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

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

3. 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

4. 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

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

6. seaward landward Mallard Island

7. seaward landward Mallard Island

8. = + = 110 X 2.7 + (-1900) = -1600 ~ 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.

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