From d4e7925292da01c30b2f6171529e26db5693b785 Mon Sep 17 00:00:00 2001 From: "hermes.herrera" Date: Mon, 22 Jun 2026 16:17:34 +1200 Subject: [PATCH] Add kriging interpolation page (CONNECTIONTYPE kriging) Document the kriging CONNECTIONTYPE: the localized NNGP method and its two output bands (predictive mean and standard deviation), the PROCESSING reference, and a self-contained, reproducible worked example. The example ships downloadable files (the complete mapfile, two sampling networks, city points and a simplified coastline) that render standalone with no external dependencies, comparing IDW, the kriging mean and the kriging standard deviation for a dense and a clustered sampling network. --- en/images/kriging-clustered.png | Bin 0 -> 63989 bytes en/images/kriging-dense.png | Bin 0 -> 78071 bytes en/output/index.txt | 1 + en/output/kriging-example/cities_major.csv | 7 + .../kriging-example/grid_nz_clustered.csv | 64 +++ en/output/kriging-example/grid_nz_regular.csv | 239 ++++++++++ en/output/kriging-example/nz_coast.geojson | 14 + en/output/kriging-example/nz_scenarios.map | 408 ++++++++++++++++++ en/output/kriging.txt | 242 +++++++++++ 9 files changed, 975 insertions(+) create mode 100644 en/images/kriging-clustered.png create mode 100644 en/images/kriging-dense.png create mode 100644 en/output/kriging-example/cities_major.csv create mode 100644 en/output/kriging-example/grid_nz_clustered.csv create mode 100644 en/output/kriging-example/grid_nz_regular.csv create mode 100644 en/output/kriging-example/nz_coast.geojson create mode 100644 en/output/kriging-example/nz_scenarios.map create mode 100644 en/output/kriging.txt diff --git a/en/images/kriging-clustered.png b/en/images/kriging-clustered.png new file mode 100644 index 0000000000000000000000000000000000000000..7b232fd48baf9bbe5afc42a4210753e06bb735b4 GIT binary patch literal 63989 zcmY&=1z1$k7A{DLlt@bqDIkrcFmy{xcY`ztNP|k}5YinYAt2o#IUtSn5Yin(H}8zz zci(-VeDcjO=bXLQUi)AF`q$bMuBt4HgGq*ogoK16FDLaD2?>=I2?==t108s0YHceL z_(g3l_f`oB$(sQQ>0=NQ(lzkb$1NlzcTOav9TOxZ!4xDU66cI2H8Ai8bTb86DWnI) zzns=@3BV_jZnJW}X2XD{GRn%eGJ8GMiVVs+mST+Rn<#X!_=Dbui*y+stif=+`uLr{*)_ zH>^ehb-|Ospb7f>UlDZ)4CVj5+)}_K{(pZHc>CkOf0F8n`yBk=SIjYltp9ERyrt$+ zVDg{a;Yox=(4k@d_mu{PLj#IdJ;OXGA1~iZ2shO&M2A)!oV5n!m=A(ZsNy^=*+v$F z+=PwnuUS*w<-)p%es^~kjy4!^c(F3j^_#1O(?fdPCio$%aMVhv&pKdn=0tRp-y3BV z@BfJG)t%rvKGjwv=vs&W0G`T_&wcnhIfUPeAba}LdhL%^;@Q|w>q9H=_ykm&&CvNX zd=p`kL=s^ym5y~VXqdY;*kG4uRQJQrLibcO1*8Nh^1gnJD^bM=_z5wG-R>J-RCSF@ zJ3iG6dz6Y#TUcP6bx9DHAe{CJRg=L_D-Fx|M|0)rh{|UU_7%o31DK0 zuwR@$R#-O&wdAhWBNnseLRIgU!Fp+APtZ|{B09M_S~^91_87canIi~UyT6>}j~K`R zcPUxkKJ(+v&wbH4f4scA0LsIYP{fLd0tS9A;(RF%zF8^lHiH{2L8Q!U>fC>LHeWeD zRSPo$j9dfBgQs8Qy?C;#{OlG4t-`sr7o`@`SC zhrtr!b?KtX^^5+~`^!(pA`w&Y7zlOzd9HV<-xYlLRWI)n))hVUh&E z;HCeq6Y|YL|1V9unW-t;yJm>mwK=#_*BOEZ`wjZWyOaFUwrH$^)>RlyL$BsL?1 z-}rWK)~nz76S!3{5@!FF2Nq=3ehQc&O?M5A7vSxQ9fv0_6Q+*=BZ6318@!H?eNIlX zI23?+Py_QQyFCu%k1tlhpVvsg3E7EFne5?z@U8sciAcJtqbStr|EwNqfAq23hT_Kv z2z<7u089h}n8)@eumfm7U4bAtipf*~JcaDrl1I}2Uf;zo#P)(1Qf;+>jzm0|F3B2~ zQ`Y)>KR4V)8JL3J^_Vp~T}?6Z(7_-FAz&$1A1DC<`C5E6hXPrdu$orLx30)O(9XgIZaRzb{e#cOO|3Vf1x=D z6$RP0v=q2wDZ+Qk^dZg92h!PUXvrsS+HMY6(81@s0YceMcPp>zLjjwq$NyXZ>n1(G zhk}b~PBsQt_K8Y?