transect (IFG- 1 ) and the multiple transect Water Surface Profile Program (IFG-2). A 

 third multiple transect model (IFG-4) was developed for use in rapidly varied flow 

 situations.^* 



The instream reach simulation takes the form of a multi-dimensional matrix 

 (corresponding to the stream cells) of the calculated surface areas of a stream having 

 different combinations of hydraulic parameters, i.e., depth, velocity, substrate, and 

 cover when applicable. This matrix calculation provides a total summation of surface 

 areas within the stream reach that have a given combination of hydraulic and 

 structural attributes. 



The significance of the hydraulic and channel structure features in each cell is then 

 evaluated using procedures similar to those suggested by Waters. '* Univariate curves 

 showing the relative suitability of various stream attributes by life stage and species 

 were compiled by IPC."' From these curves, a weighting factor for the depth, 

 velocity, and substrate in each cell is determined. These weighting factors are 

 multiplied together to estimate the composite suitability for that combination of 

 variables, and this composite index is multiplied by the surface area of the cell. The 

 product of the composite habitat suitability index and the cell surface are termed the 

 "weighted usable area" of the cell. This process is repeated for each cell, with the 

 weighted usable areas of all cells summed to determine the total weighted usable area 

 of the stream reach. 



By changing the flow, the distribution of depths and velocities changes in 

 association with various substrate types and cover objects. As the flow changes the 

 habitat value ot each cell changes and is reflected in the total weighted usable area. 

 These changes often balance out, i.e., some cells decline in usability while others 

 increase. Therefore, it is often possible to identify several discharges which provide 

 the same measure of habitat usability. 



Mathematically, the basic concept is that in any instant of time and small area of 

 the stream (dA), there exists a function 0(P) which related physical parameters (P) to 

 the suitability of the area as physical habitat for a given species. The usability of the 

 area is then: 



d(WUA) = 0(P)dA (2) 



The term WUA is "weighted usable area" which is a physical habitat index. 

 Integrating over a specified reach of stream, the weighted usable area for the reach is: 



WUA = /^ <A(P)dA (3) 



The physical parameters are simulated with predictive hydraulic models repre- 

 sented by: 



P = H(l) (4) 



The variables include depth, velocity, and substrate in the stream. The resulting 

 equation is: 



WUA = /^<//(H(l)) dA (5) 



In the simplest form, the equation for the function for any cell or element / in the 

 stream is: 



<^i - Pv(V) • Pd(D) • Ps(S) (6) 



where: 



is the habitat suitability function, 

 V is the velocity at a point, 



135 



