Harmonic Analysis – use in calibrating models Larry Smith USGS retired.

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Presentation transcript:

Harmonic Analysis – use in calibrating models Larry Smith USGS retired

Data contain variability at a number of frequencies Walnut Grove Rio Vista 15-minute Flows Julian Day

caused by sun & moon so frequencies are known location on earth influences amplitude and phase of each constituent tidal field data decompose to… Individual constituents

Model evaluation concept a Cos(wt+p)a’ Cos(wt+p’) A Cos(wt+P)A’ Cos(wt+P’) For a given w if we set (a=A, p=P), and run the model, does a’=A’ and p’=P’? from field data from model calculations

= + advection + dispersion where is tidal mean, and Q’ = Q - etc. Why does it matter? One answer comes from Eulerian flux calculations: ~

seaward landward Mallard Island

seaward landward Mallard Island

= + = 110 X (-1900) = ~ Net salt flux over the tidal cycle A 1-hour phase shift causes the dispersion term to grow from 0 to -1900! Getting correct phase shifts is an essential part of model calibration.

Particle paths are a Lagrangian calculation for which model phases and amplitudes must be accurate….