Variations in Slope Components during Large Magnitude Floods, Wisconsin

Abstract

Errors are associated with the substitution of map and water surface slopes for energy gradients in hydraulic estimation procedures. Many paleodischarge reconstruction techniques assume one-to-one correspondence between water surface slope and slope measured from a topographic map. The assumption that map slope or water surface slope, however, can be directly substituted for energy slope, involves unknown degrees of error. This research shows that energy gradients are generally overpredicted by both water surface slope (mean = 44 percent) and map slope (mean = 71 percent). At several sites in the Upper Mississippi Valley, the explained variances for the relationship between map slope and water surface slope range from 7–78 percent. Environmental factors that influence the strength of the relationship include the flood-producing mechanism (snowmelt versus convectional precipitation), the storm path through the basin, and the relative synchroneity of response between the tributaries and the trunk stream. The relationship does not systematically improve with increasing relative flood height. The strongest association between these two slope measures occurs during rainstorms distributed fairly uniformly throughout the basin, and when floods attain sufficient stage to minimize the resistance effects of floodplain vegetation and surface irregularities. During other floods, map slopes poorly approximate water surface slopes causing differences in discharge estimation that deviate by 27 percent but may reach 50 percent.