AbstractScaling can be a powerful solution for predictions in ungauged basins (PUB). Since becoming a principal scaling tool, the theory concerning the index flood method has been criticized because it requires some scaling conditions that are satisfied in few river basins. In that method, precipitation and flood discharge variability play key roles. Consequently, the coefficient of variation (CV) of annual flood peaks came to be considered after the 1990s. In this paper, we have attempted to clarify true CV characteristics of flood discharges.Using numerical simulations, we attempt to reproduce the empirical characteristics of an increase in CV with increasing catchment area for a small basin (i.e. less than 30–100 km2) and decrease in CV with increasing catchment area for a large basin. First, as a preliminary test, we developed a simple model, which is on the basis of the unit hydrograph. Results obtained using this simple model show that the CV of annual flood peaks shows a constant‐increasing‐constant pattern, but this model cannot reproduce the empirical characteristics. Secondly, we used an idealized channel network to find the cause of decreasing CV. However, results show that the ability to reproduce the empirical characteristics is unrelated to the presence or absence of a network. This was confirmed using a distributed rainfall‐runoff (DRR) model comprising a channel network. The most important cause is decreased CV of rainfall intensity with increasing catchment area.Furthermore, increasing CV of the peak discharge response (PDR) function increases the CV of annual flood peaks. However, the CV of PDR of a partial duration series does not affect the CV of annual flood peaks for smaller basins (0·1 km2 in our simulation condition); hence CV is constant for small basins. Copyright © 2008 John Wiley & Sons, Ltd.