Spatial and Temporal Variation of Groundwater and Surface Water

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					      Spatial and Temporal Variation of
  Groundwater and Surface Water Interaction
    along the Gallatin River, Four Corners,
                                        Montana
                                   Mark A. Shaffer
                             MSU Department of Earth Science




Colored infrared image of Four Corners Montana and the West Gallatin River taken in August
2000. Red areas represent photosynthesizing plants which are in contact with water during the dry
season



                                         Abstract
        As previously irrigated agricultural land is converted to residential developments
along the West Gallatin River, changes to the hydrologic system are anticipated resulting
from decreased aquifer recharge which results from decreased irrigation and increased
residential consumption of the ground water. Managing groundwater and surface water
resources conjunctively, possibly by aquifer augmentation (injecting surface water into
the aquifer), has been proposed as a means of mitigating anticipated stream flow declines,
resulting from increased groundwater withdrawals and decreased aquifer recharge. An


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 1 of 29
understanding of the current dynamic relationship between the West Gallatin River and
the West Gallatin Alluvial Aquifer is required in order to calibrate future groundwater
models which could be used to test theoretical augmentation regimes and manage the
ground and surface water conjunctively.
        This report is a preliminary characterization of the ground and surface water
interactions near Four Corners Montana during July and August of 2006 (Fig. 1). Specific
electrical conductance measured in surface water features, the W. Gallatin River’s
streambed, and the Aquifer indicate that groundwater discharge into the West Gallatin
River increased from July to August and was statistically significant at a 95% confidence
level. Significant differences also occur along the stream profile in a single month.
Statistical differences were observed between the hydrologic subgroups described by the
USGS report “Geology and ground-water resources of the Gallatin Valley, Gallatin
County, Montana” (Hackett, 1960). A statistical analysis indicates groundwater flux was
greater in the Gateway subgroup than the Belgrade subgroup during July and August of
2006.
        Ground and surface water levels corroborate the results from the statistical test of
specific conductance that groundwater flux into the Gallatin River increased from July to
August. Hydrologic gradients in the alluvial became greater towards the river from July
to August as groundwater elevations rose in the aquifer’s margin and river stage declined.
Spring creek discharge in the fluvial plain also increased from July to August. Diurnal
stream temperature fluctuation, streambed specific electrical conductance, and
potentiometric surfaces were also used to characterize the locations in the river channel
of groundwater discharge.

                                       Methods
      Specific electrical conductance (SC) was used in conjunction with water level
measurements in surface and groundwater bodies to test the hypothesis that;

1.) Groundwater discharge increases from July to August.

2.) During July and August groundwater discharge is greater in the Gateway sub-reach
than the Belgrade sub-reach.

       SC measurements and diurnal stream temperature fluctuations were also
compared with physical channel characteristics to describe the distribution groundwater
discharge along the longitudinal profile of the stream.

Specific Electrical Conductance as an Indicator of Source

        Specific conductance (SC) is an approximate measure of the dissolved mineral
matter in water. During the spring, snow melt is the primary source of surface water in
the Gallatin River and is relatively low in dissolved minerals compared to the local
groundwater. Because these sources of water differ in mineral content, SC can be
measured in the streambed or in a well and be used to approximate the water’s source,
surface or groundwater.


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 2 of 29
        In 1954, Hackett (p.168) hypothesized that, “Although there is no analytical
proof, the mineralization of groundwater in places where the water levels are directly
affected by stream flow probably varies somewhat in response to the salinity of the
surface water”. SC data collected for this study indicates that fluctuation of the SC in
wells near the West Gallatin River do fluctuate concurrently with fluctuations in the SC
of the river.
        SC values from groundwater sources are typically much higher than surface water
values. Surface water SC values ranged between 130 and 306 µS and groundwater
values ranged between 193 and 708 µS during the summer of 2006,. Observations by
Hackett (Hackett, 1960) and Slagle (Slagle, 1994) from the Gallatin Valley indicate that
dissolved solids in Quaternary alluvium are low compared to other geologic units, such as
Tertiary deposits and Precambrian bedrock.
        Hackett observed that in the Gallatin Valley water in quaternary deposits, such as
the West Gallatin Alluvium, was of the sodium bi-carbonate type and had relatively low
mineral content. SC values measured by Hackett in the alluvium ranged between 227-620
µS. Observation by Hackett and Slagle show that a slight degree of mineralization occurs
as groundwater travels down valley. Hackett observed, “In the lower part of the valley,
where streams are effluent, the total mineralization of the surface water is but slightly
greater than in the upstream part of the valley where streams are influent”(Hackett, p
166).
         In the Tertiary deposits surrounding the alluvium groundwater is also of the
sodium bi-carbonate type and initially similar to the alluvial water but that mineralization
increased with depth. Precambrian units near the study area possess the greatest degree of
mineralization. SC values measured from the Precambrian bedrock at 450 ft below the
surface were as high as are near 1,900µS (Hackett, p 170 Table 30).
        Water entering the aquifer may also increase in mineral content as it passes
through the soil profile. Therefore irrigation water recharging the aquifer will increase in
mineralization and will be higher in SC than surface waters.
        Because surface water has the lowest SC compared to other waters in the area and
water in the West Gallatin Aquifer undergoes little mineralization, elevated SC values in
alluvial and surface waters must be the result of either groundwater entering the alluvial
and stream system from sources such as regional/intermediate flow in the Tertiary and
Precambrian bedrock or irrigation water.

