Anomaly time series
Encyclopedia
In atmospheric sciences
and some other applications of statistics, an anomaly time series is the time series
of deviations of a quantity from some mean
. Similarly a standardized anomaly series contains values of deviations divided by a standard deviation
. Location and scale measures that are resistant to the effects of outlier
s are sometimes used as the basis of the transformation
.
The location and scale parameters used in forming an anomaly time-series may either be constant or may themselves be time series. For example, if the original time series consisted of temperatures measured every hour, the effect of typical daily cycles of temperature might be remove by subtracting a time series containing mean temperature values for each hour of the day: clearly, this can be extended by including seasonal variations of temperature.
In the atmospheric sciences
, the climatological annual cycle
is often used as the mean value. Famous atmospheric anomaly time series are for instance the Southern Oscillation index (SOI) and the North Atlantic oscillation
index. SOI is the atmospheric component of El Niño, while NAO
plays an important role for Europe
an weather
by modification of the exit of the Atlantic storm track
.
Atmospheric sciences
Atmospheric sciences is an umbrella term for the study of the atmosphere, its processes, the effects other systems have on the atmosphere, and the effects of the atmosphere on these other systems. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather...
and some other applications of statistics, an anomaly time series is the time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
of deviations of a quantity from some mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
. Similarly a standardized anomaly series contains values of deviations divided by a standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
. Location and scale measures that are resistant to the effects of outlier
Outlier
In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....
s are sometimes used as the basis of the transformation
Data transformation (statistics)
In statistics, data transformation refers to the application of a deterministic mathematical function to each point in a data set — that is, each data point zi is replaced with the transformed value yi = f, where f is a function...
.
The location and scale parameters used in forming an anomaly time-series may either be constant or may themselves be time series. For example, if the original time series consisted of temperatures measured every hour, the effect of typical daily cycles of temperature might be remove by subtracting a time series containing mean temperature values for each hour of the day: clearly, this can be extended by including seasonal variations of temperature.
In the atmospheric sciences
Atmospheric sciences
Atmospheric sciences is an umbrella term for the study of the atmosphere, its processes, the effects other systems have on the atmosphere, and the effects of the atmosphere on these other systems. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather...
, the climatological annual cycle
Annual cycle
In geosciences, an annual cycle is the part of a measured quantity's fluctuation that is attributed to Earth's changing position in orbit over the course of the year. Such quantities might be influenced directly or indirectly In geosciences, an annual cycle is the part of a measured quantity's...
is often used as the mean value. Famous atmospheric anomaly time series are for instance the Southern Oscillation index (SOI) and the North Atlantic oscillation
North Atlantic oscillation
The North Atlantic oscillation is a climatic phenomenon in the North Atlantic Ocean of fluctuations in the difference of atmospheric pressure at sea level between the Icelandic low and the Azores high. Through east-west oscillation motions of the Icelandic low and the Azores high, it controls the...
index. SOI is the atmospheric component of El Niño, while NAO
NAO
NAO can refer to:* National Applications Office, an agent of the United States Department of Homeland Security* National Audit Office in several nations* Nautical Almanac Office in several nations...
plays an important role for Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
an weather
Weather
Weather is the state of the atmosphere, to the degree that it is hot or cold, wet or dry, calm or stormy, clear or cloudy. Most weather phenomena occur in the troposphere, just below the stratosphere. Weather refers, generally, to day-to-day temperature and precipitation activity, whereas climate...
by modification of the exit of the Atlantic storm track
Storm track
Storm tracks are the relatively narrow zones in the Atlantic and Pacific along which most Atlantic or Pacific extratropical cyclones travel.The storm tracks begin in the westernmost parts of Atlantic and Pacific, where the large temperature contrasts between land and sea cause cyclones to form,...
.