*3.2. Link between Meteorological and Hydrological Droughts*

#### *3.2. Link between Meteorological and Hydrological Droughts 3.2. Link between Meteorological and Hydrological Droughts* 3.2.1. Establishing Regression Function

3.2.1. Establishing Regression Function The coefficient of determination (R2) and regression coefficient (a) extracted from linear regression equations (Table 1) showed that a significant relationship existed between SDI and SPI, and it increased up to the 9-month time scale and then decrease in the 3.2.1. Establishing Regression Function The coefficient of determination (R2) and regression coefficient (a) extracted from linear regression equations (Table 1) showed that a significant relationship existed between SDI and SPI, and it increased up to the 9-month time scale and then decrease in the The coefficient of determination (R2) and regression coefficient (a) extracted from linear regression equations (Table 1) showed that a significant relationship existed between SDI and SPI, and it increased up to the 9-month time scale and then decrease in the case of the 12-month time scale. The coefficient of determination (R<sup>2</sup> ) of the 6-months and the 9-month time scale was relatively higher as compared to the other two time scales. Moreover, the correlation of SPI and SDI was higher at upstream sub-basin 1 of the Soan River Basin as compared to downstream. For instance, sub-basin 1 and sub-basin 2 had 0.66 and 0.63 values of R<sup>2</sup> based on a 9-month time scale respectively. The regression lines with the related data points are shown in Figure 6 which may be utilized for the prediction of hydrological droughts using the meteorological droughts information.


the 9-month time scale was relatively higher as compared to the other two time scales. Moreover, the correlation of SPI and SDI was higher at upstream sub-basin 1 of the Soan River Basin as compared to downstream. For instance, sub-basin 1 and sub-basin 2 had 0.66 and 0.63 values of R<sup>2</sup> based on a 9-month time scale respectively. The regression lines with the related data points are shown in Figure 6 which may be utilized for the prediction

) of the 6-months and

**Table 1.** Results of Regression modeling developed between SDI on SPI. of hydrological droughts using the meteorological droughts information.

case of the 12-month time scale. The coefficient of determination (R<sup>2</sup>

*Appl. Sci.* **2022**, *12*, x FOR PEER REVIEW 8 of 14

(**a**) For Sub-Basin 1

**Figure 6.** *Cont.*

(**b**) For Sub-Basin 2

**Figure 6.** The linear relationship between SDI and SPI at the four selected time scales. **Figure 6.** The linear relationship between SDI and SPI at the four selected time scales.

3.2.2. Moving Average Analysis and Lag Time Identification 3.2.2. Moving Average Analysis and Lag Time Identification

A moving average analysis was performed at multiple time scales to better assess the correlation between SPI and SDI, see Figure 7. Results show that the variations of SPI and SDI were quite comparable; however, the differences between them do exist. In general, a strong correlation was observed between SPI and SDI at the upstream sub-basin 1, i.e., CC = 0.66. Overall based on the correlation analysis with different lag times, it was observed that at both sub-basins, the SDI was 1 month lagging behind SPI at 3-month and 12-month time scales and 2 months lagging for 6–month and 9-month time scales. This period of lagging time was in accordance with the prior study [7]. A moving average analysis was performed at multiple time scales to better assess the correlation between SPI and SDI, see Figure 7. Results show that the variations of SPI and SDI were quite comparable; however, the differences between them do exist. In general, a strong correlation was observed between SPI and SDI at the upstream subbasin 1, i.e., CC = 0.66. Overall based on the correlation analysis with different lag times, it was observed that at both sub-basins, the SDI was 1 month lagging behind SPI at 3-month and 12-month time scales and 2 months lagging for 6–month and 9-month time scales. This period of lagging time was in accordance with the prior study [7].

**Figure 7.** Moving average analysis for lag time identification between SPI and SDI at sub-basins 1 and 2 for different time scales. (**a**,**b**) 3 months, (**c**,**d**) 6 months, (**e**,**f**) 9 months, (**g**,**h**) 12 months.

### **4. Discussion**

Climate change includes the variations in the behavior of climatic parameters, e.g., precipitation, evapotranspiration, etc. [40]. Whereas anthropogenic activities include landuse/land cover changes, irrigation area expansion, increased water diversion, water conservation practices, etc. During the last decades, the Soan basin experienced precipitation and runoff variation (with a change point in 1998 [30]) due to both climate change and anthropogenic activities [30,32]. Based on the drought analysis performed in the current study, notable variations between SPI and SDI values were found over the past three decades. It could be mainly because of major changes in agricultural land, forest, settlement, water bodies, and bare land in addition to natural climate variability [41].

