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Lake Titicaca is a crucial water resource in the central part of the Andean mountain range, and it is one of the lakes most affected by climate warming. Since surface evaporation explains most of the lake's water losses, reliable estimates are paramount to the prediction of global warming impacts on Lake Titicaca and to the region's water resource planning and adaptation to climate change. Evaporation estimates were done in the past at monthly time steps and using the four methods as follows: water balance, heat balance, and the mass transfer and Penman's equations. The obtained annual evaporation values showed significant dispersion. This study used new, daily frequency hydro-meteorological measurements. Evaporation losses were calculated following the mentioned methods using both daily records and their monthly averages to assess the impact of higher temporal resolution data in the evaporation estimates. Changes in the lake heat storage needed for the heat balance method were estimated based on the morning water surface temperature, because convection during nights results in a well-mixed top layer every morning over a constant temperature depth. We found that the most reliable method for determining the annual lake evaporation was the heat balance approach, although the Penman equation allows for an easier implementation based on generally available meteorological parameters. The mean annual lake evaporation was found to be 1700 mm year−1. This value is considered an upper limit of the annual evaporation, since the main study period was abnormally warm. The obtained upper limit lowers by 200 mm year−1, the highest evaporation estimation obtained previously, thus reducing the uncertainty in the actual value. Regarding the evaporation estimates using daily and monthly averages, these resulted in minor differences for all methodologies.
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Hydrol. Earth Syst. Sci., 23, 657–668, 2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
Modelling Lake Titicaca’s daily and monthly evaporation
Ramiro Pillco Zolá1, Lars Bengtsson2, Ronny Berndtsson2, Belen Martí-Cardona3, Frederic Satgé4, Franck Timouk5,
Marie-Paule Bonnet6, Luis Mollericon1, Cesar Gamarra7, and José Pasapera7
1Instituto de Hidráulica e Hidrología, Universidad Mayor de San Andrés, La Paz, Bolivia
2Division of Water Resources Engineering and Center for Middle Eastern Studies,
Lund University, Lund, Sweden
3Department of Civil and Environmental Engineering, University of Surrey, Guildford, UK
4CNES, UMR HydroSciences, Univeristy of Montpellier, Place E. Bataillon,
34395 Montpellier CEDEX 5, France
5Laboratoire GET UMR5563, CNRS, IRD, Université Paul Sabatier, OMP, Toulouse, France
6IRD, UMR Espace-Dev, Maison de la télédétection, 500 Rue JF Breton,
34093 Montpellier CEDEX 5, France
7IMARPE, Instituto del Mar del Perú, Puno, Peru
Correspondence: Ramiro Pillco Zolá (
Received: 12 March 2018 – Discussion started: 28 March 2018
Revised: 20 September 2018 – Accepted: 15 December 2018 – Published: 6 February 2019
Abstract. Lake Titicaca is a crucial water resource in the
central part of the Andean mountain range, and it is one
of the lakes most affected by climate warming. Since sur-
face evaporation explains most of the lake’s water losses,
reliable estimates are paramount to the prediction of global
warming impacts on Lake Titicaca and to the region’s water
resource planning and adaptation to climate change. Evap-
oration estimates were done in the past at monthly time
steps and using the four methods as follows: water bal-
ance, heat balance, and the mass transfer and Penman’s equa-
tions. The obtained annual evaporation values showed signif-
icant dispersion. This study used new, daily frequency hydro-
meteorological measurements. Evaporation losses were cal-
culated following the mentioned methods using both daily
records and their monthly averages to assess the impact of
higher temporal resolution data in the evaporation estimates.
Changes in the lake heat storage needed for the heat balance
method were estimated based on the morning water surface
temperature, because convection during nights results in a
well-mixed top layer every morning over a constant temper-
ature depth. We found that the most reliable method for de-
termining the annual lake evaporation was the heat balance
approach, although the Penman equation allows for an easier
implementation based on generally available meteorological
parameters. The mean annual lake evaporation was found
to be 1700 mm year1. This value is considered an upper
limit of the annual evaporation, since the main study period
was abnormally warm. The obtained upper limit lowers by
200 mm year1, the highest evaporation estimation obtained
previously, thus reducing the uncertainty in the actual value.
Regarding the evaporation estimates using daily and monthly
averages, these resulted in minor differences for all method-
1 Introduction
Lake Titicaca, the largest freshwater lake in South America,
is located in the endorheic Andean mountain range plateau
Altiplano, straddling the border between Peru and Bolivia
(Fig. 1). The lake plays an essential role in shaping the semi-
arid Altiplano climate; feeding the downstream Desaguadero
River and Lake Poopó (Pillco and Bengtsson, 2006; Abarca-
del-Río et al., 2012); and supplying the inhabitants with wa-
ter resources for domestic, agricultural, and industrial use
(Revollo, 2001). Anthropogenic pressure on the Altiplano
water resources has increased during the last decades due
to population growth and increased evapotranspiration losses
(FAO, 2011; Canedo et al., 2016; Satgé et al., 2017) as well
as to industrial pollution (UNEP, 1996; CMLT, 2014). The
Published by Copernicus Publications on behalf of the European Geosciences Union.
658 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
Figure 1. Lake Titicaca and the TDPS system within the Altiplano.
challenge of managing water resources in the Altiplano Basin
is further exacerbated by climate conditions; annual rainfall
is highly variable (Garreaud et al., 2003), while warming in
this region exceeds the average global trend (López-Moreno
et al., 2015), which is expected to intensify the evaporation
from the lake surface and the evapotranspiration losses from
the whole basin. The combined impact of these pressures be-
comes evident at the downstream end of the system, where
Lake Poopó is situated. In recent years this lake suffered ex-
treme water shortages, including its complete drying out in
December 2015 (Satgé et al., 2017).
Lake Titicaca has a large surface area of about 8500km2
on average. Over a certain water surface level, the lake spills
out at the south-eastern end and feeds the Desaguadero River.
However, the major water output from Lake Titicaca is due
to evaporation, which accounts for approximately 90 % of the
losses (Roche et al., 1992; Pouyaud, 1993; Talbi et al., 1999;
Delclaux et al., 2007). In recent years, Lake Titicaca’s level
dropped below the outlet threshold for some periods. Thus,
a small increase in evaporation or decrease in precipitation
may turn the lake into a closed system with no outflow.
Since evaporation dominates the water balance in Lake
Titicaca, it is essential to improve the knowledge of the lake’s
evaporation. This is especially important in light of anthro-
pogenic pressure and due to the evident strong global warm-
ing that this region experiences. Previous studies of Lake Tit-
icaca’s evaporation have all been based on monthly meteoro-
logical observations. Due to the importance of lake evapo-
ration, detailed calculations using daily as well as monthly
observations may be necessary. Consequently, this paper in-
vestigates different methods for calculating evaporation us-
ing both daily and monthly data; in addition we discussed
the possibility for the appropriate evaporation models at both
timescales to be used on the study the climatic function-
ing and sensitivity. The main problem with Lake Titicaca’s
evaporation estimation is the lack of high-resolution tempo-
ral data. Taking into account only the mass transfer mod-
els for different timescale, Singh and Xu (1997) calculated
monthly evaporation. However, doing the same calculations
on a daily basis could give radically different results. For both
timescales, the evaporation estimation could be more sensi-
tive to vapour pressure. On the other hand, random errors in
input data could have a significant effect on evaporation esti-
mation at a monthly scale rather than at a daily scale (Singh
et al., 1997).
Lake Titicaca’s surface water is cold, with a temperature
that remains 12–17 C throughout the year, and below 40m
depth the temperature is almost constant (Richerson et al.,
1977). The water is usually warmer than the air during the
daytime, which means that the air immediately above the
lake is unstable. The air temperature shows large diurnal
variations, often exceeding 15 C in summer. At an aver-
age terrain elevation above 4000 m a.s.l. the solar radiation
is strong and the atmospheric pressure is low, which means
that the ratio between sensible and latent heat flux (Bowen
ratio) is lower than at sea level. To determine the evapora-
tion rate using the aerodynamic mass transfer approach, the
atmospheric vapour pressure and surface temperature must
be known. Furthermore, a wind function must be used, be-
cause the atmosphere over Lake Titicaca is unstable most of
the time. This means that the wind function may be different
from the function used for most other lakes.
