**3. Methodology**

processes like those taking place in river catchments. That is why we used regional climate models from COordinated Regional Climate Downscaling Experiment (CORDEX) [6] driven by global models from the CMIP5. As part of CORDEX framework, EURO-CORDEX initiative

**Figure 2.** Available water capacities (AWCs) (in mm water column/1 m soil) computed in the 12.5 km EURO-CORDEX grids (black circles) obtained as the sum of topsoil and subsoil AWCs (at 1 km × 1 km resolution) extracted from the European Soil Database (ESDB) and averaged over the 12.5 km × 12.5 km grid cells centered in the model grids for the

**No. Regional climatic modeling center Regional climate model** 

2 KNMI (Royal Netherlands Meteorological

3 SMHI (Swedish Meteorological and Hydrological Institute)

4 SMHI (Swedish Meteorological and Hydrological Institute)

5 SMHI (Swedish Meteorological and Hydrological Institute)

on the future evolution of water cycle components in the selected basins.

Institute)

118 Engineering and Mathematical Topics in Rainfall

areas of interest.

**(RCM)**

1 DMI (Danish Meteorological Institute) HIRHAM5 ICHEC-EC-EARTH

**Table 1.** Numerical experiments with regional and global climate models used to assess the influence of climate change

**Global climate model** 

**(GCM)**

RACMO22E ICHEC-EC-EARTH

RCA4 ICHEC-EC-EARTH

RCA4 MPI-ESM-LR

RCA4 IPSL-CM5A-MR

In our approach, we define the local water cycle components (precipitation, potential evapotranspiration, and potential runoff) based on the two-level model of the soil exploit by the Palmer Drought Severity Index (PDSI) [14], like in the approach presented in [2]. The top layer of soil is assumed to hold 25.4 mm of moisture. The amount of moisture that can be held by the two-layered soil is a soil-dependent value—available water capacity (AWC)—which must be provided as an input parameter [14].

The PDSI measures the cumulative effect of monthly precipitation deficit/surplus with respect to a value that is climatologically appropriate for existing conditions (CAFECs) in a given region [14]. The computation of the PDSI requires precipitation, air temperature, soil characteristics (i.e., available water capacity—AWC), and the latitude of the location to estimate the length of day over which the solar radiation is received (for deriving potential evapotranspiration). In order to calculate the PDSI for a certain month (i), one has first to determine the moisture anomaly index ZINDi for that month (i):

$$\text{ZINDI} = \text{k (P} - \alpha \text{PE} - \text{\ $PR\text{-}γPRO} + \text{\$ PL)} \tag{1}$$

$$\text{PDSIi} = \text{PDSIi} - 1 + \text{ZINDi} / 3 - 0.103 \text{ PDSIi} - 1 \tag{2}$$

components and related indices in the selected case studies. In this context, we analyzed the linear trends of basin-averaged PDSI and potential runoff up to 2100 to assess the impact of climate change on meteorological drought under moderate and worst-case RCP scenarios.

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**Figure 3** presents the correlation coefficients linking observation-derived components of the Palmer water balance and mean monthly streamflow (Qmed) at the gauging stations for each selected basin (Arges, Mures, Prut, Siret, and Somes). Due to data availability constraints, monthly values of ZIND, PRO, and the difference between precipitation and evapotranspiration (P-PE) are spatially averaged over the Romanian area of each river catchment, except the Prut basin where the spatial means cover the whole transboundary catchment. The monthly streamflow values are taken from available observations recorded at stations as close as possible to the river outlet. The selection of catchments and stations for streamflow observations

**Figure 3.** Correlation between monthly components of Palmer Drought Severity Index—soil moisture index ZIND (dotted line) and potential runoff PRO (black line) computed from CRU observations and observed mean monthly streamflow (Qmed) at the gauging stations associated for the basins of rivers Arges, Mures, Prut, Siret, and Somes over the Romanian territory. The analyzed intervals with available data are specified in brackets. Gray line illustrates the

correlation linking the difference between precipitation and potential evapotranspiration (P-PE) and Qmed.

**3.1. Validation of Palmer's water balance model at the catchment level**

where k is an empirical weighting factor, specific for each region; α, β, γ, and δ are coefficients for evapotranspiration, soil water recharge, runoff and water loss from the soil, computed to link the potential quantities and real ones; and P, PET, PR, PRO, and PL represent the observed precipitation, Thornthwaite potential evapotranspiration [15], potential recharge, potential runoff and potential water loss from the soil. Potential evapotranspiration (PET) is the maximum evapotranspiration in the given environmental conditions, when soil moisture is not a limiting factor. Potential recharge (PR) is the amount of moisture required to bring the soil to its AWC from the available moisture at the beginning of the month. Potential run-off (PRO) is defined as the difference between the potential precipitation and the potential recharge. Runoff is assumed to occur if the Palmer soil model reaches its available moisture capacity, AWC. Potential loss (PL) is the amount of moisture that could be lost from the soil provided that the monthly precipitation is zero [14].

