****
º
º - - ºf
T |G. |27 . | Oll - O3 Photograph courtesy of Pinedale Online
National Water-Ouality Assessment Program O 62| – ||
Prepared in cooperation with the University of Washington and the Oregon Health & Science University
LakeV00—A Computer Model to Estimate the Concentration
of Volatile Organic Compounds in Lake
By David A. Bender, William E. Asher, and John S. Zogorski
Introduction
Lakes and reservoirs are important
sources of drinking water and some are
used extensively for recreational pur-
poses. On the basis of information in the
U.S. Environmental Protection Agency’s
Safe Drinking Water Information System
database, approximately 124 million
people in the United States (47 percent
of the population served by public water
supplies) are served by public water sup-
pliers that use a lake or reservoir as one
of their source waters. Furthermore, the
drinking water of approximately 34 mil-
lion people is derived exclusively from
a lake or reservoir (Marilee A. Horn,
U.S. Geological Survey, written com-
mun., August 26, 2002). Recreational
activities on lakes and reservoirs include
Swimming, fishing, water skiing, boat-
ing, sailing, racing, and wind surfing.
Because so many lakes and reservoirs
are used for both recreation and drink-
ing-water sources, there is a need for
simplified tools to estimate the levels of
contaminants in these water bodies from
recreational activities and to evaluate
management options.
Volatile organic compounds (VOCs),
especially gasoline-related compounds,
have been found in lakes and reservoirs in
the northeastern United States (Baehr and
Zapecza, 1998; Baehr and Reilly, 2001),
Lake Tahoe, in Nevada and California
(Boughton and Lico, 1998; Lico and
Pennington, 1999), California (Reuter
and others, 1998; Dale and others, 2000),
and Texas (Mahler, 2000). Recreational
boating on lakes and reservoirs using
marine engines, especially older two-
cycle engines, introduces gasoline-related
organic compounds through emission of
non-combusted fuel, including methyl
s and Reservoirs
, SUDOCS
COLLECTION
tert-butyl ether (MTBE), benzene, tolu-
ene, ethylbenzene, and xylenes to water
bodies (Jüttner, 1988, 1994; Van Don-
kelaar, 1988; Jüttner and others, 1995a,
1995b; Dale and others, 2000; Gabele
and Pyle, 2000). Other possible sources
of gasoline-related VOCs to lakes and
reservoirs include accidental spills from
fueling operations, leaking underground
fuel storage tanks or pipelines, overland
Stormwater runoff, and streamflow and
atmospheric inputs.
The U.S. Geological Survey, in coop-
eration with the University of Washington
and Oregon Health & Science University,
developed a publicly available computer
model to estimate the concentration of a
user-selected VOC in a lake or reservoir.
The model, called LakeVOC, is specifi-
cally intended as a planning tool and can
be used by water utilities and govern-
ment agencies to estimate a time series of
concentrations of gasoline-related VOCs
expected from various intensities and
mixes of recreational watercraft. Other
sources of gasoline-related VOCs to lakes
and reservoirs also can be investigated
using LakeVOC including, for example,
accidental spills from fueling opera-
tions, leaking gasoline pipelines, leaking
gasoline storage tanks, stormwater runoff,
and atmospheric inputs. Advantages
of LakeVOC are its ease of use and the
ability to quickly evaluate a large number
of strategies to reduce gasoline-related
compounds in reservoirs and lakes.
Model Description and Input
Parameters
LakeVOC represents a lake or
reservoir as a two-layer system and
Direct Volatilization,
Addition Wet and Dry
of VOC Deposition
! . .
Absorption
(Air-water gas transfer)
| ?
Sunlight
Epilimnion
- Epilimnion
Advection to Degradation Processes Advection from
Epilimnion || ---------------------------------------- Interlayer Epilimnion
(Inflow) Stratification Exchange (Outflow)
| A
N. Hypolimnion V
(mixing between
layers)
Advection from
Hypolimnion Hypolimnion - Hypolimnion
(Inflow) Degradation Processes (Outflow)
Figure 1. Schematic diagram showing the transport, behavior, and fate processes modeled by
LakeV00 for volatile organic compounds in lakes and reservoirs.
