1. Examples, examples: Outline
Overview of todays exercises
Basic scripting
Importing data
Working with temporal data
Working with missing data
Interpolation in 1D
Some time series analysis
Linear regression
Getting started
Preparing data
Data analysis

2. Exercise Overview Today we are going to be doing lots of exercises.
Today's dataset consists of 2001 hourly buoy measurements from a buoy near Bodega Bay (#46013):
Today we will:
Import the data
Learn how matlab deals with dates and times
Deal with missing data
Fill in missing data
Do some autocorrelations of wind and air temperature
Do a linear fit between wind and air temperature

3. Basic Scripting
Matlab commands can be stored in a text file with a .m extension and then run using the filename.
Change the working directory to your student directory (z:\Home\WFCB\WFCB-??\).
Use the edit command to being editing a text file.
edit
Put some commands in the file and save it as myfile.m:
a = 1:10;
plot( a, a.^2 )
Run your commands by either hitting F5 or typing from the command line:
myfile
Get in the habit of saving commands in m-files.

4. Importing data The data for this class is located in:
z:\Pkg\WFCB\class3\46013h2001.txt
Take a look at data (use edit).
There are many ways to get data into matlab.
One popular way is through the Excel toolbox.
Many other commands: load, importdata, textread, imread (try: help fileformats)
We have used load.
Drawback: Requires rigid format.
Another more flexible command is importdata.
More flexible – tries to load data no matter what
Works on lots of different formats (text, images, HDF,...)
Exercise: Use importdata to load todays dataset.
Next slide explains the result of loading data.

5. Structures
The result of loading a text file with importdata is often a structure. Many functions return structures.
Structures are like bags of variables. If you have loaded the data into a variable “a”, then the column names would be accessed using:
a.colheaders
Structures are a convenient way to keep together related variables.
Add an “element” to a structure like so:
a.buoy_num = 46013
Take a look at the elements of the result of importdata. Which “element” contains the numerical data?

6. Temporal data
The first four columns of the data are year, month, day and hour
Matlab has its own way of dealing with dates and times
Numbers days from Year 0, January 1 at 00:00!
Noon on January 1, 2000 is to matlab.
Matlab has functions to convert to and from matlab format:
datenum: converts year, month, ... to matlab date numbers
datevec: converts numbers to individual parts
datestr: converts numbers to human readable dates
datetick: converts numeric ticks on a plot to dates
Exercises:
Put dataset dates in matlab format (datenum)
Oops – dateset dates are in GMT (subtract 8 hours for PST)
Plot PST date vs. air temp (ATMP) and fix x-axis labels (datetick)

7. Initial plot of air temperature
Looks pretty bad – air temperatures of 1000ºC are still unusual. Why does it look this way?
Try scaling y-axis limits to something more reasonable (ylim)

8. Missing Data The problem in the last plot is missing data
In this dataset, 99, 999 and 9999 all indicate missing data.
Exercises:
Create a new variable of data with all missing data replaced by NaN.
Use logical operations (last class) to do this.
== is equivalent
| is logical or
Replot data

9. Plot of air temperature with NaNs
Try zooming in on the second half of March. Hint: Use datetick('keeplimits') to create date ticks after zoom.
Do you see any data gaps? What dates?

10. Interpolation in 1D
We want to fill in all that missing data using linear interpolation.
Exercise: Use the interp1 function to fill in the missing data for air temperature and water temperature (WTMP).
Hints:
You will need to create new variables with the results.
Use isnan to remove bad data (remember ~ is logical not).
Use interp1 to get values at all points. Where data already exists, it will return the same value; elsewhere, it will interpolate.

11. Replot data Exercises:
Plot air temperature and water temperature on a figure with different line colors.
Put a black circle around all data points that were interpolated (i.e. originally missing data). Hint: use isnan and look at line styles in help plot. Don't forget to hold on to your first plot.
Zoom in on second half of March again
Can you figure out how to fill in the dots? Don't worry if you can't do this.

12. Time Series Analysis: Autocorrelations
Now we want to look first at how water and air temperatures vary in time through autocorrelations.
Autocorrelations are a measure of how well data at one point in time reflects data at a future or past point in time.
It is basically a lagged correlation.
Exercises:
Compute the autocorrelations for air and water temp (hint: use the xcov and set the scaling option to 'coeff').
Plot both autocorrelation functions on the same graph.
Label x and y axes.
Remember that lags are in hours. Zoom in to a sensible time period (i.e. a few days).
What does the slower decline of one of the autocorrelations means? What do the oscillations in the curves mean?

13. Plot of autocorrelations
Slower decline of water temp autocorrelation means that it is more stable.
Oscillations every 24 hours mean that temps have a diurnal cycle, but air temp fluctuates more.

14. Linear Regression
Exercise: Make a scatter plot of air temperature against water temperature using the plot function.
Clearly there is a relationship.
Matlab can do basic linear regression with polyfit (more robust fits need Stats Toolbox or code available online).
Exercises:
Use polyfit to regress air temp vs. water temp.
Add a red line to your scatter plot with the linear fit using the polyval function.
Can you plot the residuals of the fit?

15. Next Class For next class, we will continue working with this dataset.
Also, think about datasets and analyses that you could bring into the class and we could work on.
Must be general enough that everyone can get involved.
Must not be too complex for us to work through it in a class.
I will choose one or two to work on.