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### Details and instructions on the monthly mean climate data correlation page

Topics:
Year Range | Lead/Lag | Contour interval option | Correlation Calculation | Variables | Climate Indices
Plotting Regions | Crossections | Page Creation | Feedback
1. Variable, years and levels available
Data is available from Jan 1948 to the present for most variables and is updated the first or 2nd week of the month with the previous month's data. Sigma level variables are available only until Apr 1998 ONLY pressure and air temperature are available for the tropopause level and ONLY u and v winds, relative humidity and pressure for the surface (.995 sigma). Streamfunction, divergence, vorticity and velocity potential are available ONLY on sigma levels.
Sea Surface Temperature: This is from the NOAA OU SST data (prescribed) over the ocean. Over land it is the skin temperature (prescribed as well). Sea Ice (which varies near land) affects these values and so the plotting range may not be as great over the tropics as desired. Using a lower latitude or specifying the contour range should help.

Index time series have cover a range of years. Some go back as far as 1948 but some don't. Please check the time series for actual data.

2. How correlations are calculated
For seasonal mean correlations, a value is calculated for each year for both the index time series and the variable that is being correlated with. A correlation is then calculated from these seasonal means For monthly correlations, each individual monthly value is used. The seasonal correlation for one month season is identical to the monthly correlation. The formula for the correlation is as follows:
r=sum(xy)/sqrt[sum(x**2)*(y**2)]

where x and y have the time means removed. There ARE other ways of calculating correlations.

The time indexes are not defined for some seasons (e.g. PNA in summer). If you choose that season for the correlation, you will get back a blank plot. Likewise, any missing values for the index will not be used the the calculation. Please look at the time series before interpreting the results.
3. Year range
Default years are 1948-2011 with the exception of seasons that would begin in 1947 (e.g. DJF) and variables that do not extend over the whole time period. For the former, 1949-2011 is used and for the latter the ending year varies. You can use your own range of years up to the latest possible data. Note that there is no data before January 1948. You should get an error message if you ask for data that is not there. For example, the season DJF 1948 contains December 1947 and therefore will not be calculated. The teleconnection values and the monthly means are usually updated within the next month.
The default lead/lag is 0 months. You can specify that the index time series either lead (come before) or lag (come after) the variable being correlated with. You can specify the correlations in months only. So, if you are doing seasonal correlations of FMA, a one month lead would correspond to the index time series of JFM. Please do not specify a lead of more than 12 months. The months used are indicated on the plot.
5. Contour range/interval option
A desired contour interval and range can be input instead of the default being used. Different plots can be easily compared (and the resulting gifs could be animated). For this option to work, the interval AND the range must be input. There must be at least 2 and less than 33 contours. The contour interval must be positive and the range must go from low to high.
6. Black and white option
Black and white contours and shading are available for use on non-color printers.
7. Atmospheric and Oceanic Indices
Monthly SST and atmospheric indices (e.g. PNA) are obtained from CPC except where noted below. Please see their site for details on the time series and how they were created. Calculation methods for other time-series can be found by following links in the right column. Please reference time-series use in publications!

See Climate Indices Plotting page for a description and references for the different time series.

 Random Calculation: Calculation details The timeseries you get is a randomly calculated "red noise" timeseries. In this case, the solution is calculated from the integrated stochastic differential equation ``` dx/dt = (-1/T)x + whitenoise. ``` 1/T is set to -1/3 months or -.333 for all cases. x(0) is determined using a changing seed value and the white noise is obtained by sampling from a gaussian distribution. Values are set for all 12 months of 1958-1999 and seasonal values are calculated from that. Code was graciously provided by Cecile Penland of CDC. Other definitions of a random timeseries could have been used. The intention is to demonstrate how spatial patterns that look "reasonable" will arise during correlation analysis even if the index timeseries has no physical basis. Please do not try to do Monte Carlo tests by repeatedly running the web-page.
8. To rotate polar stereographic plots
To rotate map, choose "custom" map projection and then choose either northern or southern polar stereographic projection. For lat range, enter 0 to 90 (for northern hemisphere) or -90 to 0 for southern. For longitude, the center of the longitude range input will be at the bottom of the plot. To center along 0E, choose -180 to 180, for example. To center at 90E, choose -90 to 270. You can plot sectors as well. The longitudes -90 to 90 in the NH will plot the half hemisphere from the US across the Atlantic to Europe.
9. Instructions for crossections
1. Choose a variable with multiple levels (temperature, geopotential heights, omega, humidity, wind, or potential temp).
2. Fro 'plot region' choose latitude by height or longitude by height.
3. For latitude by height plots, choose a latitudinal extent and a range of longitudes (or a single longitude) over which to average.
4. For longitude by height plots, choose a longitudinal extent and a range of latitudes (or a single latitude) over which to average.
5. Choose level range (bottom to top). Note that humidity variables only go through 300mb and omega only goes to 100mb.
10. Plotting regions
To plot over the dateline, use values from 0 to 720. For example, to plot 180W eastward to 180W, use 180 to 540. Be sure that the western most longitude is less than the eastern., For example, to plot 100W to 70W, use -100 to -70 or 260 to 290 and NOT 100 to 70.
There are 6 custom projections:
Northern Hemisphere: 0-90N, 0-360W in using a polar stereographic projection
Globe: 90S-90N 0E-360W
United States: 20N-65N; 235-285 polar stereographic projection
Tropics: 60S-60N
Tropical Pacific: 35N-35S 100E to 60W
Indio-Pacific (20S-20N,60E-160W)
4 Corner Region US (xxS-xxN,xxE-xxW)
The main interface for this page is an HTML form. The data that are input into this form are processed by a Perl script. The script reads the inputs, tests for bad inputs and then executes a FORTRAN code that produces a correlation file (in Netcdf). This file is what is processed by a GrADS script. The GrADS script is run as a batch job with the plot created in a virtual frame buffer (to increase the quality of the GIF output). Plot options are input into the GrADS script at this time. The plot in the frame buffer is converted to GIF and this GIF is displayed as part of a HTML document. The netCDF file and the gif file are kept in a directory where the files are periodically deleted.
12. Feedback
Please let me know if find the page useful. Likewise, let me know if you think any instructions are unclear, if you think there are bugs or if you have any suggestions for improvements of any type. I would particularly like to know if you use these pages for teaching purposes and if so, how. I can be reached by email at cathy.smith@noaa.gov or by phone at (303) 497-6263
13. Note: Leads and Lags >13 were allowed by the page but not in the instructions. Leads/lags >12 returned correlations a year off. You can now do lags/leads <=24.

Back to main correlation page.