ESTIMATING RESERVOIR EVAPORATION:
CURRENT PRACTICE AND STATE-OF-THE-ART
Justin Huntington,
Associate Research Professor, DRI
&
Agencies Contributing to This Work
Lake Tahoe, NV/CA
Workshop Collaborators: Robert Grossman, Katjia Friedrich,
Peter Blanken, Ben Livneh
Introduction
• Open water evaporation is one of the most
difficult surface energy/water fluxes to
quantify, and is rarely directly measured in
the natural environment
• Reservoir operations and the development
of new storage and water accounting
strategies require estimates of evaporation
and net evaporation (E minus PPT)
• Changes in open water evaporation under
future climate are uncertain, especially if
we don’t know current evaporation rates
Boca Reservoir, CA – Truckee River Basin
Introduction
• Primary factors that govern open
water evaporation include
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net radiation
heat storage
air temperature
water surface “skin” temperature
humidity
wind speed
stability of the atmosphere
advection of water and heat in and out of
the water body
• salinity
• All of these factors are important to
consider when deciding which
technique is most appropriate given
the application and data
requirements
Washoe Lake, NV – Truckee River Basin
Windiest valley in Nevada!!
Introduction – Heat Storage
• Heat storage can alter both the rate
and timing of evaporation depending
on the volume, geometry, clarity, and
the surrounding environment
Lake Tahoe temperature profile
• For shallow water bodies, the heat
storage impact on seasonal
evaporation is minor, however for
deep water bodies it can be
significant
• Recent research at Lake Tahoe has
found that the peak evaporation is in
September-November, rather than
summer months
Figure modified from UC Davis
• Heat storage causes evaporation to
be NEGATIVE in the summer over
the Great Lakes!!
Introduction – Heat Storage
• Evaporation is a surface
process
• Heat storage occurs from
penetration of solar radiation
beneath the water surface
• Heat storage is only available
to the surface when
transferred by conduction or
convection
• Large amount of energy is
transferred to the surface during
fall in winter when Tsurface > Tair
• Energy not readily available at the
surface for immediate consumption
by evaporation
• Significant amount of stored
energy can be partitioned into
heating the air or long-waver
emission rather than to evaporation
• Important to consider heat storage
with any evaporation method..
Introduction – Common Indirect Techniques
• Common indirect techniques for
estimating evaporation include:
• Pan evaporation and pan coefficients
• Water budget
• Energy budget
• Bulk mass transfer
• Combination of energy and mass
transfer techniques
• The water budget technique is
considered the most accurate
indirect approach in arid
environments where inflows are
minimal and evaporation is a large
component of the water budget
Folsom Reservoir, CA - American River
Funded by Reclamation and Cal. DWR
Introduction – Common Direct Techniques
• The eddy covariance technique is a direct
technique, and considered the most
accurate if environmental conditions,
physical setting, and experimental design is
ideal
• Eddy Covariance, EC (Enough Corrections!!)
• Hard to collect data on shore due to fetch
issues
• Hard to collect data over water with float/buoy
due moving horizontal plane
• Subject to energy balance blues…
(Rn – G) = (LE + H)
Energy fluxes = Turbulent fluxes… but never do..
Eddy Covariance Station at American
Falls Reservoir, ID - Snake River
Funded by Reclamation
Pan Evaporation
• Historically, evaporation for operations has been estimated
using average pan evaporation data
E  Epan * Coef
• Pan data are widely known to have significant uncertainty both
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in magnitude and timing
Freezing conditions limit use of the pans
No heat storage in a pan
Often poorly sited and maintained
Must determine the pan Coef..
Rye Patch Reservoir, Nevada - Humboldt River Basin
Typical Operations Table – Truckee River
Pan Evaporation
• Proper pan siting is extremely important
• But how do you accurately represent open water
and fetch with pans? Floating pans have issues
too…
Lake Tahoe Pan and NWS COOP Station
Floating Pans?
Pan Evaporation Example for Tahoe
Old Pan
• Example of pan differences due to
pan siting
• Pier location is double that of the
NWS pan station
New Pan.. But discontinued..