It can generally be assumed that during a year the lake wa-
ter temperature returns to the value at the beginning of the
year. Thus, for the heat balance, it is sufficient to know the
annual net radiation, provided that the sensible heat flux can
be estimated from the constant Bowen ratio. When using the
method for shorter time periods, the time variation of the lake
water temperature profile must be known. The heat balance
approach and the aerodynamic method can be combined. The
Penman method is such a combined approach. A wind func-
tion must also be included in this approach.
Previous investigations
One of the first evaporation studies for Lake Titicaca ap-
plied the water balance method using measurements for the
period 1956–1973 (Carmouze et al., 1977) and estimated
a mean annual lake evaporation of 1550mm year1. Tay-
lor and Aquize (1984) applied a bulk transfer approach
for a shorter period and determined the lake evaporation
to be 1350 mm year1. The largest reported annual evapo-
ration is from using the energy balance approach. Richer-
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation 659
son et al. (1977) found the lake evaporation to be equal to
1900 mm year1. Later, Carmouze (1992) used the same ap-
proach and found the lake evaporation to be 1720mm year1.
Using observations for the period 1965–1983 and the wa-
ter balance method, Pouyaud et al. (1993) found the mean
annual evaporation to be equal to about 1600mm year1.
Thus, the mean annual evaporation has been estimated in
the range 1350–1900 mm year1. While the precipitation can
vary much from year to year, the large range of calculated an-
nual evaporation, 1350 to 1900 mm year1, is likely to be the
result of uncertainties in the evaporation estimations and in
the temporal resolution of the measurements. Recently, Del-
claux et al. (2007) studied the evaporation from Lake Titicaca
using in situ pan-evaporation measurements, energy balance,
mass transfer and the Penman methods. They concluded that
the mean annual evaporation may be about 1650 mm year1,
with low seasonal variation between 135 mm in July (winter)
and 165 mm in November (summer).
This study applies the methodologies mentioned above
using the frequent and accurate hydro-meteorological mea-
surements acquired at Lake Titicaca in 2015 and 2016, with
the aim of reducing the uncertainty in evaporation estimates
and evaluating the effect of using daily records instead of
monthly ones.
2 Study area
Lake Titicaca is a unique biosphere due to its large depth
and volume, high elevation, and tropical latitude. It is lo-
cated in the northern part of the Peruvian–Bolivian Alti-
plano, between latitudes of 15450S and 69250W. It is
surrounded by the eastern and western Andean Mountains.
The total Lake Titicaca basin area, including the lake itself,
is close to 57 000 km2, with a mean elevation higher than
4000 m a.s.l. The outlet sill is at 3807 m a.s.l. The lake vol-
ume is about 903 km3, with a corresponding mean depth of
105 m (Boulange and Aquize, 1981; Wirrmann, 1992). The
only outlet is the Desaguadero River, which ends in the shal-
low Lake Poopó. The modern Lake Titicaca consists of the
major Titicaca lake (Lake Chuquito), which is 284m at the
deepest point, and the smaller Titicaca lake (Lake Huiña-
marca). The latter lake represents 1200 km2, with a maxi-
mum depth of 35 m below the spill level. The threshold be-
tween the two lake basins is 19 m below the spill level (see
Fig. 2). The lake is described by Dejoux and Iltis (1992)
and in the Encyclopedia of Lakes and Reservoirs edited by
Bengtsson et al. (2012).
2.1 Hydrology
The Lake Titicaca watershed is a part of the TDPS system
(Titicaca, Desaguadero, Poopó and Salares) within the Al-
tiplano (Revollo, 2001). Lake Poopó is considered a termi-
nal lake, with only one discharge event into the downstream
Figure 2. Lake Titicaca basin with sub-basins and major and
smaller lakes.
Coipasa salt pan occurring in the last century (Pillco and
Bengtsson, 2006). The basin of Lake Titicaca itself includes
the sub-basins Katari, Coata, Huancané, Huaycho, Ilave,
Illpa, Keka-Achacachi, Ramis and Suchez. The largest is the
Ramis River basin, with an area of 15 000 km2, representing
30 % of the total basin (Fig. 2). The mean flow of the Ramis
River for the period 1965–2011 was 72 m3s1. The mean
outflow from Lake Titicaca through the Desaguadero River
for the same period was 35 m3s1. During those 50 years,
Lake Titicaca experienced large changes in water level, with
a mean close to 3808.1 m a.s.l., which is about 1 m above
the outlet threshold (Pillco and Bengtsson, 2006). From its
low to high water level, the Lake Titicaca water surface area
might change from a minimum of 7000 to a maximum of
9000 km2.
2.2 Climate
The northern part of the Altiplano is semiarid, while the
southern part, including the biggest salt pans in the world,
is arid (TDPS, 1993). The climate is further characterized
by a short wet season (December–March) and a long dry
season (April–November; Garreaud et al., 2003). The av-
erage precipitation over the Lake Titicaca basin is about
800 mm year1, out of which more than 70 % fall during
the wet season (Garreaud et al., 2003). Over the lake, an-
nual precipitation is assumed to vary from 1200 mm year1
in the central part to 800 mm year1along the shores (TDPS,
1993). January is the wettest (about 180 mm month1) and Hydrol. Earth Syst. Sci., 23, 657–668, 2019
660 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
Table 1. Climatological and hydrological components of Lake Titicaca for 1966–2011.
Months Ramis Inflow Outflow Lake Precipitation Air Relative Wind
flow (m3s1) (m3s1) depth (mm month1) temperature humidity velocity
(m3s1) (m) (C) (%) (m s1)
Jan 173.5 549.0 31.3 283.9 177.0 10.2 67.5 1.9
Feb 198.8 629.4 39.4 284.1 141.6 10.1 67.4 1.8
Mar 190.4 602.8 49.8 284.4 126.8 10.0 67.3 1.8
Apr 104.9 332.1 50.9 284.5 50.6 9.8 61.9 1.7
May 38.7 122.6 46.5 284.5 13.2 8.8 54.9 1.7
Jun 20.7 65.5 41.8 284.4 7.3 7.8 52.9 1.9
July 14.5 46.0 37.0 284.3 6.6 7.7 52.8 1.9
Aug 11.0 34.9 32.1 284.2 13.2 8.3 53.7 2.0
Sep 9.9 31.3 28.1 284.1 29.9 9.2 55.1 2.1
Oct 14.0 44.2 24.1 284.0 45.5 10.2 55.4 2.1
Nov 24.0 76.0 21.7 283.9 56.7 10.8 56.4 2.1
Dec 55.2 174.7 22.1 283.9 102.5 10.6 62.4 2.0
July the driest (less than 10 mm) month. In the central and
southern parts of the Altiplano, the total annual precipitation
is about 350 mm (Roche et al., 1992; Pillco and Bengtsson,
2006) and is less than 200 mm over the Salares in the south-
ernmost areas (Satgé et al., 2016). The seasonal variability
of precipitation in the basin is related to changes in the up-
per troposphere circulation. During the Austral summer, an
upper-level cyclone is established to the south-east of the
central Andes. The Bolivian high brings easterly winds and
allows influx of moisture from the central continent over the
plateau during periods, intensifying the precipitation (Gar-
reaud, 1999; Vuille et al., 2000).
The daily air temperature over Lake Titicaca is rather con-
stant throughout the year, usually varying between 7 and
12 C but sometimes up to 20 C in summer. The Titicaca
region is more humid than the more southern parts of the Al-
tiplano. The relative humidity varies between 52% to 68 % as
a monthly average, with diurnal variation between 33% and
80 %. According to Carmouze (1992), the dominant wind
on the lake is in the north-west to south-east direction, with
mean monthly wind velocity close to 2 m s1, rarely reach-
ing 5 m s1at the daily time step. The general climate and
hydrology are summarized in Table 1. The total river inflow
was estimated through a representative area approach based
on the Ramis River discharge.
