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

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 semiarid 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 water 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 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 becomes evident at the downstream end of the system, where Lake Poopó is situated. In recent years this lake suffered extreme water shortages, including its complete drying out in December 2015 (Satgé et al., 2017).

Lake Titicaca and the TDPS system within the Altiplano.

Lake Titicaca has a large surface area of about 8500 km

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 anthropogenic pressure and due to the evident strong global warming that this region experiences. Previous studies of Lake Titicaca's evaporation have all been based on monthly meteorological observations. Due to the importance of lake evaporation, detailed calculations using daily as well as monthly observations may be necessary. Consequently, this paper investigates different methods for calculating evaporation using 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 functioning and sensitivity. The main problem with Lake Titicaca's evaporation estimation is the lack of high-resolution temporal data. Taking into account only the mass transfer models 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 sensitive to vapour pressure. On the other hand, random errors in input data could have a significant effect on evaporation estimation 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

It can generally be assumed that during a year the lake water 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 function must also be included in this approach.

One of the first evaporation studies for Lake Titicaca applied the water
balance method using measurements for the period 1956–1973 (Carmouze et al.,
1977) and estimated a mean annual lake evaporation of 1550 mm year

Climatological and hydrological components of Lake Titicaca for 1966–2011.

This study applies the methodologies mentioned above using the frequent and accurate hydro-meteorological measurements 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.

Lake Titicaca is a unique biosphere due to its large depth and volume, high
elevation, and tropical latitude. It is located in the northern part of the
Peruvian–Bolivian Altiplano, between latitudes of 15

Lake Titicaca basin with sub-basins and major and smaller lakes.

The Lake Titicaca watershed is a part of the TDPS system (Titicaca,
Desaguadero, Poopó and Salares) within the Altiplano (Revollo, 2001).
Lake Poopó is considered a terminal lake, with only one discharge
event into the downstream 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 km

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 average precipitation over
the Lake Titicaca basin is about 800 mm year

The daily air temperature over Lake Titicaca is rather constant throughout
the year, usually varying between 7 and 12

Four evaporation estimation conventional methods were applied in this study: water balance, energy balance, mass transfer and the Penman method. These approaches have previously been used by other researchers to estimate Lake Titicaca's evaporation at a monthly time step (Carmouze, 1992; Pouyaud, 1993; Delclaux et al., 2007). The methods are briefly described as follows.

The energy balance approach (Maidment, 1993) which comes from the integral energy balance
equation of a reference volume at the air–water interface, the evaporation component in terms of latent heat flux
is

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

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):

The Penman equation is a combination of energy balance and mass transfer used for
evaluating open water evaporation (Penman, 1948):

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

The evaporation during individual days is not important for the water balance but is only important over longer periods like months. However, since the equations for calculating evaporation are not linear, the monthly evaporation computed from monthly mean meteorological data may differ from what is found when data with a higher time resolution are used. In the aerodynamic approach the wind speed is multiplied by the vapour deficit. The energy balance approach 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 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.

For this study, hydro-meteorological parameters and water surface
temperature were measured near Lake Titicaca's bank for 24 consecutive
months (2015–2016). Vertical lake temperature profiles were also acquired
periodically. Observations were taken at 15 min intervals. These records
were averaged to daily and monthly values. A Campbell Scientific
research-grade automatic weather station (AWS) was installed at the Isla de la Luna (latitude 16

Hydrological data, such as inflow to the lake, were observed 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

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 representative 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).

Location of observation points.

Tables 2 and 3 summarize hydrological and meteorological measurements used in this study. Subscripts for vapour pressure are “w” for water, “s” for saturated air vapour pressure and “a” for actual air vapour pressure. The computed variables required for evaporation calculations are given in Table 4.

Monthly mean of hydrological variables observed during the 2015–2016 period.

Monthly averages of main climatic variables observed during the 2015–2016 period.

Monthly average parameters for evaporation calculations for the 2015–2016 period.

Short-wave radiation was measured, while long-wave radiation 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

Monthly average radiative budget for Lake Titicaca in 2015–2016.

Detailed energy balance computations over the period 2015–2016 should give
good estimates of the total lake evaporation for that period. After 24 months the lake surface temperature 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 1700 mm year

Change of heat storage in 2015–2016.

The computed monthly evaporation using monthly average data and the energy
balance method was somewhat higher in 2016 than in 2015, 1725 mm year

Monthly evaporation computed using energy balance approach.

From the energy balance and the water balance methods, the annual
evaporation from Lake Titicaca was estimated in the range of about 1700 mm year

Comparison of monthly evaporation computed by energy balance and mass transfer method for 2015.

The monthly evaporation computed by mass transfer over the 2 years is
compared with the energy balance calculations in Fig. 7 for 2015 and in Fig. 8
for 2016. The computed annual evaporation by the last method was 1700 mm year

Comparison of monthly evaporation computed by energy balance and mass transfer method for 2016.

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 balances differs from the three other methods. The
water balance method yielded 1672 mm year

Monthly actual evaporation calculated by the four methods for the period from January 2015 to December 2016.

Descriptive statistics of monthly evaporation calculated by the four methods for the period from January 2015 to December 2016.

Water balances were computed for the long-term period and continuous
available data in 1966–2011 as well. During the computation the A

Monthly mean water balances for Lake Titicaca for the period 1966–2011.

When calculating evaporation using daily data, it was found that there are
large differences between the methods and ignoring the water balance method.
The maximum daily evaporation using the mass transfer method was 12 mm day

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 determined with high resolution. Detailed water
temperature measurements are not available, however. Instead, it was assumed
that the temperature changes at a steady rate through individual months.
August is an example, since the temperature for the whole month changed very
little (0.2

Daily evaporation computed by the mass transfer (shaded staples) and energy balance (filled staples) method.

When annual evaporation was determined using daily data instead of monthly mean data, there was hardly any difference for the mass transfer method. As indicated above it is 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 evaporation 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 balance 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 Penman 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 imagery, as reported in other lakes (e.g. Marti-Cardona et al., 2008). According to this observation, the temperatures acquired for this study are likely to be an overestimation.

The spatial distribution of Lake Titicaca's surface temperature 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 heat
storage changes. Over the larger period of air temperatures observed at
the Copacabana weather station (1966–2016), the particular months in 2015–2016
have been characterized by the strongest El Niño dry phenomena during
the last 50 years (

Due to uncertainty of most observed data such as river inflow 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
estimate 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
temperature. 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

However, for the purpose of assessing climate change effects 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
modelling the lake evaporation, the first model only depends on the
solar radiation data, and, additionally, the second one depends on the air temperature
factor; thus both models cannot be applied broadly. In the Penman model based
on the adjusted wind coefficient, the mean annual evaporation is 1620 mm year

All data can now be freely accessed through requests to rpillco@umsa.edu.bo.

RPZ coordinated the research and was directly involved in all steps, from fieldwork to proofreading. He built the database, computed the evaporation for the different models, analyzed the results, and prepared figures and tables. LB contributed to the conceptual approach and structure of the paper. He supervised and validated the calculations and contributed to the writing of the objectives and the scientific background of the paper. RB revised and validated the calculations and collaborated on the writing, mainly for Sect. 5. BMC contributed to the discussion and analysis 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 maintenance of the gauging stations and data quality assurance. MPB improved the conceptual approach of the paper. She also helped to obtain 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.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Integration of Earth observations and models for global water resource assessment”. It is not associated with a conference.

We would like to express our sincere appreciation 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