Journal of Environmental Protection, 2009, 1, 1-19
Published Online November 2009 (http://www.SciRP.org/journal/jep/).
Long-Term Study of Lake Evaporation and Evaluation of
Seven Estimation Methods: Results from Dickie Lake,
South-Central Ontario, Canada
Huaxia YAO
Dorset Environmental Science Centre, Ontario Ministry of Environment
Dorset, Ontario, P0A 1E0, Canada
Abstract
Establishing satisfactory calculation methods of lake evaporation has been crucial for research and manage-
ment of water resources and ecosystems. A 30 year dataset from Dickie Lake, south-central Ontario, Canada
added to the limited long-term studies on lake evaporation. Evaporation during ice-free season was calcu-
lated separately using seven evaporation methods, based on field meteorology, hydrology and lake water
temperature data. Actual evaporation determined during a portion of a year was estimated using a lake en-
ergy budget model, and the estimation was used as reference evaporation for evaluation of the seven methods.
The deviation of method-induced evaporation from the reference evaporation was compared among the
seven methods, and a performance rank was proposed based on the root mean squared deviation and coeffi-
cient of efficiency. As for the whole ice-free season (roughly May to November), the water balance was the
best method, followed by Makkink, DeBruin-Kejiman, Penman, Priestley-Taylor, Hamon, and Jensen-Haise
methods. As for shorter duration (a week to a month), the DeBruin-Kejiman was the best method, followed
by Penman, Priestley-Taylor, Makkink, Hamon, Jensen-Haise, and water balance method. Annual and sea-
sonal changes of energy budget terms and the compensation function of lake heat storage in evaporation flux
were also analyzed.
Keywords: Long-Term Study, Lake Evaporation, Water Balance, Energy Budget, Lake Temperature, Stream Discharge
1. Introduction
Natural lakes and artificial reservoirs provide a valuable
water resource. The quantity and quality of lake water
resource are important for agriculture, fisheries, recrea-
tion, domestic and industrial water supply, aquatic eco-
system, and hydropower [1-2]. Lake water availability is
regulated by the water balance and energy budget proc-
esses which in turn are closely tied to climate variations,
land use change or other human influences [3-5]. For
example, a common indicator of water availability-lake
water level-is influenced by four major processes or fac-
tors: 1) precipitation on the lake and its drainage water-
sheds; 2) surface and subsurface runoff generated from
the watersheds; 3) runoff leaving the lake; and 4) direct
evaporation loss from the lake surface. Therefore, it is
crucial to understand the lake evaporation process, estab-
lish satisfactory calculation methods, and identify the
effects of lake evaporation on lake level and water re-
sources.
Long-term observations and field data are important for
understanding lake evaporation, creating estimation meth-
ods, and evaluating effects of evaporation change (caused
by climate change or land use change) on water resources.
However, it is challenging or difficult to directly measure
lake evaporation for a long time, because it involves sig-
nificant financial investment in instruments, field main-
tenance, and field work on a lake. Usually lake evapora-
tion is estimated or calculated by a formula and using
regular meteorological and hydrological data. Lake eva-

H. X. YAO ET AL. 2
poration is affected not only by climatic variables, but
also by lake characteristics such as depth, surface area,
and water clarity and temperature. Lake water itself in-
fluences the energy budget and lake evaporation through
the changes in water temperature and water mixing (turn
over). Accurate accounting of energy budget processes
requires observations of temperature profiles of lake wa-
ter. As a result, these field difficulties have severely re-
stricted the number of long-term evaporation studies.
Methods, equations or models for determining lake
evaporation may be categorized into four categories: en-
ergy budget, aerodynamic transfer (or mass transfer),
combination of aerodynamic transfer and energy budget,
and empirical method. Most literature studies using one
or more of these methods have utilized short-term field
monitoring and datasets. In this paper “long-term” studies
mean those that conduct and utilize monitoring data of
multiple years to more than 5 years. Lenters et al. [6]
completed a comprehensive study of lake evaporation and
effects of climate variation by using 10 year data from a
small lake in Wisconsin USA. In the article by Lenters et
al., some long-term studies were summarized. Apart from
these summarized examples, there are other long-term
studies that have been conducted: a lake in Northwest
Territories of Canada for six years [7], the small Lake
Kinneret in Israel for five years [8], the large Lake Okee-
chobee (1732 km2) in Florida USA for five years [9], a
small reservoir (8.8 km2) in Minas Gerais State, Brazil for
three years [10], the large man-made Lake Mead (506
km2) in Las Vegas, Nevada USA for three years [11], the
large Bear Lake in Idaho and Utah, USA for two years
[12], the Cottonwood Lake Area in North Dakota USA
for 5 years [13], the Mirror Lake in New Hampshire USA
for 6 years [14], the Perch Lake in eastern Ontario Can-
ada for 11 years [15], several lakes in Minnesota USA for
11 years [16], and several more examples using two-year
data [17-19]. Scheider et al. [20-21] and Hutchinson et al.
[22] have reported on lake evaporation study of 15 years
(1976–1992) for lakes in Muskoka area of Ontario, Can-
ada.
The study examples mentioned above are listed in Ta-
ble 1, illustrating the limited number of long-term studies.
There are only 14 examples of studies in Table 1 where
five or more years of data are used. The Lake Ziway
study with the longest data record of 30 years made many
simplifications in its calculations of monthly and annual
average evaporation and did not provide details of the
evaporation process. Therefore, additional studies of lake
evaporation using long-term data are needed to describe
the evaporation process and its variability; and to confirm
and compare the applicability of available estimation
methods. A detailed analysis of 30 year (1978–2007) field
data for Dickie Lake (the lake is located in the same
Muskoka-Haliburton area as monitored and reported by
Scheider et al. and Hutchinson et al.) is presented in this
paper.
Table 1. Study examples of long-term lake evaporation.
Authors Study site Country Years of data Methods used
Vallet-Coulomb Lake Ziway Ethiopia 30 Three methods
Hutchinson et al. Muskoka Area Canada 15 Energy budget
Rasmussen et al. Cedar Lake etc. USA 11 Seven methods
Robertson et al. Perch Lake Canada 11 Energy budget
Lenters et al. Sparkling Lake USA 10 Energy budget
Robertson et al. Perch Lake Canada 10 Energy budget
Winter et al. Mirror Lake USA 6 Energy budget
Rosenberry et al. Mirror Lake USA 6 15 methods
Gibson et al. Yellowknife Canada 6 Two methods
Rosenberry et al. Cottonwood Lake USA 5 13 methods
Winter et al. Williams Lake USA 5 11 methods
Sturrock et al. Williams Lake USA 5 Energy budget
Assouline Lake Kinneret Israel 5 Two methods
Abtew Lake Okeechobee USA 5 Seven methods
Myrup et al. Lake Tahoe USA 3 Two methods
Sacks et al. Two lakes USA 3 Energy budget
Dos Reis et al. Lake Serra Azul Brazil 3 Two methods
USGS Lake Mead USA 3 Energy budget
Amayreh Bear Lake USA 2 Two methods
Hamblin et al. Lake Malawi Mozambique 2 Three methods
Keskin et al. Lake Egirdir Turkey 2 Six methods
Linacre Copenhagen Australia 2 Three methods

