§1.2 Process of Groundwater Modeling
The process of groundwater modeling involves a number of different steps and the essential steps are shown as Figure 1.1.
1.Defining purpose
Groundwater models are usually applied for predicting the consequences of the proposed actions such as groundwater development scenarios or waste disposal.Models can be used for analyzing groundwater flow system by assembling and organizing field data and formulating ideas about dynamics of flow systems.Models can be also used for studying processes in generic geologic settings like river-aquifer systems.It is essential to identify clearly the purpose of modeling so that the needs of modeling efforts and accuracy are determined.The purpose of modeling also decides on the dimensionality and time dependency of a model.
Figure 1.1 Process of groundwater modeling
Answers to the following questions will help in the determination of the types of model applications and the levels of modeling efforts：
（1）Will the model be used for the prediction of system's response，analysis of flow systems，or study of the processes in a certain generic geologic settings?（Really necessary to build a model?）
（2）What questions do you want the model to answer?（Questions to be answered by the model.）
（3）Can an analytical model provides the answer or must be a numerical model is constructed?（Analytical or numerical model?）
Examples of prediction the consequences of a proposed action：
（1）Groundwater development scenarios：Extension and magnitude of the cone of depression around a pumping station.
（2）Groundwater pollution：Plume of groundwater contaminants from a waste disposal site.
（3）Interaction between groundwater and environment impacts of a reservoir on groundwater level.
Example of interpretation：
（1）Framework for assemble field data synthesizing field data；testing assumptions about the system；indicating the further field work.
（2）Flow system analysis：pathlines，flow rate，pattern of recharge and discharge boundary conditions.
（3）Sensitivity analysis：Identification of important system parameters.
2.Building conceptual model
The purpose is to simplify the field problem and organize the associated field data so that the system can be analysis and modeled more readily.Conceptual model is a quantitative representation of groundwater systems in terms of aquifer-aquitard layers，boundary conditions hydrogeological parameters，hydrological stresses，flow patterns，and water balance components.Field visits are necessary to gain the modeler first impression about the area to be modeled.The conceptual model is simplified as much as possible yet retain the important hydrogeologic condition so that it adequately reproduces system behavior.
Steps in Building a Conceptual Model
Step 1 Construction hydrogeologic framework.
（1）Schematization of aquifer systems（geological cross sections）.
1）Defining hydrogeological units.
2）Classification of hydrogeological units.
3）Hydrogeological cross sections.
4）Types of aquifers（hydrogeological cross sections）.
5）Thickness and lateral extent of aquifers and confining beds（hydrogeological cross sections）.
Lateral extent of aquifers can be determined from cross sections and then projected on the map；Natural hydrogeological boundaries are boundaries of the extent of aquifers；Construction of contour maps of groundwater level，elevation of bottoms of aquifers and confining beds；Aquifer thickness can be calculated from contour maps，or directly calculated from cross sections；Construction of isopach map of aquifers and confining beds.
（2）Boundaries of aquifer systems（hydrogeological cross sections）.
1）Types of boundaries.
Physical boundaries（fixed）—Impermeable rocks；Impermeable faults；Large bodies of surface water.
Hydraulic boundaries（movable）—Groundwater divides；Streamlines.
2）Mathematical representation.
3）Setting boundaries.
Hydrogeological boundaries—Impermeable rocks；Impermeable faults；Large rivers，lakes，and oceans；Regional groundwater divides.
Distant boundaries—Artificial boundaries for transient simulation where head and flow are not influenced by the stresses.
Hydraulic boundaries—Groundwater divides；Streamlines；Groundwater head contour line.
4）Simulating boundaries.
Specified head boundaries—River；Lake；Ocean；Water level.
Specified flow boundaries—Seepage to stream，spring flow，underflow，seepage to/from bedrocks，local hydraulic boundaries.
No-flow boundaries—Impermeable bedrock，impermeable fault zone，seepage a groundwater divide，a streamline，a freshwater/saltwater interface.
Head-dependent flow boundaries—Leakage to/from river，lake，reservoir.
（3）Hydrogeologic parameters.
1）Parameters—Hydraulic conductivity，K；Transmissivity，T=Km；Storage coefficient，Ss；Specific yield，Sy；Porosity，n；and so on.
2）Pumping tests.
3）Laboratory tests.
4）Empirical data.
（4）Extent and rate of areal recharge（precipitation，irrigation）.
（5）Extent and rate of areal discharge（evapotranspiration）.
（6）Locations and rate of wells（discharge/recharge）.
（7）Spatial and temporal distribution of interaction between groundwater and surface water（river，canal，lakes，spring flow）.
（8）Locations of observation wells and Hydrograph of groundwater of groundwater head.
Step 2 Defining the flow system.
Conceptualize the movements of groundwater through the system.
（1）General direction of groundwater flow.
（2）Pattern of recharge and discharge.
（3）Connection between ground-surface water.
（4）Information for analysis—Groundwater head contour maps；Hydrochemical information；Isotopes；Groundwater temperature information；Hydrographs of groundwater head；Hydrographs of surface water level.
Step 3 Preparing the water budget.
Groundwater balance：Inflow+Outflow=Changes in storage.
Inflow—Precipitation；surface water；Underflow；Irrigation.
Outflow—Evapotranspiration；Spring flow；Baseflow to stream；Pumping；Underflow.
