Many engineers and scientists will use the term "model" to refer to a variety of different things. An equation can properly be called a model because it does "model" or describe the behavior of a physical system. "Model" can also be used to refer to a primary equation and additional supporting equations or graphs that are used to estimate parameters for the primary equation. A good example of this second use of model is the Snyder unit hydrograph model, described in Chapter 6. An input "model" describes how data required to solve equations is acquired, processed, and prepared for use. Finally, a computer program may also be called a "model" because is solves equations that describe a physical system. For clarity, this manual minimizes the use of the term "model" in an attempt to reduce ambiguity. These terms are used:
Method
As noted above, a mathematical model is the equations that represent the behavior of hydrologic system components. This manual uses the term method in this context. For example, the Muskingum-Cunge channel routing method described in Chapter 8 encapsulates equations for continuity and momentum to form a mathematical model of open-channel flow for routing. All of the details of the equations, initial conditions, state variables, boundary conditions, and technique of solving the equations are contained within the method.
When the equations of a mathematical model are solved with site-specific conditions and parameters, the equations describe the processes and predict what will happen within a particular watershed or hydrologic system. In this manual, this is referred to as an application of the model. In using a program to solve the equations, input to the program is necessary. The input encapsulates the site-specified conditions and parameters. With HEC-HMS, the information is supplied by completing forms in the graphical user interface. The input may also include time-series data, paired data functions, or grid data from an HEC-DSS database (USACE, 1995).
Program
If the equations of a mathematical model are too numerous or too complex to solve with pencil, paper, and calculator, they can be translated into computer code. Techniques from a branch of mathematics called numerical analysis are used to solve the equations within the constraints of performing calculations with a computer. The result is a computer program. The term model is often applied to a computer program because the particular program only solves one mathematical model. However, HEC-HMS includes a variety of methods for modeling hydrologic components. Thus it does not make sense to call it a model; it is a computer program.
Programs may be classified broadly as those developed for a specific set of parameters, boundary conditions or initial conditions, and those that are data-driven. Programs in the first category are "hard wired" to represent the system of interest. To change parameters, boundary conditions or initial conditions, the program code must be changed and recompiled. HEC-HMS is in the second category of programs—generalized so that such fundamental changes are not required. Instead, these programs are tailored to the system of interest through changes to data in a database or changes to parameters, boundary conditions, or initial conditions in the input. Also, not all methods can be applied in all circumstances and selections must be made carefully. Criteria to assist in selecting a method for a particular application are listed at the end of each chapter.