&#g}{u8cff*25%;)iVGesySc%&CUo6-@b2x@uyb zAUm?X7Lz-}#iv06gUeDLgheA|Dd7Cj>bViD-KR&akZdn2YfVzBRk80r*mRcexw=m@ zm^QX@?%YGjh*+2HG@18S^d1S{#q3SVKTR&~POR1gQ(8!KLV{j^{a#;wYz6i)0(V>heEhx0#%K&- zT$fg|%Mr6sW68yF&+uQ;)hKhMuWCrNAN@)4m3C?`)?YF%6wv28A1BMI`XW-U%_;?w zZ`VVmk{nTTtfaA+aL4xNoOy&iVo~(QBiq@c7|RlH$P8{fPTqa5aP_$~i`SVUB%9uS z0U#-GGltK=M7tt;R&F;dzX_Zbm?JmbmEXXNn4y&JOvnL_Lo_g#nYyxQ{^W{+Y8DAs za}=S&2B~A6s2OK3Rsdz2{8mRuOsw8?}>z!)lp_*7($7f1A&K?`JR9`Fo7K zPMl=us~1vXj@nt5!lydrdf@pXE-^j}yzC|M>G854zG?hO#vhcS)elF8ZD)}K0;^fT zb#j1Ly!_`CGd7_wzQY=xo6MM@i7BYl$%4F*sIEpU!58Cp!C?QraOvBgTy=5!)$y&F!=H`UY)*UzB@ zL}LDVjNN^5pvd!g(vAysa&;}~A zk==7B0NxRd|8VEMy@tEJ($%DoV%^0{|+G zd}uJ!#EY8d6 zOi&LdG!t;Rpx}QHonC)DQO!}g@VRlX(%!m%)#lCA4?Hu}@onsmAzpfGse$+R_L?E( z`}Jma#7ozAJ&pke07U5gixa@7M%r)5eD>QEbcaQO5J+`*1V=^j2YH{$*Nc`HsUkK^ z*1mx6#X~tQUpwVQWi2%Xh_1b;CEG4HbimG*j{h4zO@weSL~jLTDgE)9wAwULHKa|y zQ6|O870loF{^teE;~G%Sqrf(IF6d1^;uYKJnPQsF0?)CtjkHbPudV zC^FdT|p*YAFBV;eW$ft3UPkUJV<(gZmt{@eOWzh?rng*}gFlMTEc z+yuMGoyu~mOHb{dhxbbZya-8DbRAlxOC-F*@{s;Iwx1LUvC|Ds)9sKk$|^i=UIC

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a/en/output/index.txt +++ b/en/output/index.txt @@ -16,6 +16,7 @@ idw imagemaps kerneldensity + kriging ogr_output pdf svg diff --git a/en/output/kriging-example/cities_major.csv b/en/output/kriging-example/cities_major.csv new file mode 100644 index 00000000000..05167fdf513 --- /dev/null +++ b/en/output/kriging-example/cities_major.csv @@ -0,0 +1,7 @@ +wkt,city,annual_mm,elevation_m,weight,label +POINT(174.76 -36.85),Auckland,1169,35,39,Auckland 1169 mm +POINT(174.78 -41.29),Wellington,763,3,25,Wellington 763 mm +POINT(173.28 -41.27),Nelson,1181,4,39,Nelson 1181 mm +POINT(171.21 -42.45),Greymouth,2833,6,94,Greymouth 2833 mm +POINT(172.64 -43.53),Christchurch,531,11,18,Christchurch 531 mm +POINT(168.66 -45.03),Queenstown,1496,318,50,Queenstown 1496 mm diff --git a/en/output/kriging-example/grid_nz_clustered.csv b/en/output/kriging-example/grid_nz_clustered.csv new file mode 100644 index 00000000000..487a21d2faf --- /dev/null +++ b/en/output/kriging-example/grid_nz_clustered.csv @@ -0,0 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PROCESSING "IDW_RADIUS=250" + PROCESSING "IDW_POWER=2" + PROCESSING "IDW_COMPUTE_BORDERS=OFF" + OFFSITE 0 0 0 + CLASS + STYLE # < 250 mm + COLORRANGE "#8b0000" "#8b0000" + DATARANGE 0 8.33 + END + STYLE # 250 - 500 + COLORRANGE "#e41a1c" "#e41a1c" + DATARANGE 8.33 16.67 + END + STYLE # 500 - 750 + COLORRANGE "#ff7f00" "#ff7f00" + DATARANGE 16.67 25 + END + STYLE # 750 - 1000 + COLORRANGE "#ffe93a" "#ffe93a" + DATARANGE 25 33.33 + END + STYLE # 1000 - 1250 + COLORRANGE "#a6d96a" "#a6d96a" + DATARANGE 33.33 41.67 + END + STYLE # 1250 - 1500 + COLORRANGE "#41ab5d" "#41ab5d" + DATARANGE 41.67 50 + END + STYLE # 1500 - 2000 + COLORRANGE "#1d9182" "#1d9182" + DATARANGE 50 66.67 + END + STYLE # 2000 - 3000 + COLORRANGE "#6baed6" "#6baed6" + DATARANGE 66.67 100 + END + STYLE # 3000 - 4000 + COLORRANGE "#2166ac" "#2166ac" + DATARANGE 100 133.33 + END + STYLE # > 4000 mm + COLORRANGE "#6a3d9a" "#6a3d9a" + DATARANGE 133.33 260 + END + END + END + LAYER + NAME "km_regular" + TYPE raster + STATUS off + CONNECTIONTYPE kriging + CONNECTION "grid_regular" + MASK "landmask" + PROCESSING "RANGE_COLORSPACE=RGB" + PROCESSING "KRIGING_MODEL=EXPONENTIAL" + PROCESSING "KRIGING_TYPE=ORDINARY" + PROCESSING "KRIGING_NEIGHBORS=16" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "KRIGING_NUGGET=0" + PROCESSING "BANDS=1" + OFFSITE 0 0 0 + CLASS + STYLE # < 250 mm + COLORRANGE "#8b0000" "#8b0000" + DATARANGE 0 8.33 + END + STYLE # 250 - 500 + COLORRANGE "#e41a1c" "#e41a1c" + DATARANGE 8.33 16.67 + END + STYLE # 500 - 750 + COLORRANGE "#ff7f00" "#ff7f00" + DATARANGE 16.67 25 + END + STYLE # 750 - 1000 + COLORRANGE "#ffe93a" "#ffe93a" + DATARANGE 25 33.33 + END + STYLE # 1000 - 1250 + COLORRANGE "#a6d96a" "#a6d96a" + DATARANGE 33.33 41.67 + END + STYLE # 1250 - 1500 + COLORRANGE "#41ab5d" "#41ab5d" + DATARANGE 41.67 50 + END + STYLE # 1500 - 2000 + COLORRANGE "#1d9182" "#1d9182" + DATARANGE 50 66.67 + END + STYLE # 2000 - 3000 + COLORRANGE "#6baed6" "#6baed6" + DATARANGE 66.67 100 + END + STYLE # 3000 - 4000 + COLORRANGE "#2166ac" "#2166ac" + DATARANGE 100 133.33 + END + STYLE # > 4000 mm + COLORRANGE "#6a3d9a" "#6a3d9a" + DATARANGE 133.33 260 + END + END + END + LAYER + NAME "sd_regular" + TYPE raster + STATUS off + CONNECTIONTYPE kriging + CONNECTION "grid_regular" + MASK "landmask" + PROCESSING "RANGE_COLORSPACE=RGB" + PROCESSING "KRIGING_MODEL=EXPONENTIAL" + PROCESSING "KRIGING_TYPE=ORDINARY" + PROCESSING "KRIGING_NEIGHBORS=16" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "KRIGING_NUGGET=0" + PROCESSING "BANDS=2" + OFFSITE 0 0 0 + CLASS + STYLE + COLORRANGE "#440154" "#3b528b" + DATARANGE 0 11.25 + END + STYLE + COLORRANGE "#3b528b" "#21908c" + DATARANGE 11.25 22.5 + END + STYLE + COLORRANGE "#21908c" "#5dc863" + DATARANGE 22.5 33.75 + END + STYLE + COLORRANGE "#5dc863" "#fde725" + DATARANGE 33.75 45 + END + END + END + + #=== scenario 2: clustered network (gaps over the back-country) ======# + LAYER + NAME "idw_clustered" + TYPE raster + STATUS off + CONNECTIONTYPE idw + CONNECTION "grid_clustered" + MASK "landmask" + PROCESSING "RANGE_COLORSPACE=RGB" + PROCESSING "IDW_RADIUS=250" + PROCESSING "IDW_POWER=2" + PROCESSING "IDW_COMPUTE_BORDERS=OFF" + OFFSITE 0 0 0 + CLASS + STYLE # < 250 mm + COLORRANGE "#8b0000" "#8b0000" + DATARANGE 0 8.33 + END + STYLE # 250 - 500 + COLORRANGE "#e41a1c" "#e41a1c" + DATARANGE 8.33 16.67 + END + STYLE # 500 - 750 + COLORRANGE "#ff7f00" "#ff7f00" + DATARANGE 16.67 25 + END + STYLE # 750 - 1000 + COLORRANGE "#ffe93a" "#ffe93a" + DATARANGE 25 33.33 + END + STYLE # 1000 - 1250 + COLORRANGE "#a6d96a" "#a6d96a" + DATARANGE 33.33 41.67 + END + STYLE # 1250 - 1500 + COLORRANGE "#41ab5d" "#41ab5d" + DATARANGE 41.67 50 + END + STYLE # 1500 - 2000 + COLORRANGE "#1d9182" "#1d9182" + DATARANGE 50 66.67 + END + STYLE # 2000 - 3000 + COLORRANGE "#6baed6" "#6baed6" + DATARANGE 66.67 100 + END + STYLE # 3000 - 4000 + COLORRANGE "#2166ac" "#2166ac" + DATARANGE 100 133.33 + END + STYLE # > 4000 mm + COLORRANGE "#6a3d9a" "#6a3d9a" + DATARANGE 133.33 260 + END + END + END + LAYER + NAME "km_clustered" + TYPE raster + STATUS off + CONNECTIONTYPE