at 10 m elevation. For the purposes of stream evaporation calculations, these data were corrected for elevation
to 2-m; a depth commonly used in stream and lake evaporation studies (i.e., Lee and Swancar, 1996). A correction for
vapor pressure profiles was adapted from DeWalle (1976) to
convert vapor pressure estimates from 10 m elevation to
2 m elevation at the stream sites; the subscript w indicates
measurements at the water surface. The following equation
was used e2 m = ew + (e10 m ew) · 0.80. A similar approach
was used to correct air temperature measurements. With
T2 m = Tw + (T10 m Tw) · 0.80.
To account for the sheltering effects at streams due to
vegetation and topography a constant coefficient of 0.6
was multiplied by the wind speed previously corrected to
2 m height for all stream sites. Open wind speed varies with
distance from vegetation and density of vegetation. The
riparian vegetation found along the valley streams of the
Spring Creek watershed is typically low density and ranges
in elevation from 1 to 30 m. Sheltering due to forest vegetation may cause wind speed to drop by as much as 40% of
open wind speed (Oke, 1987 p. 244). More recently, Bogan
et al. (2003) found that for 156 streams in the eastern and
central US the median sheltering effect was approximately
a 20% reduction of open wind speed. Since the streams they
studied were larger than those found in the Spring Creek
146
M.A. O’Driscoll, D.R. DeWalle
watershed it is likely that the sheltering coefficient for
these streams reduces wind speed by more than 20% because of the lower ratio of stream width to vegetation
height in the Spring Creek watershed. It was assumed that
shelter effects fell between 60% and 20% reduction of open
wind speed and for this study a 40% reduction of open wind
speed at 2 m elevation was used. A combined coefficient
accounting for elevation (0.8) and sheltering effects (0.6)
on wind speed was 0.48 times the open wind speed measured at 10 m.
Virtual temperatures were used to calculate the evaporative energy losses as laid out in Brutsaert (1982, p. 37–
38). The virtual temperature is defined as the temperature
dry air should have in order to have the same density as
moist air at a given specific humidity, temperature, and total air pressure. Saturation vapor pressure at the water surface was estimated from the following equation from
Richards (1971): ew = 1013.25exp(13.3185 · tr 1.976 · tr2
0.6445tr3 0.1299tr4) where tr = 1 (373.15/T) in which
T is the temperature at the water surface in Kelvin. Vapor
pressure in the air was calculated by calculating saturation
vapor pressure from air temperature and multiplying by relative humidity/100.
The Bowen ratio (b) is the ratio between sensible heat
flux (Hc) and latent heat flux (Hle). The Bowen ratio was calculated from the following equation:
b = (0.61 · P(Tw Ta)/(ew ea))/1000 where P is barometric pressure in mbar, Tw is water temperature, Ta is
air temperature at 2-m height, ew is vapor pressure at
the water surface in mbars, ea is vapor pressure of the
air at 2-m height in mbars. When the difference between
ew and ea is very small, the Bowen ratio becomes excessively large; therefore a minimum value for the vapor
pressure difference was set at 0.1 for computations. Sensible heat flux (Hc) was calculated as: Hc = b · Hle. Heat
conduction in the channel bottom was assumed negligible.
Results
Hydrology and energy flux across the air–water
interface for a ground water-fed stream segment
(Thompson Run) and a seasonally losing stream
segment (Lower Buffalo Run)
For the stream segments at Thompson Run and Lower Buffalo Run, both streams had similar mean flow rates over
the study period (Thompson Run = 0.27 m3/s, Buffalo
Run = 0.30 m3/s) but differed in flow variability with
Thompson Run behaving more steadily (coefficient of variation of flow = 63%) than Buffalo Run (coefficient of variation
of flow = 125%), due to steady spring inputs from Thompson
Spring. The temperature regime was far less variable at
Thompson Run, with a coefficient of variation for weekly
average water temperature of 23% for Thompson Run, versus 60% for Lower Buffalo Run water temperatures over
the 3-year period.