To further justify, a trend analysis of precipitation, runoff, and runoff coefficient had been performed. The analysis resulted, in the case of sub-basin 1 a declining trend in precipitation was observed during the years 1983–2015, as shown in Figure 8a. For instance, the average annual precipitation decreased from 1983–1997 (1950 mm) to 1998–2015 (1570.50 mm). This decline in precipitation was significant in sub-basin 1, while little variation (no significant trend) was found in the case of sub-basin 2 with an average value of 1115 mm and 1065 mm for 1983–1997 and 1998–2015 respectively. For sub-basin 1, the annual runoff depth had a decreasing trend (i.e., an average of 174.44 mm for 1983–1997, and 84.00 mm for 1998–2015) during the study period (left panel Figure 8b) and, the runoff coefficient had no significant trend (left panel Figure 8c). Similarly, in the case of sub-basin 2, runoff depth has a decreasing trend, while runoff coefficient has no significant trend as the *p*-value is greater than alpha. The variations in the trend direction of runoff, and runoff coefficient in the case of sub-basins 1 and 2 could be mainly due to land-use changes, e.g., 71 km<sup>2</sup> and 1611 km<sup>2</sup> increase in agriculture land was observed in sub-basins 1 and 2 respectively from 1983–1997 to 1998–2015 [30].

Moreover, the higher decreasing rate in runoff compared to precipitation and change point showed the possible effect of anthropogenic activities [32]. It was anticipated because of a significant increase in the intensity of crops and the construction of large numbers of small dams from 1998- onward [27]. These significant variations were also anticipated due to the significant number of development projects under the Government of Punjab, Pakistan, which comprises the development of ponds and mini-dams for rainwater harvesting and to increase the intensity of agriculture. The initiative of these developments was to increase the storage for crop and drinking purposes, which might have caused the increase in evaporation, and water use for the growing population, ultimately decrease in surface runoff and increasing in probability of drought occurrence. In addition to that, a reservoir could decrease the frequency, duration, and severity of drought events downstream of the dam, and irrigation practices can primarily influence hydrological droughts by consuming streamflow and groundwater, which typically results in a decrease in streamflow and groundwater levels [16,42]. Hence, the Simly reservoir operation, as well as seasonal irrigation practices, could have an impact on the statistical relationship among drought indices.

The difference in SPI and SDI trends could be due to evapotranspiration or lag time between rainfall and runoff, which could predict the propagation of meteorological to hydrological droughts. Drought propagation may also be influenced by basin characteristics such as soil moisture, land use, and the relationships between streamflow and groundwater. A time lag was used to perform cross-correlation between SPI and SDI, which acknowledged the sequence between SPI and SDI and demonstrated that meteorological drought events could be used to predict hydrological droughts in relatively small watersheds with less anthropogenic activities.

(**c**)

**Figure 8.** Temporal Variation of (**a**) Precipitation, (**b**) Runoff depth, and (**c**) Runoff Coefficient at sub-basin 1 and 2. **Figure 8.** Temporal Variation of (**a**) Precipitation, (**b**) Runoff depth, and (**c**) Runoff Coefficient at sub-basin 1 and 2.

#### **5. Conclusions 5. Conclusions**

This study concludes that the frequency of both hydrological and meteorological droughts increased in the Soan River Basin during the study period. At various time scales, Sub-basin 1 was subjected to more frequent meteorological moderate drought and hydrological drought events. The current study was also designed to investigate the relationship between meteorological and hydrological drought events and SPI and SDI by developing a simple linear function between them. The results of a linear regression between SPI and SDI show an increase in regression coefficients with increasing time scale and became stronger until the ninth month. Climate change and anthropogenic activities (i.e., land use/land cover changes) are the main reasons that cause the variations between these two types of droughts. Moreover, the hydrological drought events commonly lagged 1–3 months (subject to the time scale and sub-basin) from the meteorological This study concludes that the frequency of both hydrological and meteorological droughts increased in the Soan River Basin during the study period. At various time scales, Sub-basin 1 was subjected to more frequent meteorological moderate drought and hydrological drought events. The current study was also designed to investigate the relationship between meteorological and hydrological drought events and SPI and SDI by developing a simple linear function between them. The results of a linear regression between SPI and SDI show an increase in regression coefficients with increasing time scale and became stronger until the ninth month. Climate change and anthropogenic activities (i.e., land use/land cover changes) are the main reasons that cause the variations between these two types of droughts. Moreover, the hydrological drought events commonly lagged 1–3 months (subject to the time scale and sub-basin) from the meteorological drought events. The dissimilarities between these two types of droughts became larger due to

climatic variation and might be due to human activities as well. Conclusively, this study provided drought propagation and the basis for long-term drought forecasting and, thus, can be employed for early warning water resources management and as an extension of this current study can be to assess the climate change impacts on hydrological drought at the basin scale.

**Author Contributions:** Conceptualization, A.N.S. and M.W.; methodology, M.A. and A.A.; software, M.A.; validation, M.W., J.E.L. and M.A.; formal analysis, I.A. and A.A.; investigation, F.u.H.; data curation, A.N.S. and M.W.; writing—original draft preparation, J.E.L.; funding acquisition. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2020S1A5B8103910).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data is provided in the form of tables and figures.

**Acknowledgments:** The Authors appreciate the NRPU-HEC projects.

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