Figures from Trask (2007)
Energy Balance
• Evaporation is estimated as a residual of the water body energy balance
LE  Rn  Qv  Qb  H  Qx  Qw  Q p
• Most widely used in research
• Most data intensive and complex approach due the need to consider the
entire water body as a control volume rather than just the surface in the
case of a land surface energy balance
• LE is the latent energy consumed for evaporation
• Rn is the net radiation
• Qv is the net advected energy to the water body from
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surface and groundwater inflows and outflows, and direct
precipitation (dependent on temperature and amount of
flux…linked to water budget!)
Qb is the energy exchange from bottom sediments to the
water body,
H is the energy convected and conducted between the air
and water as sensible heat
Qx is the energy that is stored in the water body
Qw is the energy advected by evaporating water (dependent
on temperature and amount of evaporating water)
Qp is the energy of precipitation
Figure modified from Stannard (2014)
Energy Balance
LE  Rn  Qv  Qb  H  Qx  Qw  Q p
Lake Mead Example
Modified from Moreo and Swancar, 2013
Energy Balance
LE  Rn  Qv  Qb  H  Qx  Qw  Q p
• Energy Balance - required measurements
• Net radiometer to measure net radiation
• Air temperature and vapor gradient over the water
• Temperature profile to measure heat storage per
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layer
Bathymetry to estimate volume weighted heat
storage per layer
Inflow and outflow volumes and water temperature
Precipitation volume and temperature (usually
ignored in arid environments)
Sediment heat storage (usually ignored in deep
reservoirs)
Lahontan Reservoir, NV – Carson River Basin
Funded by Reclamation
• Walker Lake – USGS energy balance Bowen Ratio station
Walker Lake Bowen Ratio Energy Balance Station, Photo by Allander , 2009 (USGS)
Funded by Reclamation
Water Balance
• Evaporation can be expressed as a residual of the water budget volume or depth per
unit time following the continuity equation for a generalized water body as
E  P  SWin  GWin  SWout  GWout  B  DS
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P is direct precipitation on the water surface
SWin and GWin are surface and groundwater inflows
SWout and GWout are surface and groundwater outflows
B is bank storage
DS is the change in storage
• Inflows and outflows must all
be measured or modeled
• Using modeled inflows, and
measured outflows and lake
stages can serve as a reality
check for other independent
methods
Figure modified from Robertson et al. (2003)
Aerodynamic / Bulk Mass Transfer
• Aerodynamic / Bulk Mass Transfer
is probably the most widely and
commonly used approach for
estimating evaporation
• Function of:
• surface temperature
• humidity
• wind speed
• atmospheric stability
• surface roughness
• thermally induced turbulence
• barometric pressure
• and the density and viscosity of the air
Stampede Reservoir, CA – Truckee River Basin
Funded by Reclamation and DRI
Aerodynamic / Bulk Mass Transfer
• Dalton’s (1802) general form of the mass transfer equation can be
expressed as
E  M (es  ea )
• E is the evaporation rate,
• es is the saturation vapor pressure at the temperature of the water
surface
• ea is the actual vapor pressure of the air
• M is the mass transfer coefficient and is a function of wind speed,
atmospheric stability, surface roughness, thermally induced
turbulence, barometric pressure, and the density and viscosity of the
air
Aerodynamic / Bulk Mass Transfer
The direct aerodynamic equation:
• The merit of using the aerodynamic method:
• Surface temperature can be estimated
relatively accurately to estimate qsat
𝐸 = 𝜌𝑎 𝐶𝑒 𝑢 𝑞𝑠 − 𝑞a ,
• qact and windspeed can be measured and/or
estimated fairly easily
• Ce can be estimated using Monin-Obukhov
ra = density of the air
u = windspeed
qs is specific humidity at saturation, estimated from
water surface temperature
qa is actual specific humidity, estimated from relative
humidity and air temperature measured over water
Ce is the exchange coefficient – a function of
atmospheric stability, surface roughness, thermally
induced turbulence, barometric pressure, and the
density and viscosity of the air
similarity theory or computed (calibrated) from
evaporation estimates using Energy Balance
or Eddy Covariance approaches
• Accounts for heat storage by using surface
temperature (i.e. seasonal surface
temperature variations is the result of heat
storage..)
• Can be applied at the sub-hourly or daily time
steps for near real-time operational
monitoring.. Energy balance and water
balance can only be applied at longer time
steps (weekly, monthly, annual..)
