Available via license: CC BY 4.0
Content may be subject to copyright.
Hydrol. Earth Syst. Sci., 23, 657–668, 2019
https://doi.org/10.5194/hess-23-657-2019
© 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 (rpillco@umsa.edu.bo)
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 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 method-
ologies.
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 year−1. Tay-
lor and Aquize (1984) applied a bulk transfer approach
for a shorter period and determined the lake evaporation
to be 1350 mm year−1. The largest reported annual evapo-
ration is from using the energy balance approach. Richer-
Hydrol. Earth Syst. Sci., 23, 657–668, 2019 www.hydrol-earth-syst-sci.net/23/657/2019/
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 year−1. Later, Carmouze (1992) used the same ap-
proach and found the lake evaporation to be 1720mm year−1.
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 year−1.
Thus, the mean annual evaporation has been estimated in
the range 1350–1900 mm year−1. While the precipitation can
vary much from year to year, the large range of calculated an-
nual evaporation, 1350 to 1900 mm year−1, 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 year−1,
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 15◦450S and 69◦250W. 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 m3s−1. The mean
outflow from Lake Titicaca through the Desaguadero River
for the same period was 35 m3s−1. 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 year−1, 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 year−1
in the central part to 800 mm year−1along the shores (TDPS,
1993). January is the wettest (about 180 mm month−1) and
www.hydrol-earth-syst-sci.net/23/657/2019/ 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 (m3s−1) (m3s−1) depth (mm month−1) temperature humidity velocity
(m3s−1) (m) (◦C) (%) (m s−1)
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 s−1, rarely reach-
ing 5 m s−1at 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 =Rn−Qheat
1+β,(1)
where λis the latent heat vaporization (J kg−1), Eis evap-
oration rate (mm day−1), Rnis net radiation (W m−2), Qheat
is heat storage within the water (W m−2) and βis the Bowen
ratio (Bowen, 1926):
β=γTw−Ta
ew−ea
,(2)
γ=cppa
0.622λ,(3)
where γis the psychrometric constant (mbar ◦C−1); 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 kg−1◦C−1); 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(1−albedo), where
Rsis the solar radiation reaching the lake (W m−2). 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 www.hydrol-earth-syst-sci.net/23/657/2019/
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=(1−s)+sεo(Ta, ea),(4)
s=Rs
Rs,o
,(5)
Rs,o =Rae−0.0018Pa
Ktsinφ24 ,(6)
εo=1.18ea
Ta1
7
,(7)
where sis the proxy cloudiness defined as the ratio of mea-
sured incoming solar radiation Rs(W m−2) to the solar radi-
ation received for the clear-sky conditions Rs,o (W m−2), 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 m−2). 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
Vmix
Alake
∂Tw
∂t ,(8)
where ρis density of water (kg m−3), cpis the specific heat
capacity of water and Vmix is the volume above the mixing
depth (km−3). 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 )(ew−ea), (9)
where Eis the evaporation rate, Uis wind velocity (ms−1)
and ew−eais the vapour pressure deficit (mbar). The pa-
rameter aaccounts for unstable atmospheric conditions. Car-
mouze et al. (1992) used a=0.17 (mm mbar−1day−1) and
b=0.30 (mm mbar−1s m−1).
3.3 Penman approach
The Penman equation is a combination of energy balance
and mass transfer used for evaluating open water evaporation
(Penman, 1948):
E=1
1+γ
(Rn−Qheat)
λρ +γ
1+γc(a0+b0U )(es−ea),(10)
where Eis open water evaporation. The slope of the water
pressure–temperature curve is denoted by 1(K Pa s−1), and
es−eais 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 day−1mbar).