H. X. YAO ET AL.
3
Apart from the need for long-term data, methods for
evaporation estimation should be discussed and assessed,
because more than 30 methods or equations have been
proposed and most of them perform differently for dif-
ferent geographical areas. Winter et al. [23] compared 11
well-used methods with the energy budget method by
using high-quality data for five years from Williams Lake,
and proposed a ranking based on best to least perform-
ance. Their ranking is: Penman, DeBruin-Kejiman, Mak-
kink, Priestley-Taylor, Hamon, Jensen-Haise, mass trans-
fer, DeBruin, Papadakis, Stephens-Stewart, and Brut-
saert-Stricker. Rosenberry et al. [13,14] compared as
more as 15 methods with energy-budget method using
6-year data and proposed their ranking. Rasmussen et al.
[16] compared seven methods for use in lake temperature
modeling. The evaluation of seven methods by Abtew [9]
suggested that simple models (such as the modified Turc
model only using solar radiation and maximum air tem-
perature) could perform better than Penman-combination
or Priestley-Taylor model requiring many more parame-
ters. The four methods–Priestley-Taylor, DeBruin-Keji-
man, Papadakis and Penman were compared with energy
budget by Mosner and Aulenbach [24] using single-year
data, and the Priestley-Taylor was found to be the best of
the four methods. Xu and Singh [25] tested eight radia-
tion-based evaporation models in order to estimate future
lake levels. Singh and Xu [26] evaluated 13 mass-transfer
equations against pan evaporation data. Delclaux et al.
[27] compared five monthly evaporation methods and the
best results of lake evaporation were obtained by the Ab-
tew model and Makkink model. Comparisons of estima-
tion methods were also made by Keskin and Terzi [18]
and Sadek et al. [28]. All these comparisons provided
somehow different conclusions depending on sites and
data used.
As indicated by Winter et al. [23], earlier comparisons
of evaporation methods did not use extensive or long term
data. Also comparisons have been focused more on large
lakes in arid and semiarid climates than on small lakes in
humid and sub-humid climates. The lakes in cold or bo-
real ecozones (such as those located on the Canadian
Shield) have received even less attention. The evaluation
of methods needs to be made for a longer period of time,
a wider scope of lake sizes and more climatic settings. In
our study, seven commonly used methods are compared
with each other and assessed by using long-term data
from Dickie Lake on the Canadian Shield where such
comparison has rarely been made. Only one case of
method comparison was reported for Canadian Shield:
Singh and Xu [26].
Another issue in evaporation studies is the standard or
reference that was used to verify estimation methods.
Actual lake evaporation can be measured by an instru-
ment such as the eddy covariance system, but long-term
data from the system has not been reported. A common
measure of lake evaporation is by using an evaporation
pan, with a limitation: the pan coefficient (multiplying the
coefficient with the pan evaporation data to get lake
evaporation) depends on season, location and the specific
pan in use [9]. In case a reliable and direct measure of
long-term evaporation did not exist, many reported com-
parison studies chose to evaluate methods by comparing
evaporation results with that of an energy budget method,
as the latter was considered the best method to estimate
lake evaporation [6,13,14,23,24]. In our study of Dickie
Lake, there was no data from pan evaporation or eddy
covariance instrument, the energy-budget results were
used to be the reference for evaluating performance of
other estimation methods.
Therefore, our study has three goals: 1) provide an
evaporation study using long-term 30-year datasets ob-
tained for a small lake located in the Canadian Shield
region; 2) estimate evaporation of ice-free season for 30
years using seven methods, and discuss their applicability
to cold ecoregions; and 3) compare deviations of meth-
od-calculated evaporation to the energy-budget-estimated
evaporation, and identify the better methods for estimat-
ing lake evaporation for the region.
2. Site and Data Description
The Muskoka-Haliburton study region as shown in Figure
1 is located in south-central Ontario, Canada, to the east
of Lake Huron, one of the five Great Lakes in North
America. Environmental monitoring programs including
hydrological and meteorological observations were star-
ted and managed by the Dorset Environmental Science
Centre, Ontario Ministry of the Environment in 1976, and
have been continuous till present. The program includes
nine lakes and their contributing watersheds, as represen-
tatives of inland lakes on the Canadian Shield landscape,
which typically consists of exposed bedrock and numer-
ous lakes. The lakes and watersheds in the Muskoka-
Haliburton study area drain into Muskoka River or Gull
River which contributes to Muskoka Lake and finally into
Georgian Bay of Lake Huron. The region is relatively
undeveloped by humans, with the exception of small
towns or villages like Huntsville, Bracebridge or Dorset,
and some scattered cottages alongside shorelines or in
forested areas.
The study lake, Dickie Lake, is one of the nine lakes
(Figure 1, Number 6), and is located between Bracebridge
and Dorset, about 20 km from both. The lake, streams and
drainage watersheds, and monitoring gages are shown in
Figure 2. There are five main streams going into the lake,
and their watersheds are numbered as 5, 6, 8, 10 and 11 in
Figure 2. These stream watersheds occupy a large portion
of the total drainage area. There is a weir (gauge) at the
end of each stream to monitor water levels at that par-
ticular point and the levels are converted to stream dis-

