The river bed level in low-land rivers like the Rhine branches in The Netherlands changes continuously on various spatial and temporal scales. Large-scale degradation occurs in many rivers due to river-wide engineering interventions, such as channelization, in the last decades and centuries. Local river interventions, such as the construction of side channels, affect the river's morphology by mainly causing sedimentation over the length of the intervention. This sedimentation occurs at a smaller spatial scale than the erosion due to channelization. On an even smaller spatial scale, dune-like bedforms migrate along the river bed but these have a net-zero effect on the morphology. This shows that bed-level changes occur on different spatial scales. Disentangling these spatial scales is appealing from a river management point of view since mitigating large-scale degradation requires a different river management strategy than mitigating erosion and sedimentation due to local interventions. We use detailed bed-level measurements to study the morphological changes on multiple scales using a wavelet transform. A wavelet transform is, unlike a Fourier transform, able to distinguish and disentangle the bed-level changes on different spatial scales while taking into account its spatial variation. Using the wavelet transform, we can disentangle the bed level change caused by a local intervention from the large-scale bed degradation. Both bed level changes are in the same order of magnitude and thereby difficult to determine without filtering. This allows us to study the morphological changes resulting from a single river intervention. The results show that interventions such as side channels cause an average bed-level increase around which the bed level fluctuates. This dynamic component can be up to 6 times larger than the average change. The average bed level increase is in the same order of magnitude as analytical estimations for the equilibrium bed level change. Disentangling spatial scales of bed level changes gives a better understanding of the impact of local interventions and past channelization. These insights can be used to optimize the operation and management of the river and thereby accommodate the main river functions.