عنوان مقاله [English]
Introduction: In hydrological studies, time series are observed as continuous or discrete. Groundwater level and rainfall can be considered as discrete time series. The most common way to measure the dependence between two variables in a discrete time series is to calculate the Pearson correlation coefficient (r). Pearson correlation test is a parametric test that quantitatively measures the linear relationship between variables. This coefficient is essentially a dimensionless index that describes the relationship between two variables numerically. The groundwater level is more or less influenced by rainfall, and this influence may be delayed for a variety of reasons. The process of comparing two time series in different time steps is called cross-correlation. In the cross-correlation analysis, the time-dependent relationship between the dependent and the independent variables is analyzed by computing the coefficients of cross-correlation for various time lags. Results are plotted on a graph called a cross-correlogram.
Mashhad-Chenaran aquifer with an area of about 2527 km2 is the most important aquifer in Khorasan Razavi province. Unfortunately, so far in the Mashhad-Chenaran aquifer, the recharge lag time has not been calculated due to the very complex geological and hydrogeological conditions of the aquifer. In this study, an attempt has been made to calculate the groundwater recharge lag time.
Materials and Methods: In this study, 15 years (Sep. 2001 to Sep. 2016) data of monthly depth to water-table and rainfall have been used . There is 74 active observation well in Mashhad-Chenaran aquifer. Out of 74 wells, 31 well were selected based on geological and hydrogeological conditions. To calculate the rainfall at the observation wells, the daily rainfall data from rain gauge and evaporation stations (25 rain gauge stations and 9 evaporator stations) have been used. First, the cumulative daily rainfall at each station for one month (from 15 months to 15 months later) was calculated. Then, a monthly rainfall raster was prepared using ArcGIS.Finally, the rainfall at the observation well was extracted from the raster file.
Results and Discussion: The correlation coefficient between the groundwater level and rainfall was calculated for the 31 wells at two confidence levels (α = 0.05 and α = 0.1). The lag time was calculated based on the highest correlation coefficient for the two confidence levels. Results showed that the cross-correlation coefficient varied from at least 0.129 in the Tanglshour-Morgh Pardak observation well (very weak) to 0.495 in the Kalateh Sheikhha observation well (moderate). The coefficients of cross-correlation for various time lags were plotted on the cross-correlogram. In cross-correlogram, the month zero was equivalent to October and the month 11 was equivalent to September of the next year. It was observed that the trend of correlation coefficient followed the two specific patterns. In the first group, the water table usually reacts to rainfall after the second month. Then, the correlation coefficient gradually increased. The correlation coefficient reached its maximum in the fourth and fifth months and then decreased with a gentle slope. From the seventh month to the eleventh month the correlation coefficient has become negative. Although there was a significant relationship during these months, there was no cause-and-effect relationship between changes in the water table and rainfall. In the second group, the relationship between the groundwater level and rainfall was not significant at the 95% confidence level. This group includes Doghai observation wells, Qarachah, Shurcheh, Mochenan, Yekehlengeh, Chamgard, Ghahghahe, Tangleshour - Morgh Pardak, and Shorcheh. Changes in the correlation coefficient of these wells were very irregular and the relationship between rainfall and water table changes was probably influenced by other factors. The map of lag time showed that the spatial variations of the lag time completely followed the pattern of the Iso-depth map. In general, the lag time was a function of the depth to the water-table in the Mashhad-Chenaran aquifer. With increasing water depth, the lag time also increased. A closer look at the map showed that in the northern and southern margins of the first hydrogeological unit, the lag time was more than its center. In the northern and southern hydrogeological units, the lag time showed the greatest compliance with the groundwater depth. The amount of lag time from the northern margin of the aquifer to the south gradually increased and finally reached its maximum value in the Akhlamad, Torqabeh-Shandiz.
Conclusion: As discussed previously, the groundwater level was influenced by rainfall, and this influence may be delayed for a variety of reasons. In this study, the groundwater response to rainfall has been estimated from 31 observation wells by cross-correlation method in a period of 15 years (Sep. 2001 to Sep. 2016). The correlation test results showed that after about 2 to 3 months, the effect of rainfall was gradually observed on the groundwater level and the correlation coefficient at the confidence level α = 0.05 and α = 0.1 for 77 % and 97% of wells became meaningful, respectively. The minimum lag time was 2 months and the maximum was 7 months. In general, the estimated lag time was well matched to the groundwater depth and fully followed the Iso-depth map pattern. The amount of groundwater recharge throughout the Mashhad-Chenaran aquifer was mainly controlled by the unsaturated area properties such as thickness, material, etc. Changes in groundwater depth were the major factor affecting the lag time. It seems that with the start of rainfall in late October, groundwater recharge in most wells begin in mid-autumn and continues until late spring. Most of the groundwater recharge takes place in late winter. In summer, rainfall has a very small role in groundwater recharge. In this period, the uncontrolled extraction of water from the aquifer and consequently a sharp and continuous drop in groundwater level plays a major role in water table fluctuations.