Measurement Locations of Specific Electrical Conductance

        Specific electrical conductance was sampled from June through August 2006
using a YSI incorporated YSI 30 Hand Held Salinity, Conductivity, and Temperature
System. The unit’s sensor was 1 inch in diameter and located at the end of a ten foot
cable which allowed for measurement to be made “down hole” in the 1 inch diameter
monitoring wells and streambed piezometers. Water was pumped from wells where the
depth to water was to beyond the cables reach. Comparison of SC values from wells
sampled “down hole” and pumped typically differed by less than 20 µS.

Streambed Piezometers



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 3 of 29
        65 streambed piezometers (SBPs) were installed to depths of 20-42 inches below
the bed surface, along a 10 km reach of the West Gallatin River. The 65 individual SBPs
comprise 22 set of 2 to 5 individual SBPs per site (Fig. 2). These sites are roughly spaced
0.5 km apart in pools, because installation in riffles was not possible. The individual
SBPs at each site are located to sample a variety of flow directions within each pool, the
pool head, pool tail, and intermediate position between the head and tail. This sampling
scheme was chosen because other studies (Woessner 2000, Wright et. al, 2006) indicate
that the flux of water of through in the streambed varies in regard to these positions in
the stream channel (Fig.3).
        Two sample runs were made of the entire population of SBPs in the summer of
2006. Due to the difficulty accessing all these sites, each “run” required two full days to
complete. The first run occurred on July 17th and 18th and the second run occurred on
August 23rd and 24th.

Surface Water Locations
        From June through August 2006 specific conductance was sampled in the W.
Gallatin River, an emerging spring, and two spring creeks, Elk Grove Slough and Fish
Creek. Both creeks emerge in the fluvial plain along the study reach. (Fig. 4). River SC
measurements were also recorded at each SBP location when a SBP sample was taken.

Groundwater Measurement Locations
        34 Geoprobe wells, 1” in diameter were installed along the fluvial plain for this
study (Fig. 5). These wells were located in positions adjacent to the river and up to 1 mile
away from the river in variety of settings ranging from agricultural to residential. The
wells range from 10-30 feet deep throughout the study area.
        Monitoring wells were sampled for SC from March through August 2006.
Measurements were made either “down hole”, or by pumping the water into a bucket and
sampling in the field when the depth to water exceeded 10 ft. Comparison of “down hole”
and pumped of values in individual wells, were within 10 – 20 µS of each other.

Specific Conductance Values as an Indicator of Source
       In order to qualify the degree of groundwater discharge occurring at a point in the
streambed, SC values measured in a streambed piezometer (SBP) were subtracted from
the average local groundwater value and divided from by the difference between the
average local groundwater value and the average river water value on the day of
measurement, equation 1.

Equation 1.

                           ( μlLocalGW − SBP)
                                               =Sc Proportion
                         ( μLocalGW − μRiver )

       The result, SC Proportion, is a unit-less value that describes the relative distance
of a SBP’s specific conductance from the local mean groundwater specific conductance
compared to the total difference between the local groundwater Specific conductance and


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 4 of 29
the average river water value on the day of measurement. Therefore, SC Proportion
values close to 1 are similar to river water and values closer to 0 are similar to
groundwater.
       This proportion normalizes SC values in space and time as specific conductance
values change in the aquifer and river. This proportion is needed to statistically compare
SC values measured in the streambed in different areas and on different days. By
converting actual SC values to this proportion statistical test can be conducted comparing
the mean SC Proportion values for any place or time in the study area.

Rational for Terms Used in SC Proportion Calculation

µLocal Groundwater Term
        Specific conductance varied in space and time across the study area. From June to
August, during high flows resulting from snow melt, some wells in the study area showed
declines and subsequent rises in SC values which corresponded with changes in river SC
values. Others wells remained stable during high water (Fig. 6). The wells showing a
fluctuation in SC values were assumed to be affected by surface water traveling through
the streambed into the alluvial aquifer and decreasing SC values in at the well. Wells with
a fluctuation greater than 50 µS were removed from the population of wells used to
calculate the average local groundwater SC, because they were consider not
representative of the local aquifer SC value.
        The stable wells considered representative of the aquifer SC, showed an increase
in value of SC from north to south (Fig. 7). The increase in average SC is believed to be
the result of groundwater entering the fluvial aquifer from Precambrian bedrock located
in the center of the study area, raising the ambient SC in the aquifer. In addition to the
north to south increase in SC across the study area, an east to west decreasing trend is
present in the northern monitoring wells (Fig 8).
        The east to west difference is believed to be the result of groundwater entering the
alluvial aquifer from Tertiary benches east of the study area and raising the SC values in
the aquifer. SC measured in spring features to the west in the zone of lower SC values
and on the other side of the river, remained stable during peak flows and SC lows in the
W. Gallatin River, indicating little to no influence from the river in this area of the
aquifer (Fig 9).
        Areas with similar groundwater SC values were defined by drawing lines of equal
SC through the study area (Fig. 10). The result is three distinct zones with different
groundwater mean SC values. The south western in the vicinity of Fish Creek(I), the
middle zone up gradient of the Precambrian bedrock(II), and the lower zone down
gradient of the Precambrian bedrock(III). The mean values for these zones are listed
below in Table 1.