kriging + CONNECTION "grid_clustered" + MASK "landmask" + PROCESSING "RANGE_COLORSPACE=RGB" + PROCESSING "KRIGING_MODEL=EXPONENTIAL" + PROCESSING "KRIGING_TYPE=ORDINARY" + PROCESSING "KRIGING_NEIGHBORS=16" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "KRIGING_NUGGET=0" + PROCESSING "BANDS=1" + OFFSITE 0 0 0 + CLASS + STYLE # < 250 mm + COLORRANGE "#8b0000" "#8b0000" + DATARANGE 0 8.33 + END + STYLE # 250 - 500 + COLORRANGE "#e41a1c" "#e41a1c" + DATARANGE 8.33 16.67 + END + STYLE # 500 - 750 + COLORRANGE "#ff7f00" "#ff7f00" + DATARANGE 16.67 25 + END + STYLE # 750 - 1000 + COLORRANGE "#ffe93a" "#ffe93a" + DATARANGE 25 33.33 + END + STYLE # 1000 - 1250 + COLORRANGE "#a6d96a" "#a6d96a" + DATARANGE 33.33 41.67 + END + STYLE # 1250 - 1500 + COLORRANGE "#41ab5d" "#41ab5d" + DATARANGE 41.67 50 + END + STYLE # 1500 - 2000 + COLORRANGE "#1d9182" "#1d9182" + DATARANGE 50 66.67 + END + STYLE # 2000 - 3000 + COLORRANGE "#6baed6" "#6baed6" + DATARANGE 66.67 100 + END + STYLE # 3000 - 4000 + COLORRANGE "#2166ac" "#2166ac" + DATARANGE 100 133.33 + END + STYLE # > 4000 mm + COLORRANGE "#6a3d9a" "#6a3d9a" + DATARANGE 133.33 260 + END + END + END + LAYER + NAME "sd_clustered" + TYPE raster + STATUS off + CONNECTIONTYPE kriging + CONNECTION "grid_clustered" + MASK "landmask" + PROCESSING "RANGE_COLORSPACE=RGB" + PROCESSING "KRIGING_MODEL=EXPONENTIAL" + PROCESSING "KRIGING_TYPE=ORDINARY" + PROCESSING "KRIGING_NEIGHBORS=16" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "KRIGING_NUGGET=0" + PROCESSING "BANDS=2" + OFFSITE 0 0 0 + CLASS + STYLE + COLORRANGE "#440154" "#3b528b" + DATARANGE 0 11.25 + END + STYLE + COLORRANGE "#3b528b" "#21908c" + DATARANGE 11.25 22.5 + END + STYLE + COLORRANGE "#21908c" "#5dc863" + DATARANGE 22.5 33.75 + END + STYLE + COLORRANGE "#5dc863" "#fde725" + DATARANGE 33.75 45 + END + END + END + + #=== sample sources, basemap, labelled cities ========================# + LAYER + NAME "grid_regular" + TYPE point + STATUS off + CONNECTIONTYPE OGR + CONNECTION "grid_nz_regular.csv" + DATA "grid_nz_regular" + PROJECTION + "init=epsg:4326" + END + CLASS + STYLE + SIZE [weight] + END + END + END + LAYER + NAME "grid_clustered" + TYPE point + STATUS off + CONNECTIONTYPE OGR + CONNECTION "grid_nz_clustered.csv" + DATA "grid_nz_clustered" + PROJECTION + "init=epsg:4326" + END + CLASS + STYLE + SIZE [weight] + END + END + END + LAYER + NAME "landmask" + TYPE polygon + STATUS off + CONNECTIONTYPE OGR + CONNECTION "nz_coast.geojson" + DATA "nz_coast" + PROJECTION + "init=epsg:4326" + END + CLASS + STYLE + COLOR 0 0 0 + END + END + END + LAYER + NAME "coastline" + TYPE line + STATUS on + CONNECTIONTYPE OGR + CONNECTION "nz_coast.geojson" + DATA "nz_coast" + PROJECTION + "init=epsg:4326" + END + CLASS + STYLE + COLOR 90 110 130 + WIDTH 0.6 + END + END + END + LAYER + NAME "cities" + TYPE point + STATUS on + CONNECTIONTYPE OGR + CONNECTION "cities_major.csv" + DATA "cities_major" + PROJECTION + "init=epsg:4326" + END + CLASS + STYLE + SYMBOL "circle" + SIZE 5 + COLOR 20 20 20 + OUTLINECOLOR 255 255 255 + WIDTH 1 + END + END + END + + SYMBOL + NAME "circle" + TYPE ellipse + FILLED true + POINTS 