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
Alake
∂h
∂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 day−1); Alake is water surface of the lake (km−2),
which is a function of depth; Qin is inflow to the lake; and
Qout represents the outflow from the lake (m3s−1). 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
www.hydrol-earth-syst-sci.net/23/657/2019/ 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 16◦0105900, longi-
tude 69◦0400100), 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 16◦1205800, longitude
69◦2703100), 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 16◦3000000, longi-
tude 69◦1501000) 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 (m3s−1) (m3s−1) (mm month−1)
(m)
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 www.hydrol-earth-syst-sci.net/23/657/2019/
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 s−1) (%) ewesea(W m−2)
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 ◦C−1)
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 Wm−2, varying
from 100 in winter to 200 Wm−2in 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
2015–2016.
Figure 5. Change of heat storage in 2015–2016.
1700 mm year−1. 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
www.hydrol-earth-syst-sci.net/23/657/2019/ 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-
proach.
Figure 7. Comparison of monthly evaporation computed by energy
balance and mass transfer method for 2015.
higher in 2016 than in 2015, 1725 mm year−1as compared
to 1680 mm year−1. 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 month−1, 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 year−1. 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 year−1, 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 mbar−1s m−1.
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 year−1in
2015 and 1675 mm year−1in 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 year−1as 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 year−1. 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 year−1, while energy balance gave the
highest evaporation rate, 1701 mm year−1.
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 year−1. 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 www.hydrol-earth-syst-sci.net/23/657/2019/
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 month−1) (mm month−1) Dev. of mean
(mm year−1) (mm month−1) (mm month−1) (mm month−1)
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 day−1.
Neither the energy balance nor the Penman method gave a
higher evaporation than 8 mm day−1. 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 ms−1. 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
evaporation.
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
www.hydrol-earth-syst-sci.net/23/657/2019/ 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 (m3s−1) (m3s−1) depth (mm month−1) (mm month−1)
(m3s−1) (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 (http://www.ciifen.org, 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
period.
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 year−1, and the mean
monthly evaporation is 141.8 mm month−1. 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
July–September.
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 year−1, and the mean monthly is 135 mm month−1.
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 rpillco@umsa.edu.bo.
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 www.hydrol-earth-syst-sci.net/23/657/2019/
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
References
Abarca-Del-Río, R., Crétaux, J. F., Berge-Nguyen, M., and Maiso-
grande, P.: Does Lake Titicaca still control the Lake Poopó
system water levels? An investigation using satellite altimetry
and MODIS data (2000–2009), Remote Sens. Lett., 3, 707–714,
https://doi.org/10.1080/01431161.2012.667884, 2012.
Bengtsson, L., Herschy, R. W., and Fairbridge, R. W.: Encyclopedia
of Lakes and Reservoirs, Springer Dordrecht, ISBN-13: 978-1-
4020-5616-1, 2012.
Boulange, B. and Aquize, J. E.: Morphologie, hydrographie et cli-
matologie du lac Titicaca et de son basin versant, Rev. Hydrobiol.
Trop., 14, 269–287, 1981.
Bowen, I. S.: The ratio of the heat losses by conduction and by
evaporation from any water surface, Phys. Rev., 27, 779–787,
1926.
Canedo, C., Pillco, Z. R., and Berndtsson, R.: Role of hydrological
studies for the development of the TDPS system, Water, 8, 1–14,
https://doi.org/10.3390/w8040144, 2016.
Carmouze, J. P.: The energy balance in the Lake Titicaca, in: A
Synthesis of Limnological Knowledge, edited by: Dejoux, C. and
Iltis, A., Kluwer, 131–146, 1992.
Carmouze, J. P., Arce, C., and Quintanilla, J.: La régulation hy-
drique des lacs Titicaca et Poopo, Cahiers ORSTOM, Série Hy-
drobiologique, XI, 269–283, 1977.
CMLT: Comisión multisectorial para la preservación y recuperación
ambiental del Lago Titicaca y sus afluentes, Estado de la calidad
ambiental de la cuenca del Lago Titicaca ámbito peruano, CMLT,
152 pp., 2014.
