Appendix 10. Equations used in riparian vegetation growth and competition submodel.

Changes in relative biomass density Bp,r,d(t) (with a 0-1 biomass scale per unit suitable habitat) for plant type p in reach r, and cross-sectional depth (stage) slice d are simulated, using the following discrete logistic equation for time steps t of one year:

Bprd(t + 1) = Bprd(t)[1 + Gprd(t)]Sprd(t)+s. (A10.1)

where Sprd(t) is the product of all monthly survivals through flooding events and inappropriate water table levels during year t; s is a seeding input rate (biomass colonization rate); and the logistic relative growth rate Gprd(t) is given by:

Gprd(t) = rp[1 - Bprd(t)-ΣkakpBkrd (t)]. (A10.2)

In this growth function, rp is an intrinsic rate of biomass increase for plant type p, and the akp represent competition coefficients (effect of unit of biomass of plant type k on the growth rate and carrying capacity for plant type p, app = 1). In practice, for plant type definitions used in baseline simulations, the competition coefficients have little effect; the plant types are "segregated" in habitat use by strong survival effects (Sprd) caused by assuming different tolerances or preferences for height above the water table.

The water table height Wr(m) for each month m is set as a simple average of the last month's water table height and of the mean diurnal river stage Dr(m) for each reach each month, as

Wr(m + 1) = 0.5Wr(m) + 0.5Dr(m). (A10.3)

That is, water table height is assumed to "track" changes in river stage with a modest time delay, rising somewhat more slowly than the water level and decaying with a lag of around one month during periods of falling stage. In practice, this assumption has little effect on predictions for most water management scenarios. For natural system "replays", violent seasonal stage variations cause much larger survival Sprd effects than would changes in water table depth, and most managed-system scenarios do not involve large month-to-month changes in mean stage Dr(m).

Although these equations appear to give reasonable predictions of biomass development and, hence, total reach-scale relative biomasses for substrate types that are stable on time scales of decades (rock, ancient elevated sand bars, boulder and cobble areas), they may predict too rapid a change in total reach-scale biomass for water management scenarios that cause sudden, substantial increases in sandbar area near the present high-water line (e.g., "beach-building" floods of somewhat larger magnitude than the 1996 experimental flood). That is, because the model is not keeping separate account of each substrate area by "age" of origin or deposition (a very complex data gathering and simulation problem), it will "suddenly" assign biomasses Bprd(t), predicted from past dynamics on already established sandbars, to the newly deposited area. Fortunately, this effect is relatively small in most scenarios, especially because flows that can produce large, new sand areas also cause a substantial "reset" of all Bprd(t) in affected depth slices (flooding survival effect).