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Abstract Channel networks are important landscape features that transport water, sediment, and nutrients. Their emergence and evolution are controlled by the competition between hillslope and fluvial processes on landscapes. Investigating the geomorphic and topologic properties of these networks is crucial for quantifying the roles of processes in creating distinct patterns of channel networks and developing models to predict the network dynamics under changing environment. Here, we study the response of landscapes to changing climatic forcing via numerical‐modeling and the topographic analysis of natural landscapes. We use a physically‐based numerical landscape evolution model to investigate the channel network structure for varying hillslope and fluvial processes represented by different magnitudes of soil transport () and fluvial incision () coefficients. We show that landscapes with the same Péclet number (defined as the ratio of the timescales of advective (fluvial) to diffusive (hillslope) processes) and thus the same characteristic length scale may exhibit different geomorphic and topologic characteristics. Specifically, increasingDandK(mimicking humid conditions) or decreasingDandK(mimicking dry conditions), while keeping the same Péclet number, results in distinct branching structures. These changes lead to an exponential decrease in relief under humid conditions and an increase under dry conditions. For smaller and combinations, higher number of branching channels is observed, whereas for larger and combinations, higher number of side‐branching channels is obtained. These results align with topographic analysis of natural landscapes, suggesting that varying climatic conditions imprint distinct signatures on the branching structure of channel networks.