The weekly average surface water–air temperature relations for the 3-year period differed markedly for Buffalo Run
and Thompson Run (see Table 2 and Figs. 3 and 4). Thompson Run surface waters showed much less variability with air
temperature and the slope of the water–air temperature
relationship was 0.272, compared to a value of 0.672 for
Lower Buffalo Run. Thompson Run had a water–air temperature intercept of 8.44 C, whereas Lower Buffalo Run had
an intercept of 3.61 C. A deviation from the water–air
temperature relationship occurred during the last week of
January 2000 along Buffalo Run because of an unseasonably
warm period, where daily average air temperatures almost
reached 8 C on 1/29/02.
The importance of different sources of energy losses
from the stream–air interface was similar for both Buffalo
Run and Thompson Run, with radiation inputs providing an
30
Temperature (Degrees-C)
25
AIR
BUL
TR
20
15
10
5
0
-5
-10
Oct- Dec- Mar- Jun- Sep- Dec- Mar- Jun- Sep- Dec- Mar- Jun- Sep99
99
00
00
00
00
01
01
01
01
02
02
02
Figure 3 Seasonal variation of weekly moving average air temperature and stream temperature at Lower Buffalo Run and
Thompson Run for the three-year study period (October 1999–September 2002).
St ream W ate r T empe rat ure (Degrees- C)
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
147
30
25
Lower Buffalo Run
20
15
Thompson Run
10
5
0
-10
-5
0
5
10
15
Air T emperature (Degrees-C)
20
25
30
Figure 4 Weekly average water temperature versus air temperature relationships for Thompson Run and Lower Buffalo Run sites
for the three-year study period (October 1999–September 2002).
average net input of 99 W/m2 at Thompson Run and 93 W/
m2 at Lower Buffalo Run (see Fig. 5), the difference was
due to shading. Longwave energy losses were greater at
Thompson Run (average loss of 37 W/m2) and Buffalo Run
had an average loss of 30 W/m2 over the study period due
to slightly warmer stream waters at Thompson Run (Thompson Run, 3-year average – 11.32 C; Buffalo Run, 3-year
average – 10.64 C). Latent heat losses were the next in
importance with Thompson Run having greater average latent heat losses (19 W/m2) than Lower Buffalo Run (11 W/
m2). Latent heat losses generally peaked during the winter
months due in part to large gradients in temperature and vapor, during this time of year latent heat losses were typically much larger at Thompson Run. Average sensible heat
losses were slightly lower than latent heat losses for the
3-year period (17 W/m2 – Thompson Run and 8 W/m2- Buffalo Run). Average net energy exchange for the three-year
period was 63 W/m2 for Thompson Run and 74 W/m2 for
Lower Buffalo Run. The difference is due to larger longwave
radiation, latent, and sensible heat losses from Thompson
Run during winter months.
Net energy exchange was corrected by dividing by depth
to account for different volumes of water underlying the
air–water interface for each site. When depth is considered, the net energy exchange across the air–water interface has a larger influence on Buffalo Run (see Fig. 6).
The influence is most pronounced during the summer
months. This explains the greater maximum water temperatures observed during summer at Buffalo Run and greater
diurnal variability in water temperatures when compared
to Thompson Run.
Water temperature–air temperature relations
within Spring Creek Watershed
Weekly moving average stream temperatures versus weekly
moving average air temperatures for all 12 study locations
for the period of October 1, 1999 through September 30,
Energy Flux (Watts/m2)
160
140
Thompson Run
120
Lower Buffalo Run
100
80
60
40
20
0
-20
-40
-60
Net Solar
Net Longwave
Net Radiation
Net Hle
Net Hc
Net Heat Flux
(Qn)
Figure 5 Average net energy flux across the air–water interface for Thompson Run and Lower Buffalo Run for the three-year study
period (October 1999–September 2002).
M.A. O’Driscoll, D.R. DeWalle
Energy Flux/Unit Area*Depth (Watts/m3)
148
3000
Lower Buffalo Run
2500
2000
1500
1000
500
0
Thompson Run
-500
-1000
Aug-99
Feb-00
Aug-00
Feb-01
Aug-01
Feb-02
Aug-02
Figure 6 Weekly moving average energy flux/stream depth for Thompson Run and Lower Buffalo Run for the three-year study
period (October 1999–September 2002).
