{"id":1551,"date":"2019-03-04T09:00:13","date_gmt":"2019-03-04T09:00:13","guid":{"rendered":"http:\/\/kusuaks7\/?p=1156"},"modified":"2023-07-28T09:20:55","modified_gmt":"2023-07-28T09:20:55","slug":"time-series-in-atmospheric-sciences","status":"publish","type":"post","link":"https:\/\/www.experfy.com\/blog\/ai-ml\/time-series-in-atmospheric-sciences\/","title":{"rendered":"Time Series in Atmospheric Sciences"},"content":{"rendered":"<p>&nbsp;<\/p>\n<div class=\"container-fluid main-container\">\n<div id=\"introduction\" class=\"section level3\">\n<p><em><strong>Ready to learn Time Series Analysis?\u00a0<a href=\"https:\/\/www.experfy.com\/training\/courses\/time-series-analysis-for-healthcare\">Browse courses<\/a>\u00a0developed by industry thought leaders and Experfy in Harvard Innovation Lab.<\/strong><\/em><\/p>\n<h3>Introduction<\/h3>\n<p>This blog deals with the applications of time series in atmospheric and environmental sciences. The blog will also demonstrate the use of data transformation.<\/p>\n<p>The time series data being considered is the Southern Oscillation Index (SOI) which is an index of El-Nino-Southern Oscillation (ENSO) phenomenon. The index is used by major climate research organizations in the USA and around the world. This index provides a measure of fluctuations in sea-level pressure due to El Ni\u00f1o and La Ni\u00f1a events. The El Ni\u00f1o became a household name during 1998 due to the havoc that it created in the world weather including North America. For details the reader may refer to web page by <a href=\"https:\/\/www.ncdc.noaa.gov\/teleconnections\/enso\/indicators\/soi\/\" rel=\"noopener\">National Oceanic and Atmospheric Administration<\/a>.<\/p>\n<\/div>\n<div id=\"effects-of-el-nino\" class=\"section level3\">\n<h3>Effects of El-Ni\u00f1o<\/h3>\n<p>A webpage by <a href=\"http:\/\/www.oc.nps.edu\/webmodules\/ENSO\/effects.html\" rel=\"noopener\">Naval Postgraduate School<\/a> summarizes the major effects of El Ni\u00f1o as:<\/p>\n<ul>\n<li>Weather pattern changes like rainfall, temperatures, storm intensities.<\/li>\n<li>Changes in ocean currents and temperatures.<\/li>\n<\/ul>\n<p>The above effects lead to the following social, economic and health related consequences:<\/p>\n<ul>\n<li>Incidences of fires.<\/li>\n<li>Floods and Droughts.<\/li>\n<li>Agriculture problems and crash of fisheries leading to increased cost of food and famine.<\/li>\n<li>Political and social unrest.<\/li>\n<li>Epidemics like Malaria and hanta virus.<\/li>\n<\/ul>\n<p>The El Ni\u00f1o also has some benefits like:<\/p>\n<ul>\n<li>Reduced number of hurricanes and cyclones in North Atlantic.<\/li>\n<li>Milder winters in Southern Canada and northern continental United States.<\/li>\n<li>Replenishment of water supplies in the southwestern U.S.<\/li>\n<li>Fewer epidemics in some areas due to drier weather (like malaria in southeastern Africa)<\/li>\n<\/ul>\n<\/div>\n<div id=\"computing-the-southern-oscillation-index\" class=\"section level3\">\n<h3>Computing the Southern Oscillation Index<\/h3>\n<p>An <strong>anomaly<\/strong> in atmospheric science has nothing to do with abnormality as many are likely to believe. On the contrary, a <strong>standardized anomaly<\/strong> is defined as the difference between the data and it\u2019s mean divided by the standard deviation of the data. Mathematically it is given as:<\/p>\n<p><img decoding=\"async\" src=\"data:image\/png;base64,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\" alt=\"return\" \/><\/p>\n<p>where <span class=\"math\">(Z)<\/span>\u00a0is the standardized anomaly, <span class=\"math\">(x)<\/span> is the data, <span class=\"math\">(\bar{x})<\/span> is the mean of the data and <span class=\"math\">(sd(x))<\/span> is the standard deviation of the data. The numerator in the above equation is called an anomaly.<\/p>\n<p>The following procedure is adopted to calculate the Southern Oscillation Index (SOI) values. Using the above equation, the standardized anomalies of the surface level pressure are calculated for Tahiti in the Pacific and Darwin in the Northern Territory, Australia. Then we find the difference between the values for Tahiti and Darwin. Finally, we calculate the standardized anomalies of these differenced values. Therefore, the above transformation is applied twice for computing SOI.<\/p>\n<p>The SOI is used to study the extreme weather events like rainfall patterns in the North America, Australia and several other world regions. The SOI time series is frequently used in combination with other meteorological, agriculture, and health data to forecast droughts, rainfalls, diseases and crop yields etc. This helps in managing crop cultivation, in addition to taking measures with regard to flooding, droughts and associated damages. It\u2019s also being used in relation to the spread of epidemics in several regions of the world.