**Question: **With this exercise I wanted to look at patterns in the cycles of temperature and kelp coverage in southern Oregon. I wanted to examine if these two variables fluctuate together and if they do, is that synchronization is constant throughout the timeseries.

**Tool: **To do this I used wavelet analysis and cross wavelet analysis. These analyses do not depend on stationarity, unlike many of our other spatio-temporal tools, so they can detect changes in the period and frequency of a cycling time series or pair of time series.

**Steps: **Wavelet analyses require evenly sampled data. My temperature data is sampled evenly with one mean temperature per month (for both the intertidal and satellite data sets). My kelp timeseries is based on sporadic sampling however (i.e. whenever we could get a good cloud free satellite image). So the first task I needed to do was to interpolate my kelp timeseries to have monthly average canopy cover.

To do this, I interpolated each year’s timeseries separately. I first added a low canopy coverage for all winter months that did not have a data point. For the winter months (November –April), I found the median winter month canopy coveragewas about 1200m2, so all empty winter months were assigned to this median number. Every year had at least 3 data points in the non-winter months, so between the added winter month data and the summer month points, I was able to fit a polynomial spline to each year’s kelp timeseries. I did this in R using the *lm(y~bs(x, degree = #)* function. I then interpolated the value on the 15^{th} of every month from this spline using *predict* function.

I then used the WaveletComp package in R to conduct wavelet and cross wavelet analyses on my kelp and temperature timeseries.

**Results: **

b)

Figure 1: A) Wavelet analysis of my kelp canopy timeseries. B) Wavelet Analysis of the satellite temperature timseries. For both, colors correspond to power, white contour lines to the 0.1 significance level, and black lines to the power ridge.

My interpretation of the wavelets plots is:

1) Kelp Canopy – The highest power comes at the 6 month and 12 month periods. The 12 month wavelet makes sense, considering Nereocystis is an annual species, and the 6 month period wavelet corresponds to intra-growing season changes in canopy cover, possibly due to changes resulting from wave events. These areas of high power at 6 and 12 months are not consistent throughout the data set, and only occur when there are spikes in canopy coverage, which points to years where kelp cover, even at the height of the growing season was quite low,Another result to note is that in the first half of the timeseries, there is some power at the 5 year period. This could potentially be related to a climatic oscillation such as El Nino or PDO.

2) Satellite Temperature – similar to kelp canopy, the highest power for this wavelet analysis was at the 12 month period. Unlike the kelp wavelet, this 12 month period was consistently high power for the entire duration of the timeseries.

My interpretation of the cross-wavelet plots I generated is:

1) Kelp Canopy and Satellite Temperature – kelp canopy and satellite temperature appear to both have high power at 12 month periods. The arrows in this 12 month band largely point to the right, which suggests that x and y are in phase. A few of the arrows point down to some extent as well (around -30 degrees). This band is not constant however, and the significance of this high power band is lost around 1997 and 2003-2005. This suggests neither timeseries had strong annual cycles around this time. There are also a few other periods that appear to have a great enough amplitude to be considered significant. Perhaps most interesting is that the 5 year/60 month period appears is significant throughout the series. The arrows along this band are mostly pointing to the left and upwards, indicating that the two may be out of phase and that temperature (y) may be leading x (kelp). We saw a similar trend in the wavelet analysis for kelp and may be indicative of some kind of effect of climate oscillations.

2) Kelp Canopy and Local, Intertidal Temperature – This cross wavelet analysis was done on a dataset about how as long as the kelp/satellite dataset. This cross wavelet power graph is ‘chunkier’ at the annual scale than that between kelp and satellite data. This cross wavelet shows a dip in power from 2003-2005 like the above graph did, but also a dip about 2009-2011 as well. This indicates that the two timeseries are not both cycling together as strongly as did the kelp and satellite data. However, this cross wavelet has additional high power areas in the period of 3-11 months about 2014 and at 13-32 months from 2006-2010. There also appears to be some significant power at the 5 year range, similar to several previous power graphs, although this is hard to tell with a shorter timeseries.

Overall, my interpretation would be that both temperature datasets tend to cycle with kelp most strongly on the annual timescale, which makes sense. The local, intertidal data set does not appear to cycle as strongly with kelp as the satellite derived temperature does. My guess is that we got these results because local temperature is more susceptible to interruptions by relatively small scale phenomena such as upwelling or snowmelt and therefore adhere less strongly to the strong global cycles stemming from sun angle and exposure. I also think that these power graphs taken together suggest that some kind of multi-year climate oscillations may be involved in cycles of kelp canopy cover, since several of these analyses found significant amplitude at a roughly 5 year frequency.

**Critique:** My critique of this method is that I feel like wavelet and cross wavelet analysis is less informative than I was expecting it to be. Some of the strongest results just show cycles at an annual period that have a lower amplitude some years, which is pretty obvious from just looking at the graphs. I still feel like I’m not interpreting my results correctly, and I think part of the reason is that it’s hard for me to stop thinking in terms of correlation after my first two exercises.