In Mediterranean environments, evaporation is a key component of lake water
budgets. This applies to Lake Baratz in Sardinia, Italy, a closed lake that
almost dried up in 2008 after a succession of years with low seasonal
rainfall. We used the energy budget method and Penman's equation to estimate
evaporation over Lake Baratz. We measured, using a raft station, water
temperature at the surface, at 1, 2, 4, 6 m depth and at the bottom of the lake, as well as air
temperature, relative humidity, wind speed, and net radiation over a period
of 3 years. We also compared Penman's equation and the energy budget
method in two other climatic zones using published data. Our results indicate
that mean yearly evaporation over Lake Baratz was 950 mm. On an annual
scale, evaporation estimated by Penman's method omitting heat storage as is
usually done was 18 % higher than by the energy budget method that included
heat storage, with monthly differences ranging between

Lakes in semi-arid regions like around the Mediterranean Sea are extremely
sensitive to changes in climate and land use. In the summer, low
precipitations, high temperatures and insolation contribute to high rates of
evaporation. Recent increases in drought frequency

The water level in a lake reflects the balance between water inputs
(precipitation, runoff, groundwater) and water losses (evaporation, outlet
streams, groundwater) making it a sensitive indicator of climate change

Time series of daily precipitation, lake depth (measured at centre
of lake), and modelled stream discharge into the lake

One of the most accurate methods for estimating long-term lake evaporation is
the energy budget method expressed as the Bowen Ratio Energy Budget (BREB)

A simpler method for estimating evaporation is the Penman equation. It
combines the heat and mass transfer balance equations for a wet surface and
requires meteorological parameters relatively simple to obtain such as net
radiation, air temperature, humidity and wind speed. In theory, Penman's
equation requires knowledge of the net available energy, i.e. the net
radiation minus the heat storage (see for example

Despite many energy budget studies, comparisons between BREB and Penman's
methods are few

In the present study, components of the energy budget are measured using a raft station to estimate the long-term seasonal evaporation of a Mediterranean lake. Our objectives are to: (i) assess the amount of evaporation from Lake Baratz, (ii) compare BREB and Penman's model to evaluate such evaporation losses at seasonal timescales, and (iii) compare the evaporation estimates by Penman and BREB with evaporation from other climatic zones.

Lake Baratz is a closed lake located 1 km from the Mediterranean Sea
in the northwestern part of the island of Sardinia, Italy
(40

The catchment drainage area is about 12 km

Air temperature, relative humidity, wind velocity and net radiation were
measured from both a land and a raft station 2 m above the land or water
surface. The land station, located about 2 km northeast of the lake,
has been collecting data since April 2008, while the raft station, anchored
in the middle of the lake, has been in operation since April 2011.
Atmospheric pressure and rainfall were measured from the land station only.
The raft station was equipped with a Campbell Scientific anemometer (model
05103, accuracy

Lake water temperature was measured with either a Schlumberger's Mini-Diver
DI501 or a Mini-Diver DI502 (accuracy

Water discharge and water temperature of the creek were measured by a current metre and a thermistor, respectively, installed on the stable bed of a trapezoidal concrete channel upstream of the tributary. A triangular weir was installed immediately downstream from the current metre to measure low flows, which the current metre does not do well.

Prior to February 2014 climatic data were logged every 5 min with hourly averages computed and stored. Thereafter, data were sampled every 10 min and averages recorded every hour. Logging was done by a Campbell Scientific CR1000 powered by a photovoltaic panel. On 24 September 2013 the raft sank and was only reassembled the next spring on 25 April 2014. The diver measuring the bottom temperature and the lake level kept working during that time. Surface temperature was measured again starting on 4 March 2014. When the raft was not in operation, missing meteorological data were filled with data from the land station using linearly regression (smallest values of the correlation coefficients are 0.72 for wind and 0.82 for relative humidity; for temperature, maximum temperature, net radiation, the correlation coefficients are higher than 0.93). Also the lake temperature at all depths was assumed to equal the bottom temperature based on temperature records from prior years (see Sect. 3.3).

Regarding the survey data, the variables required to use Penman's formula are net radiation, water surface and air temperatures, wind speed and relative humidity. The change in heat storage in the water body is the main cost of data acquisition and is needed to apply BREB. In our case, our fully equipped raft station (including temperature profile) was less than EUR 6000 in 2011.

The energy balance for a water body neglecting heat exchanges from
groundwater is

The heat storage term,

In Eqs. (1) and (2), all terms except

The Penman equation is used to estimate monthly evaporation from an open
water body by the sum of a radiative and an aerodynamic term

A simplified water balance for the lake can be expressed as

Figure

Time series of 14-day moving average (dark-colour lines) and mean
daily (light-colour lines) of

Monthly mean of

Net radiation,

Evaporation estimated using BREB was on average 950 mm day

Monthly evaporation,

Heat storage (

Figure

In early spring (February–March), net radiation increases more rapidly than
evaporation (Fig.

Lake temperature profiles. Black circles are daily average temperatures. Red circles represent the temperature profile on the first of the month.

Correlations between various components of the heat budget equation. Dots represent monthly data over the 3-year survey period. Dot colour indicates the season (with red in summer and blue in winter). When seasonal cycles are apparent, line segments link successive data points.

