Cirque overdeepening and their relationship to morphometry

Shape and size characteristics of cirques and their changes and mutual relationships include not only spatial and descriptive aspects but also genetic attributes. The goals of this article were to define an application of k-curve (sensu Haynes, 1968) that describes the extent of cirque overdeepening and to identify k-curve equation input variables. The k-values depend on the profile location, and hence, a clear definition of the cirque profile position is necessary. Therefore, ideal profiles were delineated through the steepest part of the cirque headwall (k-steepest, ks) or through a point on the cirque crest that had a maximal elevation (k-highest, kh). Knowledge of the cirque headwall height allows for the mathematical (theoretical) calculation of cirque overdeepening (i.e., the maximum depth of the cirque floor, sedimentary filling of the cirque floor). Further, the goal of this study was to analyse and compare cirque classification methods according to the extent of overdeepening and standard morphometric characteristics. As a training data set, 27 example cirques of the Bohemian Massif (Giant Mts., Šumava Mts., and Hrubý Jeseník Mts.) and a total of 12 morphometric characteristics were used in the analyses. Cirques were classified into two groups using cluster analysis based on the extent of overdeepening (k-values: kh and ks). A mutual relationship between cluster analysis classifications and classifications based on morphometric characteristics (L/W, H, and 3D/2D) was determined using general discriminant analysis. The classification of cirques based on other characteristics corresponded closely (in total, 81% for the first group and the cross-validation group) with cirque classifications based on the degree of overdeepening (k-value).

► This study deals with morphometry and cirque overdeepening defined by k-curve. ► We analysed k-curve function from a mathematical point of view. ► Ratio between the height of the cirque headwall and cirque floor is constant. ► The paper shows that the k-curve includes also information on development of cirques. ► Classifications of cirques based on k-values and H, L/W, and 3D/2D are similar.