D is the depth at the same point, 

 S is the substrate at that same point, and 



P , P ., and P are the functional relationships between the habitat suitability 

 and velocity, depth, and substrate in the environment. 

 These functional relationships are species specific and are referred to a habitat 

 suitability criteria. 



For discrete elements, /', the average velocity, depth, and substrate values are used 

 to solve Equation 6. The discrete elements are: 



(7) 

 (8) 

 (9) 



where v , d-, and s- are the average values for the velocity, depth, and substrate in 

 element'/. The terms Ky(i), Kj(i), and K^(i) are the solutions for element /. Thus: 



(P - Ky(i) . Kj(i) . K^(i) (10) 



where ip is the habitat suitability function for element /. 



For discharge, the velocity and depth are simulated as a function of -flow. The 

 equation for ip is solved for finite elements in the stream and the weighted usable area 

 calculated using the equation: 



n 



WUA = I 0jAj (11) 



i=l 



where ip- is the solution to Equation 6 for the element /and A- is the area of element /. 



The assumption basic to the model is that a species of fish will elect to live in 

 physical conditions that are most suitable. Although there are many important 

 physical factors, this model includes velocity, depth, substrate, and cover and, 

 therefore, is applicable only to situations where these are the principal variables of 

 concern. 



A computerized physical habitat simulation system (PHABSIM) has been devel- 

 oped based upon the above logic." While PHABSIM represents the synthesis and 

 use of techniques which already existed, the examination of incremental changes in 

 flow and habitat is new application of the technique as developed by IFG. 



Water resource management utilizes water supply information based upon annual 

 variation (annual hydrograph) and historical records (often displayed as monthly 

 flows with certain recurrence intervals). The distribution of the hydraulic parameters 

 of depth and velocity through a stream reach is a deterministic function of the flows 

 (discharges) present, and can be described as a stochastic process utilizing existing 

 hydraulic simulation techniques. The theory and application of these approaches to 

 instream flow studies are discussed by Bovee and Milhous^'' and Stalnaker.' 



Recent studies of fish habitat and channel maintenance flow requirements have 

 shown that both are a function of the dynamic flow patterns of the stream 

 hydrograph within a given year, and, most dramatically, among years. Thus, the flow 

 requirements for maintaining any desired level of stream channel fish habitat 

 structure must be dynamic and can only be protected by establishing instream flow 

 regimes for wet years (sediment and bed load transport), average years (establishes 

 the base level of fish production), and dry years (provides minimal survival 

 conditions for "seed" stock necessary for replenishing the stream reach). ^^ 



Flow requirements may differ for various fish species and life stages as well as for 

 other instream uses, thereby forcing the management agency, on behalf of the public, 

 to define the management objectives for the stream reach in question. 



136 