3 Methods
Lake evaporation models
Four evaporation estimation conventional methods were ap-
plied in this study: water balance, energy balance, mass trans-
fer and the Penman method. These approaches have previ-
ously been used by other researchers to estimate Lake Titi-
caca’s evaporation at a monthly time step (Carmouze, 1992;
Pouyaud, 1993; Delclaux et al., 2007). The methods are
briefly described as follows.
3.1 Energy balance approach
The energy balance approach (Maidment, 1993) which
comes from the integral energy balance equation of a refer-
ence volume at the air–water interface, the evaporation com-
ponent in terms of latent heat flux is
λE =RnQheat
where λis the latent heat vaporization (J kg1), Eis evap-
oration rate (mm day1), Rnis net radiation (W m2), Qheat
is heat storage within the water (W m2) and βis the Bowen
ratio (Bowen, 1926):
where γis the psychrometric constant (mbar C1); Tw
and Taare the surface water and air temperature (C), re-
spectively; ewand eaare the water surface and air vapour
pressures (Pa), respectively; cpis the specific heat capacity
(J kg1C1); and Pa is the atmospheric pressure (kg Pa).
The psychrometric constant, and thus also the Bowen ratio,
are lower at this high altitude than at sea level. The net radi-
ation is the sum of net short-wave and net long-wave radia-
tion. The net short-wave radiation is Rs(1albedo), where
Rsis the solar radiation reaching the lake (W m2). The at-
mospheric long-wave radiation as well as the back radiation
are computed from Stefan’s law. The emissivity of the wa-
ter is well known and was set to 0.98, and the emissivity at-
mosphere must be known. The emissivity of the atmosphere
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation 661
depends on humidity, temperature and cloudiness. The at-
mospheric emissivity accounting for clouds was proposed by
Crawford and Duchon (1999):
εe=(1s)+o(Ta, ea),(4)
Rs,o =Rae0.0018Pa
Ktsinφ24 ,(6)
where sis the proxy cloudiness defined as the ratio of mea-
sured incoming solar radiation Rs(W m2) to the solar radi-
ation received for the clear-sky conditions Rs,o (W m2), and
εois the emissivity in the clear-sky condition, which is deter-
mined from the vapour pressure eaexpressed in hPa and Ta
temperature in Kelvin. The 824 is the mean daily sun angle.
The constant 1.18 describes the attenuation defined for the
region according to Lhomme et al. (2007). The extraterres-
trial solar radiation Ra(W m2) is determined as a function of
local latitude and altitude and time of year, using the turbidity
coefficient Kt=0.85.
The energy equation is fairly easy to use over a full
year, since the lake water usually returns to its initial state
when computations were started or when Qheat equals zero
(W m2). When using the approach over shorter periods the
variation of the water temperature in the lake must be ac-
counted for. In Eq. (1), the change of heat storage is in-
cluded. From temperature water profiling observations, it
was assumed that the water temperature below 40 m does not
change from month to month. The temperature, Tw, above
this mixing depth, hmix (m), changes but remains almost ho-
mothermal after convective mixing during the night (Rich-
erson et al., 1977), which also is corroborated by our own
field investigations. Thus, the change of heat content can be
estimated from measured surface temperature:
Qheat =ρcp
t ,(8)
where ρis density of water (kg m3), cpis the specific heat
capacity of water and Vmix is the volume above the mixing
depth (km3). Carmouze et al. (1992) introduced the con-
cept of the exchange of heat between surface and deep water
using the energy balance concept. The results of Carmouze
et al. (1992) were compared to the calculation results in the
present study.
3.2 Mass transfer approach
The mass transfer aerodynamic approach is used in various
models based on Dalton’s law (Dalton, 1802). The latent heat
transfer is related to the vapour pressure deficit. Most often a
linear wind function is used (e.g. Carmouze et al., 1992):
E=(a +bU )(ewea), (9)
where Eis the evaporation rate, Uis wind velocity (ms1)
and eweais the vapour pressure deficit (mbar). The pa-
rameter aaccounts for unstable atmospheric conditions. Car-
mouze et al. (1992) used a=0.17 (mm mbar1day1) and
b=0.30 (mm mbar1s m1).
3.3 Penman approach
The Penman equation is a combination of energy balance
and mass transfer used for evaluating open water evaporation
(Penman, 1948):
λρ +γ
1+γc(a0+b0U )(esea),(10)
where Eis open water evaporation. The slope of the water
pressure–temperature curve is denoted by 1(K Pa s1), and
eseais the saturation deficit of the air (K Pa); here eais de-
pendent on the relative humidity (%). Delclaux et al. (2007)
applied the Penman equation to Lake Titicaca using a0=
0.26, b0=0.14 and c=1 after optimizing (mm day1mbar).
3.4 Lake water balance model
The water balance approach was applied to calculate water
levels in Lake Titicaca in a previous study by Pillco and
Bengtsson (2007). The water balance is
t =(P E)Alake +Qin Qout,(11)
where h/∂t represents change in water depth; Pis precip-
itation on the lake (mm); Eis evaporation from open wa-
ter (mm day1); Alake is water surface of the lake (km2),
which is a function of depth; Qin is inflow to the lake; and
Qout represents the outflow from the lake (m3s1). Com-
putations were carried out at a monthly timescale for two
periods, one for 1966–2011 and another for 2015–2016. As
already pointed out, the most reliable method of computing
evaporation over long periods is probably the water balance
method. However, the computation only can be general, since
the inflow to Lake Titicaca is not measured in all rivers.
3.5 Possible errors when using monthly averages
The evaporation during individual days is not important for
the water balance but is only important over longer peri-
ods like months. However, since the equations for calculat-
ing evaporation are not linear, the monthly evaporation com-
puted from monthly mean meteorological data may differ
from what is found when data with a higher time resolu-
tion are used. In the aerodynamic approach the wind speed
is multiplied by the vapour deficit. The energy balance ap-
proach includes the Bowen ratio, which may differ from day
to day and can even be negative for certain periods. If high
atmospheric vapour pressure is related to strong winds, the
aerodynamic equation using monthly means can yield lower Hydrol. Earth Syst. Sci., 23, 657–668, 2019
662 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
evaporation estimates than when daily values are used. This
is further discussed below. The Bowen ratio changes during
a month. When the net radiation is large, the air temperature
is likely to be rather high but is not necessarily related to
high vapour pressure. For this situation, the Bowen ratio is
relatively high, and the computed evaporation is higher than
it would have been using a constant monthly Bowen ratio.
This means that when using monthly averages, the computed
evaporation will tend to be low.
4 Instrumentation and data
For this study, hydro-meteorological parameters and wa-
ter surface temperature were measured near Lake Titicaca’s
bank for 24 consecutive months (2015–2016). Vertical lake
temperature profiles were also acquired periodically. Obser-
vations were taken at 15 min intervals. These records were
averaged to daily and monthly values. A Campbell Scien-
tific research-grade automatic weather station (AWS) was
installed at the Isla de la Luna (latitude 160105900, longi-
tude 690400100), near the shore of Lake Titicaca (Fig. 3).
The AWS was equipped with a rain gauge sensor, a CS215
probe for measuring relative humidity and air temperature, an
A100R vector anemometer and W200P wind vane to mea-
sure wind speed, and a Skye SP1100 pyranometer for so-
lar radiation measurement. The surface water temperature
was taken from Juli, Puno (latitude 161205800, longitude
692703100), at a distance of 42 km from Isla de la Luna. A
handheld thermometer was used to measure water surface
temperature at 8 h intervals at approximately 60 m from the
shoreline. An increased daily surface recorded temperature
is representative of heat storage changes.
Hydrological data, such as inflow to the lake, were ob-
served at the outlet of the Ramis River. The outflow through
the Desaguadero River was observed at Aguallamaya. This
is 40 km downstream of the lake outlet. However, there are
only a few tributaries between the lake and this point that
may contribute to the data uncertainty. The water level was
observed at Huatajata at the daily time step, shown as depth
in Table 1. Additional lake water temperature soundings were
carried out close to Isla de la Luna (latitude 163000000, longi-
tude 691501000) for specific days during the summer, spring
and winter of the study period, using the Hydrolab DS5 mul-
tiparameter data sonde. The sounding reached a maximum
lake depth of 95 m, with a water temperature recording for
each 5 cm at the surface and each 0.5 m below 1 m depth.
