Increased Asymmetry of Pit-Over-Peak Statistics with Landscape Smoothing

TL;DR

This study investigates how landscape smoothing affects the distribution of local elevation extremes, revealing increased asymmetry in pit-over-peak statistics as landscapes mature and become smoother.

Contribution

It provides a novel analysis linking landscape evolution, spatial correlation structures, and local extreme statistics across diverse terrains and planetary landscapes.

Findings

Spherical covariance models fit observed data well.

Pit-over-peak ratio indicates landscape aging.

Smoother landscapes show reduced pit counts.

Abstract

The local extremes (i.e., peaks and pits) of the landscape-elevation field play a critical role in energy, water, and nutrient distribution over the region, but the statistical distributions of these points in relation to landscape advancing towards maturity have received limited research attention. In this work, we first explain how the spatial correlation structure of the elevation field affects the counts and frequency distributions of local extremes. We then analyze local extremes statistics for 8 mountainous landscapes worldwide with diverse hydroclimatic forcings and geologic histories using 24 Digital Elevation Models (DEMs) and compare them with complex terrain of the Erythraeum Chaos region on Mars. The results reveal that the spherical covariance structure captures the observed spatial correlation in these cases with the peak frequency distribution agreeing well with the elevation frequency distribution. The ratio of the pit-over-peak (POP) count is linked to the degree to which the pit and peak frequency distributions match, and carries the mark of landscape aging. The relationship between the geomorphic development stage (quantified by the reduced fatness of the slope-distribution tail) and the deviation of POP values from unity in old mountainous landscapes confirms that the evolution towards smoother topographies is atypically accompanied by reduced pit counts typical of organized valley and ridge patterns.