Surface-water quality and flow Modeling Interest Group
U.S. Geological Survey
Box 25046, MS 415
Denver Federal Center
Denver, CO 80225-0046
Internet: runkel@usgs.gov
Phone: (303) 236-4882 x285
FAX: (303) 236-4912
For more information, documentation, references, mailing lists, and more on the OTIS model, please visit http://co.water.usgs.gov/otis/.
For more information on the concept of transient storage and its applications, see the Transient Storage Reader 1 and Reader 2 reference lists.
This version of the fact sheet has all of the figures inline. A version with all of the figures converted to thumbnails, with links to the larger images, is also available; the download time for the thumbnail version will be shorter, but the thumbnail figures may be less convenient for viewing and printing.
Citation:
Runkel, R.L., 2000, Using OTIS to model solute transport in streams and rivers:
U.S. Geological Survey Fact Sheet FS 138-99, 4 p.
Introduction
Model Description
Hydrologic Transport
Chemical Transformations
Model Applications
Mixing and Traveltime
Nutrient Uptake
Trace Metal Removal
References
Sources of Additional InformationThe primary assumption used within the model is that solute concentration varies only in the longitudinal direction; solute concentration does not vary with width or depth. Given this assumption, equations are developed for a one-dimensional system that consists of a series of stream segments. Conservation of mass for each stream segment yields a set of differential equations that are solved using numerical methods. Solution of the differential equations yields a general equation of the form:
where:
x is the distance,
t is time, and
C(x,t) is the solute concentration at distance x
and time t.
This equation describes the spatial and temporal variation in solute concentration as a function of several hydrologic and geochemical parameters. As discussed by Runkel (1998), parameter estimates may be obtained by nonlinear regression using a modified version of OTIS known as OTIS-P.
Transient storage has been noted in many streams where solutes may be temporarily detained in small eddies and stagnant pools of water that are stationary relative to the faster moving water near the center of the channel (fig. 1A). In addition, significant portions of flow may move through the coarse gravel of the streambed and porous areas within the streambank (fig. 1B). The traveltime for solutes carried through these porous areas may be substantially longer than that for solutes traveling within the water column. These pools of water and porous areas of the streambed are the two areas contributing to transient storage, as shown in figure 1.
Lateral inflow is any water that is added to the stream due to ground-water inflow, overland flow, interflow, or small springs. These flows act to dilute (or concentrate) solutes in the stream channel if they carry solute concentrations that are lower (or higher) than the stream-solute concentration.
Two conceptual areas are defined within the model: the main channel and the storage zone (fig. 2). The main channel is defined as the portion of the stream in which advection and dispersion are the dominant hydrologic transport mechanisms. The storage zone is defined as the portion of the stream that contributes to transient storage; that is, stagnant pools of water and porous areas of the streambed. Water in the storage zone is considered immobile relative to water in the stream channel. The exchange of solute mass between the main channel and the storage zone is modeled as a first-order mass transfer process.
Consideration of the hydrologic processes discussed above introduces
several model parameters. The main channel crosssectional area (A)
is used with estimates of streamflow to determine the average advective
velocity of transported solutes. Spreading of solute mass due to shear
stress is described by the dispersion coefficient (D). Solute mixing
due to transient storage is governed by the storage-zone cross-sectional
area (As) and the storage-zone exchange coefficient
(
). Lateral inflows are characterized by
the lateral inflow rate and the solute concentration associated with the
lateral inflow (CL).
) and (or) the storage zone
(s). Consideration of
sorption within OTIS is based on a distribution coefficient approach that
allows for sorption onto streambed sediments.
In addition to providing management information, hydrologic parameters
derived from tracer-injection data provide insight into the physical
characteristics of streams. Values of the transient-storage parameters
(As, ), for example, indicate
the degree of mixing due to stagnant pools and flow through porous areas
of the streambed. Further, model-derived estimates of traveltime indicate
the relevant time scales over which chemical reactions can potentially
affect solute concentrations.
In this section, we illustrate the use of OTIS to quantify hydrologic processes using tracer-injection data. Our first example uses data from Uvas Creek, a small pool-and-riffle stream in northern California. Bencala and Walters (1983) describe a continuous, constant-rate injection of chloride into Uvas Creek. Concentrations were monitored at several downstream locations, and streamflow was estimated by tracer dilution.
Application of OTIS to the Uvas Creek chloride injection requires
estimates of stream cross-sectional area (A), transient storage
(As, ), and dispersion
(D). Estimates of stream crosssectional area are related to traveltime
as they control the timing of the chloride profile, whereas estimates of
the transient-storage parameters represent instream mixing as reflected
by the shape of the chloride profile. During a series of simulations,
Bencala and Walters (1983) varied A, As,
, and D to obtain a match between observed
and simulated concentrations. Final simulation results at two sampling
locations are shown in figure 3.
Estimates of A and As developed from the tracer data are consistent with the pool-and-riffle characterization of Uvas Creek reported by Bencala and Walters. The pools act to produce transient storage by temporarily detaining some of the chloride. A dimensionless measure of this storage effect is obtained by calculating the ratio of storage-zone area to main-channel cross-sectional area (As/A). Values of As/A for various reaches of Uvas Creek range from 1.0 to 3.0. These values indicate that the pool areas are large relative to the main channel.
