Profile "smearing" in long residence time rivers
Robert T. Hensley1 and Matthew J. Cohen2
1 – University of Florida, School of Natural Resources and Environment
2 – University of Florida, School of Forest Resources and Conservation
Methods
H.T. Odom (1957) was the first to recognize that the spring-fed rivers of North
Florida make excellent model analogs because they exhibit large diel variation
in metabolism while their boundary concentration remains temporally stable.
Modeling was performed using a one-dimensional reactive transport model
based off the advection, dispersion and transient storage equations (Bencala
and Walters 1983). Reactive terms were added to both the channel and storage
zone (Runkle 2007).
DO (mg/L)
12.00
8.00
4.00
0.00
5/11/10 0:00
2.5 km
NO3- (mg/L)
𝝏𝑪
𝑸 𝝏𝑪
𝝏𝟐 𝑪
=−
+ 𝑫 𝟐 + 𝜶 𝑪𝒔 − 𝑪 − 𝒌𝑪 𝑪𝒏𝑪
𝝏𝒕
𝑨 𝝏𝒙
𝝏𝒙
DOsat
5/12/10 0:00
5/13/10 0:00
Time
USBC
0.65
0.50
0.35
0.20
5/11/10 0:00
5km
5/12/10 0:00
2.5 km
5/14/10 0:00
5/15/10 0:00
5km
5/13/10 0:00
Time
5/14/10 0:00
𝝏𝑪𝒔
𝑨𝑺
=𝜶
𝑪 − 𝑪𝒔 − 𝒌𝑺 𝑪𝒏𝑺
𝝏𝒕
𝑨
5/15/10 0:00
Simplification of the model required making certain assumptions
• Channel processes were driven by assimilation and zero-order. Therefore kC
was a function of insolation (modeled as a half sine wave) and nC = 0.
• Storage zone processes were heterotrophic, first-order and time invariant.
Therefore kS was constant and nS = 1.
• Re-aeration (DO model only) was a product of the saturation deficit and the
re-aeration rate constant k. k was modeled as a function of stream velocity
using an empirical formula derived for spring-fed rivers (Knight 1980).
Figure 1. Diel DO and NO3- profiles from Ichetucknee River.
12.00
8.00
4.00
0.00
4/20/13 0:00
NO3- (mg/L)
1.42
1.35
1.28
1.21
4/20/13 0:00
4 km
DOsat
4/22/13 0:00
4/23/13 0:00
Time
USBC 4 km 8km
0:00
Time
0:00
0:00
k = 0.0604u + 0.0929
8km
4/21/13 0:00
0:00
The DO model does only a fair job of fitting observed profiles, particularly in
regards to timing of peaks. We note several potential reasons
• Incorrect re-aeration. Changing re-aeration could shift the timing of the
peaks (Chapra et al. 1991). However this would also require changing GPP
to maintain correct amplitude of the signal.
• Assuming that respiration is constant over 24 hours. Respiration may be
temporally variable in response to labile C availability (Heffernan and
Cohen 2010).
The model was calibrated using data from the Silver River. We performed a
pulse release of Rhodamine WT and positioned fluorometers to record the
breakthrough curve at the 4 km and 8 km station.
4/24/13 0:00
1.50
1.40
1.30
1.20
1.10
1.00
0:00
0:00
0:00
0:00
Time
Figure 5. Results of NO3- Simulation
0:00
1.40
4/21/13 0:00
4/22/13 0:00
Time
4/23/13 0:00
NO3- (mg/L)
DO (mg/L)
USBC
12.00
10.00
8.00
6.00
4.00
2.00
0:00
Figure 4. Results of DO Simulation
NO3- (mg/L)
USBC
Results
DO (mg/L)
Introduction
4/24/13 0:00
RWT (µg/L)
40
0
15 km (projected)
10000
Distance (m)
20000
Figure 4. Simulated NO3- Longitudinal Profile
30
20
10
0
0
360
720
1080
Time (min)
1440
1800
2160
Figure 3. RWT Breakthrough curves for Silver River
What signals might we expect in longer rivers?
• Unfortunately even the longest spring-fed rivers are only on the order of 10
km long with residence times on the order of half a day. Thus predicting the
sort of signals we might observe in longer residence time rivers requires
projection using a reactive transport model.
1.20
1.10
Figure 2. Diel DO and NO3- profiles from Silver River.
Some interesting observations
• Increased mean residence time (due to greater travel time) delays the timing
of the signals. For example, note the peaks in DO occur after solar noon
(and in 8 km Silver River profile after the sun has set).
• Increased distribution of residence times (due to dispersion and transient
storage) causes a “smearing” of older and younger water along the flowpath,
attenuating the magnitude of diel variability.
• Re-aeration along the flowpath further decreases the magnitude of diel
variability in the DO signal by gradually “erasing” upstream effects.
1.30
Because RWT is a conservative tracer we could set the reactive parameters
equal to zero and fit the model to the breakthrough curve to estimate the
hydraulic parameters (A, AS, and α). The reactive parameters were then fit
using the observed DO and NO3- signals.
The NO3- model on the other hand dose a better job of fitting observed profiles,
leading us to conclude the shortcomings of the DO model are not being driven
by hydraulics. We also note several interesting features
• Diel variability initially increases with downstream distance but then begins
to decline until the signal matches the USBC at approximately 15 km.
• We observe a similar trend in the longitudinal profile (Fig 4).
• Note 15 km is the distance with mean residence time of 24 hrs (Fig 3).
• Thus all water parcels have been acted on by exactly one full daily cycle;
though the order of processes varies, the net effect is approximately equal.
• Using the two-station method, sensors placed 15 km apart would show offset
but identical signals, leading one to incorrectly assume that removal is time
invariant (all dissimilatory).