Long-term monthly temperature and wind observations
from 1960 onwards were available from the Copacabana
weather station mentioned above (Fig. 3; Table 1). The El
Alto station observations, 50 km from Copacabana, were
used to fill 2.5 % of the missing wind data for the period.
The monthly precipitation on the lake was determined using
the rain gauge at Copacabana and Puno on the lake shore.
The total inflow from all rivers was estimated from a repre-
Figure 3. Location of observation points.
Table 2. Monthly mean of hydrological variables observed during
the 2015–2016 period.
Month Lake Inflow Outflow Precipitation
depth (m3s1) (m3s1) (mm month1)
Jan 282.9 399.8 37.7 165.4
Feb 283.1 639.7 53.9 146.1
Mar 283.2 427.0 47.3 76.5
Apr 283.3 327.9 42.1 103.9
May 283.3 148.4 40.2 18.1
Jun 283.2 80.2 32.9 7.7
Jul 283.0 56.7 28.6 51.9
Aug 282.9 42.6 24.4 12.5
Sep 282.8 36.8 20.7 26.6
Oct 282.7 32.3 19.1 42.9
Nov 282.6 35.7 18.2 39.0
Dec 282.5 92.0 18.5 87.6
sentative area approach assuming the specific run-off to be
the same for all rivers entering into Lake Titicaca. The long-
term outflow from the lake was measured at the outlet of the
lake and treated by Gutiérrez and Molina (2014).
Tables 2 and 3 summarize hydrological and meteorolog-
ical measurements used in this study. Subscripts for vapour
pressure are “w” for water, “s” for saturated air vapour pres-
sure and “a” for actual air vapour pressure. The computed
variables required for evaporation calculations are given in
Table 4.
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation 663
Table 3. Monthly averages of main climatic variables observed during the 2015–2016 period.
Water Air Wind Ralative Solar
Month surface temp. velocity humidity Vapour pressure (mbar) radiation, Rs
temp. (C) (C) (m s1) (%) ewesea(W m2)
Jan 17.2 11.1 1.60 68.3 19.8 13.9 9.5 273.3
Feb 17.3 11.4 1.61 70.3 19.9 14.2 10.0 292.4
Mar 17.5 12.0 1.50 66.1 20.2 14.7 9.7 273.4
Apr 16.5 10.8 1.52 66.7 19.0 13.6 9.1 229.2
May 15.4 10.7 1.33 53.4 17.5 13.5 7.2 234.9
Jun 14.3 10.1 1.30 51.8 16.7 13.0 6.7 236.7
Jul 13.7 9.7 1.41 50.6 16.1 12.8 6.5 237.9
Aug 14.0 9.7 154 54.4 16.4 12.8 7.0 265.8
Sep 14.7 10.5 1.50 57.6 17.1 13.6 7.8 304.7
Oct 15.5 10.9 1.63 58.2 17.6 13.9 8.1 318.7
Nov 16.4 11.7 1.61 57.1 18.8 14.8 8.4 332.1
Dec 16.9 11.6 1.70 64.9 19.5 14.5 9.4 315.9
Table 4. Monthly average parameters for evaporation calculations
for the 2015–2016 period.
Month Atmospheric Bowen Slope of water
emissivity ratio vapour pressure
ε β 1 (mbar 100 C1)
Jan 0.81 0.38 87.40
Feb 0.80 0.38 89.10
Mar 0.79 0.31 91.90
Apr 0.80 0.35 86.20
May 0.74 0.22 85.20
Jun 0.71 0.19 82.50
Jul 0.71 0.18 80.70
Aug 0.72 0.21 80.60
Sep 0.74 0.21 84.60
Oct 0.75 0.23 86.60
Nov 0.76 0.21 90.70
Dec 0.78 0.30 90.00
Short-wave radiation was measured, while long-wave ra-
diation was computed as described above. The average for
all components is shown in Fig. 4. The radiation budget is
positive every day, with a mean of about 150 Wm2, varying
from 100 in winter to 200 Wm2in summer.
5 Results and discussion
5.1 Monthly data
Detailed energy balance computations over the period 2015–
2016 should give good estimates of the total lake evapora-
tion for that period. After 24 months the lake surface tem-
perature at Puno more or less returned to the temperature
at the beginning of 2015. When applying this method over
the 2 years of study the mean annual lake evaporation is
Figure 4. Monthly average radiative budget for Lake Titicaca in
Figure 5. Change of heat storage in 2015–2016.
1700 mm year1. When computing the evaporation month by
month, the change of heat storage was considered in the way
previously described. The mixing depth was set to 40 m. The
change of the heat storage is shown in Fig. 5. The values
suggested by Carmouze et al. (1992) are shown for compar-
ison. The calculated monthly heat storage agrees well with
the Carmouze estimates.
The computed monthly evaporation using monthly av-
erage data and the energy balance method was somewhat Hydrol. Earth Syst. Sci., 23, 657–668, 2019
664 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
Figure 6. Monthly evaporation computed using energy balance ap-
Figure 7. Comparison of monthly evaporation computed by energy
balance and mass transfer method for 2015.
higher in 2016 than in 2015, 1725 mm year1as compared
to 1680 mm year1. The small gap of evaporation between
2 consecutive years is mainly explained by the warmer sea-
son that occurred in autumn of 2015; otherwise the evap-
oration was fairly evenly distributed over the year, being
about 140 mm month1, with somewhat lower evaporation
rates from July to September (see in Fig. 6).
From the energy balance and the water balance meth-
ods, the annual evaporation from Lake Titicaca was esti-
mated in the range of about 1700 mm year1. The monthly
variation depends on the change of heat storage, therefore
the calculated evaporation may be high one month and low
the following month. When using the mass transfer ap-
proach, similar annual evaporation to that from the energy
balance approach may be anticipated when applying the ap-
proaches over 2 full years. This may be the case even though
there may be differences when comparing monthly calcu-
lations. However, when the coefficients suggested by Car-
mouze et al. (1992) were used, the evaporation was much
higher than 1720 mm year1, which was found from the
energy balance method. A good fit for the total evapora-
tion was found using the coefficients a=0.17 mbar and b=
0.155 mm mbar1s m1.
The monthly evaporation computed by mass transfer over
the 2 years is compared with the energy balance calculations
Figure 8. Comparison of monthly evaporation computed by energy
balance and mass transfer method for 2016.
in Fig. 7 for 2015 and in Fig. 8 for 2016. The computed an-
nual evaporation by the last method was 1700mm year1in
2015 and 1675 mm year1in 2016. Consequently, for indi-
vidual years the two methods gave similar results and similar
seasonal trends. This is expected, since the coefficients in the
mass transfer equation were chosen to fit over the 2-year pe-
riod. For individual months, there are deviations. However, it
is not possible to note any systematic differences related to
different seasons of the year. The largest difference between
the two methods for an individual month was about 30 mm.
A summary and comparison of all investigated methods
for the study period are shown in Fig. 9 and Table 5. As
seen from these, the evaporation calculated from water bal-
ances differs from the three other methods. The water bal-
ance method yielded 1672 mm year1as the average for the
tow year. As well, the same method gave the largest stan-
dard deviation. The variation in mean annual evaporation
was 1633–1711 mm year1. Since the lake water level can
be observed at best with a resolution in centimetres, individ-
ual monthly evaporation becomes highly uncertain, like in
February 2016 and May 2016. Thus, calculated annual evap-
oration is better performed using the three other methods. In
general, the mass transfer, energy balance and Penman meth-
ods gave a similar monthly variation as described above; only
the evaporation by Penman gave a smaller rate than the rest
of models, 1621 mm year1, while energy balance gave the
highest evaporation rate, 1701 mm year1.
Water balances were computed for the long-term period
and continuous available data in 1966–2011 as well. Dur-
ing the computation the Alak e parameter in the model was
assumed to be constantly equal to 8800 km2. The resulting
annual lake evaporation for the period 1966–2011 was about
1600 mm year1. The mean water balance components for
the last period at monthly mean values are shown in Table 6.