Analysis of Uvas Creek data relied on a trial-and-error approach wherein
parameter estimates were manually adjusted to produce an acceptable match
between simulated and observed tracer concentrations. In the following
example, parameter estimates are obtained by nonlinear regression using
OTIS-P. Laenen and Risley (1997) describe several studies in Oregon
streams where rhodamine WT was used to determine traveltime. In July 1992,
a slug of rhodamine was added to the Clackamas River at river mile 13.3
(RM 13.3). Water samples were collected at river miles 11.0, 9.5, and
8.0. Because rhodamine was introduced as a slug (as opposed to a continuous
injection), data at the first sampling location (RM 11.0) are used to define
the upstream boundary condition (fig. 4). Given the boundary condition,
the traveltimes (as given by A) and mixing characteristics (as
given by As, , and D)
for the two reaches ending at river miles 9.5 and 8.0 may be determined.
Use of OTIS-P requires a set of initial estimates for the parameters of
interest. Here we set A and D for both reaches equal to 50
square meters (m2) and 10 m2/s, respectively. The
exchange coefficient, , is initially set
to 0.0 such that transient storage is not considered. Preliminary OTIS
results based on these initial parameter estimates are shown as dashed
lines in figure 4. These preliminary profiles indicate that our initial
estimates of stream cross-sectional area are too large; the simulated
traveltime is overestimated at both RM 9.5 and RM 8.0. In addition, the
symmetric simulation profile at RM 8.0 is in contrast to the asymmetry
of the observed data. This observation indicates that transient storage
may be an important mixing mechanism. Both of these discrepancies may be
addressed by developing parameter estimates using OTIS-P. As expected,
application of OTIS-P results in an improved simulation (solid lines,
fig. 4) and a revised set of parameter estimates (A = 30.4,
48.1 m2; As = 7.0, 14.4 m2;
D = 2.0, 0.4 m2/s; =
2.0x10-4, 1.7x10-4/s).
= s = 0; dashed
line) and first-order loss (,
s > 0; solid line).
Under the assumption that nutrient uptake is a first-order process,
the first-order decay coefficients (,
s) in OTIS
are used to quantify the loss of nitrate. Given the hydrologic
characterization, OTIS-P is used to estimate uptake in the main
channel () and in the storage zone
(s). Reach-specific
estimates of range from
4x10-5 to 4x10-4; estimates of
s range from
3x10-6 to 2x10-3. Simulation results based on
these parameters are shown as a solid line in figure 5. Additional
mass-balance calculations based on and
s indicate that 84 to 93
percent of the nitrate loss occurs in the main channel where algal uptake
is the likely mechanism of nitrate loss. The remaining loss occurs in the
storage zone where possible mechanisms include microbial uptake and nitrate
reduction. In contrast, similar analyses indicate that phosphate loss occurs
only in the main channel (s
= 0). OTIS thus provides a framework for determining the magnitude and
location of processes controlling nutrient concentrations in Green Creek.
=
s = 0; dashed line) and
first-order loss ( = 1x10-4;
solid line).The first step in the analysis is to define the hydrology of the system. Broshears and others (1993) describe the addition of a conservative tracer that coincided with the synoptic study. Data from the tracer addition are used to determine flow rates and the hydrologic parameters. Observed data from the springs are used to set the lateral inflow concentrations, CL. OTIS then is used to develop a spatial profile under the assumption that dissolved iron is conservative (nonreactive). Results from this simulation are shown in figure 6 (dashed line). The close correspondence between observed and simulated iron concentrations in the upper portions of St. Kevin Gulch (0-500 m; fig. 6) indicates that the initial increase in iron is due to strictly hydrologic factors; that is, iron loading from the metal-rich springs. Simulated iron concentrations decrease downstream from 500 m due to the addition of water from a relatively dilute tributary but do not match the decrease in the observed data. This discrepancy indicates that chemical reactions affect dissolved iron concentrations downstream from 500 m.
A simple approach to quantifying the chemical reactions is to determine
the first-order rate at which iron is lost from the system. This is
accomplished by estimating a first-order decay coefficient for the main
channel (). A first-order decay coefficient
of 1x10-4/s results in the simulated profile shown in figure 6
(solid line). Although the decay-rate approach yields an excellent fit to
the data, it does not explicitly identify the mechanisms causing the iron
loss. Inspection of the spatial pH profile indicates an increase in pH
downstream from 500 m that could result in the precipitation of hydrous
iron oxides. This observation is confirmed by additional calculations
using a chemical equilibrium model.
Broshears, R.E., Bencala, K.E., Kimball, B.A., and McKnight, D.M., 1993, Tracer-dilution experiments and solute-transport simulations for a mountain stream, Saint Kevin Gulch, Colorado: U.S. Geological Survey Water-Resources Investigations Report 92-4081, 18 p.
Laenen, Antonius, and Risley, J.C., 1997, Precipitation-runoff and streamflow-routing model for the Willamette River Basin, Oregon: U.S. Geological Survey Water-Resources Investigations Report 95-4284, 252 p.
McKnight, D.M., and Duff, J., 1995, Hyporheic zone interactions controlling nutrient uptake by algal mats in an Antarctic stream: San Francisco, 1995 Fall Meeting of the American Geophysical Union, December 11-15, 1995, Eos Transactions, AGU Fall Meeting Supplement, 76(46), p. 226.
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, 73 p.
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