كليدواژه :
رگرسيون خطي , ضريب همبستگي پيرسون و ضريب همبستگي متقابل , واكنش آب زيرزميني نسبت به بارش , همبستگي نگار متقابل
چكيده لاتين :
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 watertable
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.
