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SAMPLING

1) Instrument of Measurement. 2) Scales to Measure. SAMPLING. Sampling Requirements:. 1) Instrument of Measurement Should produce reliable and useful data Accuracy vs. Precision   true repeatable. . . . . . . . . . . Precise but not accurate!

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SAMPLING

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

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

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

  4. 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)

  5. t 12 hrs 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

  6. 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!

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

  8. 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

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

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

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

  12. (prepared by Lonnie Thompson – Ohio State University)

  13. (prepared by Lonnie Thompson – Ohio State University)

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