U.S. Department of the Interior
U.S. Geological Survey
Advection to
63 Printed on recycled paper
Fact Sheet 104–03
November 2003





estimates the concentration of an indi-
vidual user-selected VOC in both the
epilimnion (uppermost mixed layer of
water in a lake) and hypolimnion (lower-
most mixed layer of water in a lake). The
model integrates the coupled system of
differential equations for the concentra-
tion of the VOC in the epilimnion and
hypolimnion, the total mass of the VOC
in the lake, and the volume of the epi-
limnion and the hypolimnion. LakeVOC
accounts for changes in concentration
caused by mixing between the two lay-
ers, direct addition of a VOC to the lake,
loss of a VOC through lake outflows,
air-water gas transfer of a VOC from the
lake surface, and degradation processes.
These processes are depicted schemati-
cally in figure 1.
The hydrodynamics of lake mixing
and stratification are characterized in the
model through user-entered time series
for the depth of the epilimnion, lake
depth, and lake inflows and outflows.
The total lake volume is determined from
the lake-depth time series and a separate
user-entered relation of lake-surface
area to lake depth. Water is added to
the lake by inflow and (or) precipita-
tion through a user-specified inflow
rate. Water is removed from the lake by
Table 1. LakeV00 model input parameters.
outflow and evaporation through a user-
specified outflow rate. The depths of the
user-specified inflows and outflows are
independent and may be placed in either
the epilimnion or hypolimnion through
user-specified inflow and outflow depths.
The gas transfer caused by air-water
flux of a VOC is characterized in Lake-
VOC in terms of the two-film model of
air-water exchange (Lewis and Whitman,
1924; Schwarzenbach and others, 1993;
Rathbun, 2000). Although the two-film
model oversimplifies the hydrodynamics
associated with gas-liquid transfer, it pro-
vides a useful framework for estimating
the rate of air-water exchange of VOCs.
Air-water gas transfer is characterized
in terms of the air-water concentration
difference and the wind speed using
the relation of Wanninkhof and others
(1991). Evaporation is characterized
using the wind speed relation of Schwar-
zenbach and others (1993) assuming a
relative humidity of 70 percent.
LakeVOC estimates the daily concen-
tration of a user-selected VOC in a lake
or reservoir for a year or several years.
Meteorological, hydrographical, VOC
mass-input, and VOC physical-chemical
properties are required to execute the
model. Input parameters for the Lake-
VOC model are listed in table 1. Daily,
weekly, or monthly time-series input
parameters can be used; however, daily
time-series values provide the best fit of
the model results with measured VOC
water concentrations.
The model hydrographical and meteo-
rological inputs are available from moni-
toring programs and weather stations.
The atmospheric VOC concentrations
may be obtained from state or local air-
quality monitoring program sites located
near the lake or reservoir. Recreational
watercraft VOC inputs can be estimated
on the basis of boat usage information
from the recreational management agency
for the lake or reservoir and mass emis-
sion rates reported in the literature.
Model Verification
Details of the verification of the
LakeVOC model are given in Bender and
others (2003). A short summary of simu-
lations using a hypothetical lake and an
actual reservoir from Bender and others
(2003) are provided in this section.
