SAMPLING

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= 12 hrs, then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 • sampling for waves every 5-10 seconds • 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. Continuous sampling vs. Burst sampling Continuous sampling mode: at equally spaced intervals 0 2 4 6 8 10 12 hrs Burst sampling mode: burst embedded within each regularly spaced time interval

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

10. Independent Realizations If correlated  not independent do not contribute to statistical significance of measurements