When we used the water balance approach the computed
evaporation internally varied greatly from month to month
and year to year. This is an indication that some hydrolog-
ical input data are uncertain, like the precipitation, which
can be improved from one point observation at lake shore
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation 665
Table 5. Descriptive statistics of monthly evaporation calculated by the four methods for the period from January 2015 to December 2016.
Method Mean Mean Min Max Stand. Stand. error
annual monthly (mm month1) (mm month1) Dev. of mean
(mm year1) (mm month1) (mm month1) (mm month1)
Energy balance 1701 141.8 113.0 172.0 15.4 3.1
Mass transfer 1686 140.5 120.9 165.6 13.8 2.8
Water balance 1672 139.4 96.3 189.0 29.3 4.2
Penman 1621 135.2 110.9 167.0 14.5 2.9
Figure 9. Monthly actual evaporation calculated by the four meth-
ods for the period from January 2015 to December 2016.
by the satellite observation. In any case, water balance com-
putations over a long-term period should give a reasonable
estimate of mean lake evaporation.
5.2 Using daily data
When calculating evaporation using daily data, it was found
that there are large differences between the methods and ig-
noring the water balance method. The maximum daily evap-
oration using the mass transfer method was 12 mm day1.
Neither the energy balance nor the Penman method gave a
higher evaporation than 8 mm day1. There was poor agree-
ment between the computed daily evaporation computed by
mass transfer and the corresponding results using the other
two methods.
When the mass transfer approach is used, it is straight-
forward to determine the daily evaporation. Using the energy
balance, the change of heat storage in the lake must be deter-
mined with high resolution. Detailed water temperature mea-
surements are not available, however. Instead, it was assumed
that the temperature changes at a steady rate through individ-
ual months. August is an example, since the temperature for
the whole month changed very little (0.2 C). The computed
daily evaporation is shown for August 2015 in Fig. 10. There
were 2 days with average winds exceeding 6 ms1. Conse-
quently, the evaporation was high during these days, when
the mass transfer approach was used.
When annual evaporation was determined using daily data
instead of monthly mean data, there was hardly any differ-
ence for the mass transfer method. As indicated above it is
Figure 10. Daily evaporation computed by the mass transfer
(shaded staples) and energy balance (filled staples) method.
not possible to use the energy balance method with short
time resolution when temperature changes have to be taken
in to account from day to day. However, the evaporation can
be computed while neglecting the heat change, keeping the
Bowen ratio constant throughout a month and changing the
Bowen ratio day by day. In this case, it was found that evap-
oration increased by about 2 %. The conclusion, considering
the many uncertainties involved in estimating evaporation, is
that it is sufficient to use monthly means when estimating
The evaporation computed with the Penman equation falls
between what was found by the energy balance and the mass
transfer approach, being somewhat closer to the energy bal-
ance than to the mass transfer results. Since monthly means
are sufficient for computing evaporation with the two above
methods, mean values are also sufficient when using the Pen-
man method.
It has to be noted that Lake Titicaca’s near-bank surface
temperatures have been observed to be warmer than the lake
surface’s average during daytime using satellite thermal im-
agery, as reported in other lakes (e.g. Marti-Cardona et al.,
2008). According to this observation, the temperatures ac-
quired for this study are likely to be an overestimation.
The spatial distribution of Lake Titicaca’s surface temper-
ature and its impact on the evaporation losses is currently
under analysis. However, for the energy balance method,
daily changes rather than absolute temperatures were used,
which are considered to be reasonable approximations of the Hydrol. Earth Syst. Sci., 23, 657–668, 2019
666 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
Table 6. Monthly mean water balances for Lake Titicaca for the period 1966–2011.
Month Ramis Inflow Outflow Lake water Precipitation Evaporation
flow (m3s1) (m3s1) depth (mm month1) (mm month1)
(m3s1) (m)
Jan 173.5 549.3 31.3 283.9 177.0 143.7
Feb 198.8 629.4 39.4 284.1 141.6 123.2
Mar 190.4 602.8 49.8 284.4 126.8 124.6
Apr 104.9 332.1 50.9 284.5 50.6 137.2
May 38.7 122.6 46.5 284.5 13.2 139.6
Jun 20.7 65.5 41.8 284.4 7.3 136.6
Jul 14.5 46.0 37.0 284.3 6.6 133.1
Aug 11.0 34.9 32.1 284.2 13.2 121.7
Sep 9.9 31.3 28.1 284.1 29.9 118.3
Oct 14.0 44.2 24.1 284.0 45.5 134.9
Nov 24.0 76.0 21.7 283.9 56.7 134.3
Dec 55.2 174.7 22.1 283.9 102.5 127.9
heat storage changes. Over the larger period of air temper-
atures observed at the Copacabana weather station (1966–
2016), the particular months in 2015–2016 have been char-
acterized by the strongest El Niño dry phenomena during
the last 50 years (, last access: 10 Jan-
uary 2017); in comparison to the rest of the years, the air tem-
peratures recorded were higher than the average of 10 C and
close to 20 C at the daily time step. Then the rates of evapo-
ration found might express, somehow, the indicated warmer
6 Conclusions
Due to uncertainty of most observed data such as river in-
flow to Lake Titicaca, and mainly the discharge data, it might
not be easy to improve the water balance results; thus it is
suggested that the most reliable method of determining the
lake evaporation is using the heat balance approach. To es-
timate the lake evaporation using this method, heat storage
changes must be known. Since convection from the surface
layer is intense during nights, resulting in a well-mixed top
layer every morning, it is possible to determine the change
of heat storage from the measured morning surface tempera-
ture. The lake evaporation is fairly uniformly distributed over
the year, with lows between July and September. The mean
annual evaporation is about 1700 mm year1, and the mean
monthly evaporation is 141.8 mm month1. When using the
mass transfer approach, the required coefficients in the aero-
dynamic equation was set so that the mean annual evapora-
tion agreed with that obtained from the heat balance calcu-
lations. These coefficients were found to be lower than coef-
ficients used in previous studies. Also, when using the mass
transfer approach, the evaporation was found to be lowest in
However, for the purpose of assessing climate change ef-
fects on Lake Titicaca’s evaporation, the practical approach,
rather than the two empirical models, might be the Penman
equation due to available observed data for this lake and the
integral behaviour of the equation. Also in comparison with
the two models proposed in Delclaux et al. (2007) for mod-
elling the lake evaporation, the first model only depends on
the solar radiation data, and, additionally, the second one de-
pends on the air temperature factor; thus both models can-
not be applied broadly. In the Penman model based on the
adjusted wind coefficient, the mean annual evaporation is
1620 mm year1, and the mean monthly is 135 mm month1.
So far, monthly evaporation computed using daily data and
monthly means resulted in minor differences. The most prac-
tical model for use at the daily scale might be the mass trans-
fer and the Penman models in comparison to the energy bal-
ance approach, which is of highly demanded observed data.
Particularly the Penman equation at the daily temporal scale
might correctly be applied for the climate change assessment
at this altitude. Nonetheless, according to spatial available
data from remote sensing, the evaporation equations used at
daily and monthly scales could be applied from now on to
improve the spatial pattern of the lake evaporation. Since
we had really extreme single warmer days during the pe-
riod 2015–2016 due to the El Niño phenomenon, higher daily
rates of evaporation must be expected; therefore the applica-
tion of the models at both timescales for the study period we
believe that was found the upper limits of yearly evaporation.
Data availability. All data can now be freely accessed through re-
quests to
Author contributions. RPZ coordinated the research and was di-
rectly involved in all steps, from fieldwork to proofreading. He built
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation 667
the database, computed the evaporation for the different models, an-
alyzed the results, and prepared figures and tables. LB contributed
to the conceptual approach and structure of the paper. He super-
vised and validated the calculations and contributed to the writing
of the objectives and the scientific background of the paper. RB re-
vised and validated the calculations and collaborated on the writing,
mainly for Sect. 5. BMC contributed to the discussion and analy-
sis of results and writing, especially for the Abstract and Sects. 1
and 6. FS collaborated on the analysis of results, particularly on the
interpretation of some evaporative models. He prepared the figures
depicting maps. FT was in charge of the installation and mainte-
nance of the gauging stations and data quality assurance. MPB im-
proved the conceptual approach of the paper. She also helped to ob-
tain funding for the field data acquisition. LM assisted in the paper
drafting and building the database base. He also prepared the chart
figures. CG and JP facilitated meteorological records from Peruvian
gauging stations. They contributed to the paper structure and to the
content of Sects. 1 and 5.
