The deposition limiter works by comparing how far a particle can fall in a time step versus the distance available for it to travel. The fall velocity computes how far the particle can fall in a time step, but the temporal limiter equation also requires an average vertical distance that the grain class can fall. That distance depends on the concentration profile of the grain class in the flow field (i.e. sediment is not uniformly distributed in the water column).
Rouse (1963) developed the classic concentration profile theory (below). The Rouse number z is higher for larger particles and lower for higher shear velocities. Smaller particles and higher shears distribute suspended particles over more of the water column. Grain classes with higher Rouse numbers have to fall farther to deposit. Toffaleti (1968) subdivided the \water column into four zones, computing transport separately for each zone (below). HEC-RAS uses these zones as a (coarse) integration of vertical concentration profiles. HEC-RAS adopts these four zones as the effective transporting depth for different grain sizes, assuming that the grain class is evenly mixed and in equilibrium in the zone. The model distributes grain classes smaller than fine sand throughout the entire water column (Effective Depth = 1). The model distributes fine sand over the middle, lower, and bed zone which compose the lower 40% of the water column. All coarser particles (≥Medium Sand) transport relatively close to the bed, in the lower zone and bed zone, the deepest 9%of the water column. This approach has limitations. It distributes sediment evenly throughout the zone at the beginning of each time step. This assumption simplifies the concentration gradients depicted in Rouse Concentration Profiles above. Additionally, assuming the effective depth (based on the transporting depth) is on only a function of grain size ignores the Rouse dependence on shear velocity. Finally, the algorithm mixes the transporting zone fully at the beginning of each time step, retaining no memory of how far material settled in the previous time step. Despite the limitations, however, the temporal deposition limiter improves the continuity approach, limiting the deposition with physical process.
