*2.4. Assessing Freshwater Conditions and Changes*

Temporal average *T* and *P* for the two comparative periods (*T1*, *P1* for the early period 1930–1949 and *T2*, *P2* for the recent period 1990–2009) are calculated from data on monthly *P* and *T*, as provided by the CRU TS 3.10/3.10.1 worldwide database extending over the period 1901–2009 [27]. Catchment-average values of these temporal averages are further quantified over all CRU grid cells with at least 34% of their area intersecting each considered catchment; Supplementary Figure S1 shows this CRU mask, used to extract catchment-average values of all analysed variables for each study catchment.

While period-average conditions for the atmospheric variables *T* and *P* can be calculated directly from available data series for the two comparative study periods, data on the average water fluxes in the landscape, *ET* and *R*, are not obtainable in this way for the earlier period 1930–1949. To estimate the early-period long-term average values of *ET1* and *R1* and the associated *ET* and *R* changes to the average values *ET2* and *R2* in the recent period 1990–2009, we start by evaluating the long-term average *ET2* value for 1990–2009 from the available *P* and *R* data for this period as *ET2* = *P2* − *R2* = (*ET2*/*P2*) × *P2*, based on the overarching long-term average water balance in each catchment. The data-given range of currently applicable *ET*/*P* values in Table 1 is calculated on this water-balance basis, following previous studies that have found [9,34] and assumed [5,7,8] long-term catchment-average changes in water storage to be near-zero over such long time periods.

To further estimate the change in average *ET* between the two 20-year periods, we follow the approach of previous studies [5,7,8] in estimating this total change as:

$$
\Delta ET = ET2 - ET1 \approx \Delta ETl\text{lim} + \Delta ETl\text{r.}\tag{1}
$$

The second equality is approximate in assuming that total Δ*ET* involves two main change components: Δ*ETclim* driven by climate change and Δ*ETirr* driven by irrigation changes. By evaluating these components, *ET1* can be estimated from Equation (1) as *ET1* = *ET2* − Δ*ETclim* − Δ*ETirr*.

Furthermore, from this quantification of *ET1*, the corresponding average *R1* can be consistently estimated as:

$$\begin{aligned} \text{R1} & \approx P1 - ET1 = P1 - \{ET2 - \Delta ETl\text{dim} - \Delta ETl\text{ir} \} = P1 - \{(P2 - R2) - \Delta ETl\text{dim} - \Delta ETl\text{ir} \} \\ &= R2 - \{(\Delta P - \Delta ETl\text{dim}) - \Delta ETl\text{ir} \}, \end{aligned} \tag{2}$$

with Δ*P* = *P2* − *P1* being the *P* change, and

$$
\Delta R = R\angle -R\,1 \approx \left(\Delta P - \Delta E \text{T} \text{lcm}\right) - \Delta E \text{T} \text{ir} \\
 r = \Delta R \text{lcm} + \Delta R \text{ir} \\
 r \tag{3}
$$

being the total *R* change between the two periods. The climate-driven component of total Δ*R* is thus quantified as Δ*Rclim* = Δ*P* − Δ*ETclim* and the corresponding irrigation-driven component is quantified as Δ*Rirr* = <sup>−</sup>Δ*ETirr*.

To estimate the climate-driven change component Δ*ETclim*, we further relate the period-average temperature (*T1*, *T2*) and precipitation (*P1*, *P2*) to the corresponding average potential evapotranspiration (*PET1*, *PET2*) based on the Langbein functional relationship [35] and further to corresponding *ET* conditions in each period (*ETclim2*, *ETclim1*) based on the Turc functional relationship [36]. From these quantifications, the climate-driven *ET* change can be estimated as Δ*ETclim* = *ETclim2* − *ETclim1* = *f*(*PET2*,*P2*) − *f*(*PET1*,*P1*). Alternative functional relationships for *ETclim* = *f*(*PET*,*P*) may be used for this estimation but previous work has shown small differences in resulting changes of long-term catchment-average *ET* by use of alternative such functions [34].

