Application of an S-shaped curve model to the temporal development of tafoni of salt-weathering origin

Abstract

To describe temporal change in tafone development, an S-shaped curve equation is proposed: Z=Zc [1-(n+1) exp (- β t)+n exp (- (1+1/n) β t)], where Z is observed tafone depth, Zc is ultimate tafone depth, t is time, and n and β are constants. The applicability of this model is examined using tafone data selected from seven sites, which are categorized into three different salt-weathering environments: a spray/splash-dominant (occasionally wave-affected) supra-tidal zone, aerosol-affected coastal regions, and inland desert areas. The results indicate that the equation can well describe tafone development in each of these environments. An investigation based on the values of n and β, determined through a best fit of the equation to the data, suggests that n characterizes site-specific environmental conditions and β reflects the magnitude of factors controlling the recession mechanism of tafone surfaces. It is found that (1) the maximum rate of tafone growth dramatically decreases from supra-tidal, through coastal, to desert environments, and (2) the growing mode of tafoni is different depending on the environmental settings. The erosional force to facilitate the development of tafoni at supra-tidal sites is estimated to be about 400 times greater than that in the general coastal area. © 2011 John Wiley & Sons, Ltd.