2002 are summarized in Table 2. All stream–air temperature relations were linear and R2 values ranged from 86.5%
for Upper Spring Creek, to 98.0% for Spring Creek Milesburg.
Slopes to the regression lines ranged from 0.185 (Lower Logan Run) to 0.672 (Lower Buffalo Run) with an average slope
of 0.472. Intercepts ranged from 9.07 C (Lower Logan Run)
to 3.23 C (Upper Buffalo Run) with an average intercept of
6.17 C. All p values for both slopes and intercepts were
<0.001. Several of the streams had periods when they
ceased to flow and during other periods water temperature
data were missed due to technical difficulties. Overall, n
values ranged from 502 to 1096. Sites with lower n values
were streams that dried up during summer months, the relations at these streams may be seasonally biased because
they typically contain fewer warm temperature points.
A comparison of intercepts versus slopes for the surface
water–air temperature relations for all stream measurement locations revealed that there was an inverse relationship between the slope and intercept of the surface water–
air temperature regression lines. The slope of this relationship was 10.306 with a y-intercept of 11.061 C and an R2
value of 89.4% (see Fig. 7).
12
Discharge variations within the spring creek
watershed
Discharge variations within the watershed were studied to
help determine the spatial and temporal variability of
ground water inputs in the watershed. Streamflow ceased
at several of the stream monitoring locations during the period of October 1999–September 2002. Specifically, the
stream dried up at Buffalo Run Upper (BUU) from July 7,
2001 to March 15, 2002 and from August 2, 2002–September
30, 2002 and at Slab Cabin Run Lower (SLL) from September
9, 2000 until January 29, 2001 and again from July 31, 01 until December 31, 2001 with only short periods of runoff
occurring within these periods. The stream had zero flow
at Slab Cabin Run Upper (SLU) from August 30, 2000 through
November 25, 2000, then July 15, 2001–March 19, 2002.
Several studies have shown both Buffalo Run and Slab Cabin
Run to be seasonally losing or perched (Moorshead, 1975;
Krothe and Parizek, 1979; O’Driscoll and Dewalle, 2002;
O’Driscoll, 2004).
Stream losses between nested gages occurred for brief
periods along most streams, with the exception of Logan
Intercept (C) = -10.306 (Slope) + 11.061
R2 = 0.8942
Groundwater Control
10
Intercept (C)
LOL
TR
8
LOU
SPU
SPA
SPM
6
SLL
SLU
CR
SPH
4
BUU
BUL
Meteorological
Control
2
0
0
0.2
0.4
0.6
0.8
1
Slope
Figure 7 A summary of slope versus intercept of the weekly air–water temperature relationships (October 1999–September 2002)
for the 12 study locations (site locations listed in Table 1).
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
Difference in Discharge Downstream (m3/s)
Branch and the Spring Creek Milesburg reaches. During the
period of August 24, 2005–September 16, 2005, no rainfall
occurred within the watershed. The differences in runoff
between nested gages on September 15, 2005 provided an
indication of stream reaches that were receiving the largest
ground water inputs (see Fig. 8). Based on this analysis the
greatest ground water inputs occurred between Spring
Creek Axemann and Spring Creek Milesburg and between
Upper and Lower Logan Branch. Ground water inputs were
weak or non-existent along Slab Cabin Run, Buffalo Run,
and between Upper Spring Creek and Houserville stations.
Streamflow-duration curves also reveal the differences in
streamflow variability between losing (Buffalo Run and Slab
Cabin Run) and gaining streams (Thompson Run and Logan
Branch) (see Fig. 9). The nested discharge data and flow
149
duration curves both indicate that of the streams studied
Slab Cabin Run and Buffalo Run both exhibited periods of little to no stream gains and did not commonly receive large
ground water inputs.
Discussion
Energy–flux at the air–water interface for
Thompson Run and Lower Buffalo Run
The one-dimensional heat advection equation describes
stream temperature variations in time and space (Mohseni
and Stefan, 1999):
AoT=ot þ oðQTÞ=ðoxÞ ¼ bS=qw Cpw
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
Spring
CreekUpper to
Houserville
Slab Cabin Buffalo RunSpring
Run- Upper
Upper to
Creekto Lower
Lower
Houserville
to Axemann
Logan
Branch Upper to
Lower
Spring
CreekAxemann to
Milesburg
Figure 8 The differences in streamflow between nested gages (downstream–upstream discharge) on September 15, 2002.