Table 1. Mean groundwater specific conductance values from wells with stable measurement
from June through August 2006. Mean values were used as µLocal Groundwater values in SC
Proportion calculation which was applied to SBPs located in each zone.
        Zone             Number of Samples          Mean Specific       Standard Deviation
                                                     Conductance
           I                      11                      372                  27.77
          II                      20                      461                  26.27


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 5 of 29
         III                      22                     481                     66.5

µRiver Term
        Sampling all 65 SBPs required two days to complete. During that time river SC
values were observed to have changed. In order to normalize the river SC value with
respect to this diiference, the SC of the river was measured at each SBP and the average
of all measurement for that day was used instead of the average for the both days. A daily
average was chosen in place of an individual values to avoid spatial bias.
        SC varied dramatically along the longitudinal profile of the W. Gallatin River,
especially in the southern portion of the Gateway subreach. Spring channels were
observed which confluenced with the main river channel. When these spring channels
intersected the river, a local spike in surface water SC was observed along the
longitudinal profile(Fig. 11). In order to avoid biasing an individual SBP’s SC
Proportion, the mean value for the day was assumed to be representative for all SBPs.
See Table 2 below for River SC values.
        This average is considered representative because it is assumed that groundwater
flow in the streambed (hyporheic flow) has a horizontal component and therefore, the SC
value measured in the SBP is the result of a mixture of surface water directly above and
surface water entering the streambed up gradient of the position.

Table 2. Average specific conductance values on days streambed piezometers were measured.
        Date                 Number of                  Mean                  Standard
                              Samples                                         Deviation
  July 17, 2006                 25                     251.41                   13.26
  July 18, 2006                 36                     275.36                   3.25
 August 23, 2006                25                     306.33                   14.18
 August 24, 2006                36                     303.34                   5.238

Statistical Test of SC Proportion Means

       Three statistical test of the mean SC Proportion were conducted at the 95%
confidence level to test the hypothesis that;

1.) Mean SC Proportions decreased (groundwater flux increased) from July to August.

2.) Mean SC Proportion was lower (groundwater flux was greater) in the Gateway sub-
reach than the Belgrade sub-reach in July and August.

        The position of individual SBPs cannot be considered a true simple random
sample. The impenetrable nature of the Gallatin River Alluvium would not allow for the
installations of piezometers in riffles due to the difficulties of installing the piezometers
in these locations and the larger cobbles sizes present in these features. Additionally, the
W Gallatin River is anabranched along the study reach and piezometers were only
installed in the river’s main channel. As a result inferences should not be made to other
channels along the reach. However, because the SBPs were positioned to sample
locations in the channel representing a range of groundwater flux(Pool Head, Pool Tail,


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 6 of 29
and Intermediate Pool), it is assumed that the SBP sets are reasonably effective at
estimating the true mean SC Proportion (a qualitative measure of groundwater flux) for
the pool.
         Technically speaking, the only conclusion which should be made from these
statistical tests is that average SC Proportions increased over time in the pools located in
the main channel. Another legitimate conclusion is that the average SC proportion of
pools for a sampled reach are different than average SC Proportion of pools in another
sampled reach. Furthermore due to the observational nature of this study, no cause and
effect relationships between the differences in SC proportions can be concluded from
these results.

Test of Hypothesis 1. Groundwater flux increased from July to August
        A comparison of two population means was conducted for paired SBP samples
between July and August using a T Test of the mean difference between individual SBP
SC Proportions. This test assumes dependence between the individual SBPs sampled.
        The two assumptions required for this test are that the populations are simple
random samples and that the population size of the samples is greater than 30, for
asymmetrical distributions. Population size for each sample consisted of all SBPs along
the study reach and was greater than 30 (n entire study reach= 61). Although the sample is
admittedly not a true simple random sample, the sample was collected to the best of the
researcher’s ability. However it should still be acknowledged that sampling bias may
present in this analysis.

Test of Hypothesis 2 and 3, Groundwater discharge was greater in the Gateway sub-
reach than the Belgrade sub-reach in both July and August.
        A test of the difference between mean SC proportion in pools in the Gateway sub-
reach and the Belgrade sub-reach was conducted for independent samples using a T Test
for July and August. The tests were conducted separately for each month. The
assumptions required for such test are the same as described above. Both populations
sizes are greater than or equal to 30 (n above Shed’s= 31, n below Shed’s = 30). The assumption
of the simple random sample and its’ implications are the same as discussed above for
hypothesis 1. The statistical software package R was used to conduct these three tests.
The code and out put for these test is included with this report in Appendices I, II, and III.

Change in Water Level Elevations
       Surface and groundwater levels were recorded using Solinst pressure transducers
(Barro and Level Loggers) and Tru Track capacitance rods. Measurements were recorded
hourly during the period of interest. Pressure transducer measurements are barometrically
compensated by another pressure transducer (Solinst Barro Logger) dedicated as a
barometer located in the study area.

