breakthrough curves were simulated using the transient storage model OTIS: where, C is the solute concentration in the stream (meq L-1), CS is the storage ...
Stream-upland connections and the effects of stream discharge on transient storage processes Brian L. McGlynn1, Michael Gooseff2, Cindy Hugenschmidt, and Robert S. McGlynn3
RESULTS AND DISCUSSION
PART I MODELING RESULTS
Stream–catchment connections and the linkages between stream discharge and transient storage processes remain poorly understood. We seek to investiagte stream catchment connections and the impact of discharge magnitude on transient storage dynamics. Previous studies of transient storage in streams have suggested that hyporheic exchange should dominate transient storage as discharge decreases because of reduced stream cross-sectional area relative to the cross-sectional area of the hyporheic zone. However, no direct relationships have been developed between stream discharge and transient storage influences on solute transport. We tested the hypothesis that the influence of transient storage on solute transport increases with decreasing stream discharge.
Local inflow of area to the stream channel was
Local inflow of water to the stream channel was
290m >1 ha
800
145m
700
600
0m
0m
(C)
Scale in meters
500
00 m 400 3300
100 m
Sampling point Tracer injection point
200 m
10 m Contour interval 3400
3500
3600
3700
3800
3900
DEM-BASED LOCAL INFLOW
(D) The upland area draining into each 20 meter stream cell was calculated based on topographic analysis of the catchment DEM and a 0.5 ha stream threshold. Note the variability in local inflows to the stream.
Three LiBr salt stream tracer experiments along a 290 m stream reach. Br addition rate was 105.5 meq L-1 for each experiment. Electrical conductance (EC) data was collected on a 120s interval at 145m and 290m. Grab samples for Br analysis were collected periodically throughout the experiments, based on EC. An EC-Br relationship was determined, and the Br breakthrough curves were simulated using the transient storage model OTIS:
∂C ∂C Q ∂C 1 ∂ + =− AD + α (C S − C ) + q L (C L − C ) ∂x ∂t A ∂x A ∂ x dC S A =α (C − C S ) dt AS
[Eq. 2]
where, C is the solute concentration in the stream (meq L-1), CS is the storage zone solute concentration (meq L-1), CL is the local inflow solute concentration (set to 0), Q is the stream discharge (m3 s-1), qL is the local inflow (m3 s-1 m-1), D is the longitudinal dispersion (m2 s-1), α is the storage zone exchange rate (s-1), A is the cross-sectional area of the stream (m2), AS is the cross-sectional area of the storage zone (m2), t is time, and x is the downstream distance (m) (Runkel, 1998). Because discharge is changing throughout the tracer experiment (decreasing baseflow), the following relationship was developed from Manning’s Equation:
A = cQ
0.6
[Eq. 3]
and, c is a coefficient representing a relationship among channel roughness, slope and wetted perimeter. Optimal values of AS, D, α, c, and qL were obtained using UCODE, a universal computer code for model optimization (Poeter and Hill, 1998)
3e-5 2e-5
Positive trend between α and Q.
1e-5 0
8
Local
4 2
2.5e-6
1.0
2.0e-6
0.6
Average local inflow to the stream decreased as Q decreased
1.5e-6 1.0e-6
0.8
In some instances 10 meter sampling intervals were too short for accurate calculation of local inflow concentrations because the precision of the Branalysis and the precision of the solute and isotopic data. Uncertainty analysis such as that used in hydrograph separation studies will be necessary to quantify significance from reach to reach. Despite this caveat, the data suggests that local inflows solute and δ18O concentrations are highly variable from stream reach to stream reach. We suggest that combined with transient storage modeling during multiple discharge magnitudes, synoptic sampling can elucidate stream catchment connections. More specifically, this approach can provide insight into the relationship between topographic variables such as local inflow and incremental inflows of water and solutes to stream channels.
0.4 0.2 8e+5
Average residence time of water in the storage zone decreased as Q increased
20 10 0
7e+5 6e+5 5e+5 4e+5 3e+5 2e+5
0.0
0.5
1.0
1.5
2.0
2.5
Discharge (L s )
3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
-1
Discharge (L s )
Figure 3. OTIS parameter and discharge (Q) relationships for both reaches. Symbols represent best-fit parameter estimate and mean Q, bars represent parameter 95% confidence intervals and the range of Q for a particular experiment.
• CSS values generally increase for each parameter at lower Q (except AS,1 and c2). • CSS values are highest for qLAT, and lowest for D in all experiments. • α CSS values are higher than AS CSS values for all experiments.
Figure 4. OTIS parameter composite scaled sensitivities (CSS) for each experiment. CSSs represent the potential to confidently optimize a parameter from a particular data set.
