INSTANTANEOUS UNIT HYDROGRAPH WITH NEGATIVE ORDINATES - POSSIBLE

The answer to the question posed in the title of this paper is yes, provided that some restrictions are imposed on the rainfall excess which is the input to the surface runoff system. Obviously, impulsive inputs are not admissible when the instantaneous unit hydrograph (IUH) has negative ordinates, since the IUH is the direct surface runoff response (known as the ‘Output’) to an instantaneous rainfall burst of unit volume and such runoff, by definition, cannot be negative. Is an instantaneous unit hydrograph with negative ordinates (IUHWNO) desirable? Now the answer is no, because of the restrictions that have to be imposed on the input. The purpose of this paper is not to justify the assumption of linearity, an assumption which is open to serious doubts, but rather to point out that IUHWNO can be of value if and when linearity of surface runoff systems is assumed. Two problems are considered: (1) The first is the ability of an IUHWNO to represent a real‐world surface runoff system. A ‘degenerate IUH’ does not have this ability, and hence the term ‘nondegenerate IUH’ is carefully defined in the paper. Several conditions are derived in the paper which enable decision as to the degeneracy of a given IUHWNO. (2) The second problem is the determination of the class of admissible inputs in a surface runoff system which is represented by a given nondegenerate IUHWNO. These two problems are relevant to whether or not one should explicitly introduce nonnegativity sign constraints into the IUH ordinates in the identification of a surface runoff system from input‐output records. Possible extensions to nonlinear and time‐varying systems are considered in the paper for continuous or discrete‐time systems. Copyright 1979 by the American Geophysical Union.