Competing interests. The authors declare that they have no conflict
of interest.
Special issue statement. This article is part of the special issue “In-
tegration of Earth observations and models for global water re-
source assessment”. It is not associated with a conference.
Acknowledgements. We would like to express our sincere ap-
preciation to the HASM, Research Programme – Hydrology of
Altiplano from Space to Modeling at GET-IRD and IHH-UMSA
(Instituto de Hidráulica e Hidrología, UMSA, Bolivia), financed
by the TOSCA-CNES (Centre National d’Etudes Spatiales). We
would like to thank SENAMHI-Bolivia (Servicio Nacional de
Hidrometeorología de Bolivia) for providing long-term climatic
data. Thanks also to the IMARPE-Perú (Instituto para el Mar
del Perú/Puno) for providing additional hydrological data as well
as surface water temperatures of Lake Titicaca. In addition, our
acknowledgment is directed to the project Fortalecimiento de
Planes Locales de Intervención y Adaptación al Cambio Climático
en el Altiplano Boliviano at Agua Sustentable-Bolivia for providing
the Lake Titicaca discharge data. Finally, we thank the programme
BABEL Erasmus EU for providing economic assistance and
completing this work in Sweden.
Edited by: Anas Ghadouani
Reviewed by: two anonymous referees
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... This is likely related to the fact that higher temperatures may lead to lower α + and a more positive δ E , and thus a more negative δ L . Moreover, the evaporation amount in this study was measured using a large evaporator; however, in previous MBM studies, evaporation was often calculated using the Penman equation (Valiantzas, 2006;Jones et al., 2016;Pillco Zolá et al., 2019), in which δ E may increase as temperature increases, leading to a more negative δ L if T A is used in the MBMs. Therefore, it is more appropriate to use T W in the MBMs to obtain a more realistic simulated δ L . ...
... (10)), but they also influence E, as would be expected. A higher E occurs as a result of an increase in T W or a decrease in h (Valiantzas, 2006;Jones et al., 2016;Pillco Zolá et al., 2019). However, the E, δ P , and δ A series were determined by field experiments and therefore the interactions among the input variables and the impact of multiple changes in variables on the simulated δ L are difficult to disentangle; thus, the actual variations of δ L in the sensitivity tests may be greater and more complex. ...
Hydrologic and isotope mass-balance models (MBMs) are useful tools for the simulation and quantitative interpretation of lake water δ¹⁸O (δL). Such studies of small, open lakes are important because δL may show large responses to weather-driven hydrological variability. A δL sequence was simulated for three-year and five-day interval data from Taozi Lake, a small, open lake in Changsha, in the East Asian monsoon region of China. The MBMs performed well, with the optimal model explaining 90% of the observed δL variability. However, it was necessary to parameterize the precipitation input by increasing the lake water depth during heavy precipitation events to capture the observed sharp decreases in δL. We found that the MBMs using air temperature and the equilibrated atmospheric vapor δ¹⁸O (δA) produced a more negative δL compared to the model using the surface water temperature and the observed δA, and that the equilibrated δA was somewhat arbitrary, which introduced a large error in the model output. A sensitivity test highlighted the importance of the seasonal variability of hydrometeorological and isotopic variables to reproduce the observed δL variability. Additionally, the simulated average δL showed a similar pattern of variation to the meteorological variables shifted by different ratios, but for the relative humidity, there was only a narrow window within which a realistic δL series could be reproduced. Our results show that a realistic MBM can be established based on long-term observations, with implications for studies of hydrologic processes and paleoclimate reconstruction.
... The basin is shared between Bolivia and Peru and considered as an ancient lake in the high-elevation Altiplano region with high biodiversity [11]. The lake is surrounded by the eastern and western Andean Mountains between 15 0 45′ S and 69 0 25′ W in the northern part of the Peruvian-Bolivian Altiplano [12]. In most parts of Bolivia, precipitation is the main water source for drinking water and agriculture. ...
... mean of about 764 and 527 mm for Copacabana and 599 and 408 mm for El Belen, respectively [13]. The lake has a large surface evaporation of about 1700 mm/year, which is considered a water loss affected by climate warming [12]. ...
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Drought and scarcity of water resources require innovative and sustainable solutions to secure water availability for poor people. Choice of solar energy for desalination is a promising and sustainable cost-effective alternative for improving high quality water supply. Today, almost all Latin American countries use different desalination technologies except for Bolivia. Bolivia has an arid to semiarid climate and suffers from salinity problems especially the Altiplano area. Thus, there is a need to introduce innovative solution using latest technologies such solar desalination at locations with scarcity of freshwater. This study suggests implementing a small desalination plant of about 10 m3/day as a demonstration plant and then successively extending the capacity. As well, it is suggested to build a solar energy system with bigger capacity to cater not only for the desalination plant, but also the excess energy to be benefit for homes, roads lighting, and other important purposes for the local community to improve life standard of the people.
... There are many calculation methods for water surface evaporation, including the energy balance method [10,11], mass transfer method [12,13], water balance method [14,15], and empirical method [16][17][18]. Theoretically, the water balance method is the most direct method for evaporation estimation. ...
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Free surface evaporation is an important process in regional water cycles and energy balance. The accurate calculation of free surface evaporation is of great significance for evaluating and managing water resources. In order to improve the accuracy of estimating reservoir evaporation in data-scarce arid regions, the applicability of the energy balance method was assessed to calculate water surface evaporation based on the evaporator and reservoir evaporation experiment. A correlation analysis was used to assess the major meteorological factors that affect water surface temperature to obtain the critical parameters of the machine learning models. The water surface temperature was simulated using five machine learning algorithms, and the accuracy of results was evaluated using the root mean square error (RMSE), correlation coefficient (r), mean absolute error (MAE), and Nash efficiency coefficient (NSE) between observed value and calculated value. The results showed that the correlation coefficient between the evaporation capacity of the evaporator, calculated using the energy balance method and the observed evaporation capacity, was 0.946, and the RMSE was 0.279. The r value between the calculated value of the reservoir evaporation capacity and the observed value was 0.889, and the RMSE was 0.241. The meteorological factors related to the change in water surface temperature were air temperature, air pressure, relative humidity, net radiation and wind speed. The correlation coefficients were 0.554, −0.548, −0.315, −0.227, and 0.141, respectively. The RMSE and MAE values of five models were: RF (0.464 and 0.336), LSSVM (0.468 and 0.340), LSTM (1.567 and 1.186), GA-BP (0.709 and 0.558), and CNN (1.113 and 0.962). In summary, the energy balance method could accurately calculate the evaporation of evaporators and reservoirs in hyper-arid areas. As an important calculation parameter, the water surface temperature is most affected by air temperature, and the RF algorithm was superior to the other algorithms in predicting water surface temperature, and it could be used to predict the missing data. The energy balance model and random forest algorithm can be used to accurately calculate and predict the evaporation from reservoirs in hyper-arid areas, so as to make the rational allocation of reservoir water resources.
... Winds generated by tropical cyclones surge the coastal water levels which cause flooding and damage to coastal infrastructures (Shimozono et al., 2020;Simonson et al., 2020). Also, the wind is a factor that governs evaporation losses from lakes and reservoirs (Pillco Zola et al., 2019), particularly in arid and semiarid regions (Kousari et al., 2013). Furthermore, wind speeds affect the residence time of airborne particles (Omokungbe et al., 2020) and cause sandstorms which lead to wind erosion (Sarafrazi and Talaee, 2020). ...
