{"id":3017,"date":"2026-01-26T14:35:25","date_gmt":"2026-01-26T14:35:25","guid":{"rendered":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png"},"modified":"2026-01-26T14:38:22","modified_gmt":"2026-01-26T14:38:22","slug":"picture1-3","status":"inherit","type":"attachment","link":"https:\/\/research.reading.ac.uk\/met-darc\/2026\/01\/28\/gaussian-anamorphosis-for-log-normal-distributions\/picture1-3\/","title":{"rendered":"Picture1"},"author":1167,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"__cvm_playback_settings":[],"__cvm_video_id":"","_links_to":"","_links_to_target":""},"class_list":["post-3017","attachment","type-attachment","status-inherit","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.8.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Picture1 - DARC<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Picture1 - DARC\" \/>\n<meta property=\"og:description\" content=\"An illustration of log-normal distribution. 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A negative difference means that the analysis variance is larger than the background.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\" \/>\n<meta property=\"og:site_name\" content=\"DARC\" \/>\n<meta property=\"article:modified_time\" content=\"2026-01-26T14:38:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1379\" \/>\n\t<meta property=\"og:image:height\" content=\"1034\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\",\"url\":\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\",\"name\":\"Picture1 - DARC\",\"isPartOf\":{\"@id\":\"https:\/\/research.reading.ac.uk\/met-darc\/#website\"},\"datePublished\":\"2026-01-26T14:35:25+00:00\",\"dateModified\":\"2026-01-26T14:38:22+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/research.reading.ac.uk\/met-darc\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Gaussian anamorphosis for log-normal distributions\",\"item\":\"https:\/\/research.reading.ac.uk\/met-darc\/2026\/01\/28\/gaussian-anamorphosis-for-log-normal-distributions\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Picture1\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/research.reading.ac.uk\/met-darc\/#website\",\"url\":\"https:\/\/research.reading.ac.uk\/met-darc\/\",\"name\":\"DARC\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/research.reading.ac.uk\/met-darc\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Picture1 - DARC","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png","og_locale":"en_GB","og_type":"article","og_title":"Picture1 - DARC","og_description":"An illustration of log-normal distribution. Upper left: the probability density function of log-normal distribution with the same \u03c3 and different \u00b5. Upper right: the same as upper left but with the same \u00b5 and different \u03c3. Bottom: the difference of standard deviation between background and analysis from a univariate data assimilation experiment where background and observations are sampled from a normal distribution of a truth of 0 and \u03c3 = 1 and \u03c3 = 0.9, respectively. Here, for demonstration purpose, we only show the case that the observations are larger than the truth (i.e., biased observations). 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Upper left: the probability density function of log-normal distribution with the same \u03c3 and different \u00b5. Upper right: the same as upper left but with the same \u00b5 and different \u03c3. Bottom: the difference of standard deviation between background and analysis from a univariate data assimilation experiment where background and observations are sampled from a normal distribution of a truth of 0 and \u03c3 = 1 and \u03c3 = 0.9, respectively. Here, for demonstration purpose, we only show the case that the observations are larger than the truth (i.e., biased observations). A negative difference means that the analysis variance is larger than the background.\" srcset=\"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-300x225.png 300w, https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-1024x768.png 1024w, https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-768x576.png 768w, https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png 1379w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>An illustration of log-normal distribution. Upper left: the probability density function of log-normal distribution with the same \u03c3 and different \u00b5. Upper right: the same as upper left but with the same \u00b5 and different \u03c3. Bottom: the difference of standard deviation between background and analysis from a univariate data assimilation experiment where background and observations are sampled from a normal distribution of a truth of 0 and \u03c3 = 1 and \u03c3 = 0.9, respectively. Here, for demonstration purpose, we only show the case that the observations are larger than the truth (i.e., biased observations). A negative difference means that the analysis variance is larger than the background.<\/p>\n"},"caption":{"rendered":"<p>An illustration of log-normal distribution. Upper left: the probability density function of log-normal distribution with the same \u03c3 and different \u00b5. Upper right: the same as upper left but with the same \u00b5 and different \u03c3. Bottom: the difference of standard deviation between background and analysis from a univariate data assimilation experiment where background and observations are sampled from a normal distribution of a truth of 0 and \u03c3 = 1 and \u03c3 = 0.9, respectively. Here, for demonstration purpose, we only show the case that the observations are larger than the truth (i.e., biased observations). A negative difference means that the analysis variance is larger than the background.<\/p>\n"},"alt_text":"An illustration of log-normal distribution. Upper left: the probability density function of log-normal distribution with the same \u03c3 and different \u00b5. Upper right: the same as upper left but with the same \u00b5 and different \u03c3. Bottom: the difference of standard deviation between background and analysis from a univariate data assimilation experiment where background and observations are sampled from a normal distribution of a truth of 0 and \u03c3 = 1 and \u03c3 = 0.9, respectively. Here, for demonstration purpose, we only show the case that the observations are larger than the truth (i.e., biased observations). A negative difference means that the analysis variance is larger than the background.","media_type":"image","mime_type":"image\/png","media_details":{"width":1379,"height":1034,"file":"2026\/01\/Picture1-1.png","filesize":186412,"sizes":{"medium":{"file":"Picture1-1-300x225.png","width":300,"height":225,"filesize":31798,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-300x225.png"},"large":{"file":"Picture1-1-1024x768.png","width":1024,"height":768,"filesize":171466,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-1024x768.png"},"thumbnail":{"file":"Picture1-1-150x150.png","width":150,"height":150,"filesize":12787,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-150x150.png"},"medium_large":{"file":"Picture1-1-768x576.png","width":768,"height":576,"filesize":115650,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-768x576.png"},"sow-carousel-default":{"file":"Picture1-1-272x182.png","width":272,"height":182,"filesize":24428,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1-272x182.png"},"full":{"file":"Picture1-1.png","width":1379,"height":1034,"mime_type":"image\/png","source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png"}},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0","keywords":[]}},"post":3016,"source_url":"https:\/\/research.reading.ac.uk\/met-darc\/wp-content\/uploads\/sites\/48\/2026\/01\/Picture1-1.png","filename":"Picture1-1.png","filesize":186412,"_links":{"self":[{"href":"https:\/\/research.reading.ac.uk\/met-darc\/wp-json\/wp\/v2\/media\/3017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.reading.ac.uk\/met-darc\/wp-json\/wp\/v2\/media"}],"about":[{"href":"https:\/\/research.reading.ac.uk\/met-darc\/wp-json\/wp\/v2\/types\/attachment"}],"author":[{"embeddable":true,"href":"https:\/\/research.reading.ac.uk\/met-darc\/wp-json\/wp\/v2\/users\/1167"}],"wp:attached-to":[{"embeddable":true,"post_type":"post","id":3016,"href":"https:\/\/research.reading.ac.uk\/met-darc\/wp-json\/wp\/v2\/posts\/3016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}