Climate change is causing the global sea level to rise. Research and discussion of the effects of sea level rise are often focused along coastlines. However, the effects of higher water level and changing morphodynamics can reach far inland via rivers. This study uses a one-dimensional numerical model to analyze bed level response to sea level rise. The model simulates 100 years of steady sea level rise on a 1000 km long, fixed width channel. Sea level rise creates a backwater curve which grows in the upstream and vertical directions. The transient response of the channel bed is an aggradation wave the grows in the upstream and vertical directions. We studied different cases which vary in sediment flux, flow discharge, grain size, and rate of sea level rise and found changes in the rate of growth of the aggradation in both directions. All runs start in an equilibrium state and run for 100 years.

This study finds a close relationship between the equilibrium slope and depth of the channel and the shape of the backwater curve. This relationship drives the aggradation patterns. For example, for the same amount of sea level rise, a flat, deep channel has a longer backwater curve with a smaller relative increase in depth than that of a steeper, shallower channel. The backwater curve drives the aggradation patters, such that the flat, deep channel then has aggradation over a longer reach, and a smaller increase in bed level than the steeper shallower channel.

With the cases modeled in this study, three general trends in aggradation rates emerge: (1) an aggradation mound that grows quickly upstream, with slower increase in bed level as found in flatter, deeper channels; (2) a faster increase in bed level with slower upstream growth, found in cases with steeper slope and shallower depths; and (3) faster growth in both bed level and upstream direction caused by an increased rate of sea level rise.

Since natural channels are often complex with multiple sources of discharge inputs, a tributary case is also
included. Starting from equilibrium state and applying sea level rise to the downstream boundary, the model
shows aggradation waves in the regions downstream and upstream of the confluence, starting from the downstream boundary and the confluence. There is also degradation just downstream of the confluence. The scour hole grows at first, in depth and the downstream direction then reduces. The aggradation moving upstream intersects with the degradation moving downstream and fills in the scour hole. In some cases, we see the scour fills in within the 100 year time frame, resulting in a net increase in bed level. In a tributary system, the risk of scour is greatest for tributaries with high flow discharge or low sediment flux.

The transient response of the bed level to sea level rise is aggradation. As the water level continues to rise, the bed level is expected to do the same, but at a lower rate. In this study, the nominal rate of sea level rise is 10 mm/yr. The fastest rate of bed level rise in the model results is less than 6mm/yr, creating an ever increasing water depth. This is beneficial for shipping and navigation in the channel, which would not require dredging of the aggradated material. However, the reduction in bankfull volume with rising water levels is dangerous for flood control.

Sediment nourishments have become an increasingly attractive alternative to deal with continuous bed degradation problems in the river system. When supplied to the river, sediment nourishments induce a sediment wave that propagates through the system causing changes in bed level and bed surface texture. In the present study we use a one-dimensional numerical model to analyse how the propagation of these sediment waves varies under different conditions. We find that the propagation of the sediment wave tends to be predominantly dispersive for large spatial variations of the flow, which is the dominant case when the height of the wave is large in comparison to the flow depth, or when the sediment is dispersed over a large enough reach to lead to a backwater effect. In artificial sediment nourishments the height of the sediment wave is usually limited to prevent creating an additional obstacle to navigation, and it is then that the temporal variations in the flow, due to high discharge events for example, determine the propagation of the wave. We study the morphodynamic response in a mixed-size sediment river system to a sediment nourishment, and identify the physical mechanisms that impact the propagation of mixed-sized sediment waves. In order to prevent it from being easily flushed downstream, the grain size distribution of the nourished sediment is typically selected to be coarser than the river bed. This reduces sediment mobility and enhances sediment deposition over the nourished reach, which in turn causes a deficit in sediment supply to the downstream reach and leads to the formation of a degradational wave. The propagation celerity of the degradational wave is found to be significantly faster than that of the sediment wave, which means that the effects of the nourishments in a river system can be observed significantly further downstream than from where the front of the sediment wave is found. We find that the celerities of both the sediment wave and the degradational wave are predominantly affected by the adjustments in surface grain size in the system. These adjustments migrate in the river system as a fining wave, which both accelerates the sediment wave, and decelerates the degradational wave. We learn that higher content of the finer fractions in the nourished sediment accelerate the evolution of the wave and lead to a predominantly translational behaviour. It also affects the magnitude of the incision depth, the closer the composition of the nourished sediment is to that of the bed surface, the less severe the scour. And even though it does not affect the propagation celerity of the degradational wave, it does impact how far downstream the wave travels, affecting a larger river reach the coarser the grain size composition of the sediment wave is. Finally, we analyse the results from a nourishment pilot project carried out in the Bovenrijn from 2016-2019. We find that the propagation of the sediment wave associated with the nourishment is only observed during high discharge events. The wave is predominantly dispersive, and only during a prolonged extreme discharge event did the wave show slight translational behaviour. We observe that lateral sorting mechanisms caused the tracer sediment to have a different trajectory from the sediment wave, which highlights the limitations of using a one-dimensional model. We also observe that the changes in bed level are related to the changes in surface grain size, with sediment deposition over the nourished reach and bed degradation just downstream.