Discharge is presumed to be groundwater as rainfall did not occur in the watershed between August 24 and September 16, 2002.
Daily discharge (cm/day)
1.E+01
1.E+00
LOL
1.E-01
TR
BUL
1.E-02
1.E-03
SLL
1.E-04
1.E-05
BUL
LOL
TR
SLL
1.E-06
0
20
40
60
80
Percent of time daily discharge equalled or exceeded
100
Figure 9 Streamflow-duration curves for Lower Logan Branch, Thompson Run, Lower Buffalo Run, and Lower Slab Cabin Run sites
for the period of October 1999–September 2002.
150
M.A. O’Driscoll, D.R. DeWalle
where A is the flow cross-sectional area, oT is water temperature change, ot is time interval, Q is streamflow, T is
water temperature, ox is distance downstream, b is average
stream width, S is net heat exchange across the air–water
interface, qw is density of water, and Cpw is heat capacity
of water. Streams receiving significant ground water inputs
should have large advective terms (o(QT)/(ox)) that decrease in importance with distance from the ground water
source. During the summer, ground water inputs will act
as a heat sink along a stream reach. During the winter,
ground water inputs will act as a heat source.
The importance of the advection of ground water to
stream temperatures at Thompson Run and Lower Buffalo
Run can be shown directly by a comparison of the advective
term of the heat advection equation for the two streams. At
Thompson Run large stream temperature gradients exist between Thompson Spring and the Thompson Run temperature
measurement station, in contrast to very small temperature
gradients from Upper to Lower Buffalo Run stations (see
Fig. 10). This indicates that advection of ground water is
of little importance to stream temperatures at Lower Buffalo Run, but very important to Thompson Run stream
temperatures.
Overall, the net energy gains and losses from both
streams are dominated by longwave and shortwave radiation fluxes and the latent heat and sensible heat losses were
generally of lesser importance. Greater net energy losses in
winter and gains in summer were exhibited by Thompson
Run when compared to Buffalo Run. Since Thompson Run
water temperature variations are subdued annually, periods
of extreme air temperatures in winter and summer promote
large temperature gradients and greater net energy exchange across the air–water interface.
Water temperature–air temperature relations
In the Spring Creek watershed, upstream water typically includes mountain runoff, seeps, and spring discharges. The
discharges from major springs and their constant temperatures provide large sources of energy during winter and
act as energy sinks in the summer. Meteorological energy inputs or losses gain importance with distance from the major
ground water inputs. As distance from a spring or seep increases, the meteorological influence on water temperature
increases in the absence of additional ground water inputs.
In some cases, where losing conditions are present, stream
depth may also decrease downstream and thus the meteorological influences may have greater effects on stream
temperature.
A comparison of the slope and intercept of the stream–
air temperature relationship for all 12 locations indicates
that the stream–air temperature relationship can reveal
information about the nature of the controls on stream
water temperatures, with ground water control segments
indicated by intercepts closer to the regional ground water
temperature and gentle slopes, and streams that are more
influenced by meteorological energy inputs having steeper
slopes and lower intercepts (see Fig. 7). Stream segments
with strong ground water controls on water temperature include Lower Logan Branch, Thompson Run, and Upper Spring
Creek. All are located within 2 km of springs and seeps. Buffalo Run and Slab Cabin Run are streams that have water
temperatures that are responsive to meteorological conditions, these are generally seasonally losing streams. These
streams typically cease to flow along several upland segments during dry periods, particularly in late summer. The
Spring Creek Axemann site may have artificially elevated
water temperatures due to wastewater and fish hatcheries
discharges upstream that counteract the influence of spring
inputs, particularly during summer months.
In a study of 39 streams in Minnesota, Pilgrim et al.