Palmer [14] built the index based on the simple representation of the components shaping the hydrological balance in a given area from the United States of America. We used the selfcalibrated version of the PDSI [16] that automatically calibrates the behavior of the index at any location by replacing empirical constants in the index computation with dynamically calculated values.

The water balance model proposed by Palmer uses the Thornthwaite parametrization for potential evapotranspiration [15], which is solely based on the air temperature, and the solar radiation contribution is empirically derived under the current climate conditions. Under the climate change, the Thornthwaite empirical approach seems to overestimate the upward trends in potential evapotranspiration [4, 17, 18]. The Penman-Monteith method uses a more physically oriented parametrization to estimate the potential evapotranspiration explicitly based on temperature, net radiation, air pressure, air humidity and wind data [10]. Thus, we have extracted and/or computed the Penman-Monteith version of potential evapotranspiration from the EURO-CORDEX archive [10, 19] and observed CRU data. We replaced Thornthwaite's potential evapotranspiration with the Penman-Monteith one by modifying accordingly the C++ code presented in [16]. We selected as a baseline for the PDSI computation the reference periods included in the interval 1951–2015, depending on the available data from numerical experiments and/or observations.

In our approach, the observed and simulated components of water cycle (precipitation, potential evapotranspiration, and potential runoff) and the PDSI values were spatially averaged across the studied basins, having in mind that the catchment level is a natural unit. On the other hand, the spatial averaging increases the signal-to-noise ratio while still providing useful information for water resource assessment and management.

The modeling results regarding future evolution of PDSI and its components under RCP scenarios are further used to assess their impact on drought over the catchments under climate change conditions. Usually, there are differences in the climate projections due to model-related biases and natural climate variability. To address this issue, we used the available results from the five-member ensemble taken from EURO-CORDEX archive (**Table 1**) to compute PDSI components and related indices in the selected case studies. In this context, we analyzed the linear trends of basin-averaged PDSI and potential runoff up to 2100 to assess the impact of climate change on meteorological drought under moderate and worst-case RCP scenarios.

#### **3.1. Validation of Palmer's water balance model at the catchment level**

PDSIi = PDSIi − 1 + ZINDi/3–0.103 PDSIi − 1 (2)

where k is an empirical weighting factor, specific for each region; α, β, γ, and δ are coefficients for evapotranspiration, soil water recharge, runoff and water loss from the soil, computed to link the potential quantities and real ones; and P, PET, PR, PRO, and PL represent the observed precipitation, Thornthwaite potential evapotranspiration [15], potential recharge, potential runoff and potential water loss from the soil. Potential evapotranspiration (PET) is the maximum evapotranspiration in the given environmental conditions, when soil moisture is not a limiting factor. Potential recharge (PR) is the amount of moisture required to bring the soil to its AWC from the available moisture at the beginning of the month. Potential run-off (PRO) is defined as the difference between the potential precipitation and the potential recharge. Runoff is assumed to occur if the Palmer soil model reaches its available moisture capacity, AWC. Potential loss (PL) is the amount of moisture that could be lost from the soil provided

Palmer [14] built the index based on the simple representation of the components shaping the hydrological balance in a given area from the United States of America. We used the selfcalibrated version of the PDSI [16] that automatically calibrates the behavior of the index at any location by replacing empirical constants in the index computation with dynamically

The water balance model proposed by Palmer uses the Thornthwaite parametrization for potential evapotranspiration [15], which is solely based on the air temperature, and the solar radiation contribution is empirically derived under the current climate conditions. Under the climate change, the Thornthwaite empirical approach seems to overestimate the upward trends in potential evapotranspiration [4, 17, 18]. The Penman-Monteith method uses a more physically oriented parametrization to estimate the potential evapotranspiration explicitly based on temperature, net radiation, air pressure, air humidity and wind data [10]. Thus, we have extracted and/or computed the Penman-Monteith version of potential evapotranspiration from the EURO-CORDEX archive [10, 19] and observed CRU data. We replaced Thornthwaite's potential evapotranspiration with the Penman-Monteith one by modifying accordingly the C++ code presented in [16]. We selected as a baseline for the PDSI computation the reference periods included in the interval 1951–2015, depending on the available data from numerical experiments and/or