H. X. YAO ET AL. 4
charges with calibrated level-discharge relationships. A
small portion of the drainage area, which is close to the
lake’s shoreline and does not have obvious streams, has
not been monitored by gauges. The outflow on the
south-west side of the lake is also monitored. The lake’s
water level is observed at a location off the inlet of wa-
tershed 6. The areas of the five main watersheds are 0.30,
0.22, 0.67, 0.79, and 0.76 km2 respectively, giving a
gauged drainage area of 2.74 km2. The ungauged drain-
age area is 1.32 km2 whereas the total drainage area is
4.06 km2. The lake itself has an area of 0.94 km2. The
lake’s outlet point controls a total area of 5.0 km2.
The geology of Dickie Lake drainage area is composed
of three surficial geology types [21]: shallow surficial
deposits (less than 1 m in depth) covering 78 % of the
area, deep surficial deposits (greater than 1 m in depth)
covering 3 %, and organic soils covering 19 %. Therefore,
the soil is thin and poorly developed, making surface
runoff the dominant runoff generation while groundwater
runoff from bedrock is minimal. Forest cover is almost
continuous in the watershed although it contains some
areas of exposed bedrock. The percentages of wooded
land and exposed bedrock among the whole watershed
are 83 % and 17 % respectively. Small logging operations
and dwellings around the lake and watershed exist, but
their influence on the hydrological cycle is minimal.
Consumptive use of lake and stream water is also mini-
mal.
The climate of the study area is cold and humid in fall
and winter, with less precipitation in summer than in fall
or winter, and usually has significant snow/ice melting in
spring. As presented by the data records, annual mean air
temperature is 4.9 °C, and average annual precipitation is
1010 mm.
The data collection and processing was completed us-
ing a meteorology station located at Heney Lake ap-
proximately 1.0 km away from Dickie Lake (Figure 1).
The data used for calculations include daily precipitation,
daily mean temperature, relative humidity, wind speed,
and daily global radiation. This station provides a major-
ity of data used for the Dickie Lake study. When a data
point was missing or unreliable at the Heney station, three
other nearby stations located close to Chub Lake, Plastic
Lake and Harp Lake were used to give a proper data
value. The processed data are available for 30 years:
1978–2007.
Figure 1. Locations of study area and study lake.

H. X. YAO ET AL. 5
Figure 2. Dickie Lake and its watersheds (W and F mean stream gauge type: weir and flume).
Stream water level data are obtained from field re-
cording charts which are used to provide hourly and daily
discharges for five watershed streams. Daily mean dis-
charges are available for 30 years: 1978–2007. They are
used for evaporation estimation via lake water balance
calculations.
Lake temperature profiles (water temperature at 1 m
intervals from lake surface to lake bottom) were con-
ducted at one and central point of the lake, on varying
dates throughout a year, mostly during the ice-free season.
A period between two observation dates consists of 6 to
45 days, two weeks on average. The water depth meas-
ured at the deepest and central part of the lake varies be-
tween 9 and 12 meters, therefore, the number of vertical
profile zones changes slightly in the year, with one zone
being one meter thick. Available data covers a period of
30 years (1978–2007).
Lake levels were monitored once every two or three
weeks on average, during ice-free season only, for 23
years: 1980 to 2002. They are used to calculate water
balance.
For clarification, the three timing concepts used in the
study are explained. Lake temperature profile observation
begins in early May but not fix on a specific date, ends in
mid November. The time length between any two obser-
vation dates is called a “period”. A period has a range of
6-45 days depending on actual field work, and is used for
evaporation calculations. The lake level observation be-
gins in May and ends in November (differs between years,
and differs from the lake profile observation dates). The
time length between two observation dates is called an
“interval”. A period and an interval may cover some same
days, but do not necessarily coincide completely with
each other, as water temperature and lake level may not
be observed on a same date. An interval has a range of
2-34 days, and is used for water balance calculations. The
length of whole ice-free time appointed in the study, or
the total cumulative time over all intervals in a year, is
called a “span”. It starts from the earliest day of lake level
observations that falls within the periods and ends at the
last day of level observations falling into the periods. The
span for water balance is 68 – 190 days long depending
on the year.
The concept “period” is important for calculating the
evaporation using any lake-heat-storage-based method,
because only the first day and last day of the period have

H. X. YAO ET AL. 6
observations of the lake’s temperature profile which is
needed to know lake heat storage. For those methods us-
ing lake temperature data, total evaporations in periods
have to be calculated before a daily evaporation rate av-
eraged over the period can be known or the daily rates are
approximately allocated (see a later allocation explana-
tion). For other methods not using lake temperature data,
daily evaporation can be calculated first, and the periods
are not necessarily required. However, for consistency,
the periods are used for all methods in this study.
Listed in Table 2 is the number of periods of each year,
number of consecutive days covered by the periods,
number of intervals, and span length in a year. For exam-
ple, there are 21 periods in 1980 which cover 180 con-
secutive days (from Julian day 126 to 305), and 17 inter-
vals which cover 141 days (the span from Julian day 162
to 302). There are no intervals assigned for years 1978
and 1979 as the lake level monitoring was started in 1980,
and no intervals for years 2003–2007 as recorded level
data in these years were found unreliable.
3. Methods
3.1. Reference Evaporation Derived by Energy
Budget
The energy budget is often used for lake evaporation cal-
culations. For a lake and for a given time period previ-
ously defined, its energy budget is written as
SHAHRE netsednet 



(1)
Table 2. Calculation periods and intervals.
Year Periods Days in periods Intervals span
1978 22 169
1979 23 179
1980 21 180 17 141
1981 21 171 21 162
1982 13 189 24 176
1983 13 189 26 183
1984 12 196 24 183
1985 11 171 24 161
1986 8 176 73 174
1987 6 164 44 161
1988 6 175 24 169
1989 7 189 26 183
1990 8 183 26 183
1991 7 197 27 190
1992 6 161 15 148
1993 5 180 12 169
1994 5 174 9 114
1995 5 168 9 139
1996 5 121 5 101
1997 5 177 13 153
1998 11 180 10 68
1999 13 184 12 149
2000 13 176 14 164
2001 12 166 15 160
2002 11 185 21 152
2003 11 149
2004 11 163
2005 11 190
2006 12 190
2007 12 198
Total 326 5290 490

H. X. YAO ET AL.
7
where all energy terms are in unit of Joule. λE is latent
energy used by evaporation of lake water during the pe-
riod, λ is the latent heat of vaporization (2.46×106 J kg-1),
E is the evaporation (mm) within the period, Rnet is net
radiation, Hsed is heat released by lake sediments and is
negligible for most cases, Anet is net heat advected into the
lake from precipitation, inflows and outflows, and is also
negligible, H is sensible heat transfer from lake surface to
atmosphere, and S is the change of heat stored in the lake
(due to temperature changes) during the period. The neg-
ligibility of the net heat advection Anet could be supported
by the study results of Lenters et al. [6] for Sparkling
Lake (0.64 km2, similarly small as Dickie Lake’s area
0.94 km2). They found that this advection term only had a
mean value of 0.1 W m-2 in 10 summers, very small
compared to other energy budget components (107 W m-2
of Rnet, or 89 W m-2 of λE). Although a lacking of stream
water temperature data at our site does not warrant a rig-
orous calculation of the advection term, it is believed
negligible.
The sensible heat term can be expressed as H=B· λ E,
where B is the mean Bowen ratio for the period. Remov-
ing the two negligible terms, Equation (1) is rewritten as
)1( B
SR
Enet




(2)
The net radiation is an accumulation of daily net radia-
tion in the period:
)]()()1()()1[(
1
iririrR lwu
n
i
lwdlwswdswnet  