Simulations Using a Hypothetical Lake
The LakeVOC model was verified, in
part, by using a series of controlled simu-

[“C, degrees Celsius; mº, square meters; mº, cubic meters; VOC, volatile organic compound; ppbv, parts per billion by volume; pg/L, micrograms per liter;
Pa-mº/mole, Pascals-cubic meters per mole]
Type of parameter
Parameter
Units
Time scale of input
parameters
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Meteorological Wind speed meters per second
Air temperature °C
Atmospheric pressure atmospheres
Relative humidity percent
Hydrographical Lake depth meterS
Lake surface area in relation to depth m” and meters
Epilimnion temperature °C
Epilimnion depth meters
Inflow rate and inflow depth m° per day and meters
Outflow rate and outflow depth mº per day and meters
VOC mass inputs Atmospheric concentrations ppbv
Initial lake concentration Hg/L
Physical-chemical
properties
Inputs to the lake other than the atmosphere
(motorboats and others sources)
Degradation rates in the epilimnion and hypolimnion
Henry's law constant (temperature dependent)
Molecular weight
kilograms per unit time
(day, week, or month)
per day
Pa-mº/mole
grams per mole
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
Daily, weekly, monthly
lations designed to test model character-
izations of mixing between the epilim-
nion and hypolimnion, Volume changes
due to inflow and outflow, and air-water
gas exchange. A hypothetical lake with
a constant surface area of 2,000 square
meters, a depth of 50 meters, water and
air temperatures equal to 10 degrees
Celsius, and relative humidity of 100 per-
cent were used for the simulations. The
VOC selected for these hypothetical
lake simulations was MTBE. Input time
series were given as monthly averages.
Seven lake mixing and dilution simu-
lations were done. The mass balance of
MTBE was simplified by setting the wind
speed to 0 meters per second so that gas
exchange was shut off. No anomalous
results were found for any of the mix-
ing and dilution test cases. These seven
simulations demonstrated that the char-
acterization of mixing and dilution were
implemented correctly in the LakeVOC
model.
Two simulations were used to test the
model’s characterization of air-water gas
exchange. The first simulation tested
the air-water gas flux of MTBE with a
constant wind speed as a driving force
for gas exchange. The mass balance of
MTBE in the first simulation was simpli-
fied by setting the atmospheric concentra-
tion of MTBE to zero, assuming there
were no inflows or outflows, and by
using an unstratified lake. The second
simulation tested whether the lake would
come to equilibrium with respect to an
atmospheric concentration of MTBE with
constant wind speed. These two simula-
tions showed that the characterization of
the air-water gas exchange was correctly
represented by the LakeVOC model.
Simulations Using an Actual Reservoir
Additional simulations were com-
pleted to verify results from the Lake-
VOC model for Lake Perris, located in
Riverside County, California, which is
a water-supply reservoir. Water-quality
data provided by the Metropolitan
Water District of Southern California
(MWDSC) were used in the simulations.
The model’s accuracy in estimating:
(1) the depth and volumes of the epilim-
nion and hypolimnion, and (2) the con-
centrations of a VOC with daily, weekly,
and monthly hydrographic, meteorologic,
and VOC input parameters was assessed
using two simulations.
,(A) EPLIMNION
| I i i | I I i | i i i I i i i I i i i I i i T
T -- Measured volume I
160 L - Model-estimated daily volume - T
C ------- Model-estimated monthly !-14 I
I average volume ; : I
140 E * : T
120E | . –
100E - =
80 E ; =
[ + = ; : I
60 E. : T
[ +++ + : i
40 E. : T
20E : =
0 - I I I | I I I I I I | y I | I I I | I I I -
(B) HYPOLIMNION
180 i i i I i i i I i I I
O Measured volume
— Model-estimated daily volume
------- Model-estimated monthly
average volume
160
140
120
100
80
60
40
20
O I I I | I I I | I
01/96 05/96 09/96
Å, Å 2.
wº-v-w
01/97
DATE
05/97 09/97 01/98
Figure 2. Comparison of measured and model-estimated daily and monthly-averaged lake
volumes in (A) epilimnion and (B) hypolimnion, Lake Perris, California, June 1996 through
September 1997.
In the first simulation, dissolved
oxygen (DO) was used to calibrate
Lake Perris’ hydrodynamics using the
LakeVOC model for June 1996 through
December 1998. Model calibration of
estimated-to-measured DO concentra-
tions was completed by adjusting the
values of the epilimnion depth within the
thermocline and applying a first-order
degradation rate for DO in the hypo-
limnion when the lake was stratified
(May through September). The simula-
tion reproduced the general features
of seasonal variation of DO within the
reservoir.
Once the model calibration was com-
pleted, a comparison was made of mea-
sured and estimated depths and volumes
for both the epilimnion and hypolimnion.
