SAMPLING Sampling Requirements: 1) Instrument of Measurement 2) Scales to Measure

Should produce reliable and useful data 1) Instrument of Measurement Should produce reliable and useful data Accuracy vs. Precision   true repeatable           Precise but not accurate! (repeatable)

2) Scales to Measure Measurements should be collected often enough in space and time to resolve the phenomena of interest t, x u

Sampling Interval  Choice of sampling increment t or x is important.  Sample often enough to capture the highest frequency of variability of interest, but not oversample  For any t the highest frequency we can hope to resolve is 1/(2 t) Nyquist Frequency (fN) fN = 1/(2 t) ; if t = 0.5 hrs  fN = 1 cycle per hour (cph)

This means that it takes at least 2 sampling intervals (or 3 data points) to resolve a sinusoidal-type of oscillation with period 1/ fN if 1/ fN = T = 12 hrs, then 1/(1/2 t ) = 12 hrs and t = 6 hrs, i.e., t = T/2  t 12 hrs t

In practice f = 1/(3 t) due to noise and measurement error. If there is a lot of variability at frequencies greater than f we cannot resolve such variability  aliasing For example, ■ sampling every month regardless of the tidal cycle ■ sampling for tidal currents every 13 hours Then, we should measure frequently!

■ We should sample long and often! Sampling duration We should sample to resolve the fundamental frequency (fF) fF = 1/(N t) = 1/T ■ We should sample long and often!

Δf × LOR ≤ 1 → Rayleigh Criterion LOR = length of record Sampling duration To resolve two frequencies separated by ( Δf ) Δf × LOR ≤ 1 → Rayleigh Criterion LOR = length of record e.g. Δf = 2π/12 h - 2π/12.42 h = 0.0177062 h-1 T = 2π/0.0177062 h-1 = 354.858 h = 14.786 days

Continuous sampling vs. Burst sampling Continuous sampling mode: at equally spaced intervals Burst sampling mode: burst embedded within each regularly spaced time interval 0 2 4 6 8 10 12 hrs

Regularly vs. Irregularly sampled data Regular if unknown distributions Irregular if looking for specific features

Independent Realizations If correlated  not independent do not contribute to statistical significance of measurements

(prepared by Lonnie Thompson – Ohio State University)

(prepared by Lonnie Thompson – Ohio State University)