(3)
where i is the order of any day in the period (i=1, 2, ……,
n days), rswd(i) is daily downward shortwave radiation
which is observed at the meteorological station, αsw=0.07
is the shortwave albedo of water (value taken from
Lenters et al. [6]), rlwd(i) is daily downward longwave
radiation, αlw=0.03 is the longwave albedo, and rlwu(i) is
daily upward longwave radiation. Longwave radiations
are calculated by rlwd(i)=εaσTa
4, rlwu(i)=εsσTs 4, where
εa=0.91 and εs=0.97 are emissivity of the atmosphere and
surface water respectively, Ta and Ts are daily air tem-
perature and surface water temperature (in unit of ˚K).
The daily air temperature is provided by routine monitor-
ing, while surface water temperature is observed only on
the first and last day of a period (roughly 14–21 days
long). The daily water temperature within a period is ob-
tained by interpolation between the two days’ temperature
values.
The heat storage change S in Equation (2) is calculated
by using vertical lake zones and lake temperature profiles.
Temperature profiles are observed at the central lake
where it has the deepest water. The water body is divided
into vertical zones from lake surface to lake bottom, and
the number of zones may differ a little among periods.
The heat stored in the lake on the last and first day of the
period is calculated, and their difference is the change in
heat storage,
 

12
1
111
1
1
222
2
)()()()()()(12
m
j
s
ww
m
j
s
ww jzjajT
a
c
jzjajT
a
c
SSS

(4)
where S2 and S1 are heat storage on the last and first day
respectively, ρw=1000 kg m-3 is water density, cw=4186 J
kg-1 ˚C-1 is specific heat of water, as2 and a2(j) are the lake
surface area and water area (m2) of any zone j (j=1,
2, ……, m
2 starting from the lake surface zone) on the
last day, T2(j) and z2(j) are the temperature and thickness
of zone j on the last day. Similarly, as1, a1(j), T1(j), z1(j)
are the surface area, water area, water temperature and
zone thickness respectively on the first day. Water area a
(m2) at a height h (m) from lake bottom is estimated by an
empirical relation derived from observed lake mor-
phometry data [29] as follows.
33401159210245389 23  hhha (5)
As in Equation (6), the period-mean Bowen ratio B is
calculated from daily Bowen ratios which is derived from
air and lake surface temperatures [30].




n
isass
as
ieie
iTiT
n
B
1)()(
)()( 
(6)
where γ is psychrometric constant (67 Pa ˚C-1), n is the
number of days in a period, i is any day within a period,
Ts(i) and Ta(i) are daily mean temperature (˚C) of lake
surface and air above the lake respectively, ess(i) and esa(i)
are saturated vapour pressure (Pa) at the lake surface and
air temperatures. The saturated vapour pressure is calcu-
lated with the Arden Buck Formula [31]:
]
14.257
)5.234/678.18(
exp[21.611
a
aa
sa T
TT
e

 (7)
Daily evaporation is not obtained by using Equation (2)
as the field collection of lake temperature profiles is not
conducted every day in a period. After the total evapora-
tion E is calculated as above, daily evaporation is allo-
cated from the total amount based on a distribution pat-
tern. Hamon method is the easiest way to estimate daily
evaporation and uses only air temperature. Therefore, a
time series of daily evaporation is created by using the
Hamon method (described later), their summation gives a
total amount, and the ratio of daily evaporation to total
evaporation is determined. By applying the same ratios to

H. X. YAO ET AL. 8
the total amount value obtained from the energy budget
method, daily evaporations for the energy budget method
are obtained. A further discussion on the allocation caveat
will be provided in the Discussion section.
3.2. Evaporation Methods
Seven methods are selected for calculation of lake evapo-
ration at Dickie Lake and are later compared to each other.
They are Hamon (HM), Penman (PM), Priestley-Taylor
(PT), DeBruin-Kejiman (DK), Jensen-Haise (JH), Mak-
kink (MK) and water balance (WB). These methods are
commonly used and once compared in literature, but they
have not been compared or evaluated for lakes on the
cold Canadian Shield, using dataset as long as 30 years.
Water balance method has not been compared with other
methods in the published reports. Calculations are con-
ducted for the defined periods of each year, and two val-
ues are estimated – the total evaporation amount in a pe-
riod, and daily evaporation rates for the period. Depend-
ing on individual methods, the total evaporation is given
first, then daily rates are calculated from the total value;
or the daily evaporation rate is calculated first, then the
total value is derived from daily rates. Comparisons of the
seven methods are made on basis of interval and span, not
on daily basis. However, daily evaporation rate is re-
quired to provide the evaporation amount within an in-
terval, as the dates in an interval are different from the
dates in a period.
3.2.1. Hamon Method
It is often used to estimate lake evaporation or watershed
potential evaporation because of its simplicity [32]. For a
given lake, daily evaporation e (mm) is calculated from
daily temperature Ta (˚C) as follows.
273
5.7
21063.0 
a
a
T
T
De (8)
where D is the ratio of maximum sunshine duration (hour)
to 12 hours, and is determined by latitude of the lake and
the date:
)]}360
365
80
sin(45.23tan[)tan(arccos{
90
1 
 J D 
(9)
where φ is the latitude (45.13˚ for Dickie Lake), J is the
Julian day of any date of interest.
Total evaporation E in a period is the sum of daily
evaporations of all included days.
3.2.2. Penman Method
A format of Penman equation, once recommended by
Food and Agriculture Organization [33], is used and
slightly modified to calculate lake evaporation. The
modification is an addition of the lake heat storage
change rather than taking only the net radiation. The
evaporation in a period is written as
nequ
SR
Esa
net 






)1()54.01(0026.0



(10)
where Rnet and S are the net radiation (Joule) and lake heat
storage change in the period, u is the mean daily wind
speed (m s-1) for the period, q is the mean daily relative
humidity (≤1.0), sa
e is the mean daily saturated vapour
pressure (Pa), Δ is the mean slope of the saturated vapour
pressure – temperature curve at the air temperature, and n
is number of days in the period. The two terms related to
the slope Δ and psychrometric constant γ are expressed as
empirical relations of air temperature [34]:
aa TT 01119.05495.001124.0439.0 







(11)
Total evaporation is obtained first as the lake heat
storage change in a period (S) is included in Equation (10).
The total evaporation E is allocated to each day of the
period as done for the case of energy budget.
3.2.3. Priestley-Taylor Method
Evaporation is estimated based on radiation and heat
storage only, as done by Winter et al. [23].

