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

2. 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)

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

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. 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

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. ■ 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!

8. 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 = h-1
T = 2π/ h-1 = h = days

9. Continuous sampling vs. Burst sampling
Continuous sampling mode: at equally spaced intervals
Burst sampling mode: burst embedded within each regularly spaced time interval
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)