Volcanic lakes are different from the common reservoirs of meteoric origin because of the interaction with the hydrothermal system of the volcano. The hot fluids (gas + liquid) of volcanic origin rise through the bottom of the lake resulting in strong acidic water and a variable temperature usually tens of degrees above the ambient. Contrariwise, the water of the lake infiltrates through the soil and changes the thermodynamics and the path of hydrothermal circulation. The balance established in this complex system is very delicate: the survival of the lake depends on the particular combination of meteoric recharge, runoff, water loss by infiltration within the volcanic edifice (seepage) and evaporation from the lake surface. The water level of the lake and its temperature are closely linked to the activity of the deep magmatic source and surveillance of the lake can provide important information for the monitoring of the volcano. Not all of the factors influencing the evolution of the lake are directly measurable, as several authors have addressed. In particular the seepage is unmeasurable, as it is sublacustrine. These unknown fluid fluxes can only be estimated from the calculation of the mass and energy balances of the lake. Numerical simulations can help to study the temporal evolution of the lake and to understand the physical dynamics behind seepage. Our simulations are based on the model of Poás volcanic system (National Park in Costa Rica), hosting Laguna Caliente. This volcano is well known, and long-term monitoring has shown that the crater lake is particularly active, and well represents the main features of volcanic lakes, in general.
The simulations were obtained with a multiphase, multicomponent integral finite differences simulator, TOUGH2. We focused mainly on the effects of the different thermodynamic conditions of the hydrothermal source and on the permeability of the rocks that make up the volcanic cone and surround the lake. Due to the geometry of the conical summit of the volcano, the simulations are carried out on a two dimensional domain representing the axial section of the system. The computational domain assigned to the simulation of the lake extends to 125 m from the axis of symmetry to a depth of 50 m, while the whole domain is 1 km wide and 250 m deep, for a total of 2288 elements. The base of the domain communicates with a source of fluid (water and steam) that is hot and pressurized. In this way we simulate the ascent of deep fluids of the hydrothermal system of Poás. A first set of simulations is run considering a stationary lake, whose temperature and water level are fixed in time. This is useful to investigate how the presence of the lake affects the hydrothermal circulation of the volcano. The volcanic lake, however, is an important boundary condition that changes through time as a function of its interaction with the volcano itself. To describe this effect, we included the lake in the computational domain in a second group of simulations. In these simulations the same porous media flow model is used to approximate the dynamics of the lake, assuming a very high permeability and a porosity of 1. In this way, the model describes the changes in water level and temperature as a result of the interaction between meteoric water and hydrothermal system. Even if this is an elementary representation, it shows the development of convective cells in the simulated lake. The calculation of the Rayleigh number shows that the real lake is definitely in convection, hence, to achieve a realistic simulation this efficient heating mechanism cannot be overlooked. In a third group of simulations we introduced the contribution of the rain. The meteoric recharge, in fact, strongly affects both temperature and water level of the lake. In this way it is possible to simulate the birth of Laguna Caliente, moreover, this contribution can hardly be neglected for a realistic description of the lake evolution. For each group we performed multiple simulations with different permeability along the bottom of the lake to simulate a greater or lesser "waterproofing", mainly due to the presence of chemical compounds dissolved in water (in particular molten sulphur pools). Other simulations have been made instead to study the changes of the volcano and Laguna Caliente in function of the temperature and pressure of the hydrothermal source. Therefore, we simulated the injection of fluids, hottest and most pressurized corresponding to a higher activity of the volcano, and the injection of fluids with lower temperature and pressure to simulate periods of lower activity. The results show that the mutual interaction between the hydrothermal system and the lake is very narrow. Changes in characteristics and thermodynamic conditions in depth are recorded by the volcanic lake and they involve a different evolution over time.

1. crater lake seepage
2. numerical modeling
3. TOUGH2