SR
Enet  


 26.1 (12)
where the variable Δ/(Δ+ γ) is estimated in Equation (11).
3.2.4. DeBruin-Kejiman Method
The DeBruin-Kejiman equation is written as [23,35]

SR
Enet  


63.095.0 (13)
where the slope of saturated vapour pressure curve Δ
could be estimated by using Equation (11), and net radia-
tion and lake heat storage change have been estimated in
the energy budget calculations.
3.2.5. Jensen-Haise Method
Daily evaporation is first calculated by the following
Equation [23].

swd
a
r
Te  ]5.0)328.1(014.0[ (14)

H. X. YAO ET AL. 9
where Ta is daily temperature (°C), rswd is daily shortwave
radiation as used in Equation (3). The total evaporation in
a period is the sum of the daily rates.
3.2.6. Makkink Method
Daily evaporation is calculated as [23]
012.061.0 




swd
r
e (15)
And then the total evaporation is obtained.
3.2.7. Water Balance Method
As shown in Figure 2, the lake’s inflows from five major
streams are measured, the inflows from ungauged water-
sheds can be prorated from measured flows, and the lake
outflow, lake level and precipitation are also known.
Therefore, the lake evaporation during a time span (or
interval) can be estimated by using a water balance equa-
tion for the lake.
Water balance analysis is made for a time in ice-free
season (early May – mid November) as long as the lake
level data are available. For a span in a year, the water
balance is expressed as
LORPEWB  (16)
where EWB is the total evaporation (mm) during the span,
P is the precipitation volume (mm) during the span, R is
the runoff (mm) from all watersheds (gauged and un-
gauged), O is the outflow volume at the lake outlet, and
ΔL is the level change over the span.
The span length of a year varies with years, because the
starting date and ending date may differ between years.
Water balance estimation must begin and end at a day
when the lake level is known. After an estimation is com-
pleted for a year (May to November usually), a new esti-
mation for the next year is made. Regarding the inflow
from ungauged watershed area, a proration method was
applied to the study area [20,22] to derive discharge from
ungauged area based on the assumption: the areal runoff
is equal among the lake’s watersheds. An evaluation of
errors originated by the proration was made by Devito
and Dillon [36] using two lakes other than Dickie Lake in
the same region, and the errors were within 10% of the
annual runoff measured. Therefore, we use the same
method to get an estimation of the ungauged runoff.
Groundwater inflow and outflow, or groundwater net
flow to the lake, are not included in Equation (16) as they
are assumed negligible. This assumption was applied to
the study area before [20,22,36], and was used in other
regions [37]. The characteristic shallow surficial till and
largely impermeable bedrock in the Canadian Shield re-
gion support the assumption, as it is supported by the
small ratio 0.07 of groundwater inflow against surface
water inflow to Lake Michigan [38], and by a satisfactory
analysis of water balance in 30 years for Dickie Lake
without including groundwater flow [Yao et al., Data
Report in editing, Ontario Ministry of Environment].
A similar equation as Equation (16) is applied to any
interval within a span, and the evaporation amount of the
interval is obtained.
3.3. Comparison and Evaluation of Seven Methods
The difference of method-calculated evaporations from
the energy-budget EWB values is used as an accuracy in-
dex of an evaporation method. Comparing the differences
of seven methods will provide a quantitative evaluation of
their performance and accuracy. The root mean square
deviation (RMSD) is a frequently-used measure of the
differences between values predicted by an estimator and
the values observed from the thing being estimated.
Another indication of how well the estimator
follows/predicts the variations in the measured values
could be given by a coefficient of efficiency (CE) as
proposed and applied by Nash and Sutcliffe [39]. This CE
index is expressed as




 2
2
)(
)(
1
meanref
refest
EE
EE
CE (17)
where Eest and Eref are the estimated and reference (or
measured) evaporation for a span (or interval) respec-
tively, and Emean is the mean of reference evaporations. A
larger CE number indicates a more accurate estimator.
Both indexes RMSD and CE are used in our study to
evaluate and compare the accuracy and performance of
the seven evaporation methods, and a performance rank is
then proposed. The estimated evaporation is plotted
against the reference evaporation for examining each
method’s bias and errors. The comparison is conducted
separately for the span (longer time) and interval (shorter
time) because a method might perform quite differently
between the two time scales.
4. Results
Results of energy budget calculation for 30 years
(1978–2007) and the resulted reference evaporation used
for comparison are presented first. They are followed by
the results of evaporation estimated with the seven meth-
ods. Then method comparison results are presented.
4.1. Energy Budget
Span-mean values of energy budget variables (net radia-
tion, sensible heat flux, evaporative heat flux, and lake
heat storage rate) and meteorological variables are illus-
trated in Figure 3 to show their inter-annual changes.
Figure 3(a) shows the meteorological variables, and Fig-
re 3(b) shows the energy budget fluxes, with the source u

H. X. YAO ET AL. 10
0
2
4
6
8
10
12
14
16
18
20
22
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Year
T
a
, T
s
(
0
C), U (m s
-1
)
0
20
40
60
80
100
120
140
160
180
200
Humidity (%)
Ta Ts URH
(a )
-160
-120
-80
-40
0
40
80
120
160
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Year
NETR, NETR-S (W m
-2
)
0
40
80
120
160
200
240
280
320
E, E+H (W m
-2
)
NETR NETR - SEE + H
(b )
Figure 3. Span averages of (a) meteorological variables, and (b) energy budget variables.
ems in upper section and consumptive items in lower change although it increases slightly, nor does wind speed it
section. Air temperature and lake surface temperature
change in an identical way, as is usually expected. Net
radiation flux changes coincidently with temperature.
Very little correspondence is seen between humidity (or
wind speed) and temperature (or net radiation). Further-
more, lake heat storage rate possesses a tiny portion in
source energy (net radiation - heat storage). For a major-
ity of 30 years, the lake heat storage contributes very little
to the energy source on annual basis. For this reason, the
consumptive term (E or E+H) has a strong correspon-
dence to net radiation flux: climbing or dropping in the
same years.
Daily mean values of meteorological and energy
budget variables (the 30-year mean for any day between
the Julian day 121 and 319) are illustrated in Figure 4 to
show seasonal changes. Air temperature has some fluc-
tuations while demonstrating a clear curving. Corre-
sponding to air temperature, the lake surface temperature
has a similar changing curve, but smoother. To their con-
trast, relative humidity does not have clear seasonal
have clear changes.
The seasonal patterns of energy terms demonstrate two
phenomena. 1) The energy source (net radiation minus
lake heat storage change, NETR - S) determines how
much energy could be consumed by sensible and evapo-
rative fluxes, therefore the source term NETR-S and con-
sumptive term E+H have the same changing pattern –
climbing in the summer to their peaks in mid July (around
day 200) and dropping in the late summer and fall. 2)
There is a time lag between net radiation NETR and con-
sumption E+H, because of the function of lake heat stor-
age. Unlike E+H, net radiation is high in May and June,
and then decreases quickly in July and August till No-
vember. By dividing the curves at the Julian day 200
(July 20), lake water uses net radiation to increase its
temperature or increase heat storage over the first section
of the curve, the usable energy source for evaporation and
sensible heat conduction is less than the net radiation, and
therefore, the high radiation rate does not produce a high