In this study, characteristics of 10 m height wind speeds (Wsp10) and outdoor human thermal sensation taking wind speeds into account were studied over the period 1995–2021 considering 43 stations in Poland. For estimating hourly Wsp10 from wind speeds measured at different heights, first, the power law exponent was calculated using hourly 10 m and 100 m wind speeds obtained from the ERA5 reanalysis project. The power law exponent was much smaller over the Baltic Sea compared to that over Poland. The power law exponent was often larger than 1/7 in Poland, and it varied spatiotemporally. During the period 1995–2021, at 19 of the 43 stations statistically significant monotonic linear trends were observed in Wsp10. It is speculated that land use changes may be one of the causes of these trends in Wsp10, although the land use – Wsp10 relationship was not straightforward. In all seasons, at all stations, except at Kasprowy Wierch (the most elevated station) daytime Wsp10 was higher than the night‐time wind speed. In winter and autumn, the highest Wsp10 occurred around 13:00 UTC. In spring and summer, the highest Wsp10 occurred after 13:00 UTC. This was probably because in spring and summer the peak temperature occurs later. In all seasons, low/high Wsp10 values were more/less frequent. According to the Beaufort scale and the Parczewski scale, it was understood that both low and high extreme wind conditions have reduced over the period 1995–2021. The Effective Temperature scale indicated increasing/decreasing monotonic linear trends in relatively warm/cold thermal sensation categories. The Wind Chill Temperature exposure risk scale indicated decreasing monotonic linear trends in wind chill. The rising temperature and declining frequency of strong winds are seen as the main causes of these trends.
... Lakes larger than 104 m 2 constituted 85% of superficial water in the park, and 10 lakes deeper than 18 m contained 50% of the water sources We did not find studies on the role of PAs in addressing climate-related impacts on freshwater ecosystems, only studies related to water losses by evaporation and the increase in the number of lakes due to glacier retreat in the tropical Andes. For instance, higher evaporation rates (1700 mm year -1 ) over Lake Titicaca were reported (Pillco Zolá et al. 2019). Moreover, 201 sites might become lakes in the future due to glacier retreat in Peruvian cordilleras (Colonia et al. 2017). ...
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Although protected areas (PAs) play an important role in ecosystem conservation and climate change adaptation, no systematic information is available on PA protection of high-elevation freshwater ecosystems (e.g., lakes and watersheds with glaciers), their biodiversity and their ecosystem services in the tropical Andes. We therefore combined a literature review and map analysis of PAs of International Union for Conservation of Nature (IUCN) and national systems of PAs and freshwater ecosystems. We found that seven national parks were created for water resources protection but were not designed for freshwater conservation (i.e., larger watersheds). High-value biodiversity sites have not been protected, and new local PAs were created due to water resource needs. We quantified 31 Ramsar sites and observed that PAs cover 12% of lakes, 31% of glacial lakes and 12% of the total stream length in the tropical Andes. Additionally, 120 watersheds (average area 631 km ² ) with glaciers and 40% of the total glacier surface area were covered by PAs. Future research into the role of PAs in ecosystem services provision and more detailed freshwater inventories within and around PAs, especially for those dependent on glacier runoff, will fill key knowledge gaps for freshwater conservation and climate change adaptation in the tropical Andes.
Evaporation from the surface of water is a vital component of the hydrological cycle. Accurately simulating evaporation is crucial for modeling hydrological processes, ensuring ecosystem water efficiency, and managing water resources. Previous methods for evaluating evaporation have generally been limited to a single site and on a regional scale. Based on eddy covariance measurements of 14 boreal flux sites, the accuracy of 26 methods for simulating daily water surface evaporation was comprehensively evaluated in this study. Most methods accurately simulated daily evaporation at most sites with a KGE greater than 0.60. The combination methods with simultaneous calibration of the energy and aerodynamic terms and the double-parameter aerodynamic methods based on the linear and exponential functions showed the best performance, with the median KGE of the evaluated sites ranging from 0.72 to 0.76. The Bowen ratio energy balance (BREB) method embedded with Tw, Rs-based two-variable empirical methods, double-parameter aerodynamic methods, and the combination method of the energy term based on net radiation (Rn) and the aerodynamic term based on the exponential function method performed better than the other methods of the same type. The relative error (RE) simulated by most methods was generally within ±30%, with the median RE of all sites within ±10% for each method. The combination methods tended to overestimate the level of evaporation, whereas the BREB-type and aerodynamic methods tended to underestimate the extent of evaporation. The simulation accuracy of the daily evaporation showed significant variance among the sites. It showed the best model performance at two FLUXNET and two sites taken from the literature, in which 75% of the methods were able to accurately simulate daily evaporation with a Kling–Gupta efficiency (KGE) larger than 0.80. All methods performed poorly at the three sites from the literature and were mainly due to the lack of measured variables with a strong correlation with the latent heat flux (LE). The FLUXNET sites generally showed better performance. The observed LE of the sites with the best model performance generally showed a unimodal distribution throughout the year. The simulation accuracy of non-unimodal distribution sites mainly depended on the correlation between the LE and related variables. The combination of the energy term based on Rn and the aerodynamic term based on the power function method showed the best model stability. This finding indicated that the calibrated method was robust and showed high stability in simulating daily evaporation, and it was recommended for application in other sites or regions. The optimization of parameters calibrated in this study may improve the accuracy of simulating the daily evaporation for the application of the Penman and Priestley–Taylor equations when the water heat storage measurement is missing.
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Lakes help increase the sustainability of the natural environment and decrease food chain risk, agriculture, ecosystem services, and leisure recreational activities locally and globally. Reliable simulation of monthly lake water levels is still an ongoing demand for multiple environmental and hydro-informatics engineering applications. The current research aims to utilize newly developed hybrid data-intelligence models based on the ensemble adaptive neuro-fuzzy inference system (ANFIS) coupled with metaheuristics algorithms for lake water-level simulation by considering the effect of seasonality on Titicaca Lake water-level fluctuations. The classical ANFIS model was trained using three metaheuristics nature-inspired optimization algorithms, including the genetic algorithm (ANFIS-GA), particle swarm optimizer (ANFIS-PSO), and whale optimization algorithm (ANFIS-WOA). For determining the best set of the input variables, an evolutionary approach based on several lag months has been utilized prior to the lake water-level simulation process using the hybrid models. The proposed hybrid models were investigated for accurately simulating the monthly water levels at Titicaca Lake. The ANFIS-WOA model exhibited the best prediction performance for lake water-level pattern measurement in this study. For the best scenario (the inputs were $${X}_{t-1},\; {X}_{t-2}, \;{X}_{t-3}, \;{X}_{t-4}, \; {X}_{t-12}$$ X t - 1 , X t - 2 , X t - 3 , X t - 4 , X t - 12 ) the ANFIS-WOA model attained root mean square error (RMSE $$\approx$$ ≈ 0.08 m), mean absolute error (MAE $$\approx$$ ≈ 0.06 m), and coefficient of determination ( R ² $$\approx$$ ≈ 0.96). Also, the results showed that long-term seasonal memory for this lake is suitable input for lake water-level models so that the long-term dynamic memory of 1-year time series for lake water-level data is the best input for estimating the water level of Titicaca Lake.
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The isotopic composition of precipitation is used to trace water cycling and climate change, but interpretations of the environmental information recorded in central Andean precipitation isotope ratios are hindered by a lack of multi‐year records, poor spatial distribution of observations, and a predominant focus on Rayleigh distillation. To better understand isotopic variability in central Andean precipitation, we present a three‐year record of semimonthly δ¹⁸Op and δ²Hp values from 15 stations in southern Peru and triple oxygen isotope data, expressed as ∆′¹⁷Op, from 32 precipitation samples. Consistent with previous work, we find that elevation correlates negatively with δ¹⁸Op and that seasonal δ¹⁸Op variations are related to upstream rainout and local convection. Spatial δ¹⁸Op variations and atmospheric back trajectories show that both eastern‐ and western‐derived air masses bring precipitation to southern Peru. Seasonal d‐excessp cycles record moisture recycling and relative humidity at remote moisture sources, and both d‐excessp and ∆′¹⁷Op clearly differentiate evaporated and non‐evaporated samples. These results begin to establish the natural range of unevaporated ∆′¹⁷Op values in the central Andes and set the foundation for future paleoclimate and paleoaltimetry studies in the region. This study highlights the hydrologic understanding that comes from a combination of δ¹⁸Op, d‐excessp, and ∆′¹⁷Op data and helps identify the evaporation, recycling, and rainout processes that drive water cycling in the central Andes.
