Ray K. Linsley was formerly the Head of the Department of Civil Engineering at Stanford University . As a professor, and later as a consulting engineer, he was a pioneer in the development of hydrologic simulation. He authored numerous papers and textbooks and has received world-wide recognition for his contributions to the field of hydrology.

The following paper was written during his tenure at Hydrocomp, Inc. Although it was written thirty years ago, in 1976, many of Linsley's points are equally valid today. While computers have become increasingly affordable, powerful, and fast, hydrologic simulation remains an underutilized tool for hydrologic analysis.

Why Simulation?

(Adapted from Ray K. Linsley, "Why Simulation?", Hydrocomp Simulation Network Newsletter, Volume 8, Number 5, September 1976.)

The question is often asked, why should we use simulation in hydrology? What is wrong with conventional techniques which have been in use for many years? Doesn't simulation require a lot more data? Doesn't it cost more and take more time? Is it really worthwhile to use computer simulation when we have so little data?

A Brief History

Simulation techniques in hydrology started about 1960 in research at Stanford University . After preliminary research had indicated that it was feasible to write a computer program which would simulate hydrologic processes and compute streamflow from rainfall data, we selected a number of target specifications for this program. (1) First, we decided that the program should run continuously to simulate many years of streamflow. This requirement is necessary because the only logical way to correctly simulate the runoff in a particular storm is to start with the antecedent conditions created by previous storms. Second, since long records are a key to adequate determination of probability in hydrology, the program must be designed to run rapidly enough to minimize the cost of simulating periods of 30 or 50 years. Third, the program should be physically based to allow the hydrologist to extrapolate beyond the range of observed data. It should represent the physical processes of hydrology with such fidelity that the user feels confident that if it reproduced streamflow in the range of observed flows, it would also accurately reproduce flows in the very high or very low ranges which are not ordinarily observed.

The general characteristics of a simulation model are based on concepts that were developed many years ago but could not be utilized because of computational limitations. The concept of infiltration which is the heart of continuous simulation was first proposed by Horton in 1933. The idea of continuous soil moisture accounting was suggested by Linsley and Ackermann in 1942. In 1934 Zoch first introduced the use of routing to construct the runoff hydrograph. The basic concepts of computer simulation were recognized as preferable approaches to hydrologic analysis long before the computational ability was available.

Traditional Analysis vs Hydrologic Simulation

Prior to the development of simulation, a number of techniques were used in hydrology to arrive at estimates of flow when no observed values existed. All of these procedures utilize approximations because the work had to be done with pencil and paper, and it was not possible to deal in detail with the problem and expect a solution within a reasonable time. Classical methods resorted to simplification of procedures. For example, in the unit hydrograph technique for constructing a graph of streamflow, it was assumed that flow rate was in linear proportion to volume of runoff. This assumption conveniently permits superposition of runoff from several storm increments. This is not absolutely correct, however, and in watersheds where large flood plains exist the errors may be very large. The computer permits a much more detailed calculation using kinematic routing which relies on the actual stream cross-sections and the theory of flow in channels.

Similarly, in estimating the runoff from rainfall, relatively simple relationships were employed. The most complex of these used time of year, an antecedent precipitation index, and the duration of rain as parameters in a statistically derived relationship. By contrast, simulation allows for the continuous calculation of soil moisture, infiltration, and the movement of moisture in overland flow to the stream. A detailed computation represents the actual physical processes realistically, and consequently provides a more reliable basins for extrapolation in time or space.

The development of the computer has permitted the modern hydrologist to approach hydrologic problems without making many of the simplifying assumptions that are inherent in the classical solutions. For example, the calculation of runoff should be carried forward on a relatively short time interval. However, for pencil and paper computations it was customary to use time intervals no shorter than 6 hours and more frequently 12 or 24 hours. With modern computer simulation it is routine to compute on a one-hour interval which more accurately deals with infiltration and hydrograph characteristics for small watersheds.