Crawford, T. and Duchon, C. E.: An improved parametriza-
tion for estimating effective atmospheric emissivity for use
in calculating daytime downwelling long-wave radiation, J.
Appl. Meteorol., 38, 474–480, https://doi.org/10.1175/1520-
0450(1999)038<0474:AIPFEE>2.0.CO;2, 1999.
Dalton, J.: Experimental essays on the constitution of mixed gases,
Manchester Literary and Philosophical Society Memo, 5, 535–
602, 1802.
Dejoux, C. and Iltis, A. (Eds.): Lake Titicaca, A synthesis of Lim-
nological Knowledge, Springer Science, Kluwer Academic Pub-
lisher, 1992.
Delclaux, F., Coudrain, A., and Condom, T.: Evaporation estimation
on Lake Titicaca: a synthesis review and modeling, Hydrol. Pro-
cess., 21, 1664–1677, https://doi.org/10.1002/hyp.6360, 2007.
FAO: The state of the world’s land and water resources for the food
and agriculture (SOLAW) – Managing system at risk, Food and
organization of the United Nation, Rome and Earthscan, London,
ISBN-13: 978-92-5-106614-0, 2011.
Garreaud, R.: Multiscale Analysis of the Summertime
Precipitation over the Central Andes, Mon. Weather
Rev., 127, 901–921, https://doi.org/10.1175/1520-
0493(1999)127<0901:MAOTSP>2.0.CO;2, 1999.
Garreaud, R., Vuille, M., and Clement, A. C.: The climate of the
Altiplano: observed current conditions and mechanism of past
changes, PALAEO, 194, 5–22, https://doi.org/10.1016/S0031-
0182(03)00269-4, 2003.
Gutiérrez, C. B. and Molina, C. J.: Final report: Balance hí-
drico y escenarios de cambio climático en el lago Titi-
caca, Project: Fortalecimiento de Planes Locales de inver-
sión y adaptación al cambio climático en el Altiplano bo-
liviano, IDRC-CRDI, Agua Sustentable, La Paz, Bolivia,
https://doi.org/10.13140/RG.2.2.24230.22083, 2014.
Lhomme, J. P., Vacher, J. J., and Rocheteau, A.: Es-
timating downward long-wave radiation on the An-
dean Altiplano, Agr. Forest Meteorol., 145, 139–148,
https://doi.org/10.1016/j.agrformet.2007.04.007, 2007.
www.hydrol-earth-syst-sci.net/23/657/2019/ Hydrol. Earth Syst. Sci., 23, 657–668, 2019
668 R. Pillco Zolá et al.: Modelling Lake Titicaca’s daily and monthly evaporation
López-Moreno, J. I., Morán-Tejada, S. M., Vicente-Serrano, J.,
Bazo, C., Azorin-Molina, J. I., Revuelto, A., Sánchez-Lorenzo,
F., Navarro-Serrano, E., Aguilar, E., and Chura, O.: Recent tem-
perature variability and changes in the Altiplano of the Bolivia
and Perú, Int. J. Climatol, 36, 1773–1796, 2015.
Maidment, D. R.: Handbook of Hydrology, Mc-GRAW-HILL,
INC., ISBN-13: 978-0-07-039732-3, 1993.
Marti-Cardona, B., Streissberg, T. E., Schladow, S. G., and Hook,
S. J.: Relating fish kills to upwellings and wind patterns at the
Salton Sea, Hydrobiologia, 604, 85–95, 2008.
Penman, H. L.: Natural Evaporation from open water, Bare
Soil and Grass, P. Roy. Soc. A-Math. Phy., A193, 120–145,
https://doi.org/10.1098/rspa.1948.0037, 1948.
Pillco, Z. R. and Bengtsson, L.: Long-term and extreme water levels
variations of the shallow Lake Poopó, Bolivia, Hydrolog. Sci. J.,
51, 98–114, https://doi.org/10.1623/hysj.51.1.98, 2006.