H. X. YAO ET AL. 11
the difference in span length (number
E+H rate in May and June. In July the lake is not absorb-
ing net radiation and the high radiation finally creates the
highest evaporation rate. Contrarily, lake water reduces
its temperature over the second section of the curve, and
releases its stored heat to compensate for the decreasing
radiation. The usable energy source is more than the net
radiation. E+H does not decrease as quickly as the net
radiation because of the lake heat compensation. Espe-
cially in late October and November, energy provided by
lake water overrides the net radiation to maintain a small
evaporation flux.
The total reference evaporation in a span of a year, as
calculated with the energy budget equations, fluctuates
irregularly because of its natural changes with meteoro-
logical inputs and
of days in a span differs, see Table 2). The reference
evaporation in a period among the 30 years (totally 326
periods) has large fluctuations too, because a period can be
in the hot summer or cold fall, and the period length can
be quite different. Therefore, these total reference evapo-
rations are not plotted in a figure. But they will be the ba-
sis for methods comparison. In order to illustrate the in-
ter-annual variations in evaporation rates, all daily evapo-
ration rates within a span of a year (121–198 days de-
pending on the year, see Table 2) is averaged to obtain the
annual average rate, and the average rates over 30 years
are shown in Figure 5. The rate varies between 2.0 – 3.5
mm/d, with lower rates in 1979–1986 and 1999–2004, and
higher rates in 1987–1992 and 2005–2007. Not a clear
increase or decrease trend is found.
0
2
4
6
8
10
12
14
16
18
20
22
24
121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311
Julian da
y
T
a
, T
s
(
0
C), U (m s
-1
)
0
20
40
60
80
100
120
140
160
180
200
Humidity (%)
Ta TsURH
(a)
-200
-160
-120
-80
-40
0
40
80
120
160
200
121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311
Y
ea
r
NETR, NETR-S (W m
-2
)
0
40
80
120
160
200
240
280
320
360
400
E, E+H (W m
-2
)
NETR NETR - SEE + H
(b)
Figure 4. Seasonal changes and patterns of (a) meteorological variable, and (b) energy budget variables, the mean values of
daily variables over 30 years.

H. X. YAO ET AL. 12
0
1
2
3
4
d)
1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Year
Reference average rate(mm/
Figure 5. Annual reference evaporation rate averaged over all the days in the span of a year (the bar showing averaged evapo-
ration rate in mm/d, the solid line showing an inter-annual variation pattern of the rates).
200
300
400
500
600
700
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
Evaporation (mm)
HM PM
DK JH
Ref
(a)
200
300
400
500
600
700
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
Evaporation (mm)
WB
PT
MK
Ref
(b)

H. X. YAO ET AL. 13
-30
-20
-10
0
10
20
30
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Ye ar
Deviation (%)
0HM PM
DK JH
(c )
-30
-20
-10
0
10
20
30
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
Deviation (%)
0WB PT MK
(d )
Figure 6. Comparison of method-estimated evaporation with reference evaporation for each of the 30 years: (a) span evapora-
tion (mm) by four methods (HM, PM, DK, JH), (b) span evaporation (mm) by remaining three methods (PT, MK, WB), (c)
percent deviation of estimated evaporation from the reference (with HM, PM, DK, JH), and (d) percent deviation of estimated
evaporation from the reference (with PT, MK, WB).
Table 3. RMSD and CE values of estimated vs. reference evaporations, and ranked performance of seven evaporation methods
when used to span length. The rank of six methods as appeared in Winter et al. study and Rosenberry et al. study are also listed
for comparison.
Method RMSD (mm) CE Rank Rank by Winter Rank by Rosenberry
WB 32.8 0.84 1 N/A N/A
MK 56.5 0.54 2 4 5
6 6 6
JH 89.2 -0.15 7 7 7
DK 58.3 0.51 3 3 3
PM 68.1 0.33 4 2 4
PT 75.6 0.17 5 5 2
HM 80.6 0.06

H. X. YAO ET AL. 14
-100
-50
0
50
100
150
050100 150
Interval reference evaporation (mm)
Estimated evaporation (mm)
WB
HM
PM
Linear (WB)
Linear (HM)
Linear (PM)
(a)
-100
-50
0
50
10
150
0
050100 150
Interval reference evaporation (mm)
Estimated evaporation (mm)
PT
DK
JH
MK
Linear (PT)
Linear (DK)
Linear (JH)
Linear (MK)
(b)
Figure 7. Comparison of interval evaporations against the reference: (a) evaporations from WB, HM and PM and their linear
trends, (b) evaporations from PT, DK, JH and MK and their trends.
Table 4. RMSD and CE values and ranked performance of seven methods when used to interval evaporation.
Method RMSD (mm) CE Rank
DK 3.5 0.94 1
PM 4.1 0.92 2
PT 4.7 0.89 3
MK 5.6 0.85 4
HM 6.4 0.80 5
-0.66 7
JH 7.3 0.74 6
WB 18.6
4.2. E
Method Comparison
Among the seven methods, six prde evaporatii-
mations for 30 years (1978–20Hamon (HMen-
man (PM), Priestley-Taylor (PT), DeBruin-KejimK),
Jensen-Haise (JH) and Makkink (MK), as they rely on
meteorological data. The waterance (WB) pdes
estimations for 23 years (1980–2002) because the lake
level observation data is availay for these y ars.
Therefore, the results from these 23 years are presented
and used for comparison. Estimated evaporations in an-
divided
into two groups in the figure to provide a better distin-
guis, as all resulted on one figure would make
the lines difficult to be distinguished. One group includes
fou HM, PMDK and JH, the other group in-
cludree methodsT, MK and WB. Results of
evaporation obtained from the seven methods and the
reference evaporation energy budget are shown in
Figa) and (b). Eorations from WB are mostly
close to reference evaporations, results of Penman,
PrieTaylor, DeBn-Kejiman and Makkink meth-
ods are away from the reference, whereas results of
vaporation from Seven Methods and nual spans are shown in Figure 6. The results are
ovi
07):
on est
), P
an (D
balrovi
ble onle
hingts plot
r methods:,
es th: P
from
ure 6(vap
stley- rui