1 1 END + END +END diff --git a/en/output/kriging.txt b/en/output/kriging.txt new file mode 100644 index 00000000000..64c32a7c7fc --- /dev/null +++ b/en/output/kriging.txt @@ -0,0 +1,242 @@ +.. _kriging: + +***************************************************************************** + Kriging interpolation +***************************************************************************** + +.. contents:: Table of Contents + :depth: 2 + :backlinks: top + +Introduction +============ + +.. versionadded:: 8.8 + +Kriging turns scattered vector features into a continuous raster surface, like +:ref:`idw`, but it is a *geostatistical* interpolator: it fits a model of the +data's spatial correlation and returns, together with the interpolated value, +an estimate of how uncertain that value is. + +It is implemented as a localized **Nearest-Neighbor Gaussian Process (NNGP)**: +each output pixel is predicted by ordinary (or simple) kriging using only its +``m`` nearest input samples, so cost scales with the neighbour count rather +than with a dense solve over the whole dataset. + +It produces **two raster bands**, selected with ``PROCESSING "BANDS=n"``: + +- band **1**: the predictive **mean**, the interpolated surface; +- band **2**: the predictive **standard deviation** (the kriging standard + error), close to zero at the sample locations and rising across the gaps + between them. + +Configuration +============= + +Set the `LAYER` `CONNECTIONTYPE` parameter to `KRIGING`. As with :ref:`idw`, +the samples come from another vector `LAYER` referenced by `CONNECTION`, and +each sample's value is read from that layer's ``STYLE SIZE [attribute]`` +binding (see the corresponding section of :ref:`kerneldensity`). + +The interpolation takes the following parameters: + +- **CONNECTION "layername"** : reference to the `NAME` or `GROUP` of a `LAYER` + to use as an input vector datasource. The referenced layer should be a + `TYPE` `POINT` layer. + +- **PROCESSING "KRIGING_MODEL=EXPONENTIAL"** : the covariance model, one of + ``EXPONENTIAL`` (Matern nu=1/2, the default), ``GAUSSIAN`` or ``SPHERICAL``. + +- **PROCESSING "KRIGING_TYPE=ORDINARY"** : ``ORDINARY`` (the default) assumes an + unknown, locally constant mean; ``SIMPLE`` assumes a known (zero or + pre-detrended) mean. + +- **PROCESSING "KRIGING_NEIGHBORS=16"** : the number of nearest samples ``m`` + used to predict each pixel. Larger values approach a full kriging solve at + higher cost (roughly ``O(m^3)`` per pixel). The default is 16. + +- **PROCESSING "KRIGING_RANGE=numeric"** : the practical range of the + covariance model, in pixels: the lag beyond which samples are effectively + uncorrelated. The default auto-fits to about a third of the image diagonal. + +- **PROCESSING "KRIGING_SILL=numeric"** : the partial sill, the variance the + covariance model reaches at large lags. The default auto-fits from the + sample variance. + +- **PROCESSING "KRIGING_NUGGET=numeric"** : the nugget. ``0`` (the default) + makes the surface interpolate the samples exactly; a positive value smooths + through them and stabilises the solve where samples are dense or coincident. + +- **PROCESSING "BANDS=1|2"** : which output band to render: ``1`` for the mean + (the default), ``2`` for the standard deviation. + +Worked example: two sampling networks +====================================== + +The example interpolates annual rainfall over New Zealand from the same field +two ways, to show both what kriging adds over IDW and how the uncertainty band +responds to the sampling layout. Each scenario is rendered as three panels: +IDW, the kriging mean (band 1) and the kriging standard deviation (band 2). + +Example files +------------- + +Download the files into one directory and render the example as is; no +preprocessing step and no external data are required. + +- :download:`nz_scenarios.map `: the complete + mapfile (the IDW, kriging-mean and kriging-SD layers for both scenarios, plus + the point sources, land mask, coastline and city points). +- :download:`grid_nz_regular.csv `: the + dense, evenly spaced network (238 samples). +- :download:`grid_nz_clustered.csv `: + samples kept only near six cities (63 samples), leaving the West Coast, + Fiordland and inland Southland unsampled. +- :download:`cities_major.csv `: six cities, + drawn as points for orientation. +- :download:`nz_coast.geojson `: a simplified + coastline, used for both the land mask and the outline. + +Each sample's value is the annual rainfall scaled to the 0-255 byte range +(rainfall in mm divided by 30); the kriging layer reads it through +``STYLE SIZE [weight]``. + +Mapfile +------- + +The complete mapfile is the download above. Its essential elements are the +point layer that holds the samples and the two kriging layers that read it. +``KRIGING_RANGE`` and ``KRIGING_SILL`` are pinned so the two scenarios share one +covariance model and their SD bands stay comparable: + +.. code-block:: mapfile + + # the sample layer; each point's value is taken from SIZE [weight] + LAYER + NAME "grid_regular" + TYPE point + CONNECTIONTYPE OGR + CONNECTION "grid_nz_regular.csv" + CLASS + STYLE + SIZE [weight] + END + END + END + + # band 1: the interpolated mean, drawn with the rainfall isohyet palette + LAYER + NAME "km_regular" + TYPE raster + CONNECTIONTYPE kriging + CONNECTION "grid_regular" + MASK "landmask" + PROCESSING "KRIGING_MODEL=EXPONENTIAL" + PROCESSING "KRIGING_TYPE=ORDINARY" + PROCESSING "KRIGING_NEIGHBORS=16" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "BANDS=1" + # CLASS with the rainfall isohyet ramp (see the full mapfile) + END + + # band 2: the standard deviation, drawn with a viridis ramp + LAYER + NAME "sd_regular" + TYPE raster + CONNECTIONTYPE kriging + CONNECTION "grid_regular" + MASK "landmask" + PROCESSING "KRIGING_RANGE=40" + PROCESSING "KRIGING_SILL=2000" + PROCESSING "BANDS=2" + CLASS + STYLE + COLORRANGE "#440154" "#fde725" + DATARANGE 0 45 + END + END + END + +The clustered scenario uses the same layers reading ``grid_nz_clustered.csv``. + +Rendering +--------- + +Render the six panels (each is a surface plus the coastline and city points), +then combine them into the two triptychs with ImageMagick: + +.. code-block:: bash + + # six panels: IDW, kriging mean and kriging SD, for each