Research Project Next Year Three is probably the limit for any instructor, and 2 is more reasonable Think about what you really want—you can do nearshore GIS, or Arctic weather, or remote sensing anywhere

From NIH, in Nature

Hourly Observed Tides Solomon’s Island Red Annapolis Blue

Lag =0, r=0.583

Lag = 3 R=0.927

Correlogram

Peaks at 3,16,28,40,53……. What is the interval and why is it important? Difference positive and negative lags?

Big peak at 438 (r=0.807) This is 435 hours from biggest peak at 3 Or days Real or artefact?

Troughs lag = 9, r=0.184

Lab Tasks Resample to common interval, which is required for time series analysis (cross correlation) –Think about the best sampling interval –If you sampled every 10 minutes, resampling to 1 minute does not make it more accurate Break wind into components –Do you have to worry about the angle conventions?

Autocorrelation Relative peaks at 75 hours (3.125 days) 149 hours (6.2 days) Total length 624 hours (26 days)—what does Nyquist tell us about this? Can we see the monthly period in the tides

Fourier curve fitting Level points center of series Matched with 5, 10, and 50 sin curves (min periods 10, 10, and 2 m)

Fourier Limits Periods longer than sampling duration Periods shorter than sampling interval Periods not captured exactly

Cross/Auto Correlation Limits at the ends of the series—they “hang out” and there are few points to compare Use for tree rings

Fig. 3 The principle of the construction of a tree-ring chronology. The inner tree-rings from a sample overlap in time with the outer tree-rings of an older sample. Fig. 4 Cross-correlation of the tree-ring series from a timber building to the period As the timber contains bark, the felling year of the trees must have occurred during the winter 1747 – 1748

Bristlecone Pine—9000 year chronology (~5000 years for Methuselah, more for Prometheus)

We have a number of tools for looking at time series and searching for periodicity in the data. The Nyquist Sampling Theorem relates the frequency at which you sample the time series to the frequencies in the original data series that you can resolve.Nyquist Sampling Theorem We will consider a time series to be a sequence of readings of some parameter at equally spaced points in time, although in many cases we could also consider a series of equally spaced values of the parameter along a horizontal distance axis. Waves represent time series that we can visualize either on a time or distance axis: on a time axis we remain at a fixed point and see how the water surface varies at discrete points in time, and on a distance axis we freeze the water surface and see how the surface varies at discrete distances along it. Tides represent time series that we can visualize on a time axis: we remain at a fixed point and see how the water surface varies at discrete points in time. We look at time series for two reasons: Search for periodicity in the data, both for objective confirmation that the data is periodic, and to determine the period or frequency of the regular pattern. Search for the relationship between two time series, and in particular to determine if there is a time “lag” between the two relationships. A change in one parameter may cause a change in another, but it may take time for the effect to be seen. For instance an El Niño will cause a change in the water levels on the east side of the Pacific, but it takes time for the water to cross the Pacific in a Kelvin wave. Thus the water level changes may lag the changes in pressure or wind speed. If we had clean data this would be an easy process, but real world data can be very noisy and we need mathematical assistance.