Studying the distributions of DTM derivatives of cinder cones: a statistical approach in volcanic morphometry

&amp;lt;p&amp;gt;In 2020 we celebrate the 40&amp;lt;sup&amp;gt;th&amp;lt;/sup&amp;gt; anniversary of the seminal works of Wood (1980a,b) who was one of the first researchers who considered the shapes of volcanoes in a global point of view. These four decades have seen a number of new approaches that were made possible by the ever increasing computer power and the improvements in Digital Terrain Model (DTM) production. The improving resolution and accuracy of the DTMs of various volcanic fields (VF) opened the way of wide variations of volcanic geomorphometric considerations. However, the differences in approach and, even more importantly, the differences in DTM production technology and resolution make the comparative studies and especially global considerations very difficult.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;We have envisioned a global geomorphometric analytical methodology to analyse cinder cone morphometry in terms of shape versus age: The aim is to establish a relationship between the age of scoria cones age and their morphometry. This is knowingly a rather difficult undertaking and we have made only the first steps yet, but our methodological advancements are always developed with this demand in mind.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;For the sake of diversity, in the current study four volcanic areas were considered with different age ranges, four different resolution DEMs and different number of cones:&amp;amp;#160; San Francisco Volcanic Field, Arizona, USA (SFVF, 30 m horizontal resolution, 313 pcs), the Cha&amp;amp;#238;ne des Puys, France (CdP, &amp;amp;#160;0.5 m, 26 pcs), the central-eastern part of the Sierra Chichinautzin, Mexico (SCVF, 5 m, 152 pcs) and Kula Volcanic Field, Turkey (KVF, 12.5 m, 64 pcs). As age data we had either age ranges or measured ages of the individual cones.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;A great number of derivatives (mostly related to slope angles) have been calculated for the individual cones. Their most important statistics and their distribution were computed. Irregularities and, especially, cone degradation modify the original statistical distribution; these distributions can be compared in statistical way. A quantitative distance (metric) has been introduced to study the similarity or dissimilarity of the cones.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;For the comparison, we have grouped the cones in several ways &amp;amp;#8211; they have been observed individually, by areas and by age groups (based on previous researches). For every cone boxplot diagrams, histograms and cumulative histograms were made to detect differences together with average and median values. These age groups were subjects of the Mann &amp;amp;#8211; Whitney statistical test to discriminate statistically independent or dependent samples in the populations. The test showed some clear relations between erosion (shape) and age.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;We created a cinder cone viewer for visualization purposes. This tool can display the aforementioned distributions and helps in picking pairs or groups of cinder cones to compare. As expected, the intra-VF comparisons are typically more successful as inter-VF comparisons. However, promising new morphometric derivatives (e.g., sectorial distributions) are under development.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Wood, C. A.: Morphometric evolution of cinder cones, J. Volcanol. Geoth. Res., 7, 387&amp;amp;#8211;413, 1980a.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Wood, C. A.: Morphometric analysis of cinder cone degradation, J. Volcanol. Geoth. Res., 8, 137&amp;amp;#8211;160, 1980b.&amp;lt;/p&amp;gt;