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SAMPLING

Learn about the important factors to consider when using instruments of measurement and scales to ensure reliable and useful data. Understand the concepts of accuracy vs. precision, sampling interval, sampling duration, continuous vs. burst sampling, and regularly vs. irregularly sampled data.

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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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