IRI
Statistical Analysis Tutorial
Table of Contents
Measures of Central Tendency
Running and Weighted Averages
Climatologies and Standardized Anomalies
Data Homogeneity
Data Stationarity
Measures of Dispersion
Correlation
Climate Indices
Frequency Distributions
Singular Value Decomposition
Interpolation Techniques
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Climatologies and Standardized Anomalies


  1. Introduction
  2. Climatologies
  3. Composites
  4. Standardized Anomalies

Introduction

Climatology is commonly known as the study of our climate, yet the term encompasses many other important definitions. Climatology is also defined as the long-term average of a given variable, often over time periods of 20-30 years. Climatologies are frequently employed in the atmospheric sciences, and may be computed for a variety of time ranges. A monthly climatology, for example, will produce a mean value for each month and a daily climatology will produce a mean value for each day, over a specified time range. Anomalies, or the deviation from the mean, are created by subtracting climatological values from observed data.

When seasonal variations are present within a set of data, it often helps to express the data in terms of standardized anomalies. Standardized anomalies, also referred to as normalized anomalies,are calculated by dividing anomalies by the climatological standard deviation. They generally provide more information about the magnitude of the anomalies because influences of dispersion have been removed. It is not necessary that a dataset have a particular distribution to express it in terms of standardized anomalies. 

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Climatologies


Example: Generate monthly vapor pressure climatologies over world landmasses from Jan 1901 to Dec 1995.

Locate Dataset and Variable
  • Select the "Datasets by Catagory" link in the blue banner on the Data Library page.
  • Click on the "Atmosphere" link.
  • Select the UEA CRU New CRU05 dataset.
  • Click on the "monthly" link under the Datasets and Variables subheading.
  • Select the "vapor pressure" link under the Datasets and Variables subheading. CHECK
Select Domains
  • No ranges will be adjusted in this example.
    The dataset will be analyzed over its entire temporal and spatial grids.
Manually Generate Periodic Mean Function of the Data (Climatology)
  • Click on the "Expert Mode" link in the function bar.
  • Type the following command under the text already there:

    T 12 splitstreamgrid
  • Press the OK button. CHECK
    This command splits the time grid into two new time grids. The T grid has a period of 12 months and a step of 1. This grid represents data from January, Februrary, March, etc. The T2 grid has a step of 12 and represents the years from the beginning of the dataset (1901) to the end of the dataset (1995).
  • Select the "Filters" link in the function bar.
  • Choose the Average over "T2" command. CHECK EXPERT
    Taking the average over T2 will generate a mean vapor pressure field for each month. In this example, the mean function is called the monthly climatology.
View Climatologies
  • To see your results, choose the viewer with coasts drawn. CHECK
  • You may cycle through the climatologies of different months by using the buttons above the viewer window.
Monthly Climatologies of Vapor Pressure from January 1901 to December 1995
         

The animated image above shows the monthly climatology. You may create animated loops such as this by entering "Jan to Dec" in the text box above the viewer window.

Create Climatologies via Shortcut
  • Click on the box titled "vapor pressure" in the source bar on the dataset page. CHECK
    This operation will undo the splitstreamgrid and average commands, erasing the monthly climatologies.
  • Click on the "Filters" link in the function bar.
  • Choose the Monthly Climatology command. CHECK EXPERT
    Using the "Monthly Climatology" link under the Filters menu is a more direct way of computing monthly climatologies of the data.
 

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Composites


Example: Generate a composite of Oct-Dec seasonal average monthly zonal surface wind anomalies from the 1951-2006 climatology for Oct-Dec El Niño seasons (based upon the Climate Prediction Center definition) during that range of years.

Locate Dataset and Variable
  • Select the "Datasets by Catagory" link in the blue banner on the Data Library page.
  • Click on the "Historical Model Simulations" link.
  • Select the NOAA NCEP-NCAR CDAS-1 dataset.
  • Click on the "MONTHLY" link under the Datasets and Variables subheading.
  • Select the "Diagnostic" link under the Datasets and Variables subheading.
  • Select the "above-ground" link under the Datasets and Variables subheading.
  • Select the "zonal wind" variable link under the Datasets and Variables subheading CHECK
Select Domains
  • Click on the "Data Selection" link in the function bar.