(1998) studied weekly stream–air temperature relations
and found an average intercept of 1.7 C and slope of
0.99. In a similar study, for 11 streams within the Mississippi
River basin, Stefan and Preud’homme (1993) found an average intercept of 2.9 C and slope of 0.86. These analyses
were based on records from US Geological Survey gaging
stations, which are likely along larger streams than those
within the Spring Creek watershed. Within the Spring Creek
watershed the average intercept was 6.14 C and the aver-
0.0003
degrees-C/second
0.0002
Thompson
Run
0.0001
0
-0.0001
-0.0002
Lower
Buffalo
Run
-0.0003
-0.0004
-0.0005
Jul99
Nov- Mar99
00
Jul00
Nov- Mar00
01
Jul01
Nov- Mar01
02
Jul02
Oct02
Feb03
Figure 10 The influence of advection on water temperatures as indicated by stream velocity (U) times the downstream
temperature gradient (dT/dx). Missing data for Buffalo Run from July 2001–March 2002 is due to the lack of streamflow at Upper
Buffalo Run.
Stream–air temperature relations to classify stream–ground water interactions in a karst setting
age slope was 0.47. The differences in stream–air temperature relations in the Spring Creek watershed are related
to the importance of ground water inputs to streamflow.
In a recent study by Webb et al. (2003) four streams in
the Exe Basin, Devon, UK, were found to have weekly
stream–air temperature regression slopes of 0.590–0.946
and intercepts ranging from 1.27 to 4.24 C for ground
water-fed stream catchments ranging from 2.1 to 601 km2.
To illustrate the importance of ground water inputs to
the stream–air temperature relationships within the Spring
Creek watershed a two-component mixing model was used
with Lower Buffalo Run data to simulate the response of
the stream–air temperature relationship to increased
ground water inputs. Regional ground water temperature
is approximately 10.9 C in the Spring Creek watershed
(Langmuir, 1971). Simulations mixed incremental fractions
of 10.9 C ground water with stream water of measured
temperatures (average for October 1999–September 2002)
at Lower Buffalo Run using the following equation:
Simulated mixed temperature
¼ ½ð1 fraction of ground water inputÞ
measured stream temperature at Lower Buffalo Run
þ ½ðfraction of ground water inputÞ
ground water temperature ð10:9 CÞ
Intercept (degrees-C)
Ground water inputs of 10–90% of total streamflow were
simulated at 10% increments. The slopes of the simulated
stream–air temperature relationship ranged from 0% for
100% ground water, to 0.672% for 100% stream water (see
Fig. 11). The relationship of the slope versus intercept
was represented by a line with a slope of 11.064 and an
intercept of +10.9. This line is very similar to the line representing the range of slope and intercept stream–air temperature relationship values calculated for the 12 points in the
Spring Creek watershed (see Fig. 7) with a slope of 10.306
and an intercept of +11.061. These simulations support the
importance of advection of ground water as a control on
stream temperatures in this valley, assuming that other factors are not contributing to the water temperatures.
The link between stream–air temperature relations and
hydrology in Spring Creek Basin is more directly shown by
12
100%
11
10
9
8
7
6
5
4
3
0.0
90%
151
comparing average hydrologic yield (streamflow/watershed
area) and the slope and intercept of the stream–air temperature relationship (see Fig. 12). Streams with large hydrologic yields have significant ground water inputs that are
translated to the gaging stations and damp the effects of
meteorological controls on stream temperature. Lower
hydrologic yield streams such as Buffalo Run and Slab Cabin
Run tend to lose water through their channels, more drainage occurs in the subsurface; therefore they have lower
ground water inputs, lower flow rates, and stream depths
allowing stream temperatures to be more influenced by
meteorological conditions.
Based on an equilibrium temperature analyses, Mohseni
and Stefan (1999) found that the slope of the air temperature–equilibrium temperature relationship for streams
where advective inputs are not significant heat sources is related to the ratio of the emission of thermal radiation from
the atmosphere plus the sensible heat loss versus the emission of longwave radiation from the water body plus the sensible heat loss. The intercept is a complicated function that
relates solar and longwave radiation inputs, evaporative,
and sensible heat losses. In the Spring Creek watershed,
large springs and seeps are common and the slope and intercept of the air–stream temperature relationship is related
to the magnitude of ground water inputs, the distance from
the ground water input source, as well as the meteorological conditions. These results indicate that the slope and
intercept of the stream–air temperature relationship are
good indexes of the importance of ground water inputs to
streams in karst settings. A direct comparison of the importance of the meteorological influence on stream temperatures between two streams can be obtained by the
comparison of the slopes of their stream–air temperature
relationship.