Aerodynamic / Bulk Mass Transfer
• Pros:
• Probably the most cost effective
approach for operational monitoring
due to low instrument maintenance
needs, low instrument cost, and daily
time steps
• Cons:
• Theory is not ideal for reservoirs with
limited fetch and located in highly
advective environments..
• But no other approach works well in
these situations either..
• Data needs to be collected over
water
Notable Aerodynamic Study
• Harbeck (1962)
USGS Study
Combination Approaches
• Combination energy-aerodynamic mass transfer methods are commonly used for land
applications and are typically based on Penman (1948; 1956) and Penman-Monteith
formulations
Radiative component:
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SW radiation
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LW radiation
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Ground heat flux
Δ
Advective component:
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Temperature
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Wind Speed
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Humidity
γ
λE = Δ+γ 𝑅𝑛 − 𝑄𝑥 + Δ+γ 𝐸𝐴
Rn = net radiation (shortwave + longwave)
Qx = heat storage of water
λ = latent heat of vaporization
Δ = slope of saturation vapor pressure-temperature curve
γ = psychrometric constant
EA = drying power of air term f (uz)(es – ea))
Combination Approaches
• Morton modified Penman’s combination approach for practical and
operational estimates of evaporation (Morton, 1983)
• Morton’s approach is based on Penman’s combination equation with a
simple heat storage procedure, and relies on feedbacks between the
over passing air and the evaporating surface termed the complementary
relationship lake evaporation model (CRLE) (Morton, 1983a,b; Morton et
al., 1985; Morton, 1986)
• Because CRLE requires limited input data (monthly solar radiation,
temperature, humidity) the approach has been fairly popular
• Also, the CRLE is not very sensitive to differences in temperature,
humidity, and windspeed from land to water, therefore it overcomes
shortcomings of the mass transfer method and combination approach,
and instead relies on the strength of the Priestly-Taylor available energy
approach in which wind speed and vapor pressure are not used
CRLE Model
CRLE Model
CRLE Model
Approach
• Fortran program
and well
documented
• Recently
converted to
Python by DRI
funded by
Reclamation
Annual Evaluation of CRLE
Evaluated CRLE model for historical periods - compares well to previous estimates
of evaporation (water budget, mass transfer, Bowen ratio energy balance)
Average Annual Comparison
Ratio of Average Annual CRLE Estimated to Research E:
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Range = 0.9 -1.13
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Average = 1.02
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STD = 0.08
WWCRA - Reclamation, 2015
Seasonal Evaluation of CRLE
• Compared CRLE to USGS bi-weekly
energy balance estimates of E at Upper
Klamath Lake (Stannard, 2014) funded
by Reclamation
WWCRA - Reclamation, 2015
Other CRLE Comparison Studies
• Most studies found CRLE to be fairly accurate at the annual time
step, and less accurate at the seasonal
• Very useful for water bodies with limited weather and hydrologic data
Limitations of CRLE
• Advected heat from inflows and outflows should be considered
• Does not account for advection of heat from surrounding water
limited environment (negative H)
• Does not account for freezing conditions
• Heat storage function is based on mean water body depth
(area weighted depth) and a simple lag function so seasonal
evaporation estimates are more uncertain than annual
estimates
Seasonal Variation
• Heat storage is a significant source of uncertainty in most models
• Aerodynamic approaches relies on surface temperature… so it must be observed or
modeled…
• Evaporation can be negative in summer!!
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Lake Superior
Like condensation on a cold beer glass on a hot humid day
Lake Tahoe
Trask (2007) – UC Davis Dissertation
Blanken et al. (2015) – Journal of Great Lakes Research
Heat storage variations for different lakes in Japan
Lakes in Japan - Kondo (1994)
What Model To Use?
• Depends on the situation and data
available…
• Don’t pick a highly empirical model
that is known to have issues.. be
smart about it..
• For a model to be good it must have
the right ingredients..