<\/p>\n<\/div>\n<div id=\"exploratory-analysis\" class=\"section level3\">\n<h3>Exploratory Analysis<\/h3>\n<p>Here I have performed exploratory analysis of the Southern Oscillation Index. The data was obtained from the website of <a href=\"https:\/\/www.ncdc.noaa.gov\/teleconnections\/enso\/indicators\/soi\/\" rel=\"noopener\">National Oceanic and Atmosphere Administration<\/a>.<\/p>\n<pre class=\"r\"><code>soi &lt;- read.csv(\"data.csv\")\r\n# The data is a data frame.\r\nclass(soi)<\/code><\/pre>\n<pre><code>## [1] \"data.frame\"<\/code><\/pre>\n<pre class=\"r\"><code>head(soi)<\/code><\/pre>\n<pre><code>##     Date Value\r\n## 1 195101   1.5\r\n## 2 195102   0.9\r\n## 3 195103  -0.1\r\n## 4 195104  -0.3\r\n## 5 195105  -0.7\r\n## 6 195106   0.2<\/code><\/pre>\n<p>When dealing with a time series it is recommended to convert the data to \u201cts\u201d object.<\/p>\n<pre class=\"r\"><code>soi.ts &lt;- ts(soi[,2], start = c(1951,01), frequency = 12)\r\nclass(soi.ts)<\/code><\/pre>\n<pre><code>## [1] \"ts\"<\/code><\/pre>\n<p>Plotting the time series.<\/p>\n<pre class=\"r\"><code>plot(soi.ts, main = \"Southern Oscillation Index\", xlab = \"Year\", ylab = \"Southern Oscillation Index\", type=\"l\")<\/code><\/pre>\n<p><img decoding=\"async\" title=\"\" 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alt=\"experfy-blog\" width=\"672\" \/><\/p>\n<p>Since El-Ni\u00f1o usually peaks at the end of the calendar year, I will also plot the January values for all the years using R\u2019s \u201cwindow()\u201d function.<\/p>\n<pre class=\"r\"><code># Extracting the Southern Oscillation Index time series values for the January.\r\nsoi.jan &lt;- window(soi.ts, start = c(1951,1), frequency = TRUE)\r\nplot(soi.jan, main = \"Souther Oscillation Index for January\", xlab = \"Year\", ylab = \"SOI for January\")<\/code><\/pre>\n<p><strong>Conclusion<\/strong><\/p>\n<\/div>\n<div id=\"conclusion\" class=\"section level3\">\n<p>In the figures above you can spot the large negative value corresponding to the 1982\/83 El Ni\u00f1o. The occurence was in December\/January 1982\/83. There is also a relatively large reading\u00a0for 1998. The large negative values are a consequence of eastward movement of the precipitation activity from near Darwin to near Tahiti with higher than normal pressure at Darwin and lower than normal pressure at Tahiti. There are several other measures of the ENSO like the Oceanic Ni\u00f1o index (ONI) which is being used by the US National Oceanic and Atmospheric Administration.<\/p>\n<p>For a general review of the applications of statistical and machine learning methods please refer to \u201cStatistical Methods in Atmospheric Sciences\u201d by Daniel Wilks. For people wishing to delve deeper into the topic, there is an excellent graduate level text \u201cThe El Ni\u00f1o-Southern Oscillation Phenomenon\u201d by Sarachik and Cane. It contains an overview of the theory in addition to the forecasting methods generally used. I have not read the latter but it\u2019s on my reading list in 2016.<\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Predictive analytics can save lives, and Majid Khattak demonstrates how to do just that by using an index of the El-Nino-Southern Oscillation phenomenon to predict weather patterns that lead to severe storms.&nbsp;<\/p>\n","protected":false},"author":516,"featured_media":4030,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","footnotes":""},"categories":[183],"tags":[140],"ppma_author":[2455],"class_list":["post-1551","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-ml","tag-predictive-analytics"],"authors":[{"term_id":2455,"user_id":516,"is_guest":0,"slug":"majid-khattak","display_name":"Majid Khattak","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/?s=96&d=mm&r=g","user_url":"","last_name":"Khattak","first_name":"Majid","job_title":"","description":"Majid has over a decade of experience in machine learning and data science. He is currently an Assistant Professor of Mathematics based in Lahore, Pakistan."}],"_links":{"self":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/1551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/users\/516"}],"replies":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/comments?post=1551"}],"version-history":[{"count":3,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/1551\/revisions"}],"predecessor-version":[{"id":29740,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/posts\/1551\/revisions\/29740"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/media\/4030"}],"wp:attachment":[{"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/media?parent=1551"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/categories?post=1551"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/tags?post=1551"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.experfy.com\/blog\/wp-json\/wp\/v2\/ppma_author?post=1551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}