In our approach, the observed and simulated components of water cycle (precipitation, potential evapotranspiration, and potential runoff) and the PDSI values were spatially averaged across the studied basins, having in mind that the catchment level is a natural unit. On the other hand, the spatial averaging increases the signal-to-noise ratio while still providing use-

The modeling results regarding future evolution of PDSI and its components under RCP scenarios are further used to assess their impact on drought over the catchments under climate change conditions. Usually, there are differences in the climate projections due to model-related biases and natural climate variability. To address this issue, we used the available results from the five-member ensemble taken from EURO-CORDEX archive (**Table 1**) to compute PDSI

ful information for water resource assessment and management.

that the monthly precipitation is zero [14].

120 Engineering and Mathematical Topics in Rainfall

calculated values.

observations.

**Figure 3** presents the correlation coefficients linking observation-derived components of the Palmer water balance and mean monthly streamflow (Qmed) at the gauging stations for each selected basin (Arges, Mures, Prut, Siret, and Somes). Due to data availability constraints, monthly values of ZIND, PRO, and the difference between precipitation and evapotranspiration (P-PE) are spatially averaged over the Romanian area of each river catchment, except the Prut basin where the spatial means cover the whole transboundary catchment. The monthly streamflow values are taken from available observations recorded at stations as close as possible to the river outlet. The selection of catchments and stations for streamflow observations

**Figure 3.** Correlation between monthly components of Palmer Drought Severity Index—soil moisture index ZIND (dotted line) and potential runoff PRO (black line) computed from CRU observations and observed mean monthly streamflow (Qmed) at the gauging stations associated for the basins of rivers Arges, Mures, Prut, Siret, and Somes over the Romanian territory. The analyzed intervals with available data are specified in brackets. Gray line illustrates the correlation linking the difference between precipitation and potential evapotranspiration (P-PE) and Qmed.

was constrained by the data availability—they are mostly over the Romanian territory. In the case of Prut transboundary catchment, we used observations from two hydrometric stations: Dranceni in Romania and Brinza in Republic of Moldova. In general, there are quite large correlation coefficients illustrated in Figure 9 showing that the PDSI represents reasonably well the local process taking place in the analyzed catchments.

An interesting feature is the fact that ZIND correlations with Qmed are systematically larger than the correlation of P-PE with the Qmed, which implies that the Palmer model brings added value in assessing anomalies of the water deficit or surplus (ZIND) compared with the simple difference between precipitation and potential evapotranspiration (P-PE). Also, PRO correlations with Qmed are, in general, larger in cold season months compared to ZIND correlations with Qmed. This can be explained by the fact that the Palmer model does not take snow, frozen soil, and related processes into consideration—the precipitation is immediately transferred into the soil. That is why in winter months, any simultaneously precipitation-related correlations with Qmed are low. On the other hand, PRO depends on soil recharge linked to soil available capacity. Remarkably high correlations all over the year link basin-averaged PRO with Qmed at the Brinza station in the Prut catchment. An explanation could be that Brinza station is very close to the Prut outlet. Streamflows recorded at the Brinza station are integrating the runoff from the whole basin which is not the case for the streamflows recorded at the Dranceni station. However, the time interval used to compute these correlations at the Brinza station is shorter (1985–2015), implying lesser statistical significance. The results presented in **Figure 3** suggest that ZIND and PRO values could be used, at least for certain months and catchments, as simple and robust indicators of anomalies in water cycle components (such as soil moisture and runoff) at the basin level.

However, the fact that the multiannual pattern of the two water cycle components (precipitation and potential evapotranspiration) is reproduced, to some extent, by the regional climate models provides a certain level of confidence when analyzing their future evolution and

**Figure 5.** Observed and simulated multiannual means (1970–2005) of monthly precipitation (in mm/month) averaged over the Prut basin. The shaded band illustrates the simulated values from the five-member ensemble of regional climate experiments taken from the EURO-CORDEX archive (see **Table 1**). The black line represents the observation-derived

values of potential evapotranspiration based on IMDROFLOOD gridded precipitation data.

**Figure 4.** Observed and simulated multiannual means (1970–2005) of monthly evapotranspiration (in mm/month) averaged over the Prut basin. The shaded band illustrates the simulated values from the five-member ensemble of regional climate experiments taken from the EURO-CORDEX archive (see **Table 1**). The black line represents the

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related drought indices in the area of interests under climate change scenarios.

observation-derived values of potential evapotranspiration based on CRU data.