Reality of Uncertainties –
Example for Lake Tahoe
3.6 ft
2.6 ft
Figure from Trask (2007)
Uncertainties
• Uncertainties are important to consider…
• Skin temperature and windspeed (aerodynamic)
• Heat storage (energy balance)
• Inflows outflows (water balance / energy balance)
• Solar radiation / Net radiation (combination energy / aerodynamic)
• Humidity and temperature (combination / aerodynamic)
Future Directions
• Combining remote sensing of water surface temperature with
gridded weather data and physically based models of
evaporation
• Model has to have the right type and with the right ingredients
to be useful for operations
Model
Samani et al. (2009)
Use Satellite Imagery to Track Freezing Conditions
From Huntington and McEvoy (2011)
Landsat TIRS Based Open Water Evaporation
• Initial tests of Landsat /MODIS TIRS aerodynamic evaporation
from Lake Mead compared to USGS eddy flux measurements
Photo by M. Moreo - USGS
Initial results suggest that a TIRS
based aerodynamic approach can
simulate open water evaporation
fairly well, while capturing the lag
in evaporation due to the heat
storage effect…
Looking into Nov, 2010 and 2011..
How Good is the Gridded Weather Data
for Lakes and Reservoirs??
• NLDAS/METDATA (Abatzoglou, 2011) comparison to in-situ eddy station
weather data at Lake Mead
Huntington et al. (2015) – in prep.
How Good is the Gridded Weather Data
for Lakes and Reservoirs??
• NLDAS/METDATA (Abatzoglou, 2011) comparison to in-situ buoy station
weather data at Lake Tahoe -- Bias Correction / Conditioning??
Huntington et al. (2015) – in prep.
Net Evaporation; Net E = E - PPT
• Ultimately we need to estimate net
evaporation for operations and for
predicting lake stage
• Precipitation varies significantly
across many lakes
• We need to measure / model
precipitation!!
• Quality precipitation
measurements or modeling is
often forgotten about during our
rigorous and expensive flux
measurement campaigns..
Future Projections of Evaporation
• Try to understand the past before we understand the future…
• How do we estimate evaporation in the future using a defensible
approach (water budget, energy budget, aerodynamic methods)
• Water budget requires estimating all future inflows, outflows, and
storage changes..
• Energy budget requires estimating lots of future variables (net
radiation, heat storage, and sensible heat flux… hard ones..), and
water inflows and outflows
• Aerodynamic requires future surface temperature, windspeed,
and humidity
Future Projections of Lake Tahoe Evaporation
• CRLE forced with 112 climate model projections (many estimated variables)
• Lake Tahoe ensemble median and 5th and 95th percentile annual precipitation, temperature,
reservoir evaporation, and net evaporation.
WWCRA - Reclamation (2015)
Future Projections of Lake Tahoe Evaporation
• Lake Tahoe mean monthly ensemble median and 5th and 95th percentile
reservoir evaporation and net evaporation.
WWCRA - Reclamation (2015)
Need for Representative Data!!
• In talking about the lack of data to
estimate evaporation Morton (1994)
says….
“After all, if physicists can discuss such
esoteric subjects as quarks and black
holes, why can't the environmental
scientists know what is happening right
under their noses?”
“The tragedy is that this
misapprehension causes the financial
resources and scientific skills to be
directed toward the development of
techniques that can only provide trivial or
dubious answers, at the expense of the
kind of long-term original research that is
needed before worthwhile answers can be
expected”
Recap
• Common indirect techniques include:
• Pan evaporation and pan coefficients
• Proper sitting important
• Must select pan coefficients based on
lake/reservoir characteristics..
• Not really reliable..
• Water budget
• Inflows outflows and stages must be
measured..
• Energy budget
• Net radiation, heat storage, inflows / ouflows,
humidity & temperature gradients must be
measured
• Aerodynamic
• Surface temp, over water wind, and humidity
• Combination of energy and mass transfer
techniques (all of the above…or use model
that estimates.. like CRLE..)
DRI / Reclamation / California Department of
Water Resources buoy weather station for energy
balance and bulk mass transfer evaporation
estimates, Folsom Reservoir, American River, CA.
Summary
• Estimating open water evaporation is not easy!!
• True measurements of it are rare..
• Important that models be chosen wisely based on
environmental conditions and available data
• Weather models and gridded weather data have biases
and need to be known
• Remote sensing of surface temperature can help
constrain models or be used directly
• Perhaps multiple models should be used… but only those
that have “good” ingredients..
Thanks – Questions/Suggestions?
Justin Huntington, Desert Research Institute, justinh@dri.edu, 775-673-7670