H. X. YAO ET AL. 15
Hamon and Jensen-Haise are evrther from the refer-
ence.
Another feature that is seen frigure 6(a) and (b) is
e inter-annual change. Except for the Hamon method,
enti-
cal ch in 1984 and 1998, very
igh in 1983, 1991 and 2002. The major reason for this
mate evaporation in shorter
tim
comaller in the water balance items (compared to
precipn, runoff, outflow, lake level change), and
infl of data mises or observation uncertainties
become more obvious. For instance, if the evaporation is
water balance account-
in
raft
fa
pans have been ensured by the method itself.
Secondly, although the Hamon evaporation amount for a
en fa
om F
th
evaporations of the other six methods have almost id
anging patterns: very low
h
similarity is that they use a controlling meteorological
factor – solar radiation which has had the inter-annual
change. The Hamon uses only air temperature which does
not show such a change style.
The percent deviations (or errors) of method-estimated
evaporation from the reference evaporation are shown in
Figure 6(c) and (d). The WB deviations are scattered
around the zero level (zero error level), with both positive
and negative errors, being the best evenly scattered over
the 23 years. The PM or PT or DK deviations are scat-
tered above the zero level (over estimated) for all 23 years.
The overestimation of Penman and Priestley-Taylor met-
hods are often reported [9]. The HM, JH and MK devia-
tions are scattered below the zero level (under estimated)
for all years except for 1998.
Values of root mean squared deviation (RMSD) be-
tween estimated and reference span evaporation, and val-
ues of coefficient of efficiency (CE) are listed in Table 3.
A lower RMSD value or a higher CE value indicates a
lower error between the estimated and observed evapo-
ration, i.e. a better performance in evaporation calculation.
Therefore, a performance rank from best to least is deter-
mined by the RMSD and CE values, and the rank is: WB,
MK, DK, PM, PT, HM, and JH.
Method comparison results with regards to span
evaporation might differ from a comparison using interval
evaporation. The estimated evaporations for 490 intervals
in the 23 years are illustrated in Figure 7 against their
corresponding reference evaporations, with three methods
in Figure 7(a) and other four methods in Figure 7(b). A
linear trend line is shown for each method’s result, and
the slope 1:1 center line is also drawn. Surprisingly, the
results from WB scattered greatly around the center line,
indicating the worst result (opposite to being the best re-
sult with the span comparison), although its trend is
mostly close to the center line. Method PM, PT and DK
tend to overestimate evaporations, while method HM, JH
and MK tend to underestimate evaporations.
Similarly to span comparison, the RMSD and CE val-
ues of estimated interval evaporation vs. the reference are
summarized in Table 4. The rank is: DK, PM, PT, MK,
HM, JH and WB. The performance and ranking of seven
methods, when applied to esti
e duration, are different from the performance when
applied to estimate evaporation in longer duration.
Why the water balance calculations do not give reliable
evaporations for intervals? When the time duration be-
comes shorter, the magnitude of evaporation item be-
in a magnitude of 30 mm for an interval of 10 days, then
any single mistake in lake level, precipitation or discharge
could reach to 5 mm, and the mistake could cause a 17%
influence on evaporation through
es sm
itatio
uence tak
g. Combined influence of multiple mistakes could cause
severer error in evaporation result. But for an evaporation
of 500 mm in a span of 7 months, the influence of the
same mistake would be 1%.
Collectively assessing Table 3 and Table 4, it is noted
that the method HM and JH perform comparatively worse
in both cases of span and interval, and should be avoided
if other methods are applicable. The DK, MK, PM and PT
perform either the best or better than other methods in
both cases, and therefore should be well applied to lake
evaporation calculation. The water balance WB can be
satisfactorily used to long duration (annual, open water
season), but should not be used to short duration (weeks,
month).
5. Discussion
There may be concerns about the collection location of
meteorological data or the distance of the weather station
to the lake. Our data are from a station located approxi-
mately 1.0 km away from Dickie Lake, not from a
cility on the lake. This concern was addressed by the
study results of Winter et al. [23]. They used 11 evapora-
tion methods including six we used here, and they com-
pared the differences caused by using raft-based,
land-based (near the lake) and remote-site-based (60 km
away) data. Their results indicated that the usage of raft-
and land-based data did not result in marked differences
in evaporation rates for those six methods. Therefore, the
location of our meteorology station on land instead of on
lake is not a concern, although raft-based data would have
been desirable.
As indicated before, the energy-budget equations only
calculated a total evaporation amount within a period
because of limited number of lake temperature profiles,
and the daily evaporation rate in the period was allocated
by using daily rates estimated from the Hamon formula.
These allocated daily evaporations used as reference rates
could contain potential errors associated with the alloca-
tion, since Hamon formula only utilized air temperature
and could have large bias from true evaporation rate. Two
rational are suggested to argue for the daily allocation.
Method comparison in the study was made on the basis of
annual span evaporation or interval evaporation, not daily
rates. The high accuracy of energy-budget results for pe-
riods and s