The difference between the measured epi-
limnion depths and the calibrated model
epilimnion depths ranged from 0 to 3.15
meters. The differences in the epilimnion
depths were within the range of the mea-
sured thermocline of the stratified reser–
voir. The lake volumes also compared



well, with the model-estimated daily
and monthly average lake Volumes not
changing as rapidly as the measured lake
volumes but following the observed trend
(fig. 2). The large drop in the epilimnion
volume and large increase in the hypo-
limnion volume between November 1996
and January 1997 in figure 2 are associ-
ated with lake destratification (turnover).
In the second simulation, boating
activity and estimated mass-emission
rates from marine engines were used to
estimate the concentrations of MTBE
in the epilimnion and hypolimnion of
Lake Perris using the LakeVOC model.
California Park Service information
(California Park Service, written com-
mun., February 16, 1999) was used
to estimate the number of boats using
the main boat ramps at Lake Perris. A
marine-engine mass-emission rate of
5.5 micrograms of MTBE per boat per
hour was assumed and was based on
the estimates made by Anderson (1997)
specifically for Lake Perris. The Califor-
nia Park Service boat count estimates and
the Anderson (1997) mass-emission rate
(A) EPLMNON
were combined to estimate the temporal
MTBE mass-load inputs for Lake Perris.
Atmospheric MTBE concentrations were
averaged from the four nearest California
Air Resources Board sites.
The measured MTBE concentrations
for Lake Perris on specific monitoring
dates were averaged vertically over the
calibrated epilimnion and hypolimnion
depths and spatially across the reservoir
to obtain an average concentration for
each of the two layers within the reser-
voir. These measured-averaged concen-
trations were compared to the model-
estimated MTBE concentrations using
daily, weekly, and monthly time series for
required model inputs. Only the results
of the calibration and verification process
for daily input time series are shown in
this report.
The model was calibrated for June
1996 through December 1997 and pro-
duced median differences between the
measured-averaged and model-estimated
MTBE concentrations of 0.15 microgram
per liter for the epilimnion (fig. 3A)
and -1.1 micrograms per liter for the
5
O
-
5
-1
0
-1
5
B) HYPOLIMNION
(
1
5
TT T TI I I
E A V
O Calibration
1
O
5
0 - H O -
T o A T
–5 [. T
-10 ET E E E E T
T ; ; ; ; T
-15 [ . . . . . . . . . . . | | | | | | | | | | | T
01/96 07/96 01/97 O7/97 01/98 07/98 01/99 07/99 01/00
DATE
Figure 3. Differences in measured-averaged and model-estimated MTBE concentrations from
daily model inputs in (A) epilimnion and (B) hypolimnion, Lake Perris, California, June 1996 through
September 1999.
MTBE and other VOCs can be released into
lakes and reservoirs directly from boat and
personal watercraft engines, as well as
from accidental spills at fueling stations
(Photograph by John S. Zogorski,
U.S. Geological Survey).
hypolimnion (fig. 3B). Based on the
median difference and the large range in
the model-estimated concentrations in the
epilimnion (fig. 4A), the model calibrated
reasonably well for the epilimnion. In
contrast, a narrow range in the model-
estimated concentrations compared to a
wider range in the measured-averaged
concentrations is evident for the hypolim-
nion (fig. 4B). The poorer calibration in
the hypolimnion could be caused by the
model not characterizing episodic mixing
events across the thermocline or mixing
that does not change the mean epilimnion
depths.
The model was verified for the period
January 1998 to September 1999 and
produced median concentration differ-
ences between the measured-averaged
and model-estimated MTBE concentra-
tions of -2.5 micrograms per liter for the
epilimnion (fig. 3A) and -1.1 micrograms
per liter for the hypolimnion (fig. 3B).