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Lake Titicaca is an important water ecosystem of South America. Due to uncertainties in estimating the evaporation losses from the lake, surface water storage calculations are uncertain. In this paper, we try to improve evaporation loss estimations by comparing different methods to calculate daily and monthly evaporation from Lake Titicaca. These were: water balance, heat balance, mass transfer method, and the Penman equation. The evaporation was computed at daily time step and compared with estimated evaporation using mean monthly meteorological observations. We found that the most reliable method of determining the annual lake evaporation is using the heat balance approach. To estimate the monthly lake evaporation using heat balance, the heat storage changes must be known in advance. Since convection from the surface layer is intense during nights resulting in a well-mixed top layer every morning, it is possible to determine the change of heat storage from the measured morning surface temperature. The mean annual lake evaporation was found to be 1700 mm. Monthly evaporation computed using daily data and monthly means resulted in minor differences.
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In 2015, an emergency state was declared in Bolivia when Poopó Lake dried up. Climate variability and the increasing need for water are potential factors responsible for this situation. Because field data are missing over the region, no statements are possible about the influence of mentioned factors. This study is a preliminary step toward the understanding of Poopó Lake drought using remote sensing data. First, atmospheric corrections for Landsat (FLAASH and L8SR), seven satellite derived indexes for extracting water bodies, MOD16 evapotranspiration, PERSIANN-CDR and MSWEP rainfall products potentiality were assessed. Then, the fluctuations of Poopó Lake extent over the last 26 years are presented for the first time jointly, with the mean regional annual rainfall. Three main droughts are highlighted between 1990 and 2015: two are associated with negative annual rainfall anomalies in 1994 and 1995 and one associated with positive annual rainfall anomaly in 2015. This suggests that other factors than rainfall influenced the recent disappearance of the lake. The regional evapotranspiration increased by 12.8% between 2000 and 2014. Evapotranspiration increase is not homogeneous over the watershed but limited over the main agriculture regions. Agriculture activity is one of the major factors contributing to the regional desertification and recent disappearance of Poopó Lake.
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The South American Altiplano in the Andes is, aside from Tibet, the most extensive high plateau on Earth. This semiarid area represents important water resources storages, including the Lakes Titicaca and Poopó located in the northern and central Altiplano, respectively. The two lake basins and the southern saltpans constitute a large watershed, called the Lake Titicaca, Desaguadero River, Lake Poopó, and Coipasa Salt Flat System (TDPS hydrologic system). The Altiplano climate, topography, and location determine the TDPS hydrologic functioning. Scarce data and high spatial variability represent challenges to correctly simulate the TDPS water budget. Consequently, there is an important need to improve the understanding of the water resources in current and future climate over the area. The paper provides a comprehensive state-of-the-art regarding current knowledge of the TDPS hydro-socioeconomic system and summarizes the data needs to improve the current hydrological understanding.
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At an altitude of 3809 metres above sea level, Lake Titicaca, the northern lake basin on the Altiplano (a high endorheic plateau in Peru and Bolivia) is the largest navigable water body in the world Iying at over 3000 metres. Following brief descriptions by Spanish chroniclers, the first scientific observations were undertaken by A. d'Orbigny during his voyage in South America (1826-1833). Until the turn of the century the map considered to be the most reliable was that made by Pentland, following two voyages on the lake (1827-28/1837-38). Further brief or multidisciplinary expeditions then took place, notably those of Agassiz and Garman (1876) and Créqui de Montfort and Sénéchal de la Grange, reported by Neveu-Lemaire in 1906. Each of these attempted to describe the precise geographical setting, with greater or lesser success. Following the last great multidisciplinary expedition, the "Percy Sladen Trust Expedition" (1936-39), more specialised studies started to be carried out. Only the most recent data are taken into account in this synthesis chapter. The main reference work is that of Boulangé and Aquize Jaen (1981), the cartographic material used being the 5 maps at 1/100,000 published in 1978 by the Hydrological Services of Peru and Bolivia (Hidronav, 1978) which were drawn from 7000 soundings to the nearest 0.1 m, based on the average measurements over 41 years of observations.
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This work analysed the changes in air temperature in 25 meteorological stations in the Altiplano and the surrounding Andean slopes of Bolivia and Peru, and their relationship with El Niño-Southern Oscillation (SO) and the Pacific Decadal Oscillation (PDO). The analysis focused on annual, warm season (DJF) and cold season (JJA) maximum and minimum temperatures. All analyses were undertaken during 1965–2012, but some analyses were also from 1945 and 1955 when data were available. Principal component analysis was applied to the annual and seasonal series to identify spatial differences of changes in maximum and minimum air temperature. There was an overall increase of temperatures since the mid-20th century. The most intense and spatially coherent warming was observed for annual and warm season maximum temperature, with warming rates from 0.15 to 0.25 °C decade−1. Changes in the cold season maximum temperature were more heterogeneous, and statistically significant trends were mostly in the Bolivian Altiplano. Minimum temperatures increased, but there was higher spatial variability and lower rates of warming. Maximum temperature was negatively correlated with the Southern Oscillation index (SO) in the warm season, and positively correlated with the SO in the cold season; there were less statistically significant correlations with the PDO, that exhibited inverse sign than those for SO. The strongest correlations were in the region near Lake Titicaca. The negative correlation of minimum temperatures with SO and the positive correlation of minimum temperatures with PDO were lower than the observed for maximum temperature. The changes in temperature and correlations with SO and PDO were highly dependent on the selected period, with stronger trends in the last 30–40 years. This suggests reinforcement of warming rates that cannot be only explained by SO and PDO variability.
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The term “playa” or “pan” applies to individual arid zone basins of varying size and origin that are subject to ephemeral surface water flows (Shaw and Thomas, 1989) such that lakes may occur within playas as permanent or ephemeral features. Playas in Australia are often geologically young (Quaternary) features developed in arid environments and are often dry due to evaporation (Boggs et al., 2006). Although playas are a response to tectonics, climate change, and eolian and fluvial processes, the majority of the scientific literature considers either their origin within a regional context, or the development dynamics of individual playas (e.g., Bettenay, 1962). However, where playas are developed within paleodrainage channels, they may exist as isolated features, but more often they exhibit a degree of hydrological interconnectivity with other playas to form “playa chains” such that the development history of an individual playa cannot be addressedwithout consideration of its neighbors.
An improved parameterization is presented for estimating effective atmospheric emissivity for use in calculating downwelling longwave radiation based on temperature, humidity, pressure, and solar radiation observations. The first improvement is the incorporation of an annual sinusoidal variation in effective clear-sky atmospheric emissivity, based on typical climatological variations in near-surface vapor pressure. The second is the continuous estimation of fractional cloudiness by taking the ratio of observed solar radiation to a modeled clear-sky solar radiation. Previous methods employed observer-estimated fractional cloudiness. Data from the Atmospheric Radiation Measurement (ARM) program were used to develop these improvements. The estimation of cloudiness was then used to modify the effective clear-sky atmospheric emissivity in order to calculate 30-min averages of downwelling longwave radiation. Monthly mean bias errors (mbe's) of 9 to +4 W m2 and root-mean-square errors (rmse's) of 11-22 W m2 were calculated based on ARM data over a 1-yr period. These mbe's were smaller overall than any of the six previous methods tested, while the rmse's were similar to the best previous methods. The improved parameterization was then tested on FIFE data from the summer of 1987. Although the monthly mbe's were larger, the rmse's were smaller.It is also shown that data from upper-air soundings can be used to calculate the effective atmospheric emissivity rather than specifying the aforementioned sinusoidal variation. Using ARM upper-air soundings, this method resulted in larger mbe's, 7 to +11 W m2, especially during the summer months, and similar rmse's. The success of the method suggests that it has application at any observing site within reasonable proximity of an upper-air sounding, while removing the empiricism used to specify the annual sinusoidal variation in emissivity.