 NOTE: The data used for this report and analysis is provisional and is subject to revision.
Monitoring well positions have not been located using survey precision instruments. Water levels
from pressure transducers have not yet been corrected for instrument drift. As this study
continues well positions will be located using survey grade GPS technology and pressure
transducer will be corrected for drift.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 7 of 29
Surface water Levels
       Surface water levels were recorded in the West Gallatin River at Axtell Bridge, in
Fish Creek near the confluence with the W. Gallatin, and in two locations on the Elk
Grove Slough (Fig. 12).

Groundwater Levels
       Groundwater levels for 18 well were available for this analysis. Water level
measurements were recorded hourly. The depths of wells ranged from 20 – 30 feet below
ground surface. A potentiometric map was produced “by hand” from this data of
groundwater flow in July and August. Transect perpendicular to the groundwater gradient
were produced a locations and used to corroborate the results of the statistical analysis.

Diurnal Stream Temperature Fluctuation
        Stream temperature was recorded hourly from Midnight 9/14/2005 to 9/17/2005,
for purpose of assessing differences in diurnal fluctuation at four different sites as method
of qualifying the relative amounts of groundwater discharge at each site. This technique
is described by Constantz in his application of this technique to asses groundwater
discharge into alpine (Constantz, 1998).
        Although these temperatures were not recorded during the time frame of this
analysis, the information provided is relevant for describing the nature of the physical
distribution of groundwater discharge into the Gallatin River within the study area.
Temperatures were recorded using Solinst Level Loggers equipped with temperature
sensors.


                               Results & Discussion
Statistical Analysis of SC Proportions

Test of Hypothesis 1. Groundwater flux increased from July to August
        The Matched Paired t-test, conducted at a 95% confidence level, indicates that on
average the SC proportion decreased (groundwater flux increased) at streambed
piezometer sites between July and August 2006. The mean difference between individual
sites was --0.1234. See Appendix I for the R code and output used run this analysis. See
Appendix IV for individual SBP measurements and differences.
        The increase of groundwater flux into the stream from July to August was not
ubiquitous along the study reach. In August the minimum SC proportion was lower
groundwater flux higher however, the maximum August value is higher, groundwater
flux lower (Tab. 3,Fig. 14).
        The highest and lowest ground groundwater flux in August were both located in
the northern portion of the study area, where on average the greatest increase in
groundwater flux was concentrated (Fig. 15). The highest groundwater flux occurred near
the vicinity of the Precambrian bedrock outcrop which corresponds with the narrowest
section of the alluvial aquifer in Set 6, Site # 18. See Appendix VI for individual SC
values.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 8 of 29
        The lowest groundwater flux was situated upstream of the highest in Set 3(Fig
16). High SBP values however, should not be mistaken for aquifer recharge or a total
absence of groundwater flow toward the river along the reach in question. Waters
sampled with large SBP values are similar to river, however this water may be hyporheic
and follow a flow path which leads it back to the river channel after intersecting a
groundwater flow path.



Table 3. Minimum, maximum, mean, and difference between minimum and maximum for SC
prop values in July and August.
                             Minimum                Maximum                      Mean
      July                     -0.0500                 1.0728                    0.8113
     August                    -0.8923                  1.123                    0.6869
   (Aug – July)                 -0.84                  0.0502

Statistical Test 2 and 3.Groundwater discharge was greater in the Gateway sub-reach
than the Belgrade sub-reach in both July and August.

       The evidence indicates that the mean SC Proportion was significantly greater in
the Gateway sub-reach than the Belgrade subreach in both July and August at a 95%
confidence level. See Table 4 below, for mean values for the sub-reaches in July and
August.

Table 4. Mean SC proportions for the hydrologic subgroups described by Hackett
                                         Gateway                         Belgrade
           July                           .7700                           .85705
          August                          .6224                            .7582

Water Level Elevations

        Lines of equal head indicate that groundwater flow changes from converging on
the river in the Gateway sub-reach, transitions to roughly parallel near the vicinity of
Four Corners, and turns laterally flowing almost perpendicular to the river near the
northern boundary of the study area. The accuracy of these lines is questionable however
due to the lack of controls and reliable well positions. However these gradients still
manage to corroborate the SC proportions depicting increased groundwater flux when
groundwater flow converges on the river channel (Fig, 17, 18, and 19).
        Fluctuation of groundwater levels through out the study area was not great enough
from July to August to warrant adjusting the lines of equal head for these two periods.
However, plotting the change in what levels in at the wells and the river indicates that
groundwater levels rose on the up gradient fringes of the aquifer and groundwater levels
declined close to the river. The decline in the river stage was 0.5 ft. (Fig.20).
        These observed change in head would result in an increased hydrologic gradient
and flux towards the Gallatin River in the northern portion of the study area. This



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 9 of 29
information corroborates the statistical test that groundwater flux increased from July to
August (Fig. 17).

Down Gradient Transect of Change in Groundwater Elevations
        Plotting well logs located along the groundwater flow path in the southern portion
of the study area illustrates that between July and August recharge exceeded discharge
during this period and water levels rose. However, as the water levels increased down
gradient, the Elk Grove Slough increased in discharge tipping the ratio between recharge
discharge and water levels equalized. (Fig. 21).