As shown in figure 3, a seasonal variation
of the concentration differences occurs








100 I T T TTTTT I
+ Calibration
(A) EPILIMNION
I * Verification
1
O
l | | | | | | | | I
TTTTTTI I I I
2:
-
| | | | |
1
(B) HYPOLIMNION
10
O
- I TTTTTTTI
I o Calibration
T A Verification
10 T
- A O O A º
- A AQAAA LM
1 | | | | | | | | | |
| | | | |
| | | | | | | | | |
0.1 1
10 100
MEASURED-AVERAGED MTBE CONCENTRATION, IN MICROGRAMS PER LITER
Figure 4. Comparison of model-estimated and measured-averaged MTBE concentrations from
daily model inputs in (A) epilimnion and (B) hypolimnion, Lake Perris, California, June 1996 through
September 1999.
with larger concentration differences in
both the epilimnion and hypolimnion
occurring during the Summer, or high
recreational-use period when MTBE con-
centrations are highest. Part of the larger
differences in the verification process
likely was caused by the lack of complete
boat use information for the verifica-
tion period (compared to the calibration
time period) and, possibly, to a partial
fleet changeover to newer marine engine
technology, with lesser emissions of
gasoline-related compounds, during the
verification time period.
Collectively, the simulations based
on daily model input parameters showed
that the LakeVOC model adequately
estimated concentrations for the epilim-
nion with a larger range in the differences
between the measured-averaged and
model-estimated concentrations for the
hypolimnion. As the time scale of the
model inputs increased (daily to weekly
to monthly), the median and range of dif-
ferences between the measured-averaged
concentrations and the model-estimated
concentrations increased, especially for
the hypolimnion (Bender and others,
2003). Because of the increasing differ-
ences as the time scale is increased, daily
model inputs will produce more accurate
model-estimated concentrations.
Model Compatibility and
Availability
The LakeVOC computer code is
written in Fortran and compiled using
Compaq Visual Fortran V 6.6a'. Lake-
VOC has been tested under all 32-bit
versions of Microsoft Windows operating
systems through Windows XP (Home
and Professional). Documentation of the
LakeVOC model is available as a U.S.
Geological Survey Open-File Report
(Bender and others, 2003). This docu-
mentation, along with the executable
Version and example input parameter
files, can be accessed on the Internet at
the following web site address:
http://pubs. water.usgs.gov/ofr03-212/
"The use of firm, trade, and brand names in this
report is for identification purposes only and does
not constitute endorsement by the U.S. Government.
References Cited
Anderson, Michael, 1997, Predicted
MTBE concentrations in the Eastside
Reservoir: Soil and Environmental
Science, April, p. 2–7.
Baehr, A.L., and Reilly, T.J., 2001, Water
quality at lakeside communities in
Sussex and Morris Counties, New
Jersey, 1998-1999, with emphasis on
methyl tert-butyl ether (MTBE) and
other fuel related compounds: U.S.
Geological Survey Water-Resources
Investigation Report 01-4149, 86 p.
Baehr, A.L., and Zapecza, O.S., 1998,
Methyl tert-butyl ether (MTBE) and
other volatile organic compounds
in lakes in Byram Township, Sus-
sex County, New Jersey, summer
1998: U.S. Geological Survey
Water-Resources Investigation Report
98-4264, 8 p.
Bender, D.A., Asher, W.E., and Zogorski,
J.S., 2003, LakeVOC–A determinis-
tic model to estimate volatile organic
compound concentrations in lakes and
reservoirs: U.S. Geological Survey
Open-File Report 03-212, 283 p.
Boughton, C.J., and Lico, M.S., 1998,
Volatile organic compounds in Lake
Tahoe, Nevada and California, July-
September 1997: U.S. Geological
Survey Fact Sheet 055–98, 2 p.

Angostura Reservoir, South Dakota (Photograph by
Gregory C. Delzer, U.S. Geological Survey).
Dale, M.S., Koch, Bart, Losee, R.F.,
Crofts, E.W., and Davis, M.K., 2000,
MTBE in Southern California water—
Motorized recreational watercraft were
the predominant mode of contami-
nation in reservoirs: Journal of the
American Water Works Association,
v. 92, no. 8, p. 42–51.
