The Beaumont number of mountain belts – quantifying the interaction between surface processes and tectonics during orogenesis

To first order mountain belts grow by crustal thickening and gain their elevated topography through isostatic compensation. High and rising topography in turn modifies the global wind circulation system and is the main locus of (orographic) precipitation. The ensuing flow of water (or ice) redistributes mass through erosion and deposition, counteracts orogenic growth, shapes the appearance of the landscape, and most importantly provides a feedback-loop between surface processes and tectonics. However, it remains debated whether surface processes or lithospheric strength control mountain belt height, width, and longevity, reconciling high erosion rates observed for instance in Taiwan and New Zealand, low erosion rates in the Tibetan and Andean plateaus, and long-term survival of mountain belts for several 100s of million years. Here we use a tight coupling between a landscape evolution model (FastScape) and a thermo-mechanically coupled mantle-scale tectonic model (Fantom) to investigate mountain belt growth. Based on several end-member models and the new non-dimensional Beaumont number, Bm, we provide a quantitative measure of the interaction between surface processes and tectonics, and define three end-member orogen types: Type 1, non-steady state, strength controlled (Bm > 0.5); Type 2, flux steady state, strength controlled (Bm ≈ 0.4−0.5); and Type 3, flux steady state, erosion controlled (Bm < 0.4). Bm can be assessed without complex measurements or assumptions, but simply by knowing a mountain belt’s convergence rate, height, width, first order shortening distribution, and widening rate. In turn, assessing Bm of an orogen provides information about its crustal strength and average fluvial erodibility and gives insight into the factors controlling orogen type: In Himalaya-Tibet , high convergence rates dominate over efficient surface processes (Type 1), in the Central Andes low convergence rates dominate over low fluvial erosional efficiency (Type 1), efficient surface processes balance high convergence rates in Taiwan (likely Type 2), and surface processes dominate in the Southern Alps of New Zealand (Type 3). Our results provide a simple unifying framework quantifying how surface processes and tectonics control the evolution of topography of mountain belts on Earth.