Furthermore, to estimate the irrigation-driven change component Δ*ETirr* = *ETirr2* − *ETirr1*, we quantify the average irrigation water withdrawal per irrigated area in each period (*Iww1*, *Iww2*) based on: the data and associated best-fit function for the temporal *Iww* evolution (Figure 2c); the area actually irrigated in absolute terms (*Aai2* from Figure 3a for recent period 1990–2009) and relative to total cell area (*Aai\_rat2* from the map in Figure 3b for the recent period); and the assumption that more or less all water used for irrigation feeds back into the average *ET* over each period. The latter assumption is supported by previous studies of different irrigated areas of the world [17,22,23], as well as by recent findings of *ET* variations correlating well with concurrent, independently determined transpiration variations [16]. As irrigation is applied precisely for feeding into transpiration, it is reasonable to assume that it largely does so, or otherwise feeds into increased evaporation, either directly from soil water, or from potentially added surface water runoff; in any case, the applied irrigation water may be expected to largely feed into the total *ET* of each catchment. Moreover, a wide range of different possible *Iww* and *Aai\_rat* evaluation scenarios are investigated (as described further in the following uncertainty analysis section) and may be expected to also cover uncertainty effects associated with varying parts of the irrigation water use (*Iww*) and / or the relative irrigated catchment area (*Aai\_rat*) feeding into *ET* in each catchment. In general, based on these considerations and assumptions, an irrigation-driven part of total *ET* in each period is estimated as *ETirr* ≈ *Iww* × *Aai\_rat*. The difference between the resulting values of *ETirr* for each of the two periods then provides the irrigation-driven change Δ*ETirr* = *ETirr2* − *ETirr1*.

In the absence of available data on the spatial distribution of irrigated area in the earlier period 1930–1949, we assume that the relative grid-cell irrigated area in that period (*Aai\_rat1*) is some fraction (*αirr*) of the corresponding relative irrigation area in the recent period (i.e., that *Aai\_rat1* = *Aai\_rat2* × *αirr*). The fraction *αirr* is further assumed to be more or less the same for all grid cells and is estimated as such from the total irrigated area over Greece (Figure 3a) in the early period (total Greek *Aai1*) relative to that in the recent period (total Greek *Aai2*), that is, as *αirr* ≈ (total Greek *Aai1*)/(total Greek *Aai2*).

Table 2 summarizes a set of estimated input variables values, needed in the above-described calculations for each study catchment. Footnotes to Table 2 explain how these values are estimated and this evaluation is in the following referred to as the base case scenario for each catchment. This scenario is obtained using mean (or other relevant characteristic) values of the main input variables for each catchment and time period. In general, values that to some degree differ from those in the base case scenario may also be estimated for uncertain variables, depending on choices of data and assumptions made for the variable evaluation. To account for such evaluation uncertainty, we also consider possible alternative values of main uncertain variables, as explained further in the following section.


*◦***C)** 12.1 12.4 11.7 12.1 15 14.8 14.4 14.4 11.6 12 *P* **c (mm/year)** 676 630 663 622 773 693 861 767 637 602 *ET***/***P* **d** 0.59 0.59 0.62 0.59 0.59 *Iww* **e (mm/year)** 0.692/2736 = 253 8.25/13,963 = 591 253 591 253 591 253 591 253 591

*T* **c (**


*Aai* **(km2)** 2736 e 11,046 f 2394 g 9665 f 342 g 1381 f 547 g 2255 f 2189 g 8791 f *Aai\_rat* 0.015 h 11,046/178,984 = 0.062 0.015 h 9665/157,550 = 0.061 0.016 h 1381/21,434 = 0.064 0.017 h 2255/31,958 = 0.071 0.015 h 8791/147,026 = 0.06 a Spatial extent of each catchment. b *Per1*: 1930–1949, *Per2*: 1990–2009. c Spatio-temporal averages from the monthly CRU TS3.10.01 data set [27]. d Using the mean *ET*/*P* value from the three local catchments with data over mainland Greece and that from the Peloponnese local catchments over the Peloponnese. e From the national reported data on irrigated areas and irrigation water withdrawals [30,31] (Figure 2). f Spatial average values for each catchment with the area actually irrigated obtained from the GMIAv5.0 map dataset [32] (Figure 3). g Assuming that the ratio of areas actually irrigated in this catchment relative to that in the mainland Greece and the Peloponnese is more or less the same in 1930–1949 as in 1990–2009. h With *Aai\_rat1* estimated from: *Aai\_rat1* = *Aai\_rat2* × *αirr* and *αirr* ≈ *Aai1*/*Aai2* = 0.25 in the base case scenario.
