Harmonic Analysis – use in calibrating models

Harmonic Analysis –use in calibrating models Larry Smith USGS retired

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

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

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

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

Mallard Island seaward landward

Net salt flux over the tidal cycle <QC> = <Q> <C> + <Q’C’> = 110 X 2.7 + (-1900) = -1600 ~ landward! 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 calculationfor which model phases and amplitudes must be accurate….

Harmonic Analysis – use in calibrating models