QS—Underground contribution

This contribution is an unknown quantity in the balance. It is calculated by Equation (1) in this form:

$$\mathbf{Q\_s} = \mathbf{E\_{LC}} + \Delta \mathbf{H} - \mathbf{P\_{LC}} - \mathbf{R\_s} - \mathbf{I}\mathbf{R\_E} - \mathbf{R\_{IR}} + \mathbf{Q} \tag{2}$$

ELC—Evaporation from the lake and evapotranspiration from the reed bed

Evaporation from the lake (or from the free water) was calculated using the energy balance method which hypothesizes a regime in which the net solar radiation absorbed by the water for a certain period of time is partly released as sensible heat to land and air in contact with the water, and partly used to transform the water into vapor [26]. The calculation was performed using temperature, global solar radiation, and reflected solar radiation data, measured at the Candia meteorological station. As we mentioned above, the reed bed grows on the lake and is always saturated with water, so that its evapotranspiration is linked to the evaporation of the lake. The ETC (evapotranspiration of the reed bed) was thus given an equal value to that of the lake evaporation multiplied by 1.7 in the months when the reed bed is growing, i.e., June, July, August, and September, and exactly equal to the evaporation from the lake in the other months of the year when it is not growing [27]. The two values obtained, multiplied by the relative area covered by the reed bed, were added and included into the balance equation together.

#### ΔH—Variations in the lake level

The daily variations in the level of the lake, obtained from the values registered by the water gauge of Candia, were calculated to obtain the actual monthly variation of the lake volume. The variation is taken with its sign, i.e., if the level falls, there will be a corresponding decrease in the volume and the value will be negative, while an increase in volume is calculated as positive.

#### Q—Surface discharge (outflow)

The last term in the balance Equation (2) is the discharge at the outlet, i.e., the quantity of water exiting the lake. The discharge is measured using the weir at the closing section of the lake that regulates its activity, and is connected with the levels of the lake that are continuously measured through the equation.

By inserting each term of the balance in the Equation (2), we could obtain the value of the monthly and annual underground contribution for different years, from 1993 to 2019. The underground contribution thus obtained takes account both the contribution of groundwater via resurgences and any hyporheic flow of infiltration water returning to the lake underground. These two contributions must be separated if we want to estimate only the groundwater source. Thus, to identify the groundwater source it is necessary to use a general hydrological balance equation, applied not only on the lake but on the whole catchment, so we consider a control volume represented by a volume that has the base coinciding with the waterproof layer of the aquifers and the upper limit above the vegetation; the general equation of water balance follows:

$$\mathbf{P} = \mathbf{E}\mathbf{T} + \mathbf{Q} + \Delta\mathbf{V} \tag{3}$$

where

P is the precipitation on the whole control volume;


Thus, using the general balance equation [20], which also includes evapotranspiration and the quantity of infiltrated water, and applying Thornthwaite's method for determining the annual soil water cycle, we defined the portion of hypodermic discharge, which allowed us to determine the effective contribution of groundwater source to the lake:

$$\mathbf{G}\_{\overline{S}} = \mathbf{Q}\_{\overline{S}} - \mathbf{D}\_{\overline{i}} = \mathbf{Q} + \mathbf{E}\_{\mathbf{L}\overline{C}} - \mathbf{R}\_{\overline{S}} - \mathbf{I}\mathbf{R}\_{\overline{E}} + \boldsymbol{\Delta V} - \mathbf{P}\_{\mathbf{L}\overline{C}} - \mathbf{R}\_{\overline{R}\overline{R}} + \mathbf{E}\mathbf{T} + \mathbf{I}\mathbf{R} \tag{4}$$

where


$$\text{ET}\_{\text{P}} = 16 \ast \text{K} \ast \left(\frac{10 \ast \bar{\text{T}}}{\text{I}}\right)^{\text{s}}$$