H. X. YAO ET AL. 16
accurate than that of energy budget,
thdistribution pattern of daily rates within the period is
nd Penman are among the better methods,
as seen from Figure 6 could be improved by ad-
ju
ba
period might be less
e
usually similar between the two methods. The similar
distribution is used to allocate daily rates for energy
budget method. Resulted daily rates would not be exactly
the same as the values that would be calculated on daily
basis if there were available water temperature data,
however, the resulted rates should be quite close to those
values.
The performance rank of the six methods (not includ-
ing WB) recommended by Winter et al. [23] and the rank
of same six methods recommended by Rosenberry et al.
[14] are also listed in Table 3. It would be understandable
that the three ranks may be different because the lakes are
in different locations, and the datasets used are different.
However, the three ranks are similar to some extent. De-
Bruin-Kejiman a
with DK being the 3rd position among all three ranks;
Hamon and Jensen-Haise are among those showing
poorer results, positioned at 6th and 7th among all ranks.
If comparing two ranks, the difference between our rank
and Winter rank is that Makkink, DeBruin-Kejiman and
Penman are positioned at 2, 3 and 4 in our rank, against 4,
3 and 2 in Winter rank. The difference between our rank
and Rosenberry rank is that Makkink and Priestley-Taylor
are positioned at 2 and 5 in our rank, against 5 and 2 in
Rosenberry rank. In other words, it is more possible and
reliable to use an evaporation method from the en-
ergy-aerodynamics combination group, such as Penman,
DeBruin-Kejiman and Priestely-Taylor. A method from
the two-parameter (solar radiation and temperature) group,
such as Makkink, may provide a satisfactory estimation
of lake evaporation. But a method from the tempera-
ture-only group, such as Hamon, provides poorer estima-
tions.
An effort is tried to interpret physical or logic reasons
to why the methods perform in a way as shown in Table 3,
why some methods perform better than other ones. First
of all the accuracy of the reference method-energy budget
would not be doubted, as it is based on strictly-defined
theories and has been proved by many researchers. It pro-
vides reliable evaporation reference provided that the
input data are correctly collected. The best performer-
water balance method (Equation (16)) has the ability to
provide good evaporation estimations, if the in and out
items are well measured. The runoff coming from 2/3
watershed area of Dickie Lake has been well monitored,
precipitation and outflow are well monitored too, and lake
level is measured too. This data information ensures that
estimated evaporation in spans is reasonable and reliable.
The second-ranked Makkink method (Equation (15)) has
a simple empirical format and uses only air temperature
and short-wave radiation as input. These two factors are
the most important among many meteorological factors.
Its equation has a fairly correct description of the two key
factors, and the equation applies well to the lake in the
Canadian Shield as it did to its original datasets. Although
it gives fairly good evaporation estimates, it has a draw-
back of underestimation. Probably a minor adjustment to
the equation (i.e. change the constant 0.61) can improve
this drawback.
The third-ranked DeBruin-Kejiman method is an em-
pirical equation similar to Makkink, considers more af-
fecting factors (temperature, short- and long-wave radia-
tions, lake heat storage) than MK does. Its performance is
accepted just because it can be applied to the studied lake
without equation adaption. Actually the overestimation
problem
sting the equation. The fourth-ranked Penman method
(Equation (10)) has been widely used to estimate lake
evaporation or watershed potential evapotranspiration,
having taken consideration of all affecting factors. There
might be two reasons leading to its overestimation prob-
lem: the function in relation to the wind speed and the
period-averaging treatments in wind speed and air humid-
ity. The fifth-ranked Priestley-Taylor method (Equation
(12)) is an empirical equation similar to DK. Its not-good
performance means that probably it needs adjustment to
be well applied to the study area, for example changing
its constant 1.26. One common concern for the three
methods (DK, PM, PT) which all overestimate evapora-
tion is noted but has not been identified: they all include a
net radiation in their equations. If the net radiation were
not correctly measured or calculated, a systematic overes-
timation would have occurred.
The sixth-ranked Hamon method (Equation (8)) does
not give good estimates simply because it only considers
air temperature as the controlling factor. Unless the mete-
orological data is severely restricted, this method is not
recommended for lake evaporation. The seventh-ranked
Jensen-Haise method (Equation (14)) includes very site-
dependent parameters, and may be not applicable to our
study lake without proper adjustment. The evaporation is
dly underestimated.
The data length of 30 years would remind that a timely
trend analysis may be worthwhile. All meteorological and
energy budget variables were checked to find potential
trends or periodic cycles in the 30 years, but none has
been found to have a significant trend at Dickie Lake.
Linacre [40] proposed that lake-evaporation rate is gener-
ally decreasing at around 0.1 mm/d per decade around the
world, chiefly on account of reduced solar radiation. The
estimated rates by energy budget method for Dickie Lake
do not show such a reduction. The averaged daily rate in
ice-free season for three decades (1981–1990, 1991–2000,
2001-2007, with the third decade being 7 years only) is
2.66, 2.57 and 2.74 mm/d respectively, the rate decreases
by 0.09 mm/d from the first to second decade, but in-
creases 0.17 mm/d from the second to third decade.

H. X. YAO ET AL. 17
Except for some situations
su
ng the Makkink method (it needed
ai
water
en
absorbed energy in the fall to compensate for evaporation.
e lag, or between temperature and the heat flux.
From year to year, the lake heat storage did not play a
budgeting, and lake evaporation or
was controlled by the net radiation.
pp.
nd C. J. Bowser, “Effects of
evaporation: Results from a
Apart from the traditional methods such as the energy
budget and seven methods used here that need meteoro-
logical data, a newer way to estimate lake evaporation is
by using isotope technology. Saxena [41] estimated
evaporation from a central Swedish lake by measuring
oxygen-18 content in lake water, stream inflows and out-
flow, and precipitation. The results of isotope method
were further compared with results of bulk-aerodynamic
and Bowen ratio methods [42].
ch as high-precipitation events, high-outflow periods or
rapid lake-volume change periods, the evaporation esti-
mated from the three methods agreed. A similar experi-
mental study was conducted by He et al. (personal corre-
spondence with one of the authors, 2009) for Dickie Lake
by measuring oxygen-18, and their results gave a total
evaporation 660 mm for year 2003 (January 1 to Decem-
ber 31). For comparison, a total evaporation for the same
year was calculated usi
r temperature and radiation data, not needing lake tem-
perature), and the calculated evaporation was 451 mm.
This reveals a significant difference between isotope-
estimated evaporation and Makkink-estimated evapora-
tion.
6. Conclusions
The 30 year dataset from Dickie Lake provided a valuable
opportunity to conduct a long-term study on lake evapo-
ration. Evaporations in longer spans and shorter intervals
during ice-free season were calculated separately using
seven evaporation methods, based on field meteorology,
hydrology and lake water temperature data. A reference
value of the evaporation was provided by a lake
ergy budget, and was used to evaluate the performance
of the seven methods. The deviations of method-induced
evaporation from reference evaporation were compared
among the seven methods, and a performance rank was
proposed based on the comparison. For purpose of
evaporation in long time duration such as a span or a year,
the best-to-least methods were ranked as: water balance,
Makkink, DeBruin-Kejiman, Penman, Priestley-Taylor,
Hamon, and Jensen-Haise. For purpose of evaporation in
short time such as an interval or a month, the best-to-least
methods were ranked as: DK, PM, PT, MK, HM, JH and
WB. Overall, four methods (MK, DK, PM and PT) work
better than other three methods.
Details of energy budget, correspondences between
energy terms and meteorological variables, annual or
seasonal changes of these terms and variables, and the
compensation function of lake heat storage in evaporation
flux were also analyzed and illustrated. Within the
ice-free duration of a year, lake water absorbed a portion
of net radiation in early and mid summer, and released the
Strong correspondence existed between net radiation and
consumptive heat flux (latent and sensible heat) but with
a tim
notable role in energy
consumptive heat flux
Our study results have shown a similar energy budget
pattern as other studies in similar climatic regions, and
identified a performance rank for the evaporation calcula-
tion methods to be used for lakes in Canadian Shield.
7. Acknowledgements
The author would like to thank Robert Girard for his as-
sistance in lake morphometry and profile data, and thank
Joe Findeis and Ron Ingram for their assistance in mete-
orology data. Thank Peter Dillon, Lance Aspden and
Christiane Guay for their discussion and comment. Nu-
merous former governmental staff and university partners
have contributed to the data collection and management.
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