Gabele, P.A., and Pyle, S.M., 2000,
Emissions from two outboard engines
operating on reformulated gasoline
containing MTBE: Environmental
Science and Technology, V. 34, no. 4,
p. 368–372.
Jüttner, Friedrich, 1988, Motor-boat-
derived volatile organic compounds
(VOC) in lakewater: Z. Wasser-
Abwasser-Forsch., v. 21, p. 36–39.
Jüttner, Friedrich, 1994, Emission of aro-
matic hydrocarbons and aldehydes into
the water by a four-stroke outboard
motor—quantitative measurements:
Chemosphere, v. 29, no. 2, p. 191–200.
Jüttner, Friedrich, Backhaus, Diedrich,
Matthias, Uwe, Essers, Ulf, Greiner,
Rolf, and Mahr, Bernd, 1995a, Emis-
sions of two- and four-stroke outboard
engines—I. Quantification of gases
and VOC: Water Research, V. 29,
no. 8, p. 1976–1982.
Jüttner, Friedrich, Backhaus, Diedrich,
Matthias, Uwe, Essers, Ulf, Greiner,
Rolf, and Mahr, Bernd, 1995b, Emis-
sions of two- and four-stroke outboard
engines—II. Impact on water quality:
Water Research, v. 29, no. 8, p. 1983–
1987.
Lewis, W.K., and Whitman, W.G., 1924,
Principles of gas adsorption: Industrial
and Engineering Chemistry, v. 16,
no. 12, p. 1215–1220.
Lico, M.S., and Pennington, Nyle, 1999,
Concentrations and distribution of
manmade organic compounds in the
Lake Tahoe Basin, Nevada and Califor-
nia, 1997–99: U.S. Geological Survey
Water-Resources Investigations Report
99–4218, 12 p.
Crater Lake, Oregon (Photograph by Alisa J. Tesch).
JNVEEsº
DEPOS, ſtiº º :
UNITED STATES OF AMERICA
.
Mahler, B.J., 2000, Determining the
occurrence of pesticides and volatile
organic compounds in public water-
supply source waters in Texas: U.S.
Geological Survey Fact Sheet 010–00,
2 p.
Rathbun, R.E., 2000, Transport, behavior,
and fate of volatile organic compounds
in streams: Critical Reviews in Envi-
ronmental Science and Technology,
v. 3, no. 2, p. 129–295.
Reuter, J.E., Allen, B.C., Richards, R.C.,
Pankow, J.F., Goldman, C.R., Scholl,
R.L., and Seyfried, J.S., 1998, Con-
centrations, sources, and fate of the
gasoline oxygenate methyl tert-butyl
ether (MTBE) in a multiple-use lake:
Environmental Science and Technol-
ogy, v. 32, no. 23, p. 3666–3672.
Schwarzenbach, R.P., Gschwend, P.M.,
and Imboden, D.M., 1993, Environ-
mental organic chemistry: New York,
Wiley-Interscience, 681 p.
Van Donkelaar, P., 1988, Comments
on an article by Friedrich Jüttner
“Motor-boat-derived volatile organic
compounds (VOC) in lakewater”:
Z. Wasser-Abwasser-Forsch., v. 21,
p. 255–256.
Wanninkhof, R., Ledwell, J., and Crusius,
J., 1991, Gas transfer velocities on
lakes measured with sulfur hexafluo-
ride, in Wilhelms, S.C., and Gulliver,
J.S., eds., Air-water mass transfer:
New York, American Society of Civil
Engineering, p. 441–458.
Information on MTBE and other
volatile organic compounds sampled
by the U.S. Geological Survey’s
National Water-Quality Assessment
Program can by found at:
http://water.usgs.gov/nawqa/vocs
For more information about the
LakeVOC model, detailed report, and
supporting files contact:
David A. Bender
U.S. Geological Survey
1608 Mt. View Road
Rapid City, SD 57702
(605) 355-4560 ext. 248
dabender@usgs.gov
UNIVERSITY OF MICHIGAN
O
3 9015 08543 6163