(C)
Using UCODE to obtain 95% confidence intervals for parameter estimates and CSS values allowed us to evaluate the relative confidence in the OTIS model parameterization. Our results suggest that in general, at lower discharges, there is greater information available within data sets for D, a, A (or c), and qLAT. Estimates of AS were not as robust, as evidenced by the CSS value trend and the larger 95% confidence intervals obtained. This suggests that comparisons of AS/A should be made with great caution when comparing different reaches, particularly in different streams.
TRACER TEST #I
0.020
4 Lateral Inflow (liters/meter) Stream discharge
0.015
3
0.010
2
0.005
1
0.000
0 0
(D)
Stream bed slope %
580 meters
50 40 30 20
5% 7.3%mean slope
6.5%mean slope
7.8%mean slope
10 0
0
100
200
300
400
500
Distance downstream in meters (0m = streamflow initiation, 580m = weir)
(B)
2.0 Local inflow of area to stream ha
1.5 1.0 0.5 0.0 0
100
200
300
400
500
Distance from stream initiation m
100
200
300
400
500
TRACER TEST #II
(C) 0.020
4
Lateral inflow of water (liters/meter) Stream discharge liters/second
0.015
3
0.010
2
0.005
1
0.000
0 0
(D)
0
-5
100
200
300
400
500
Distance from stream initiation m 0
-5
-10
-10 δ18O in lateral inflow 18 Streamflow δ O
δ18Ο in lateral inflow 18 Stream δ O
-15 0
100
200
300
400
-15
500
Distance from stream initiation m
0
(E)
(E) 20
100
200
300
400
500
Distance from stream initiation m 20 15
15 10
10 5
5
Later inflow SiO2 Stream SiO2
Lateral inflow SiO2 Stream SiO2
0 0
100
0 200
300
400
Distance from stream initiation m
500
0
100
200
300
400
500
Distance from stream initiation m
CONCLUSIONS •
The storage zone area to stream area ratio (AS/A) increased with decreasing stream discharge and average local inflows to the stream decreased as stream discharge decreased. This effect was more pronounced in the headwaters where baseflow decreased at a higher rate than in reaches closer to the catchment outlet.
•
We also tested the linkage between local subsurface water inflow to the stream channel and local upland accumulated area. We found suggestion of a linkage between topography and incremental changes in discharge. We plan to more fully assess the significance of this relationship.
•
We found pronounced variability in δ18O and of SiO2 concentrations in local inflow of water to each stream reach. Uncertainty analysis is required for quantitative assessment, however our results suggest local inflows can be highly variable. This information is masked in synoptic stream sampling results that do not include high resolution quantification of incremental changes in stream discharge.
DISCUSSION OF MODELLING RESULTS: These results support previous assertions that hyporheic exchange potential increases at lower discharge, as evidenced by 1) positive relationships between a and Q and 2) increasing CSS values for a in each sequential (lower Q) experiment. However, the uncertainty associated with AS parameterization in Reach 2, and the negative relationship between AS and Q in Reach 2, but a generally positive relationship between AS and Q in Reach 1, suggests that greater relative storage zone area at lower discharge is an equivocal conclusion.
Reach 4 435 meters
0%
Stream discharge liters/second
-1
3.0e-6
(Qupstream )(Cupstream ) (Qdownstream )(Cdownstream ) C local inflow = Qlocal inflow
Because A (or c) decreased with increasing Q, AS/A decreased with increasing Q
Reach 3 290 meters
Distance from stream initiation m
δ18O
and SiO2 inflow to the stream channel Local inflow solute and δ18O concentrations were calculated based on synoptic stream samples and calculated local inflow of water (incremental increases in discharge). This approach allows for calculation of the mass and concentration of solutes entering the stream between each sampling point.
6
1.2
Br stream
Qlocal inflow = Qupstream − Qdownstream
10
1.4
-
Local inflow was then calculated for each reach by subtracting the upstream discharge from the downstream discharge.
12
3.5e-6
(Q injectate )( Br − injectate )
145 meters
δ18O
Area Coefficient, c
4e-5
-1
[Eq. 1]
0.00 14
30
Stream Tracer Solute Transport Modeling
Qstream =
0.04
5e-5
40
MODELLING METHODS
0.08
Reach 2
0 meters
8.9%mean slope
SiO2 PPM
900
0.04
0.12
AS/A
0 ha
1000
0.06
Ls (m-1)LS=(m) Q/(A*α)
(D)
580 m
Exchange Coef, α (s )
weir
(C)
1100
(C) The locations of the 4 study reaches are indicated on the topographic map of the 16.9 ha K catchment.
0.08
0.02
-1
(B)
0.10
computed from synoptic stream samples collected every 10-20 meters during the first two steady state Br- tracer injections. The following equation was used to calculate discharge at each synoptic sampling point.