Diurnal Temperature and the Physical Distribution of Groundwater Discharge to the
Gallatin River Channel
        Diurnal stream temperatures measured in September of 2005 illustrate an import
aspect of the groundwater discharge into the stream channel. Not all groundwater
discharge enters the river through the streambed channel. Small channels have been
observed which confluence with the main river channel along the entire study reach
data from one such channel in the Gateway sub-reach illustrates that at these confluences
daily stream temperature is stable, like groundwater compared to temperatures measured
in other part of the stream (Fig. 22). Additionally, these features explain the spikes
observed in the longitudinal profile of river specific conductance in Figure 11. The spike
of SC values in Figure 11 occurs in just down stream from the stable diurnal temperature
measured in Figure 22.

Specific Conductance Fluctuation in Wells as an indicator of losing
segments
        A qualitative relationship can be observed between the fluctuations of SC values
in monitoring wells and groundwater flow direction in the aquifer. In the Gateway
subreach were groundwater gradients converge on the river, SC fluctuation is less. Down
gradient of the bed rock high, where groundwater flow diverges from the river, a higher
fluctuation in SC can be observed (Fig. 23).

                                      Conclusion

         A statistical analysis of the groundwater flux into the Gallatin River indicates that
flux increased from July to August along the entire study reach. Additionally a higher
proportion of flux occurred in the Gallatin Gateway sub-reach during both periods. These
statistical results were corroborated by groundwater flow directions in the alluvial
aquifer. Groundwater may enter Gallatin River through multiple pathways; including
spring creeks, side channels discharging groundwater, or the as flux through the river
bed. The observed fluctuation of specific electrical conductance in monitoring wells
corresponds with groundwater directions diverging on from the river and low
groundwater flux values estimated by SC proportion method described. The use of the SC
proportion is an effective means to statistical test of the qualitative amount of
groundwater contributions to the Gallatin River as variables change in space and time.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 10 of 29
                                  Future Analysis
        Data collected from the SBPs in November will also be incorporated into the data
sets from July and August for the analysis described below. Future data analysis will
include examining temperatures and vertical head gradients measured from the SBPs.
This data will be used to gain a better understanding of the relationship between
groundwater flux, the river and the hyporheic zone. The effects of channel characteristics,
such as channel slope and sinuosity, upon the specific conductance, vertical head
gradient, temperature will also be conducted as part of this projects final analysis.
Seepage run data, stream discharge measurements, collected in July and August will be
used to assist in interpretation measurements from the SBPs. Finally the relationship
between irrigation, changes in groundwater temperature, elevation, and specific
conductance, and groundwater flux into the W. Gallatin will also be examined.

                                         References
Conant, B. 2004. Delineating and Quantifying Groundwater Discharge Zones using
Streambed Temperatures. Ground Water 42 no. 2: 243-257.

Constantz J. 1998. Interaction between stream temperature, streamflow, and groundwater
exchanges in alpine streams. Water Resources Research 34 no.7:1609-1615.

Hackett, O.M., Visher, F.N., McMurtrey, R.G., and Steinhilber, W.L., 1960, Geology and
ground-water resources of the Gallatin Valley, Gallatin County, Montana: U.S.G.S.
Water Supply Paper 1482, 282 p.

Slagle, S.E. 1992. Geohydrologic conditions and land use in the Gallatin Valley,
Southwestern Montana, 1992, 1993: U.S.G.S. Water resource investigations report 95-
4034.

Woessner, W. 2000. Stream and Fluvial Plain Groundwater Interactions: Rescaling
Hydrogeologic Thought. Groundwater Vol. 8, no 3. 423 -429.

Wright, K.K., Baxter, C.V., Li, J.L. 2006. Restricted hyporheic exchange in an alluvial
river sytem: implications for theory and management. Journal of American Benthological
Society, 24 no 3, 447-460.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 11 of 29
                                     Appendices

Appendix I. R code and output used for Paired t-test of the mean difference between
individual SBPs in July and August
> t.test(sc_prop_july,sc_prop_aug2,conf.level=.95,paired=T,alternative="greater")
      Paired t-test
data: sc_prop_july and sc_prop_aug2
t = 3.1882, df = 60, p-value = 0.001138
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 0.0592122       Inf
sample estimates:
mean of the differences
          0.1243984

Appendix II. R code and output used to for Two Sample t-test of the average SC
Proprtion values, measured in pools above and below Shed’s Bridge in July.
 > t.test(sc_prop_july~hackett,conf.level=0.95,var.equal=T,alternative="greater")

 Two Sample t-test
data: sc_prop_july by hackett
t = 1.7183, df = 59, p-value = 0.0455
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 0.002386104        Inf
sample estimates:
mean in group Belgrade mean in group Gateway
         0.8569517           0.7700125

Appendix III. R code and output used to for Two Sample t-test of the average SC
Proprtion values, measured in pools above and below Shed’s Bridge in August.
> t.test(sc_prop_aug2~hackett,conf.level=0.95,var.equal=T,alternative="greater")
      Two Sample t-test
data: sc_prop_aug2 by hackett
t = 1.4793, df = 59, p-value = 0.07219
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 -0.01761156       Inf
sample estimates:
mean in group Belgrade mean in group Gateway
         0.7582000           0.6223719




