Labs Sediment Transport Mechanics

Greg Tucker, Bob Anderson, Spring 2013

Modeling assignment # 1. Experiments with water volume balance in buckets and basins

Goals: You will gain experience with: setting up a code in IRF format; setting up simple arrays; stepping incrementally in time; and in plotting your results.
a) Write a MATLAB code that answers the following question: given a fixed input of water to the bucket, and a hole in the base of the bucket, how will the water level in the bucket evolve? Assume that the bucket starts with no water in it. Produce a plot of water level as a function of time.

b) Now allow the inputs to vary through time, in particular allow the input to oscillate sinusoidally. Specify a period and amplitude of the oscillation about the mean. Again, answer how the water level in the tank will vary through time. Produce a two-part plot in which you display both input and output of water on a top plot, and the water level on the lower plot.

Answers to Leaky Bucket assignment # 1a &1b.

1.Bob Anderson's demonstration code

Now let’s take this to a little bit more real setting, a closed basin lake in which there is input solely from runoff from the surrounding landscape, and outputs solely from evaporation from the lake surface. One of the most famous examples in the US is Mono Lake in eastern California at the foot of the Sierras.

We start with a generic lake basin, and move on to a more real basin after developing a simple model.

The lake basin: Consider a simplistic closed lake basin, called Snowcone Basin, shown in the figure below. The drainage basin has an area Ab. There are no outlets. The geometry of the basin is a cone, with the tip of the cone at an elevation of 1000 m, and a spread angle for the cone of .

The climate: On the average, it precipitates in the basin, uniformly (by which I mean evenly over the entire area), at a rate P (in meters of water equivalent per year). The climate is such that it also evaporates off any standing water in the basin at a mean annual rate E (also in meters per year).

The runoff: The precipitation is imperfectly converted to runoff when the precipitation falls on any surface but the lake itself, some of it being lost to transpiration and evaporation from the surface of the basin and its vegetation before the water can make it to any lake in the basin. The conversion factor, called the runoff coefficient, is . Of course, any precipitation that falls on the lake is not