From a watershed management perspective, stream
shading would be less effective in moderating stream temperatures in strongly ground water-fed segments (revealed
by gentle slopes and large intercepts) but more effective
along losing reaches or stream reaches distant from ground
water inputs, as indicated by the air–water temperature
relationship. Ground water withdrawals that affect springflows also have the potential to affect stream temperatures, the loss in ground water inputs would result in
80%
70%
intercept = -11.064(slope) + 10.9
60%
50%
40%
30%
20%
10%
0.1
0.2
0.3
0.4
0.5
0.6
0%
0.7
Slope
Figure 11 The computed relationship of slope versus intercept of the weekly air–water temperature relationship for a twocomponent mixing model with end members consisting of 10.9 C ground water and stream temperatures measured at Lower Buffalo
Run over the course of the three-year study period. Each fraction indicates a 10% increase in groundwater input.
M.A. O’Driscoll, D.R. DeWalle
Intercept (degrees-C) and
Slope
152
10
9
8
7
6
5
4
3
2
1
0
intercept = 17208(hydrologic yield) + 4.0945
2
R = 0.7273
Intercept
Slope
0
0.00005
0.0001
slope= -1529.2(hydrologic yield) + 0.6572
2
R = 0.6634
0.00015
0.0002
0.00025
0.0003
0.00035
3
Hydrologic Y ield (m /s/ha)
Figure 12 The relationships between average hydrologic yield (October 1999–September 2002) of the 12 study locations and the
associated slope and intercept of the water–air temperature relationship for those locations.
greater meteorological controls on stream temperature and
greater water temperature variability. For example, using
the simple two-component mixing model for Buffalo Run,
for a mid-summer week, if ground water flows to the stream
dropped 30%, then weekly average stream temperatures
would rise more than 3 C.
Conclusions
Hydrological and water temperature data revealed a large
degree of spatial and temporal variability in the stream–
ground water interactions in this carbonate watershed.
Streams only several kilometers apart showed large differences in streamflow and water temperature regimes, a
characteristic of carbonate watersheds. Correction of
stream energy fluxes for streams with significant riparian
shade are especially problematic and significant due to vegetative impacts on wind speeds and both longwave and
shortwave radiative fluxes. Subdued temporal variations in
surface water temperature alone can be indicative of
ground water inputs, but consideration of the stream–air
temperature relationship can help to indicate the strength
and proximity of the ground water input signal.
Stream settings ranged from strongly ground water-fed
to seasonally losing. The nature of the stream–air temperature relationship indicated the importance of ground water
advection versus meteorological controls on stream temperatures. The slopes and intercepts of the stream–air temperature relations indicated that an effect of ground water
advection is apparent in their range of slopes and intercepts
as is evident by the maximum intercept of 9.07 C at Lower
Logan Branch.
As a management tool, stream–air temperature relations can reveal the importance of ground water inputs, particularly in smaller watersheds where the travel time of
surface waters is short enough to allow surface waters to
carry thermal evidence of ground water inputs. Records of
stream–air temperature relations over time can be indicative of changing hydrological regimes. For instance, if
ground water withdrawals were pirating significant amounts
of ground water from a stream, the slope and intercept of
the air–water temperature relationship at a point along a
channel would increase and decrease, respectively. At a lar-
ger scale, the spatial and temporal variability of water temperature in a carbonate watershed may be estimated by
remote sensing. Watershed scale mapping of surface water
temperatures over time can reveal ground water inputs
across the landscape and their seasonal variability.
Acknowledgments
We thank Katie Ombalski at the ClearWater Conservancy
and also the US Geological Survey for providing three years
of streamflow and water temperature data. We also express
our gratitude to the Water Resources Monitoring Committee
for their data collection efforts and willingness to share
data. In addition, we acknowledge the SURFRAD network
for three years of radiation and meteorological data. We
also thank the reviewers who provided comments that
helped to greatly improve the manuscript.
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