## 1 Introduction  
Hydroologic models have been developed and implemented for simulating surface water and groundwater dynamics and assessing the interactions between them. The quantification of surface water and groundwater interactions (SGIs) typically considers the influences of rainfall, evapotranspiration, or groundwater pumping in a specific groundwater basin [1]. With the advantages of computational technologies, the integrated hydrologic models (IHMs) have made the coupled solutions possible to analyze complex water resource problems relevant to the interactions of surface water and groundwater systems. The processes included in the IHMs can be the overland flow, surface runoff, infiltration, evapotranspiration, soil zone flow, or groundwater interactions and others [2]. In IHMs, the coupled surface and subsurface flow equations are solved either simultaneously or iteratively [3]. These types of models are physical-based models because the physical mechanisms are considered based on the concepts of mass, momentum, or energy conservations. The parameters in the equations can represent physical properties in either the surface water or the groundwater systems. Depending on the complexity of the developed models, the coupled equations in IHMs can be one- or multi-dimensional problems. The implementations of IHMs require comprehensive knowledge of the detailed theory of the IHMs so that the practical problems can be accurately solved. Intensive studies have developed numerous IHMs to assess interactions between surface water and groundwater systems. These widely used models include the SWATMOD model [4], parallel groundwater flow (PARFLOW) model [5], MODHMS model [6], 3D fully coupled groundwater-surface model (an acronym for catchment hydrology model, CATHY) [7], HydroGeoSphere model [8], WetSpass-MODFLOW [9], J2000-MODFLOW model [10], GSFLOW model [11], and MIKE SHE [12]. The SWATMOD model couples the soil water assessment tool (SWAT) model [13] with the three-dimensional groundwater simulation (MODFLOW) model [14]. The MODHMS model considers two-dimensional diffusion surface flow and has been integrated into the MODFLOW model. The main focus of the MODHMS is the dynamics of the surface water flow that provide detailed sources for the MODFLOW model. MIKE SHE is an integrated water resources model that enables the simulations of coupled surface and subsurface water dynamics. The particle-based random walk approach was used in the model to simulate the processes that affect surface water quality. The HydroGeoSphere model allows for simulating stream and surface drainage networks that physically connect rivers to the groundwater systems. The special feature of the model is that the model avoids the problems related to the riverbed-conductance concept, which is a challenging task for most practical implementations. The CATHY model is a process-based model that focuses on quantifying the spatio-temporal variability of soil moisture, groundwater flow and surface runoff. The WetSpass-MODFLOW model is used to evaluate the feasibility of water replenishment through natural reservoirs. The model integrated a spatially-distributed water balance model (WetSpass-M), and a groundwater flow model (MODFLOW-NWT). J2000 is a package that is developed based on the software environment of the geographical information system (GIS). The model is a hydrological model that provides the water balance near the land surface for the MODFLOW focusing on the large catchment areas. The GSFLOW model has integrated the Precipitation Runoff Modeling System (PRMS) [15] with MODFLOW to account for interactions between surface water and groundwater. The GSFLOW model is also a physical-based model developed by the U.S. Geological Survey (USGS). The advantages of the GSFLOW model are the efficiency of PRMS modules and the well-developed MODFLOW-2005 packages that can provide detailed dynamics of groundwater flow. The model uses a flexible and adaptive modular design framework and allows simulations to be performed by only PRMS or MODFLOW-2005, or both.