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 12 of 29
Appendix IV. Table of SC Prop values in July and August, and Differences used to
test hypothesis #1.
Sit SC Prop           SC Prop   Differenc   Sit   SC Prop    SC Prop      Differenc
e     July            Aug       e           e     July       Aug          e
3     0.6500          0.3538    0.2962      36    0.5215     0.4241       0.0975
4     0.5167          -0.3231   0.8397      37    0.8978     0.8544       0.0434
5     1.0500          0.9231    0.1269      38    0.8978     0.7342       0.1637
6     0.6333          1.0154    -0.3821     39    0.8441     0.9241       -0.0800
7     0.9083          0.9077    0.0006      40    0.3548     0.4177       -0.0629
8     1.0000          1.1231    -0.1231     41    0.9301     0.8608       0.0693
9     0.9083          1.0769    -0.1686     42    0.9126     0.9045       0.0081
10 0.9333             0.8769    0.0564      43    0.8932     0.7809       0.1123
11 0.9333             0.3538    0.5795      44    0.8835     0.8315       0.0520
12 1.0417             0.0923    0.9494      45    0.6408     0.0618       0.5790
13 -0.0500            -0.2462   0.1962      46    0.9612     0.9326       0.0286
14 0.9000             0.6615    0.2385      47    0.8495     0.8202       0.0293
15 0.6917             0.8769    -0.1853     48    0.9757     0.9326       0.0431
17 0.8250             0.9077    -0.0827     49    0.9223     0.8202       0.1021
18 0.7417             -0.8923   1.6340      50    0.9806     0.6348       0.3458
19 0.8417             0.7385    0.1032      51    0.8786     0.7247       0.1539
20 0.8083             0.5538    0.2545      52    0.7427     0.8483       -0.1056
21 0.8417             0.6308    0.2109      53    0.9806     0.9551       0.0255
22 1.0000             1.0308    -0.0308     54    0.9126     0.6910       0.2216
23 0.6507             0.9419    -0.2912     55    0.7184     0.6910       0.0274
25 0.9330             0.9032    0.0298      56    0.9903     0.9438       0.0465
26 0.3780             0.5355    -0.1575     57    0.6359     0.4157       0.2202
27 0.3971             0.2194    0.1778      58    0.7621     0.5225       0.2397
28 0.6555             0.7355    -0.0800     59    0.8350     0.5562       0.2788
29 0.7512             0.9097    -0.1585     60    0.6748     0.6180       0.0568
30 0.8565             0.4581    0.3984      61    1.0728     1.0281       0.0447
31 0.8852             0.5935    0.2916      62    0.9563     0.8708       0.0855
32 0.9474             0.8903    0.0570      63    0.8883     0.7921       0.0962
33 0.5968             0.8774    -0.2806     64    0.9466     0.8989       0.0477
34 0.9301             0.7975    0.1326      65    0.9126     0.9213       -0.0087
35 0.9624             0.9684    -0.0060




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 13 of 29
Appendix V . Set, position, and SC values in July and August for all streambed
piezometers.
site   Set     Position   SC July   SC Aug   site   Set   Position   SC July   SC Aug
3      2       Head       294       348      36     13    Head       364       394

4      2       Middle     310       392      37     13    Middle     294       326
5      2       Tail       246       311      38     13    Tail       294       345
6      3       Tail       296       305      39     14    Head       304       315
7      3       Head       263       312      40     14    Middle     395       395
8      3       Middle     252       298      41     14    Tail       288       325
9      4       Head       263       301      42     15    Middle     293       320
10     4       Middle     260       314      43     15    Middle     297       342
11     4       Tail       260       348      44     15    Tail       299       333
12     5       Tail       247       365      45     16    Head       349       470
13     5       Head       378       387      46     16    Middle     283       315
14     5       Middle     264       328      47     16    Tail       306       335
15     6       Middle     289       314      48     17    Middle     280       315
17     6       Tail       273       312      49     17    Middle     291       335
18     6       Tail       283       429      50     17    Tail       279       368
19     7       Head       271       323      51     18    Head       300       352
20     7       Middle     275       335      52     18    Middle     328       330
21     7       Middle     271       330      53     18    Tail       279       311
22     7       Tail       252       304      54     19    Head       293       358
23     8       Head       325       315      55     19    Middle     333       358
25     8       Tail       266       321      56     19    Tail       277       313
26     9       Head       382       378      57     20    Head       350       407
27     9       Tail       378       427      58     20    Middle     324       388
28     10      Head       324       347      59     20    Tail       309       382
29     10      Middle     304       320      60     21    Head       342       371
30     11      Head       282       390      61     21    Middle     260       298
31     11      Middle     276       369      62     21    Tail       284       326
32     11      Tail       263       323      63     22    Head       298       340
33     12      Head       350       325      64     22    Middle     286       321
34     12      Middle     288       335      65     22    Tail       293       317
35     12      Tail       282       308




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 14 of 29
                                           Figures




Figure 1. Location map, study area
Boundary defined by black line (Bozeman 1:100K)




Figure 2. Streambed piezometer locations along the Gallatin River. Flow is from right to
left. North is the left side of the map.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 15 of 29
Figure 3. Schematic of the scales of groundwater exchange along a hypothetical
longitudinal profile in a alluvial stream. Wright et. al.




