Different interpolation methods applied to the same data can\nproduce different results. Therefore, it is necessary to\nevaluate the comparative relevance of these methods.
\nThe\ninterpolation methods are based on the principle of spatial autocorrelation,\nwhich assumes that the closer the points, the more similar they are.\nIn the literature you will find many methods of interpolation,\nthey\nare generally classified into two categories: local and global methods.\n
\nLocal\nmethods predict the value of a point based on the values \u200b\u200bof points in the\nneighborhood. The most used local methods\nare: <\/p>\n\n\n\n
\u0095\nthe inverse of the weighted distance (IDW) method, <\/p>\n\n\n\n
\u0095\nthe local polynomial method, <\/p>\n\n\n\n
\u0095\nthe natural neighbour method (NN), and <\/p>\n\n\n\n
\u0095\nradial basic methods (Spline). <\/p>\n\n\n\n
On the other hand, global interpolation methods, such as\npolynomial interpolation functions, use all available sampling points to\ngenerate forecasts for a particular point. These\nmethods facilitate the evaluation and elimination of global phenomena (such as\ntrend) in physical data.
\nAll\nthese methods are also called deterministic as opposed to geostatistical\nmethods. <\/p>\n\n\n\n
Kriging<\/strong>\n<\/p>\n\n\n\n It is a geostatistical interpolation method that uses a\nvariogram ( analysis of the variability of the data according to the distance\nbetween them). The variogram depends on the\nspatial distribution of the data rather than the actual values. When\napplying the kriging method one can see results for input points different from\nthe input value. <\/p>\n\n\n\n The IDW method<\/strong>\n<\/p>\n\n\n\n It is a local deterministic interpolation technique that\ncalculates the value of a point by averaging the values \u200b\u200bof the neighbouring points\nweighted by the inverse of the distance at the calculated point: the closer the\npoints, the more the affected weighting is strong. The natural neighbour method<\/strong>\n<\/p>\n\n\n\n This method searches for the subset of samples closest to a\npoint and applies a weighting based on the area where they are located.\nIt is a local deterministic method and the interpolated\nheights are necessarily within the range of values \u200b\u200bused. It\ndoes not produce peaks, pits, ridges or valleys that are not already present in\nthe input samples and adapts locally to the input data structure.\nIt does not require any configuration by the user and works\nequally well for data distributed regularly as well as irregularly.\n<\/p>\n\n\n\n The Spline interpolation\nmethod<\/strong> <\/p>\n\n\n\n This method uses a mathematical function to minimize the\ncurvature of the surface and produces a smooth surface that matches exactly the\nentry points. <\/p>\n\n\n\n The ANUDEM method (topo to\nraster of ArcGis 3D Analyst)<\/strong> <\/p>\n\n\n\n This method uses an interpolation technique specifically\ndesigned to create a surface that best represents a natural drainage surface\nand preserves both ridge lines and stream networks. <\/p>\n\n\n\n Results of the comparison\nof interpolation methods<\/strong> \n\nWe compared the different\nmethods with the IGN repository for several projects, calculating the mean\nsquare error. In general, we can say that IDW<\/strong> methods\nand\nKriging<\/strong> adapt quite well, whatever the variations of\nterrain. Other methods are generally more sensitive to variations.\nThe ANUDEM<\/strong> method has excellent performance when it\nwas a question of the calculation of ridges and areas of flow stream ..\n As you must have already reckoned, we are particularly interested in the transition of the territorial data to 3D. The ArcGis Pro output with two side-by-side windows (2D window ArcMap type and 3D window ArcScene type)…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"give_campaign_id":0,"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"sfsi_plus_gutenberg_text_before_share":"","sfsi_plus_gutenberg_show_text_before_share":"","sfsi_plus_gutenberg_icon_type":"","sfsi_plus_gutenberg_icon_alignemt":"","sfsi_plus_gutenburg_max_per_row":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1260],"tags":[],"class_list":["post-8025","post","type-post","status-publish","format-standard","hentry","category-non-classe-en"],"aioseo_notices":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p6XU0A-25r","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/posts\/8025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/comments?post=8025"}],"version-history":[{"count":0,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/posts\/8025\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/media?parent=8025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/categories?post=8025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sigterritoires.fr\/index.php\/wp-json\/wp\/v2\/tags?post=8025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nIt\nconsiders that the points closer to the location to be calculated will have\nmore influence. <\/p>\n\n\n\n
\nIn\norder to study the sensitivity of the interpolation methods according to the\nnature of the terrain, we grouped the results according to three types of\nslope: zones with little slope, zones of steep slope, and zones having a\nmixture of the two. The results are presented in\nqualitative form (stars) but it can be said that the best results have an EQM\nof the order of 50 cm and the least good an EQM of the order of 2m.\n\n\n\n\n<\/p>\n\n\n\n![\"\"](\"https:\/\/i0.wp.com\/www.sigterritoires.fr\/wp-content\/uploads\/2019\/02\/51.png?resize=525%2C77&ssl=1\")
<\/figure>\n\n\n\n
\nIn\nlow slope areas, Kriging<\/strong> and the Natural Neighbor<\/strong>\ngive very good results, and we advise to adopt them in this case.\nIn areas of steep slope, the average differences are less\nmarked and must analyze them more on a case-by-case basis. The Natural\nNeighbor is<\/strong> best applied on small areas of study. For\nthe calculation of the flow zones the ANUDEM<\/strong> method gives\nthe best results.
\nThe\nnatural neighbour<\/strong> method showed almost optimal values \u200b\u200bon smooth\nsurfaces.
\nSpline-<\/strong> based methods fit a minimum curved surface\nthrough the entry points. It preserves trends in the\nsample data and adapts to rapid changes in gradient or slope.
\nIn\nall cases , kriging<\/strong> gives good results, even for steep declivity areas\nas well as for areas with both steep and steep slopes. This\nmethod takes into account the auto-correlation structures of the heights of the\nzone, in order to define the optimal weights. But,\nin return, the method needs a qualified user, with good knowledge of\ngeostatistics. <\/p>\n","protected":false},"excerpt":{"rendered":"