Physical and numerical issues in river plume modeling Rob Hetland Rocky Geyer Rich Signell

Outline “You’ve got to be vary careful if you don’t know where you’re going, because you might not get there.” -Yogi Berra Motivation Basic test case. Metrics for measuring model performance. ‘Physical’ modifications to the basic case. –Tides, wind, background properties, and geometry. ‘Numerical’ modifications to the basic case. –Advection scheme, grid resolution, and closure scheme.

Gulf of Maine - surface salinity

Base case The base case represents the least complicated river plume. It is not intended to simulate reality. Estuary –1 km wide –10 m deep –1000 m 3 s -1 fresh water flux. Coastal sea: –10 m deep at coast –1/500 slope. –0.05 m s -1 background flow. –32 psu, unstratified water.

Domain schematic

Metrics Does it ‘look’ right? –Eliminate obviously bogus solutions. Bulge diameter –Measure furthest offshore extension of plume Density anomaly/sea surface salinity –A proxy for net vertical mixing. Down-coast fresh water transport –Measure the fresh water flux downstream of the bulge. Dense water formation. –Measure the ‘unmixing’ effects of numerical dispersion.

Physical modifications. Tides and wind will effect mixing in the plume. Geometry effects the evolution of the plume (e.g., if the plume feels the bottom, there are strong PV constraints as well as increased drag). Background properties effect the offshore extent of the plume (mean flow), as well as being fundamental in R d (background density). Numerical model configurations must be robust over a wide range of physical forcing.

Effects of different forcing

Numerical modifications Grid resolution: What is the lowest resolution requirements for reliable simulation. Advection scheme: We want to minimize dissipation while maintaining reasonable levels of dispersion. (Closure scheme)

Grid convergence test Grid size near the estuary mouth –Low resolution: dy ~ 500 m –High resolution: dy ~ 200 m –Extremely high resolution: dy ~ 50 m Model setup: –4 th order advection with A H = 50 m 2 s -1 –Q R = 1000 m 3 s –No tides.

Resolution comparison

Bulge diameter vs. resolution

Advection scheme test ‘High’ resolution grid setup. Test high-order advection schemes with horizontal diffusion. –3 rd order and 4 th order –A H = 0 to 500 m 2 s -1 Use tidal modulation of the river discharge (Q R = / m 3 s -1 ) as a more stringent test of advection.

Different advection schemes

Different advection schemes (tides)

Spurious fresh water formation

Bulge diameter vs. advection scheme

Conclusions “I didn’t really say everything I said” -Yogi Berra Changes in physical forcing fundamentally alter the structure of the river plume, however, non- realistic cases can be used to examine the fidelity of numerical algorithms. Different advection schemes (and accompanying horizontal diffusion) give similar bulk metrics, except for numerical dispersion. Grid resolution must be fine enough to resolve the cross-channel structure at the estuary mouth.