An edge ordering of a graph \( G \) is an injection \( f : E(G) \to \mathbb{Z} \), where \( \mathbb{Z} \) denotes the set of integers. A path in \( G \) for which the edge ordering \( f \) increases along its edge sequence is called an \( f \)-\({ascent}\); an \( f \)-ascent is maximal if it is not contained in a longer \( f \)-ascent. The \({depression}\) of \( G \) is the smallest integer \( k \) such that any edge ordering \( f \) has a maximal \( f \)-ascent of length at most \( k \). We apply the concept of ascents to edge colorings using possibly less than \( |E(G)| \) colors and consider the problem of determining the minimum number of colors required such that there exists an edge coloring \( c \) for which the length of a shortest maximal \( c \)-ascent is equal to the depression of \( G \).