scenario + for s in idw_regular km_regular sd_regular \ + idw_clustered km_clustered sd_clustered; do + map2img -m nz_scenarios.map -l "$s coastline cities" -o "$s.png" -i png + done + + # one triptych per scenario + montage -label 'IDW' idw_regular.png \ + -label 'Kriging mean' km_regular.png \ + -label 'Kriging std dev' sd_regular.png \ + -tile 3x1 -geometry +8+8 idw_vs_kriging.png + montage -label 'IDW' idw_clustered.png \ + -label 'Kriging mean' km_clustered.png \ + -label 'Kriging std dev' sd_clustered.png \ + -tile 3x1 -geometry +8+8 idw_vs_kriging_clustered.png + +Scenario 1: a dense, even network +--------------------------------- + +.. figure:: ../images/kriging-dense.png + :width: 100% + + IDW, kriging mean and kriging standard deviation from 238 evenly spaced + samples. + +With samples everywhere, IDW and the kriging mean agree closely (kriging is a +little smoother), and both resolve the dominant west-east pattern: the Southern +Alps wring out the prevailing westerlies, so the West Coast is very wet (the +purple spine) while Canterbury sits in the rain shadow. The standard-deviation +band is low and uniform across the country (every pixel is close to a +measurement), so the surface is well supported everywhere. + +Scenario 2: a clustered network +------------------------------- + +.. figure:: ../images/kriging-clustered.png + :width: 100% + + The same three panels from 63 samples clustered near the cities (the dots). + +Now the network covers only the populated areas. IDW and the kriging mean still +look plausible, but both have lost the West Coast high: with no samples there, +the South Island reads uniformly dry, and the mean alone gives no hint that +anything is wrong. The standard-deviation band does: it stays dark over the +city clusters (the dots) and turns bright over the unsampled West Coast, +Fiordland and Southland. This is the practical value of kriging over IDW: it +reports not only an estimate but also where that estimate is unsupported by +data. + +Technical notes +--------------- + +- IDW's per-sample bullseyes stand out against the kriging mean's smoother + bands because both are drawn with the same isohyet palette. +- ``KRIGING_RANGE`` is pinned smaller than the gaps in the clustered network, + which is why the clustered SD rises over those gaps. Left unset it auto-fits + to about a third of the image diagonal. +- ``KRIGING_SILL`` is pinned to the sample variance so the SD scale is the same + in both scenarios and the two SD panels stay comparable. +- Output bands are 8-bit (0 to 255). The mean is the value within the layer's + ``DATARANGE``; the standard deviation is in the same units, so the SD layer's + ``DATARANGE`` is the expected range of the standard error. + +References +========== + +- Datta, A., Banerjee, S., Finley, A. O., Gelfand, A. E. (2016). Hierarchical + Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets. + *Journal of the American Statistical Association* 111(514), 800 to 812. +- Vecchia, A. V. (1988). Estimation and Model Identification for Continuous + Spatial Processes. *Journal of the Royal Statistical Society: Series B* + 50(2), 297 to 312.