The theory of stochastic differential equations driven by multiplicative Markovian dichotomous noise and a number of geomorphological relationships of river basins are used to investigate the geomorphological patterns of the width of riparian zones and the associated riparian vegetation biomass. Under the assumption that the scaling relationship between the river flow fluctuations, represented by the standard deviation of the flows, sigma(Q), and drainage area holds, i.e., sigma(Q) similar to A(s), we find that the scaling exponent s plays an important role in determining the patterns of the riparian width and vegetation biomass. In particular, high values of s, i.e., when the fluctuation grows relatively fast with drainage area, could result in the riparian zones of high-magnitude streams being completely void of vegetation, whereas low values of s result in the riparian zones increasing in width with the stream magnitude. For very low s such an increasing trend of riparian width scales with the stream magnitude with an exponent approaching the negative value of the scaling exponent of the stream bank slope. The analysis presented here offers a potentially useful tool that can be used in watershed management, especially under changing climatic conditions, which may induce larger flow fluctuations and extreme events.