3.Selecting computer code
A computer code is a computer programme which solves the mathematical model of groundwater flow or contaminant transport numerically.There are many computer codes available.The selection of a suitable code depends on the complexity of the conceptual model and the purpose of study.The main considerations are：
（1）Types of model：flow model，particle tracking or solute transport model.
（2）Time dependency：steady or transient model.
（3）Dimensionality：one，two，quasi-three，or fully three dimensional model.
（4）Ability to describe the aquifer properties：homogeneous or heterogeneous；isotropic or anisotropic media.
（5）Ability to include various hydrological stresses.
（6）User friendliness.
（7）Requirements on the computer facility.
Widely-applied model—MODFLOW；MOC3D；MT3D；MODPATH；Processing Modflow（PM）；Visual Modflfow（VM）；Groundwater Modeling System（GMS）；Finite Element Modflfow（FEM）.
4.Designing numerical model
The design of numerical model includes the selection of modeling area，design of model grids，selection of stress periods and time steps，setting model boundaries and initial conditions.The conceptual model will be the bases for the design of the numerical model.The purpose of the modeling will dictate the sizes of grids and time steps.The memory and computing time of computers and the computer code may have limitations on total number of grids and time steps.
5.Determination of model inputs
The inputs to the model include initial and boundary conditions，hydrogeological parameters，and hydrological stresses.The data for all these inputs have to be entered to all grid points for all stress periods.
（1）Data for defining physical framework.
Geologic map and cross sections showing the areal and vertical extent and boundaries of the system.
1）Topographic map showing surface water bodies and divides.
2）Contour map of land surface elevation.
3）Contour maps showing the elevation of the base the stratigraphic units.
4）Maps showing the extent and thickness of stream and lake sediments.
（2）Hydrogeologic framework.
1）Schematization of aquifer systems.
2）Thickness and lateral extent of aquifers and confining beds.
3）Boundaries of aquifer systems.
4）Maps and cross sections showing the storage properties of the aquifers and confining beds.
5）Maps and cross sections showing the distribution of hydraulic conductivity/transmissivity.
6）Maps showing the extent and thickness of stream and lake sediments.
7）Groundwater head contour maps.
8）Locations of observation wells and measurements.
（3）Hydrological stresses.
1）Extent and rate of areal recharge（precipitation irrigation）.
2）Extent and rate of areal discharge（evapotranspiration）.
3）Locations and rate of wells（discharge/recharge）.
4）Spatial and temporal distribution of interaction between groundwater and surface water（river，canal，lakes）.
5）Spatial and temporal distribution of springs.
6）Locations of observation wells and hydrographs of groundwater head.
6.Calibration of the model
（1）Why to calibrate the model?The purpose of calibration is to establish the model that can reproduce the field measured groundwater heads or concentrations.
（2）How to calibrate the model?The calibration forces the model calculations approximate the field measured values through the adjustment of aquifer parameters or stresses by trial-and-error method or automated parameter estimation method requiring the measurements of groundwater heads or concentrations.
（3）Assessment of calibration.Mean error；maximum error；root mean square error（RMS）.
（4）Sensitivity analysis.Objectives—Uncertainty of model parameters on model results；Identification of most important parameters.
Sensitivity coefficients—Head or concentration；RMS（root mean square）.
Procedures for sensitivity analysis—Before and after model calibration；Systematic vary parameter values.
7.Verification of the model
To check whether the calibrated model has the predictive power，the calibrated model is applied to another period of time where a second field data are available.The model should also be able to reproduce the field measured values of groundwater heads or concentrations with hydrological stresses in this period.
8.Application of the model
The calibrated model is used to predict the response of the aquifer system to future events.In the prediction the model is run with calibrated aquifer parameters and future hydrological stresses.Some hydrological stresses are the proposed actions（such as abstraction）.Others are natural uncontrolled stresses（such as recharge from precipitation）.
9.Presentation of results
Clear presentation of modeling processing and results is essential for the effective communication of the modeling effort.The report on the modeling study should include chapters like：
（1）Introduction.
（2）Hydrogeological conceptual model.
（3）Numerical model setup.
（4）Model calibration.
（5）Model application.
（6）Summary and conclusions.
10.Postaudit
（1）Validation of the model prediction.
（2）Not yet a normal part of modeling.
（3）Groundwater models did not accurately predict the future due to ① error in conceptual model or/and ② errors in estimation of assumed future stresses.
Groundwater modeling is an iterative process.Steps outlined above may have to be repeated.Assumptions and even simplifications are necessary in the modeling because of the complexity of hydrogeological formations on the one hand and the lack of sufficient field data on the other hand.Models are only approximations of reality，but not reality itself.Therefore，groundwater modeling is not only a science but also an art.The science behind modeling can be learned relatively easily from many standard text books or short courses.However，the art of modeling can only be learned from practicing how to apply models.A successful modeler will have to know the science of the modeling and practice the art of modeling.
Great progress has been made in numerical modeling of groundwater in China since 1970's.Compared with the work done in some foreign countries，the numerical modeling of groundwater in China overlooked work steps of model purpose definition，sensitivity analysis，model postaudit and redesign.These steps play an important role in model validation and refinement.Groundwater model shouldn't be only constructed for answering pressing questions，it should be also developed for the purpose of groundwater system management and improved successively as new information source.