Figure 4. Spring feature specific conductance measurement locations.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 16 of 29
Figure 5. location of SC measurements taken from monitoring wells. North is to the right
of the map. The W Gallatin Flows from South to North.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 17 of 29
                                              F luctuation of S E C M easurments from
                                                                Individual W ells
                                                           J une through A ugust 2006
                           14                                                                  100.00%
                           12                                                                  90.00%
                                                                                               80.00%
                           10
  F requency




                                                                                               70.00%
                                   8                                                           60.00%          F requency
                                                                                               50.00%
                                   6                                                           40.00%          C umulative %
                                   4                                                           30.00%
                                                                                               20.00%
                                   2                                                           10.00%
                                   0                                                           0.00%
                                          25          75          125          175

                                                    SEC microsiemens

Figure 6. Histogram of the change in specific conductance observed in all wells through
out the study area.


                                               North to South Distribution of the SEC values of Individual
                                                             Monitoring Wells August 2006
                                        650



                                        600
      Specific Electrical Conductance




                                        550
              (micro siemens)




                                        500



                                        450



                                        400
                                                                                                                 y = 0.0107x - 53849
                                                                                                                     R2 = 0.2232
                                        350



                                        300
                                        5050000       5052000       5054000          5056000         5058000         5060000           5062000
                                                                              UTM Easting (NAD 27)


Figure 7. North to south increasing trend in SC measured in wells which have little to
know connection to the river, and are therefore considered representative of the true
groundwater local aquifer SC value.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 18 of 29
                                              East to West trend in Groundwater Specific Conductance values
                                                           Measured in Stable Monitoring Wells
                                    700




                                    600
  Specific Electrical Conductance




                                    500




                                    400




                                    300




                                    200

                                                                                               y = 0.0257x - 12019
                                                                                                     2
                                                                                                   R = 0.1592
                                    100




                                     0
                                     483000        483500    484000     484500        485000      485500          486000       486500

                                                                       UTM Easting (NAD 83)


Figure 8. West to east increasing trend in SC measured in wells which have little to
know connection to the river, and are therefore considered representative of the true
groundwater local aquifer SC value.


                                                    Specific Electrical Conductance of Surfacewater Features
                                                                           Spring 2006

 500


 450


 400


 350


 300                                                                                                       Axtell Bridge Wetlands
                                                                                                           Stone House Spring
 250
                                                                                                           Fish Creek
 200                                                                                                       Gallatin River at Axtell Bridge

 150


 100


        50


                       0
        3/4/2006 3/24/2006 4/13/2006 5/3/2006 5/23/2006 6/12/2006 7/2/2006 7/22/2006 8/11/2006


Figure 9. Specific conductance of spring features in Zone I and the Gallatin River during
spring run off. These features showed little to no response to the River and were assumed
to be representative of true groundwater SC values.


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 19 of 29
Figure 10. Lines of equal specific conductance, inferred from values in the displayed
wells. The wells used to draw the lines of equal SC were chosen because they exhibited
little fluctuation in SC as the Gallatin River’s SC declined and rose dramatically in
response to spring runoff. These wells were considered representative of the true
groundwater SC values because they were not directly connected to the river. The lines



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 20 of 29
on this map were used to delineate the three families of local groundwater value used in
the SC proportion calculation.


                                          Longitudinal Profile of River Specific Electrical Conductance

                                    380


                                    360
  Specific Electrical Conductance




                                    340


                                    320


                                    300                                                                   July
                                                                                                          Aug I
                                    280
                                                                                                          Aug II
                                    260


                                    240


                                    220


                                    200
                                    50 469
                                    50 455
                                    50 455
                                    50 842
                                    50 831
                                    50 832
                                    50 864
                                    50 463
                                    50 441
                                    50 770
                                    50 720
                                    50 781
                                    50 520
                                    50 512
                                    50 606
                                    50 042
                                    50 035
                                    50 096
                                    50 122
                                    50 456
                                    50 484
                                    50 775
                                    50 785
                                    50 258
                                    50 289
                                    50 032
                                    50 048

                                            2
                                         09
                                      52
                                      52
                                      52
                                      52
                                      52
                                      52
                                      53
                                      53
                                      53
                                      53
                                      53
                                      53
                                      54
                                      54
                                      54
                                      55
                                      55
                                      55
                                      55
                                      55
                                      55
                                      55
                                      55
                                      56
                                      56
                                      57
                                      57
                                      57
                                    50




                                                           UTM Northing (NAD 27)

Figure 11. Approximate longitudinal profile of specific conductance in W. Gallatin River
from Axtell to Shed’s Bridge on three separate days. The left end of the x axis represent
Axtell Bridge and the right end Shed’s. The river generally flows north in this reach,
therefore flow is left to right on the graph above. The spike in conductance occurs at the
SBP Site 9.