Reach 1, 0-145 m Reach 2, 145-290 m
0.16
-1
42 degrees S
Positive trend between D and Q
0.20
3
(A-B) The Maimai catchments are located in NW New Zealand, on the South Island.
Maimai
Inflow, qLAT (m s m )
SITE LOCATION
1200
-1
Figure 1.
N
New Zealand
0.12
(h) ts (h-1) =tSAs/(α*A)
172 degrees E
(A)
0.14
2
STUDY SITE
0.16
Dispersion (m s )
5) Synoptic sampling during the two steady-state tracer was used to measure variability in later inflow quantity, δ18O, and silica concentrations.
Lateral inflow of water (liters/meter)
2
Storage Zone Area, AS (m )
4) Terrain analysis was used to quantify stream morphology and local inflow area along the stream.
Reach 1
15%
10%
Later inflow of water liters/meter
Figure 2. Br observed (points) and simulated (black line) breakthrough curves and hydrographs at 145m and 290m from injection point. During the three experiments, discharge decreased from 1.11 to 0.14 L s-1 at the injection point, and from 2.52 to 0.72 L s-1 at 290m. Br concentration plateaus were increasing due to a decrease in discharge.
computed from the catchment digital elevation model by calculating the incremental increase in catchment area from stream cell-to-stream cell in a downstream direction. The range of local inflow is greatest in the headwaters where the catchment exhibits the greatest topographic convergence and decreases toward the catchment outlet. The pattern of local inflow area reflects the highly dissected nature of the catchment topography. The catchments at Maimai are comprised of regularly alternating spur-hollow sequences with greatest topographic convergence in the headwaters.
STREAM MORPHOLOGY
(A)
Area entering stream from adjacent uplands ha
demonstrate the variability in stream gradient for each reach. The average slope ranges from 9% to 6.5% from reach to reach, but more importantly, the range of variability for each 10 meters of stream section is 4% to 14%. Stream morphology is hypothesized to be a strong driver of stream hyporheic exchange.
δ18O
3) Discharge decreased from 1.11 to 0.14 l s-1 at the injection point, and from 4.5 to 1.5 l s-1 at 580 m over the course of the three tracer tests.
Figure 5A-E. We synoptically sampled the stream every 10 meters from the tracer injection point to the catchment outlet during the first and second steadystate tracer tests. We surveyed the stream channel elevation at each sampling point and calculated streambed slope. In addition, we calculated the incremental increase in catchment area for each stream cell (20 meters) along the stream. (A) Streambed slope and cumulative stream elevation, (B) Local inflow of area along the stream, (C) Computed later inflow of water along the stream network, (D) δ18O in streamwater and local inflow, and (E) SiO2 in streamwater and local inflow.
Streambed slope and cumulative elevation
1) Three separate conservative tracer stream additions with LiBr during baseflow recession (over 12 days) in a 16.9 ha headwater catchment, at Maimai New Zealand. 2) Breakthrough of bromide was measured and simulated with OTIS for 2 sub-reaches within the 580 m study reach (145 m, 290 m, 425 m, and 580 m from the injection).
PART II STEADY STATE SYNOPTIC SAMPLING
FIELD/DEM ANALYSIS RESULTS/DISCUSSION
SiO2 PPM
INTRODUCTION
Institut für Hydrologie Albert-Ludwigs-Universität Freiburg i. Br.
C um ulative elevatio n m eters
1. Department of Land Resources & Environmental Sciences, Montana State University, Bozeman 2. Department of Aquatic, Watershed, and Earth Resources, Utah State University 3. Institute for Hydrology, Freiburg University, Germany 4. Department of Earth Sciences, Dartmouth College
Stream discharge liters/second
Utah State UNIVERSITY
A more enhanced understanding of transient storage within particular reaches is possible with analysis of stream–upland connections and repeated solute tracer experiments at varying discharge. One test at one discharge does not provide adequate comparison to either the same reach at another discharge, or another stream system.
References: Poeter E. P., and M. C. Hill. 1998. Documentation of UCODE, a computer code for universal inverse modeling. Water Resources Investigation Report 98-4080. U.S. Geological Survey, Denver, Colorado. [http://water.usgs.gov/software/ucode.html] Runkel, R. L. 1998. One-dimensional transport with inflow and storage (OTIS): A solute transport model for streams and rivers. U.S. Geological Survey. Water Resources Investigations Report 98-4018. [http://co.water.usgs.gov/otis/] Acknowledgements: We extend our thanks to Paul Schuster for sample analysis, John Payne, Jagath Ekanayake, and Breck Bowden of LandCare Research, NZ for logistical, technical, and collaborative support, and to Jamie Shanley for guidance and field equipment. We also thank Rob Runkel for valuable input on modelling methods. This work was made possible by NSF grant EAR-0196381 and the 2001 AGU Horton Research Grant awarded to BLM.
