About Recursive Digital Filter Method About BFI_max

One parameter digital filter method (Lyne and Hollick, 1979; Nathan and McMahon, 1990; Arnold and Allen, 1999)

q_k = a * q_k-1 + (1 + a)/ 2 * (y_k - y_k-1)

Where,

q_k: Direct runoff at time step k,
q_k-1: Direct runoff at time step k-1,
y_k: Total streamflow at time step k,
y_k-1: Total streamflow at time step k-1,
a : Filter parameter.

The recursive digital filter method (Eckhardt, 2004)

b_k = [ ( 1 - BFI_max) * a * b _k-1 + ( 1 - a ) * BFI_max * y_k ] / ( 1 - a * BFI_max)

Where,

_k

_k-1

_k

_max

In order to minimize the subjective influence that a user of the filter technique experts on the results by his choice of BFI_max, one has to find typical BFI_max values for classes of catchments that can be distinguished by their hydrological and hydrogeological characteristics. Based on a preliminary analysis, it is suggested to select BFI_max

0.80 for perennial streams with porous aquifers,
0.50 for ephemeral streams with porous aquifers,
0.25 for perennial streams with hard rock aquifers.

References:
Arnold, J. G. and Allen, P. M., 1999. Validation of automated methods for estimating baseflow and groundwater recharge from stream flow records. Journal of American Water Resources Association. 35:411-424.
Lyne, V. D. and Hollick, M. 1979., Stochastic time-variable rainfall-runoff modeling. Hydro. And Water Resour. Symp. Institution of Engineers Australia, Perth. Pp. 89-92.
Eckhardt, K., 2004. How to construct recursive digital filters for baseflow separation. Accepted for Hydrological Processes.
Lim, K. J. and Engel, B. A., 2003. Development of the Web-based Baseflow Separation System, iSep Web GIS. Ag. and Biological Engineering Departmental Report, ABE, Purdue University.
Nahatan, R. J. and McMahon, T. A., 1990. Evaluation of automated techniques for baseflow and recession analysis. Wat. Resour. Res., 26, 1465-1473.
Muthukrishnan, S., Lim, K. J., Harbor, J., and Engel, B. A., 2004. iSep: A Simple GIS Enabled, Internet-Based Hydrograph Separation Tool. In Reivew for Journal of Computers & Geosciences.