Pillco, Z. R. and Bengtsson, L.: Doctoral theses: Response of Boli-
vian Altiplano Lakes to Seasonal and Annual Climate Variation,
Lund University Publications, 1, 107 pp., 2007.
Pouyaud, B.: Lago Titicaca, Programa estudios TDPS: misión
d’evaluation sur la prise en compte de l’evaporation, GIE Hydro
Consult International, GIE ORSTOM-EDF, 1993.
Revollo, M. M.: Management issues in the Lake Titicaca and
Lake Poopó System: Importance of development a water budget,
Lakes and Reservoirs: Research and Management, 6, 225–229,
https://doi.org/10.1046/j.1440-1770.2001.00151.x, 2001.
Richerson, P. J., Widmer, C., and Kittel, T.: The Limnology of the
Lake Titicaca (Perú-Bolivia), a Large, High Altitude Tropical
Lake, Institute of Ecology Publication, 14, 82 pp., 1977.
Roche, M. A., Bouges, J., and Mattos, R.: Climatology and hydrol-
ogy of the Lake Titicaca basin, in: Lake Titicaca a Synthesis of
Limnological Knowledge, edited by: Dejoux, C. and Iltis, A.,
Kluwer Academic Publisher, 63–88, 1992.
Satgé, F., Espinoza, R., Pillco, Z. R., Roig, H., Timouk, F., Molina,
J., Garnier, J., Calmant, S., Seyler, F., and Bonnet, M.-P.:
Role of climate variability and human activity on Poopó Lake
droughts between 1990 and 2015 assessed using Remote Sensing
Data, Remote Sens., 9, 1–17, https://doi.org/10.3390/rs9030218,
2017.
Singh, V. P. and Xu, C.-Y.: Sensitivity of mass transfer-based evap-
oration equations to errors in daily and monthly input data, Hy-
drol. Process., 11, 1465–1473, 1997.
Talbi, A., Coudrain, A., Ribstein, P., and Pouyaud, B.: Calcul de la
pluie sur le bassin-versant du lac Titicaca pendant l’Holocène,
Comptes Rendus de l’Accadémie des Sciences, Paris, Sciences
de la Terre et des Planètes, 329, 197–203, 1999.
Taylor, M. and Aquize, E. A.: Climatological energy Budget of
the Lake Titicaca (Peru/Bolivia), Internationale Vereinigung für
Theoretische und Angewandte Limnologie: Verhandlungen, 22,
1246–1251, https://doi.org/10.1080/03680770.1983.11897478,
1984.
TDPS: Climatología del sistema de los lagos Titicaca, Desaguadero,
Poopó y Salares Coipasa y Uyuni (TDPS), Comisión de comu-
nidades de europeas, Repúblicas del Perú y Bolivia, convenios
ALA/86/03 y ALA/87/23, LP, Bolivia, 1993.
UNEP.: Diagnóstico Ambiental del Sistema Titicaca-Desaguadero-
Poopó-Salar de Coipasa (TDPS) Bolivia-Perú, División de
Aguas Continentales del Programa de las Naciones Unidas para
el Medio Ambiente y Autoridad Binacional del Sistema TDPS,
Washington, DC, USA, p. 192, 1996.
Vuille, M., Radley, R. S., and Keiming, F.: Interannual climate vari-
ability in the Central Andes and its relation to tropical Pacific and
Atlantic forcing, J. Geophys. Res.-Atmos., 105, 12447–12460,
https://doi.org/10.1029/2000JD900134, 2000.
Wirrmann, D.: Morphology and bathymetry, in: Lake Titicaca, In
a synthesis of Limnological Knowledge, edited by: Dejoux, C.
and Iltis, A., Monographiae Biologicae, 68, Kluwer Academic
Publisher, Dordrecht, 16–22, 1992.
Hydrol. Earth Syst. Sci., 23, 657–668, 2019 www.hydrol-earth-syst-sci.net/23/657/2019/
