Conceptual and theoretical models for landscape evolution suggest that fluvial topography is sensitive to climate. However, it remains challenging to demonstrate a compelling link between fluvial topography and climate in natural landscapes. One possible reason is that many studies compare erosion rates to climate data, although theoretical studies show that, at steady state, climate is encoded in the relationship between erosion rate and topography rather than erosion rate alone. We use an existing global compilation of 10Be basin-averaged erosion rates to isolate the climate signal in topography as a function of erosion rate for morphologically steady-state, fluvially dominated basins underlain by crystalline bedrock. Our results show that the relationship between erosion rate (a proxy for rock uplift rate) and the normalized river channel steepness index (a proxy for fluvial relief) becomes increasingly nonlinear with increasing mean annual precipitation and decreasing aridity. This result indicates that erosional efficiency increases in wetter and more humid climates, lowering fluvial relief for a given erosion rate. When interpreted in the context of detachment-limited bedrock incision models that account for incision thresholds and stochastic flood distributions, this systematic pattern can be explained by a decrease in discharge variability in wetter and more humid landscapes, assuming incision thresholds are important on a global scale.