<p>Dynamic climates featuring spatially and temporally variable precipitation patterns are ubiquitous in mountain settings. To understand the role of climate on landscape evolution in such settings, and how climate change-related signals might be translated into the sedimentary realm, this variability must be addressed. Here, we present an analysis of how spatial gradients and temporal changes in rainfall combine to affect both the steady state form and transient evolution of river profiles of large transverse river basins as predicted by the stream power model. Where rainfall is uniform, the stream power model predicts that topographic metrics, like fluvial relief and normalized channel steepness index (k<sub>sn</sub>), vary inversely and monotonically with rainfall at steady state. In contrast, we find that these relationships are more complex and can be inverted in many circumstances, even at steady state, in the presence of orographic rainfall gradients. An important consequence of this is that correlations between average rainfall (climate) and topography are always weaker in catchments that experience rainfall gradients relative to expectations based on uniformly distributed rainfall. Moreover, dispersion caused by rainfall gradients is systematic, varying both with the polarity (i.e., generally increasing vs. decreasing downstream) and intensity of the gradient. Therefore, even in quasi-steady-state, rainfall gradients have the potential to obscure or distort the influence of climate on landscapes if they are not accounted for. In addition, we find that temporal changes in spatially variable rainfall patterns can produce complex erosional and morphological responses that can be contrary to expectations based on the change in mean rainfall. Specifically, enhanced incision and surface uplift may occur simultaneously in different parts of a landscape in a pattern that evolves during the transient response to climate change, complicating prediction of the net erosional and topographic response to climate change. Thus, transient responses to the orographic distribution of rainfall may misleadingly appear inconsistent with erosional or morphological responses expected for a relative change in average climate. Additionally, topographic indications of transient adjustment, even to a dramatic change in orographic precipitation, can be subtle enough that a landscape can appear to be in quasi-steady-state. In such cases, spatial gradients in erosion rate driven by a change in orographic precipitation pattern may be mistakenly interpreted as recording spatial gradients in rock uplift rate, potentially at once obscuring an important influence of climate and misinterpreting tectonic drivers of landscape evolution. Finally, we explore the use of a variant of normalized channel steepness index (k<sub>sn-q</sub>) that is able to incorporate the influence of spatially variable in rainfall based on the stream power model. Importantly, we find that k<sub>sn-q</sub> preforms well to help diagnose and quantify the role of climate acting in a landscape, in particular during transient adjustment to changes in rainfall patterns where the standard channel steepness metric (k<sub>sn</sub>) may be misleading.</p>
Role of the on-site pinning potential in establishing quasi-steady-state conditions of heat transport in finite quantum systems