  • Enter the text Jan 1951 to Dec 2006 in the Time grid text box.

  • Press the Restrict Ranges button and then the Stop Selecting button. CHECK
Calculate the
Monthly Zonal Wind
Anomalies
  • Select the "Filters" link in the function bar.
  • Choose the "anomalies" calculates the difference between the (above) monthly climatology and the original data command. CHECK EXPERT
    For each gridbox this step calculates the difference between each monthly zonal wind value and the monthly climatology calculated over the 1951-2006 period. This is the monthly zonal wind anomaly.
    •
Calculate 3-Month
(Seasonal) Running
Averages
  • If you are not already in Expert Mode, click on the "Expert Mode" link. EXPERT
  • In the Expert Mode text box, under "yearly-anomalies" type in the following command:

    • T 3 runningAverage
  • Press the OK button. CHECK

Select the Oct-Dec
El Niño Seasons
to Composite
  • In the Expert Mode text box, after the existing text, type in the following command to initially select all Oct-Dec seasons from 1951 to 2006:

    • T (Oct-Dec) VALUES
  • The table on the following page at the Climate Prediction Center (CPC) website identifies historical El Niño and La Niña periods by 3-month season: Cold & Warm Episodes by Season. In the Expert Mode text box, after the existing text, type in the following command to select the Oct-Dec El Niño seasons identified in the CPC's table:

    • T (1951) (1957) (1963) (1965) (1968) (1969) (1972) (1976) (1977) (1982) (1986) (1987) (1991) (1994) (1997) (2002) (2004) (2006) VALUES
  • Press the OK button. CHECK
Average Over the
Selected Seasons
  • In the Expert Mode text box, after the existing text, type in the following command to average over the selected El Niño seasons to create the composite:

    • [T] average
  • Press the OK button. CHECK
  • To see your results, choose the viewer with coasts drawn. CHECK
Composite of Zonal Surface Wind Anomalies During Oct-Dec El Niño Seasons, 1951-2006
          

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Standardized Anomalies


Example: Calculate monthly sea surface temperature standardized anomalies from Jan 1984 to Dec 2003.

Locate Dataset and Variable
  • Select the "Datasets by Catagory" link in the blue banner on the Data Library page.
  • Click on the "Air-Sea Interface" link.
  • Select the NOAA NCEP EMC CMB GLOBAL Reyn_Smith dataset.
  • Select the "Reyn_SmithOIv2" link under the Datasets and Variables subheading.
  • Click on the "monthly" link again under the Datasets and Variables subheading.
  • Select the "Sea Surface Temperature" link again under the Datasets and Variables subheading. CHECK
Select Domains
  • Click on the "Data Selection" link in the function bar.

  • Enter the text Jan 1984 to Dec 2003 in the appropriate text boxes.

  • Press the Restrit Ranges button and then the Stop Selecting button. CHECK
Compute Anomalies
  • Click on the "Filters" link in the function bar.
  • Choose the anomalies command. CHECK EXPERT
    This operation calculates the difference between monthly climatology and the original data. These anomalies are not standardized.
Standardize Anomalies
  • Click on the "Expert Mode" link in the function bar.
  • Type the following command under the text already there:

    [T] standardize
  • Press the OK button. CHECK
    The standardize function divides each anomaly by the standard deviation of the data, removing influences of dispersion. The result is a dataset of standardized sea surface temperature anomalies.
View Standardized Anomalies
  • To see the result of these operations, choose the viewer with land shaded in black.
  • In the text box above the viewer window, enter the text Nov 1988. CHECK
  • Click on the Edit "plot" button in the table at the bottom of the page. CHECK
  • Select "sstacolorscale" in the Plot pull-down menu.
  • Click on the "plot" button. These steps select a default colorscale for sea surface temperature anomalies.
  • Click on the "more options" button.
    This button returns the users to the main viewer interface.

November 1988 Global Standardized Sea Surface Temperature Anomalies



 Standardizing anomalies facilitates the comparison of observations at two different locations. For example, an anomaly of 2° Celsius may be insignificant off the east coast of Peru and highly significant in the Central Atlantic Ocean. A standardized anomaly of 2 has the same relative significance at both locations. Note that the below average sea surface temperatures in the Central and Eastern Pacific are indicative of the 1988 La Niña event.


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