events recorded on a hydrograph. These 

 events could result from either, or a combina- 

 tion of, rainstorms, snowmelt, or excessive 

 evapotranspiration. The analytical technique 

 is completely automated; the results are de- 

 pendent entirely on the flow rates shown on 

 the hydrograph. The hydrologist can influ- 

 ence the results in only one way: by increas- 



ing or decreasing the number of sampling 

 points along the hydrograph. 



The technique used in the computer pro- 

 gram was tested on hydrographs of typical 

 runoff events in many regions in the United 

 States; it was considered successful because 

 the computed separation curves crossed the 

 recession limbs of the hydrographs at their 

 points of inflection. 



BASIC ASSUMPTIONS 



Two basic assumptions underlie the com- 

 putations: that both increment in base flow 

 and the ratio of surface runoff to interflow 

 depend essentially on the hydrograph 's rate of 

 rise. A rapid rise indicates a proportionately 

 smaller increment in base flow than does a 

 moderate rise. On the other hand, the ratio of 

 surface runoff to interflow is large when the 

 stream rises rapidly; this ratio is small when 

 the stream rises slowly. 



We also assume that (a) surface runoff 

 (including channel interception) ends at the 

 first inflection point following peak flow, and 

 that (b) interflow ends at the lower inflection 

 point on the recession limb of a simple hydro- 

 graph. Our research was directed towards de- 

 fining equations that — if based on the first 

 two assumptions — would meet the criteria of 

 the third and that would be applicable to any 

 hydrograph. 



ESSENTIAL ELEMENTS 

 OF THE SEPARATION TECHNIQUE 



The heart of this program consists of a se- 

 ries of calculations to determine the consecu- 

 tive positions of points along two curves: the 

 base flow curve (which separates base flow 

 from stormflow) and the interflow curve 

 (which separates interflow from rapid flow.) 

 Figure 1 is used to illustrate the parameters 

 entering the calculation of points along both 

 the base flow and interflow lines. 



Base Flow Computations 



The rate of flow at any point (Pi) on the 

 base flow line is equal to the sum of the rate 



at a prior time (P^. ) plus an incremental val- 

 ue (Ui): 



Pi=Pi-,+ Ui (1) 



where 



Ui = expl-(1.0 + sin A)]x(Af x AR x tan B)'/^ (2) 

 where (see fig. 1) 



A = arctan (AR/^t) 

 B = (H xA -/SR)/H 

 H = (AR^ + At^ )'/2 



2 



