Regional groundwater flow is critical for understanding a variety of geologic processes. Unfortunately, few studies have considered the impact of gradual decrease in hydraulic conductivity (K) with depth on groundwater flow. In this study, regional groundwater flow through a basin is analyzed under conditions of exponentially decaying K with depth. We found that the development of local versus regional flow systems is sensitive to the decay exponent of K. With higher rates of decrease in K with depth, the penetration depth of local flow systems increases, the regional flow weakens, the amount of recharge decreases, and less water reaches the regional discharge zone. Therefore, the depth decay of K should not be neglected when analyzing hydrologic problems related to regional groundwater flow.

The existence of stagnation points in nested flow systems is relevant to a range of geologic processes. There has been no analytical study on the characteristics and locations of stagnation points in nested flow systems. We derived analytical solutions for hydraulic head and stream function in basins with isotropic and depth‐decaying hydraulic conductivity. The solutions of hydraulic head and stream function are used to identify the positions of stagnation points and discuss the dynamics of groundwater around the stagnation points. Three types of stagnation points are identified by analytical and graphical means. For stagnation points on the basin bottom below the valley, only two regional flow systems converge from opposite directions. For stagnation points on the basin bottom below the regional high, only two regional flow systems part toward opposite directions. In contrast, for stagnation points under counterdirectional local flow systems, flow systems converging from and parting toward opposite directions coexist, and these stagnation points move deeper as the water table configuration becomes more rugged and the decay exponent of hydraulic conductivity increases. Moreover, the dividing streamlines around stagnation points under counterdirectional local flow systems are used to divide the local, intermediate, and regional flow systems accurately, from which the penetration depths of local and intermediate flow systems are precisely determined. A clear understanding of the location of stagnation points is critical for characterizing the pattern of hierarchically nested flow systems and has potential implication in studying solute and mineral concentration distributions in drainage basins.

Near- and off-shore fresh groundwater resources become increasingly important with the social and economic development in coastal areas. Although large scale (hundreds of km) submarine groundwater discharge (SGD) to the ocean has been shown to be of the same magnitude order as river discharge, submarine fresh groundwater discharge (SFGD) with magnitude comparable to large river discharge is never reported. Here, we proposed a method coupling mass-balance models of water, salt and radium isotopes based on field data of ²²³Ra, ²²⁶Ra and salinity to estimate the SFGD, SGD. By applying the method in Laizhou Bay (a water area of ~6000 km²), we showed that the SFGD and SGD are 0.57 ~ 0.88 times and 7.35 ~ 8.57 times the annual Yellow River flux in August 2012, respectively. The estimate of SFGD ranges from 4.12 × 10⁷ m³/d to 6.36 × 10⁷ m³/d, while SGD ranges from 5.32 × 10⁸ m³/d to 6.20 × 10⁸ m³/d. The proportion of the Yellow River input into Laizhou Bay was less than 14% of the total in August 2012. Our method can be used to estimate SFGD in various coastal waters.