In classical procedures it was customary to start with average rainfall over the watershed although it was recognized that when the actual rainfall varied widely above and below this average, the computation could not be correct. It is now possible to use computer simulation to calculate runoff independently over many segments of the watershed. Each segment represents an area of different rainfall, soil conditions, vegetative cover, or any one of many factors which might influence runoff. The degree to which the watershed is divided is limited only by the fact that each additional segment requires a complete repetition of the simulation and thus does increase computer time.

Simulation models of the continuous type permit the generation of streamflow for watersheds of any size for as long as is required. Streamflow synthesis for a period of 500 years has been undertaken in connection with research at Stanford University . The procedure yields the equivalent of an observed flow record which can be used for planning purposes in the same way that an observed record would be used.

One of the weaknesses of observed streamflow records lies in the fact that changing conditions in the watershed may have so altered streamflow that the records collected 25 or 30 years ago are no longer comparable to the records collected today. For planning and design it would be desirable to be able to use flows which might be expected in the future as a result of prospective changes in the land use or other factors which might change streamflow. Streamflow records cannot provide such information but simulation can. By calibrating a simulation model to the streamflow of the last three or five years, simulated streamflow for a period extending as far back as the available rainfall records can represent flows which would have occurred under current conditions. Flows for future conditions can be simulated by adjusting the parameters of the simulation model to assumed future conditions.

Issues of Data and Cost

The comments above offer many reasons why simulation is to be preferred over conventional methods. What about the charge that it is more difficult and more costly? Simulation requires input of a considerably larger quantity of data than is normally used in most conventional hydrologic studies. However, in the conventional study an equal volume of data is usually reviewed, but because of difficulties of hand computation, only selected data items are actually used--usually much less than 10 percent of the available data. It is a relatively simple matter to get the required streamflow and rainfall data from responsible federal agencies.(2) The actual work of preparing the data for use may, in fact, be less than that of selecting from this same mass of data the cases to be studied by conventional means.

It is often implied that because one has limited data, one should use approximate methods. However, there is nothing about approximate methods that makes better use of the limited data and most such approximate methods have been demonstrated to be highly unreliable. There are many techniques which can be used to adapt the limited data to simulation. By careful use of a simulation program, data of poor quality can be checked, missing records completed, and a considerable extension of the record can be made. The most critical data for simulation are the rainfall data. Without rainfall data, it is impossible to carry out a simulation study. However, it is also impossible to carry on a study by any other reasonably adequate hydrologic technique without rainfall.

Simulation techniques cannot compete with the use of empirical formulae for computation of design flows on the basis of time and cost, but can easily compete with conventional methods such as rainfall-runoff relations and unit hydrographs. It will usually take no more time to develop the necessary data for simulation than it will require to develop the estimates desired. Meanwhile, one simulation run will provide an abundance of data which can answer many hydrologic problems. Although the data from the run may not be required in all its detail for a study of flood flows, it may subsequently have considerable value in dealing with streamflow volumes or minimum flows. If one wishes to explore the effect of changing vegetal cover on the watershed, of increasing the amount of urban land use, or other possible land use changes, this is easily done with simulation. Using conventional methods, is would be difficult, if not impossible, to estimate the effect of such changes.


In summary then it can be said that the answer to "Why simulate?" is given by the following points:

  1. Simulation is generally more adequate because it involves fewer approximations than conventional methods.
  2. Simulation gives a more useful answer because it gives a more complete answer.
  3. Simulation allows adjustment for change which conventional methods cannot do effectively.
  4. Simulation costs no more than the use of reliable conventional methods (excluding empirical formulae which should not be used in any case).
  5. Data for simulation is easily obtained from the Climatic Data Service or the Geological Survey.(2)
  6. No more work or time is required to complete a simulation study than for a thorough hydrologic analysis with conventional methods. Often the time and cost requirements are less.
  7. In any case, if the time and cost are measured against the quality and completeness of the results, simulation is far ahead of the conventional techniques.
  8. Even though the available data are limited, simulation can still be useful because the data are used in a physically rational computational program.


(1) Norman H. Crawford and Ray K. Linsley developed the earliest hydrologic simulation models at Stanford University .

(2) Hydrometeorologic data are now readily available on CD-ROM databases.

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