Figure 12. Surface water level measurement locations


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 21 of 29
Figure 13. Stream temperature measurement locations




Figure 14. Box and whisker plot of SC portions for the entire study reach in July and
August 2006.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 22 of 29
Figure 15. Change in the SC proportion from July to August. Black lines of equal head
inferred from 18 wells. The amount of groundwater fluctuation was not significant
enough to adjust the low resolution lines of equal head.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 23 of 29
Figure 16. Comparative boxplots of SC proportions by set in July and August 2006. Sets
are numbered from upstream near Axtell Bridge downstream to the study area’s northern
boundary. Shed’s Bridge, the boundary between the two hydrologic groups described by
Hackett, crosses the study reach between sets 12 and 13.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 24 of 29
Figure 17. SBP proportions in July and lines of equal groundwater head in aquifer for
July and August. The amount of groundwater fluctuation was not significant enough to
adjust the low resolution lines of equal head.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 25 of 29
Figure 18. SC proportions in SBPs August and lines of equal head in July and August.
The amount of groundwater fluctuation was not significant enough to adjust the low
resolution lines of equal head.




Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 26 of 29
Figure 19, Change in water level elevations (feet) , from July to August, at the Gallatin
River and surrounding monitoring wells. Red features indicate declines, grey is relatively
little change, and Blue is a rise in level. The change in elevation of the river is the change
in stage at the Axtell Bridge site. This value is then used as a rough estimate of the
change along the entire reach. The result of the water level changes in the river and
aquifer is an increased groundwater flow down gradient created by the decline in and
along the river and water levels rise up gradient of the river in the fringes of the alluvial
aquifer.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 27 of 29
                                                                             Gallatin River Staff Guage at Axtell Bridge

                                      4.5                                                                                                                                                               25


                                           4

                                                                                                                                                                                                        20
                                      3.5


                                           3

                                                                                                                                                                                                        15
 Stage (FT)




                                      2.5




                                                                                                                                                                                                              Temp (C)
                                                                                                                                                                                                                           Stage
                                                                                                                                                                                                                           Temp
                                           2
                                                                                                                                                                                                        10

                                      1.5


                                           1
                                                                                                                                                                                                        5

                                      0.5


                                           0                                                                                                                                                            0
                                       3/24/06      4/13/06      5/3/06 0:00   5/23/06       6/12/06     7/2/06 0:00    7/22/06       8/11/06     8/31/06                                9/20/06   10/10/06
                                        0:00          0:00                      0:00          0:00                        0:00          0:00       0:00                                   0:00       0:00
                                                                                                         Date/Time




Figure 20. Gallatin River stage and temperature at Axtell bridge. Stage decline between
the July and August is approximately 0.5 feet.




                                                         Change in Groundwater & Elkgrove Slough Water Level Elevations
                                                                gw flowpath transect (#1) of the Southeastern section
                                      11                                                                                                               0.90


                                                                                                                                                                                                              224069 #1
                                                                                                                                                       0.80
                                       9



                                                                                                                                                       0.70
                                       7
                                                                                                                                                                                                              224087 #2
                                                                                                                                                       0.60
   Change in Groundwater Level (FT)




                                       5
                                                                                                                                                              Change in EGS Stage (FT)




                                                                                                                                                       0.50
                                                                                                                                                                                                              224091 #3
                                       3

                                                                                                                                                       0.40


                                       1
                                                                                                                                                       0.30                                                   Lower Elkgrove
                                                                                                                                                                                                              Slough
                                      -1
                                                                                                                                                       0.20



                                      -3                                                                                                                                                                      Upper Elkgrove
                                                                                                                                                       0.10                                                   Slough


                                      -5                                                                                                               0.00
                                       1-Nov     2-Dec   2-Jan       2-Feb     5-Mar     5-Apr   6-May       6-Jun     7-Jul      7-Aug   7-Sep    8-Oct
                                                                                             Month




Figure 21. Down gradient arrangement of groundwater hydrographs. All data is
equalized to zero datum to illustrate the relative time when recharge exceeds discharge in
a well and the water level rises. The numbers indicate position up grasdient so that #1 is
the furthest up gradient and 3 the furthest down gradient. Notice the water level rise in
the Elk Grove Slough when well # 2 begins to rise.


Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 28 of 29
           Diurnal Stream temperature Fluctuations at Four Sites along the West
                                     Gallatin River
                                                                           16
                                                                           15




                                                                                Temperature (Degrees C)
                                                                           14
      Site 1                                                               13
                                                                           12
      Site 2
                                                                           11
      Site 3                                                               10
      Site 4                                                               9
                                                                           8
                                                                           7
                                                                           6

                      Midnight 9/14/05 through Midnight 9/17/05

Figure. 22. Diurnal stream temperature fluctuation at 4 sites along the W. Gallatin River.
Site 4 which shows no diurnal fluctuation was positioned in a tributary spring channel.
This location coincides with SBP Site 9, where the spike in river specific conductance
occurs in Figure 11.




Figure 23. Change, from June to August 2006, in groundwater specific electrical
conductance measured in wells. Specific conductance measured in the W Gallatin River
increased from 134µS in June to 306 µS in August.



Mark Schaffer, MSU Earth Science Dept., Geol 583 Term Paper, 12/2006, Page 29 of 29