{"id":765,"date":"2019-07-12T12:24:03","date_gmt":"2019-07-12T11:24:03","guid":{"rendered":"http:\/\/35.193.178.118\/?page_id=765"},"modified":"2019-07-29T16:53:05","modified_gmt":"2019-07-29T15:53:05","slug":"introduction-to-the-effects-table-pt4","status":"publish","type":"page","link":"https:\/\/research.reading.ac.uk\/fiduceo\/archive\/tutorials\/introduction-to-the-effects-table\/introduction-to-the-effects-table-pt4\/","title":{"rendered":"Introduction to the effects table"},"content":{"rendered":"\r\n<h2 class=\"wp-block-heading\">Example effects table<\/h2>\r\n\r\n\r\n\r\n<p>In the second tutorial in this series, we examined an <a href=\"https:\/\/research.reading.ac.uk\/fiduceo\/considering-sources-of-uncertainty-effects\/example-uncertainty-analysis-tree\/\">Uncertainty Tree Diagram for the Advanced Very High Resolution Radiometer<\/a> (AVHRR). On this page will see how we might go about filling in an effects table for one of the error effects identified in this Uncertainty Tree Diagram. Specifically, we will look at the effect of detector noise on counts when measuring the calibration target, which contributes to uncertainty, <span class=\"katex-eq\" data-katex-display=\"false\">C_\\mathrm T<\/span>.<\/p>\r\n\r\n\r\n\r\n<p>In order to fill in an effects table for this effect, we need three pieces information:<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>The uncertainty associated with the effect<\/li>\r\n<li>The sensitivity coefficient, which allows us to propagate uncertainties associated with that effect to uncertainties associated with the measurand<\/li>\r\n<li>The error correlation structure over spatial, temporal and spectral dimensions for this effect<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>We\u2019ll look at each of these pieces of information in more detail in the sections below.<\/p>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\">The associated uncertainty<\/h3>\r\n\r\n\r\n\r\n<p>The detector noise is variable and at different times can be much smaller or larger than the nominal figure that is widely assumed. Within the FIDUCEO project we use an approach based on the Allan Deviation to estimate the uncertainty due to evolving noise. More information on this technique can be found at this <a href=\"\/sites\/default\/files\/publications\/noise_and_allan_variance_report.pdf\">link<\/a>.<\/p>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\">The sensitivity coefficient<\/h3>\r\n\r\n\r\n\r\n<p>To determine the sensitivity coefficient for this effect, we can simply differentiate the measurement equation with respect to the calibration target counts. Note when the sensitivity coefficient is evaluated it will differ for each pixel since it is dependent upon the on the Earth count measured.<\/p>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\">The error correlation structure<\/h3>\r\n\r\n\r\n\r\n<ol class=\"wp-block-list\">\r\n<li>The fourth tutorial in this series, we saw that error correlation can be structured differently in different spatial and temporal dimensions. A summary of the error correlation structure for our chosen effect for different dimensions is given below.<\/li>\r\n<\/ol>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>Within scanline \u2013 Since the calibration target is only measured once per scanline, the noise error is the same for all pixels across a given scanline. Therefore, we have an error correlation of 1 across the whole scanline for this effect. The correlation type is therefore \u2018rectangular absolute\u2019, extending over the full range of this dimension, so we record the correlation scale as in this as <span class=\"katex-eq\" data-katex-display=\"false\">[- \\infty,+ \\infty]<\/span>.<\/li>\r\n<li>Between scanlines \u2013 The measurements of the calibration target counts are averaged in a rolling average as in the example in Tutorial 4. As we saw there this results in a \u2018triangular relative\u2019 correlation form, in this case with a base width of a defined number of scanlines, <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span><\/li>\r\n<li>Between orbits \u2013 Outside the averaging window there is no correlation<\/li>\r\n<li>Between channels &#8211; There is no correlation between channels<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<p>Bringing together<\/p>\r\n\r\n\r\n\r\n<p>We now have all of the information required to fill in an effects table for our chosen effect. The completed effects table is shown below.