Monthly evaporation for BREB and Penman with other terms of the heat
budget and Bowen ratio. Units are W m

The heat storage in the lake is an important component of the energy balance
and shows strong seasonality. Heat storage is driven by net radiation but
controlled by sensible heat exchange between lake water and air and thus by
lake water dynamics and mixing. Water movement is driven by variations in the
density of water (convection). The warmest, less-dense layers remain at the
top while cooler water sinks. Figure

Figure

Evaporation is highest in August while net radiation reaches its maximum in
July. Evaporation is lowest in February when net radiation is smallest. The
hysteresis in evaporation is likely due to the dependence of evaporation on
the seasonal variations of

Sensible heat also shows a seasonal correlation with net radiation
(

Although sensible heat is well correlated to the temperature difference
between lake and air (Fig.

Another hysteresis loop is also evident in the relation between evaporation
and heat storage (Fig.

At a monthly scale, evaporation and sensible heat are relatively well
correlated (

Figure

Figure

Table

In winter, the difference between BREB and Penman is lower and can become
negative (Fig.

When comparing BREB and Penman's methods, it is clear that the
differences originate from neglecting heat storage (

As stated in our introduction, theoretically the net radiation term in
Penman's equation (Eq. 7) should be replaced with the net available energy

Annual components of the lake water balance for the five
hydrological years.

Comparison of BREB and Penman's method for six lakes in three
different climatic zones. Climate type is based on Köpper classification.
The ratio

Monthly mean evaporation,

Water follows two main pathways. Water input, runoff and precipitation are
concentrated during a short cool wet season from about November to March.
Water losses, mainly by evaporation, occur throughout the year but are
highest in summer. The annual volumetric lake water balance is shown in
Table 3 as an update to the table presented in

Evaporation is calculated using the Penman equation for the first 3 years
and the energy budget method thereafter

The differences in evaporated volume at an annual scale between the
simplified energy budget method and BREB is of the order of about
33

In Table 3, all terms in the lake water balance are of the same order of
magnitude. In the first 3 years surface runoff is high because the
rainfall–runoff model of

We compare six lakes (including Lake Baratz) in three different climatic
zones for evaporation. For three African lakes (Ziway, Victoria, Bosumtwi),
the study areas are classified as tropical savanna

Table

Monthly mean evaporation estimated using BREB and Penman's equation for six lakes in different climatic zones.

Except for Lake Baratz, the maximum ratio of Penman's evaporation over BREB evaporation is slightly above 1 and Penman's method compares well with BREB (ratio equal or less than 1.25). For Lake Baratz, however, Penman's estimate is 1.6 times BREB and standard deviation is 1 order of magnitude higher than at other lakes. This difference motivates us to compare seasonal evaporation trends for different climatic zones.

Figure

For the North American and Mediterranean climates, the shapes of the evaporation curves are similar, with highs in the summer and lows in winter, but the range of evaporation is twice larger in the Mediterranean climate. In tropical Africa, lake evaporation is high year long and the shape of the evaporation curve shows an inverted trend due to the monsoon season.

Climate is not the only factor influencing the value of the ratio of Penman
to BREB evaporation (Table

In terms of water circulation both Lake Williams

Figure

Annual cumulative bias on evaporation estimate (BREB minus Penman) for the six lakes.

In contrast, the seasonal difference between BREB and Penman at Lake Baratz
or Mirror lake is clearly visible in the change of slope at the end of
summer. In these cases, correction to Penman's formula is more difficult. For
Williams Lake in continental North America, the effort to calculate
evaporation rate using BREB does not seem justified given the small bias of
Penman's method

We estimate evaporation for Lake Baratz, a Mediterranean lake in Sardinia,
Italy, using the energy budget method (BREB) and Penman's method relying on
new measurements from a raft station over a period of 3 years.
Evaporation occurs year-round with a maximum in July, a minimum in December,
and an annual mean of 950 mm day

Our objective in this paper was to evaluate the Penman equation when data are
scarce (no measure of heat storage) even though we have the data to correct
the energy term. It is unfortunate that no papers address the issue of
including or not the heat storage term (see

Figure A1 shows the position of the temperature sensors in the lake and the thickness of the layers used to compute the heat storage term.

Layer thickness and temperature sensor locations (black circles). Sensors for layers 1, 2, 3, 4 and 5 are attached to the raft. The thickness of layer 6 varies with lake level and is taken into account in the calculation of the heat storage term (see Eq. 4).

We compared the Bowen ratio calculated with and without the wind. The wind
correction for the Bowen ratio using

Monthly average of BREB evaporation computed with and without the effect of wind.

To estimate monthly mean evaporation for other lakes
(Fig.

Estimations of BREB often rely on few measurements and several assumptions.
A common parameter neglected in tropical climate studies is the change in
energy stored into the lake

This study was supported by grants from the Municipality of Sassari and the Sardinian Region, project PIT SS.1: Recovery of natural areas, the Lake Baratz, responsible Marge Cannas. The authors gratefully acknowledge Luisa Secci for providing help with water temperature survey data management during the first year of this project. We also thank Roberto Marrosu for his assistance in maintaining the raft structure and instrumentation. This paper benefited from reviews by W. James Shuttleworth and P. Le Moigne. Edited by: J. Carrera