**3. Results**

Before assessing the performance of the RegCM4 (in simulating the PET), it is important to quantify the RegCM4 model bias concerning the simulated SW and T2m (as inputs of the HS equation). Figure S1 shows the simulated SW with respect to ERA5 and

ERA5land as well as the difference between ERA5 and ERA5land themselves for the seasons: March −April −May (MAM), June −July −August (JJA), September −October −November (SON) and December −January −February (DJF). From Figure S1, it can be noticed that the RegCM4 is able to reproduce the spatial pattern of the SW with respect to ERA5 and ERA5land in all seasons (Figure S1a–c,g–i,m–o,s–u). Additionally, the RegCM4 overestimates the SW in the MAM season by 10–30 W m<sup>−</sup><sup>2</sup> (Figure S1d,e). In the JJA and SON, the RegCM4 bias ranges from 20 to 40 W m<sup>−</sup><sup>2</sup> (Figure S1j,k,p,q). Lastly in the DJF, the RegCM4 bias becomes 10–20 W m<sup>−</sup><sup>2</sup> with respect to both products (Figure S1v,w). Further, there is no noted difference between ERA5 and ERA5land in all seasons (Figure S1f,l,r,x). It can be noted that the RegCM4 bias is maximized in the JJA and SON and it is minimized in the DJF.

Like SW, the RegCM4 shows a good ability to capture the spatial pattern of the simulated T2m with respect to reanalysis products in all seasons (Figure S2a–c,g—i,m–o,s–u). Additionally, there is no observable difference between ERA5 and ERA5land (Figure S2f,l,r,x), which means that the resolution of the observational dataset does not affect the evaluation of the RegCM4. In addition, an obvious warm-bias is noted in all seasons ranging from 3 to 7 ◦C (Figure S2d,e,j,k,p,q,v,w) with mostly pronounced warm bias during the summer. Such noted bias can be attributed to the fact that land cover of Egypt is mostly represented by desert leading to a low specific/relative humidity. As a result, the convective activity is affected, producing low total cloud cover (not shown), high SW approaching the earth surface and eventually warming the earth surface and the adjacent air layer close to the earth surface. Another possible reason is that the Holtslag scheme is characterized by high turbulent activity, leading to an enhancement of the warming effect produced by the SW.

### *3.1. Influence of Lateral Boundary Condition*

To examine the influence of the lateral boundary condition on the simulated PET, Equation 1 was used to compute the simulated PET. Figure 2 shows the simulated PET (by the EIN15-RegCM4 and NNRP2-RegCM4, respectively) with respect to the ERA5. From Figure 2, it can be noted that the RegCM4 shows good consistency in reproducing the spatial pattern of the simulated PET in comparison with the ERA5 product (see Figure 2a−c,g −i,m −o,s −u). Additionally, it can be observed that there is no significant difference between EIN15 and NNRP2 in all seasons (Figure 2f,l,r,x). Such behavior can be attributed to two reasons: 1—RegCM4 has a similar performance when it is driven either by EIN15 or NNRP2 [23] and 2—RegCM4's physical parameterization dominates over the lateral boundary condition [24]. In addition, it can be observed that both simulations have a bias of 1–2.5 mm day−<sup>1</sup> in the March −April −May season (MAM; Figure 2d,e).

The bias approaches its maximum in the June −July −August season because the RegCM4 shows a bias of 1–4.5 mm day−<sup>1</sup> overall Egypt (JJA; Figure 2j,k). In the September-October-November (SON) season, the bias ranges between 1 and 3 mm day−<sup>1</sup> over coastal regions and middle Egypt and 1–1.5 mm day−<sup>1</sup> over Upper Egypt (see Figure 2p,q). Lastly, in the December-January-February (DJF) season, the bias is around 0.5–2 mm day−<sup>1</sup> over majority of Egypt (Figure 2v,w). From a simple check between Figures S1 and S2 and Figure 2; it can be noted that the PET spatial pattern is more consistent with the SW than T2m. Therefore, calibrating the SW coefficient is more effective than T2m (see Equation (2)). This point will be discussed briefly in Section 3.2.

