At-a-station Hydraulic Geometry of the Mahi River with Special Implication to Annual Maximum Series

Abstract

Hydraulic geometry is of fundamental importance in flood hydrology and geomorphology. It refers to the rate of change of hydraulic variables, namely width, mean depth, and mean velocity, as discharge increases. An attempt has been made to find out at-a-station hydraulic geometry of the Mahi River with special reference to Annual Maximum Series (AMS).Data regarding hydraulic variables associated with annual peak discharges are available for six sites on the Mahi River and its tributaries. These data have been used to derive at-a-station hydraulic geometry equations. The b/f ratio, m/f ratio and total variance have been computed. The hydraulic geometry exponents (b, f, and m) were plotted on Rhode’s ternary diagram. The results of the analysis for all the sites clearly show that the rate of change in mean velocity (m) and mean depth (f) with discharges are greater and the rate of change in width (b) are very slow except one site i.e. Rangeli on the Som River. The rate of change in width (b) with discharge is much slower for Khanpur, Padardi Badi and Mataji sites on the Mahi River which are attributed to nearly box-shaped nature of channels. The rate of change in width (b) with discharge is moderate on the Anas River at Chakaliya and Jakham River at Dhariawad indicating semicircular channel form. However, the rate of change in width (b) with rising discharge is much higher for the Som River at Rangeli. This is attributed to wide open channel of the river. The b/f ratios indicate that the rate of change in width is always lower than the rate of change in mean depth which has important implications for efficiency of the channel since the flood power is directly related to the flow depth. The higher m/f ratios reveal that there is more rapid increase of measured sediment load with increase of discharge. The total variance values for three sites namely Rangeli, Dhariawad and Chakaliya are closer to the theoretical value (0.33). This suggests that the effects of changes in discharge are absorbed equally by all the three variables. However, the total variance values for the remaining three sites namely Khanpur, Padardi Badi, and Mataji are not absorbed equally by all the three variables, but by one or two hydraulic geometry variables. This fact, therefore, suggests that the alluvial river channel of the Mahi River is not a true alluvial channel, which is self-formed through the independent adjustment of the morphological variables. The b-f-m or ternary diagram indicates that three sites fall in sector 6, two sites in sector 2 and a site in sector 3. The sector 6 represents the channel where Froude number and slope-roughness ratio increases and width-depth ratio and velocity-area ratio decreases with increasing discharge.Thesector2 reveals the decrease in width-depth ratio and increase in competence, Froude number, velocity-area ratio, and slope-roughness ratio with rising discharge. Whereas, sector 3 shows the channel characteristics where width-depth ratio, competence, Froude number, and slope-roughness ratio increase and velocity-area ratio decrease with increasing discharge.