Reply to “Comments on ‘Scaling Water Characteristic and Hydraulic Conductivity Based on Gregson‐Hector‐McGowan Approach’”

We certainl y appreciat e the comment s of Dr. A.P. Meissner for bringing into focus and clarifying the key features of the scaling approach we presente d in Abuja and Williams (1991). We do disagre with Dr. Meissner' s conclusion drawn in the last paragraph of the comments , and we also wish to clarify some other points. First, the clarifications. Dr. Meissner states: "However, in the field or in 'real soils' , the values of i/fe and i/fs are measure d with error". We do not believe it is primarily the measuremen t of i/»e and i/fs with errors that causes the values of these parameter s to differ from location to location within a soil type or a group of soils, but rather it is a resul t of natural variability in real soils. The real soils do not follow the perfect linear relationshi p between a and b of Eq. [2] of Meissner . In Table 1, Dr. Meissner gives effective average values for i/»e and i/»s calculated from our p and q values for the different soils. For Lakeland and Norfolk soils, the effective i/»s values shoul d be 0.276 and 0.374 m 3 m~, respectively, since these soils had a residual water content , i/»r, of 0.02 (Ahuja and Williams, 1991, Table 1). We may also point out that the rather low value of effective «/>s of Lakeland soil was probabl y a resul t of poorer fitting of experimenta l ln( e) and — ln(6s) for p and q in Eq. [4] of Ahuja and Williams, you arrive at the equality of ln(6) = ln(6)." The problem is that Eq. [4] of Ahuja and Williams is written for a fixed location for real soils, and p and q values for a soil type are not equal to ln( —i/»e) and — ln(i/»s) at that location in real soils. [The/> and q are equal to effective average values of ln(i/fe) and — ln(i/»s) acros locations. ] Hence, the substi tution called for in the second sentenc e of the above statement of Dr. Meissner cannot be made. Only for an imaginary set of perfect soils wil l the ln(^e) and —\n(if/s) be the same at all locations, equal top and q, respectively. In that case, the above-note d substitution into Eq. [4] of Ahuja and Williams (1991) wil l indeed lead to the identity ln(6) = ln(6), a 1:1 relationshi p between ln(6) and scaled ln(-i|>). But this identity simply indicates perfect scaling, the way it shoul d be. We also take this opportunit y to sugges t a more appropriate name for the type of scaling presente d in Ahuja nd Williams (1991). The scaling is based on the propert y of all ln( — »|») vs. ln(8) straight-line functions within a soil type or group, below the air-entry values, to converge within a narrow band around a point (p, —q), p and — q being the effective average values of ln( —i|»e) and ln(6s), respec tively. We, therefore, sugges t that this scaling technique be called convergence scaling. Received 6 Apr. 1992.