\u00a0<\/p>\r\n\r\n\r\n<table id=\"tablepress-7\" class=\"tablepress tablepress-id-7 dataTable no-footer\">\n<tbody class=\"row-hover\">\n<tr class=\"row-16\">\n<td class=\"column-3\">\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<thead>\n<tr class=\"row-1 odd\">\n<th class=\"column-1\" colspan=\"2\">Table descriptor<\/th>\n<th class=\"column-3\">How this is codified<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2\">\n<td class=\"column-1\" colspan=\"2\">Name of effect<\/td>\n<td class=\"column-3\">Calibration target counts radiometric noise<\/td>\n<\/tr>\n<tr class=\"row-3\">\n<td class=\"column-1\" colspan=\"2\">Affected term in measurement function<\/td>\n<td class=\"column-3\">Calibration target counts ($C_\\mathrm T$)<\/td>\n<\/tr>\n<tr class=\"row-4\">\n<td class=\"column-1\" colspan=\"2\">Channels \/ bands<\/td>\n<td class=\"column-3\">Channel 3B, 4 and 5 (3.7\u00b5m, 11\u00b5m and 12\u00b5m)<\/td>\n<\/tr>\n<tr class=\"row-5\">\n<td class=\"column-1\" rowspan=\"4\">\n<ol>\n<li style=\"list-style-type: none\">\n<ol>\n<li>Correlation type and form<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/td>\n<td class=\"column-2\">within scanline [pixels]<\/td>\n<td class=\"column-3\">Rectangular absolute<\/td>\n<\/tr>\n<tr class=\"row-6\">\n<td class=\"column-2\">from scanline to scanline [scanlines]<\/td>\n<td class=\"column-3\">Triangular relative<\/td>\n<\/tr>\n<tr class=\"row-7\">\n<td class=\"column-2\">between images\/orbits [orbits]<\/td>\n<td class=\"column-3\">None<\/td>\n<\/tr>\n<tr class=\"row-8\">\n<td class=\"column-2\">between channels \/ bands<\/td>\n<td class=\"column-3\">None<\/td>\n<\/tr>\n<tr class=\"row-9\">\n<td class=\"column-1\" rowspan=\"4\">\n<ol start=\"2\">\n<li style=\"list-style-type: none\">\n<ol start=\"2\">\n<li>Correlation scale<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/td>\n<td class=\"column-2\">within scanline [pixels]<\/td>\n<td class=\"column-3\"><span class=\"katex\"><span class=\"katex-mathml\">&#8211; \\infty,+ \\infty<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">\u221e<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<tr class=\"row-10\">\n<td class=\"column-2\">from scanline to scanline [scanlines]<\/td>\n<td class=\"column-3\">$\\pm N$<\/td>\n<\/tr>\n<tr class=\"row-11\">\n<td class=\"column-2\">between images\/orbits [orbits]<\/td>\n<td class=\"column-3\">None<\/td>\n<\/tr>\n<tr class=\"row-12\">\n<td class=\"column-2\">between channels \/ bands<\/td>\n<td class=\"column-3\">None<\/td>\n<\/tr>\n<tr class=\"row-13\">\n<td class=\"column-1\" colspan=\"2\">Uncertainty PDF shape<\/td>\n<td class=\"column-3\">Digitised Gaussian<\/td>\n<\/tr>\n<tr class=\"row-14\">\n<td class=\"column-1\" colspan=\"2\">Uncertainty units<\/td>\n<td class=\"column-3\">Counts<\/td>\n<\/tr>\n<tr class=\"row-15\">\n<td class=\"column-1\" colspan=\"2\">Uncertainty magnitude<\/td>\n<td class=\"column-3\">Estimated from Allan deviation from calibration target views accumulated over a complete orbit.<\/td>\n<\/tr>\n<tr class=\"row-16\">\n<td class=\"column-1\" colspan=\"2\">Sensitivity coefficient<\/td>\n<td class=\"column-3\"><span class=\"katex\"><span class=\"katex-mathml\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\partial&amp;space;L_{E}&amp;space;}{\\partial&amp;space;C_{T}}=\\frac{a_{1}L_{T}-a_{2}C^{2}_{T}}{C^{2}_{T}}C_{E}+\\frac{a_{1}L_{T}--a_{2}C^{2}_{T}}{C_{T}}\" alt=\"\\frac{\\partial L_{E} }{\\partial C_{T}}=\\frac{a_{1}L_{T}-a_{2}C^{2}_{T}}{C^{2}_{T}}C_{E}+\\frac{a_{1}L_{T}--a_{2}C^{2}_{T}}{C_{T}}\" align=\"absmiddle\" \/><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Example effects table In the second tutorial in this series, we examined an Uncertainty Tree Diagram for the Advanced Very High Resolution Radiometer (AVHRR). On this page will see how&#8230;<a class=\"read-more\" href=\"&#104;&#116;&#116;&#112;&#115;&#58;&#47;&#47;&#114;&#101;&#115;&#101;&#97;&#114;&#99;&#104;&#46;&#114;&#101;&#97;&#100;&#105;&#110;&#103;&#46;&#97;&#99;&#46;&#117;&#107;&#47;&#102;&#105;&#100;&#117;&#99;&#101;&#111;&#47;&#97;&#114;&#99;&#104;&#105;&#118;&#101;&#47;&#116;&#117;&#116;&#111;&#114;&#105;&#97;&#108;&#115;&#47;&#105;&#110;&#116;&#114;&#111;&#100;&#117;&#99;&#116;&#105;&#111;&#110;&#45;&#116;&#111;&#45;&#116;&#104;&#101;&#45;&#101;&#102;&#102;&#101;&#99;&#116;&#115;&#45;&#116;&#97;&#98;&#108;&#101;&#47;&#105;&#110;&#116;&#114;&#111;&#100;&#117;&#99;&#116;&#105;&#111;&#110;&#45;&#116;&#111;&#45;&#116;&#104;&#101;&#45;&#101;&#102;&#102;&#101;&#99;&#116;&#115;&#45;&#116;&#97;&#98;&#108;&#101;&#45;&#112;&#116;&#52;&#47;\">Read More ><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"parent":751,"menu_order":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":"","footnotes":""},"coauthors":[6],"class_list":["post-765","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.8.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Introduction to the effects table - Fiduceo<\/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\/fiduceo\/archive\/tutorials\/introduction-to-the-effects-table\/introduction-to-the-effects-table-pt4\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Introduction to the effects table - Fiduceo\" \/>\n<meta property=\"og:description\" content=\"Example effects table In the second tutorial in this series, we examined an Uncertainty Tree Diagram for the Advanced Very High Resolution Radiometer (AVHRR). 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