Where 



C = a IXn matrix of cost or return associated with each activity 



X = an mXl matrix of activity levels 



A = an mXn matrix of technology coefficients and relations among 



activities 

 B = an mXl matrix of constraint levels 

 K = identification of costs, returns and quality, set optimized, K= 1 to 



9 (identifies objective optimized) 

 L = identification of sector, L = 1 to 7 

 P = identification of constraint levels (RHS), P = 1 to 27 (4 areas and 



sub-areas, 3 river-flow levels, 2 river-quality levels, and projection 



to 1980) 

 R = river flow, coliform, biochemical oxygen demand, and suspended 



solids in river 

 Y = a 7Xn matrix of annual effects including income (value added), 



recreation day usage, employment, and water use 

 m varies between areas 

 n varies between areas 



A schematic of the model is shown in Figure 2.2. The model can be visualized 

 in terms of seven independent sectors physically interrelated by the river's 

 flowing through the watershed, with flow and quality constraints imposed on 

 all sectors. 



2.2 Flow Levels 



In order to recognize the most limiting river-water flow and use situation 

 likely to be encountered, use and flow data for the month of August were 

 utilized. This is a period when the high demands of industrial, domestic, and 

 recreational use are being imposed on relatively low-river flow. As a result the 

 values, quantities, and coefficients in the model are monthly figures, with the 

 exception of impact equations which are on an annual basis. Furthermore, the 

 model was felt to be reasonably representative of areas in southern New Hamp- 

 shire, and appropriate constraint values or right-hand side values were developed 

 for analysis of the median flow of the Lamprey River. The same A matrix, Y 

 matrix, and C matrix were used in all of the analyses. 



Three flow levels were analyzed, one representing dry years, the 10th per- 

 centile of 36 years of August flow records; the median flow to approximate 

 normal river flow; and the 90th percentile flow to estimate high-flow years. 



Table 2.1 shows a summary of the distribution of 1934-1969 monthly flows 

 of the Ashuelot River with respect to the flow-level assumptions used in the 

 model. For the four months summarized (July through October; 36 years of 

 records), the level of river flow was between low flow (10th percentile) and 

 high flow (90th percentile) for 84 percent of these months. For the months 

 not shown in Table 2.1 (November through June), only six months had less 

 than the August median flow of 2,850.5 million gallons. The river-flow levels 

 for the 432 months in the 36 years of records were between low flow and high 

 flow 50 percent of the time. 



The above observations support the conclusion that the flow levels assumed 

 in the model were representative of the conditions in which water quahty and 

 quantity would be most limiting on the surface-water-related uses in the basin. 



