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constituents. all averaged over the stream cross seCllon for . a specified time period. In a few models. attempts have heen madc to include certam aspects of the hlOlogical enVIf()TI- ment. with variables such as food supply. competitive spe- cies. and predators, Most riverine habitat models are one-dimensional: the value assigned to a variable represents the average condition for a single cross section, or sometimes for a short reach of stream (<5-7 times channel width). Examples of com- monly used one-dimensional models are the Wetted Perime- ter Model (Nelson 1984)3, the Instream Temperature Model (Theurer et a\.. 1982), the Habitat Quality Index (Binns and Eiserman, 1979). and the Habitat Evaluation Procedures (USFWS 1980). A few are two-dimensional, where both the longitudinal and lateral distributions of vari- ables are measured and analyzed. Two examples of two- dimensional physical microhabitat models are the Washing- ton method (Collings 1972) and the Physical Habitat Simu- lation System (Stalnaker 1979; Milhous 1979). At least one habitat modeling system--the Instream Flow Incremental Methodology (IFIM) described by Bovee (1982) - com- bines the use of one-dimensional and two-dimensional models. No three dimensional habitat models are now in use, although PHABSIM can potentially be modified to incorporate three dimensions. Physical process models in three dimensions that provide input to three-dimensional microhabitat models are not yet operational. The multitude of riverine habitat models were discussed by Wesche and Rechard (1980), Loar and Sale (1981), and Morhardt (1986). A further distinction among riverine habitat models can be made by considering whether they are empirical or based on physical processes. The investigator who uses an empiri- cal model typically must remeasure the model variables to quantify the habitat whenever the river flow changes. A physical process model is useful for predicting (simulating) changes in the environment under conditions that were not (or could not be) measured. Most often, these simulations are restricted to unmeasured discharges and hydrologic events, but can also demonstrate changes in channel mor- phology, waste water treatment, or the discharge of altered thermal effluents (among a myriad of possibilities). An advantage of the empirical approach is that the investi- gator does not need to understand why a variable changes, but merely know how to measure it when it does change. It is also possible to include many variables in an empirical , model, since functional linkages among them are not neces- sary. Most empirical models for river management simula- tions have three primary disadvantages: 1) They are data intensive, requiring the remeasurement of all variables whenever conditions change. 2) The total range of conditions for each variable is difficult to describe e~pirically and thus resists generalization. Consequently, any variables included in the model that are untested over a range of conditions tend to reduce 3Nelson, F. A. 1984. Guidelines for using the wened perimeter (WETP) computer program of the Montana Department of Fish, Wildlife, and Parks. Bozeman, MT. 25 p. + appendices. Avail- able from Montana Fish and Game Department, Helena, MT, USA. 16 transferability and the model reprcscnts only the condi- tions that prevailed at a specific time and place. :; l Perhaps most imp()nanl. empIrical m()dcls are con- strained in their capabilities 10 quantify habilat condi- tions resulting from unique combinations of variables that were not measured. This third problem is illustrated by the inability of a purely empirical model to estimate the impact of a new water development project until after the project has been built and operated. Such a constraint severely limits the utility of the model for planning. and usually leads to a request for severe "constraints" being placed on the operational flexibility of new projects. This can also lead to conflicts between instream uses of water and the development of water. The use of physical and chemical processes to derive models for habitat analyses overcomes many of the disad- vantages of empirical models, although the different models vary widely in accuracy and precision. These models gener- ally require fewer data. are capable of more generalization, and (when used properly) enable predictions of changes in the habitat under conditions when no measurements were made. The most serious drawback is their being based on mathematics, and thus requiring that the user have substan- tial skill and understanding. Use of these models often requires considerable judgment regarding the reliability of the results, based on knowledge of model limitations, per- formance, and calibration accuracy - in contrast to empiri- cal models, which are rather straightforward but require multiple data sets. Hydraulic Models Many aspects of the hydraulic component of habitat ana- lyses in rivers are similar, regardless of the size of the stream. However, the procedures for measurement and prediction of certain variables differ and some of these differences are size related. The primary hydraulic variables of concern are the water surface elevation (stage), and the distribution of velocities. Water Surface Elevations (Stage) - To determine the depth distribution in a stream, one needs two types of infor- mation: the cross sectional bed elevations and the water sur- face elevation. The depth at any point on the cross section can be calculated merely by finding the difference between the bed elevation and the water surface. Bed elevations can be determined by surveying or sounding techniques. Because water surface elevations change whenever the flow changes, determinations of the water surface elevations at unmeasured discharges are a necessity. Three methods are routinely used to determine the rela- tion between water surface elevation and discharge: (1) Step-backwater models, which incorporate the Manning equation and energy balancing concepts (Chow 1959); (2) Models that use the Manning equation at a cross section (Chow 1959; King and Brater 1963; Morisawa 1968); and (3) Regression models that relate water surface elevation to discharge (Leopold et al. 1964; Carter and Davidian 1968). Each of these approaches has its strengths and limitations, and its applicability is a function of the stream characteris- tics. The step-backwater model is most applicable in low gradient rivers with uniform to gradually varied flow, and F' -