Although information on total annual sediment loads is available I have been unable to find information on how seddment loads are distributed throughout a typical hydrological year.
At the risk of oversimplification, sediment loads are usually flow dependent. Thus, as a first approximation, loads will track the seasonal flow patterns at your site.It has been my experience that suspended sediment concentrations are a non linear (e.g. exponential ) function of flow, so if I were to guess, I would say you are likely to see a disproportionate amount of most of your annual sediment load during high flow events.
I concur. And on an annual budget, most of the sediment over time moves during bankfull flow, the channel forming flow, on streams with an active floodplain. Bankfull flow elevation is typically defined by point bars. On entrenched channels such as gullies that lack floodplain, the flow energies continue to increase above bankfull flow, so the exponential power function of gullies streams continues above bankfull. In low gradient, braided systems, sediment movement is more difficult to analyze, as the channel has and continues aggradation, lost capacity, keeps changing and shifting, etc. So sediment loading may also be dependent on channel type (e.g., Rosgen channel types). Rivermorph is an example of software that can help convert channel metrics into stream power values, sometimes useful. Some stream sediment loading is limited by stream power, and other stream sediment loads are limited due to lack of sediment sources. Sediment sources can come from channel sources or land erosion sources. There are many studies and books on sediment. If you have water quality agency or environmental resource study Universities, researchers, hydrologists, they may have some data or information useful to you.
The previous two answers are very good. You should also consider if your site is located downstream from a dam, lake or other sediment trap. Depending on the flow conditions, dams may release sediment-starved effluent during low or ordinary flows and sediment-rich effluent during high flows.