**Figure 2.** The figure shows the potential evapotranspiration over the period 1981–2017 (PET; in mm day−1) for: MAM season in the first row (**<sup>a</sup>**−**f**); JJA in the second (**g**−**l**); SON in the third (**<sup>m</sup>**−**<sup>r</sup>**); and DJF in the fourth (**<sup>s</sup>**−**<sup>x</sup>**). For each row, EIN15 is on the left, followed by NNRP2; ERA5 is the third from left, EIN15 minus ERA5, NNRP2 minus ERA5 and the difference between NNRP2 and EIN15. Significant difference/bias is indicated in black dots using student *t*-test with alpha equals to 5%.

#### *3.2. Added Value of the Calibrated HS Equation*

As noted in Section 3.1, there is no significant difference between the two simulations. Therefore, the RegCM4-EIN15 simulation was taken (as an example) to examine the added value of the calibrated HS equation compared to ERA5. Figure 3 shows the simulated PET before calibration (HS), after calibration (HSnew) in comparison with the ERA5 and the difference between HSnew and HS. In general, both simulations are able to capture the spatial pattern of the simulated PET against the ERA5 (Figure 3a–c,g–i,m–o,s–u). However, HSnew shows added value over the HS in all seasons particularly in the JJA. Such value is indicated in two points: 1—better ability to reproduce the PET spatial pattern relative to HS and 2—the RegCM4 bias is significantly reduced in all seasons (particularly in the JJA) compared to the HS. For instance, in the MAM season, the HS shows a bias of 1–2.5 mm day−<sup>1</sup> over the entire domain (Figure 3d). On the other hand, the HSnew shows a bias of 0.5 mm day−<sup>1</sup> over the majority of Egypt, with some regions approaching 0.5–1 mm day−<sup>1</sup> and 0.5 to −1.5 mm day−<sup>1</sup> around Lake Nasser (Figure 3e). Qualitatively, the HSnew reduces the PET by 0.6–1.2 mm day−<sup>1</sup> relative to the HS (Figure 3f).

**Figure 3.** The figure shows the potential evapotranspiration over the period 1981–2017 (PET; in mm day−1) for: MAM season in the first row (**<sup>a</sup>**−**f**); JJA in the second (**g**−**l**); SON in the third (**<sup>m</sup>**−**<sup>r</sup>**); DJF in the fourth (**<sup>s</sup>**−**<sup>x</sup>**). For each row, HS is on the left, followed by HSnew; ERA5 is the third from left, HS minus ERA5, HSnew minus ERA5 and the difference between HSnew and HS. Significant difference/bias is indicated in black dots using student *t*-test with alpha equals to 5%.

In the JJA and SON seasons, the HS overestimates the PET over all of Egypt by 1–4.5 mm day−<sup>1</sup> (see Figure 3j,p). After calibration, the HSnew reduces the PET bias to 0.5–1.5 mm day−<sup>1</sup> over the north coast of Egypt and the western desert and −0.5 mm day−<sup>1</sup> around Lake Nasser and middle Egypt (see Figure 3k,q). From a qualitative point of view, the HSnew approximately reduces the simulated PET by 1.6–2.2 mm day−<sup>1</sup> in the JJA (Figure 3l) and by 0.8–1.6 mm day−<sup>1</sup> in the SON (Figure 3r). Lastly, in the DJF, it can be observed that HSnew shows its added value over the HS in middle and upper Egypt where the bias was 0.5–2 mm day−<sup>1</sup> prior to calibration (Figure 3v) and became 0.5–1 mm day−<sup>1</sup> post calibration (Figure 3w). Further, the HSnew approximately reduces the PET by 0.4–1.2 mm day−<sup>1</sup> relative to the HS (see Figure 3x). Overall, it can be noted that the added value of the HSnew (over the HS) can be arranged according to season in the following order: 1—JJA; 2—SON; 3—MAM; and 4—DJF. These findings are in agreemen<sup>t</sup> with the results reported in Figure S1.

To further explore the added value of the calibrated HS, the climatological annual cycle (Figure 4) of the simulated PET of the HS and HSnew (compared to ERA5) was plotted for locations reported by [3]. Only Port-Said was not mentioned because it shows missing values. From Figure 4, it can be observed that the performance of HS/HSnew varies with location and month. For instance, the HS is close to ERA5 in the months of January, February, November and December, while HSnew is close to ERA5 for the rest of the months in Alexandria. For Arish, Marsa-Matruh and Ismailia; HSnew is closer to ERA5 than HS. In Giza and Asswan, the situation is quite different because HS performs better than HSnew in all months. Further, HSnew shows an improved performance over HS in Assyut. Additionally, the situation in Luxor is similar to the one observed in Alexandria. Finally, in Siwa, Dakhla and Kharga, HSnew shows an improved performance (relative to the HS) in comparison with the ERA5.

**Figure 4.** The figure shows the climatological annual cycle of the simulated PET for HS and HSnew compared to ERA5 for locations reported by [3].

### **4. Discussion and Conclusions**

Potential evapotranspiration (PET) is important for monitoring hydrological and meteorological droughts as well as assessing the crop irrigation needs. Additionally, it is a major component in the global terrestrial hydrology cycle. Therefore, the availability of long-term records of PET on a hierarchy of time scales (ranging from hourly to seasonal) is important. The authors of [2] recommend the PM model to compute the PET because it is based on the physical exchange of water and energy between vegetation and atmosphere; however, it requires a large number of meteorological variables (which may not be available for a long time for a variety of locations). Further, uncertainty of the involved meteorological variables may induce a source of uncertainty in the computed PET (and in particular if they are derived from reanalysis products/regional climate models). In addition, it requires a surplus of soil moisture (which is not suitable for the domain of the present study). Hence, there was an urgen<sup>t</sup> need to compute the PET with a simple empirical method (only needs a few meteorological inputs).

Among various empirical methods, the HS model was chosen in this study because it gives a good performance with observational datasets of the PM [7–11]. However, the HS has not been calibrated in Egypt until today. In the present study, the regional climate model (RegCM4) was used to compute the PET comparing between the non-calibrated/calibrated HS with respect to ERA5. The influence of the lateral boundary condition on the simulated PET was also examined. The results showed that switching between EIN15 and NNRP2 did not show a considerable impact on the simulated PET (Figure 2). Spatially, the calibrated HS showed its added value (relative to the original HS model) particularly in the JJA season; such value can be seen by a reduction in the PET bias with respect to the ERA5 (Figure 3). On a point scale, the HS/HSnew performance varies with location and month (Figure 4). Nevertheless, the calibrated HS model can be recommended to construct a regional map of PET of Egypt, predict the daily PET for locations (where station observations are not available) and project the future PET under different global warming scenarios [10,15]. To ensure more robust results of the simulated PET (using the calibrated HS model), a future work will consider the following points:


**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10.3390/ ECWS-7-14253/s1, Figure S1: global incident solar radiation, Figure S2: 2-m mean air temperature.

**Author Contributions:** Conceptualization, S.A.A.; methodology, S.A.A.; software, S.A.A.; validation, S.A.A.; formal analysis, S.A.A. and I.L.; investigation, S.A.A. and I.L.; resources, S.A.A.; data curation, S.A.A.; writing—original draft preparation, S.A.A. and I.L.; writing—review and editing, S.A.A. and I.L.; visualization, S.A.A.; supervision, S.A.A. and I.L.; project administration, S.A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Egyptian Meteorological Authority (EMA) is acknowledged for providing the computational power to conduct the model simulations. Hourly potential evapotranspiration (hPET) was retrieved from the web link https://data.bris.ac.uk/data/dataset/qb8ujazzda0s2aykkv0oq0ctp (accessed on 18 October 2022). However, the monthly mean can be acquired from the authors upon request.

**Conflicts of Interest:** The authors declare no conflict of interest.
