Bestand:Wrc.svg

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Beschrijving

BeschrijvingWrc.svg	English: calculated diagram of soil with model formula (van Genuchten, 1980) ^[1] Deutsch: Der Saugdruck von Sand, Schluff, Lehm und Ton. Neu berechnetes Diagramm verschiedener Bodenarten mit Modelldaten gemäß van Genuchten, 1980
Datum	13 augustus 2015
Bron	Eigen werk
Auteur	FMoeckel, DufterKunde
Toestemming (Hergebruik van dit bestand)	http://de.wikipedia.org/wiki/Datei:Wrc.svg
Andere versies	Wrc.jpg

W3C-validity not checked.

Van Genuchten model of soil water retention ( $\theta$ – relative soil water content, $\Psi _{\mathrm {m} }$ – soil matric potential):

\theta =\theta _{r}+{\frac {\theta _{s}-\theta _{r}}{\left(1+\left(\alpha \,{\frac {\left|\Psi _{\mathrm {m} }\right|}{\mathrm {hPa} }}\right)^{n}\right)^{m}}}

with

m=1-{\frac {1}{n}}\;.

Parameter List
Soil	Soil	$\theta _{r}$	$\theta _{r}$	$\alpha$	$n$	$m$
Ss	Sand	0.043019	0.370687	0.087424	1.57535	0.36522
Uu	Silt	0	0.421256	0.003405	1.34475	0.25637
Lu	Loam-Silt	0	0.421217	0.013345	1.12614	0.11201
Tt	Clay	0	0.550541	0.006812	1.08155	0.07540

GNU Octave source code

function van_genuchten()
	%* Encdoing: UTF-8.
	%* Written by DufterKunde
	%  https://de.wikipedia.org/wiki/Benutzer:DufterKunde
	%  to produce a corrected version of
	%  https://commons.wikimedia.org/wiki/File:Wrc.svg .
	%  It is supposed to be run in GNU octave 4.0,
	%  but it should also work with older versions of octave as well.
	%  Only minor changes are needed to make it run with Matlab.
	%* The plot shows the matric potential Psi_m
	%  of different types of soil as a function of the
	%  relative soil water content theta.
	%  It is based on the equation and parameters from
	%  {{cite web
	%  | url=https://www.bgr.bund.de/DE/Themen/Boden/Netzwerke/Adhocag/Downloads/Ergaenzungsregel_1_18.pdf
	%  | title=Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung
	%  | accessdate=2015-07-29
	%  | author=Ad-hoc-AG Boden
	%  | coauthors=
	%  | date=2004-09-17
	%  | format=PDF, 242 KiB
	%  | publisher=Staatlichen Geologischen Dienste und BGR
	%  | language=German
	%  }}
	%  theta = theta_r + (theta_s - theta_r)/(1 + (alpha*(-psi))^n)^m
	%  with
	%  m     = 1 - 1/n .
	%* Ss = Sand, Uu = Silt, Lu = Loam-Silt, Tt = Clay.
	%* Compliance of the output with the svg-standard validated by:
	%  https://validator.w3.org/
	%  and practical functionality tested with
	%  - Mozilla Firefox for Ubuntu 40.0,
	%  - Chromium 43.0.2357.130 Ubuntu 15.04 (64-bit)
	%  - eog (“Eye of Gnome”) 3.14.4,
	%  - Inkscape 0.91 r13725, and
	%  - SVG Check: https://tools.wmflabs.org/svgcheck/ (rsvg 2.36.1).
	
	% parameters:
	pF         = [  0     6];
	N          = 10*diff(pF) + 1;
	psi        = -logspace(pF(1),pF(2),N);
	x          = [  0     0.55];
	y          = pF;
	X          = [ 70   550   ];
	Y          = [390   30   ];
	DY         = diff(Y)/diff(y);
	Tick       =   8;
	tick       =   6;
	lgnd_wdth  =  95;
	lgnd_hght  = 120;
	lgnd_strk  =  35;
	lgnd_pad   =   4;
	lgnd_Pad   =  12;
	today      = clock();
	
	% Sand:
	theta_r_ss = 0.043019;
	theta_s_ss = 0.370687;
	alpha_ss   = 0.087424;
	n_ss       = 1.57535;
	theta_ss   = theta_vg(psi, theta_r_ss, theta_s_ss, alpha_ss, n_ss);
	
	% Silt:
	theta_r_uu = 0;
	theta_s_uu = 0.421256;
	alpha_uu   = 0.003405;
	n_uu       = 1.34475;
	theta_uu   = theta_vg(psi, theta_r_uu, theta_s_uu, alpha_uu, n_uu);
	
	% Loam-Silt:
	theta_r_lu = 0;
	theta_s_lu = 0.421217;
	alpha_lu   = 0.013345;
	n_lu       = 1.12614;
	theta_lu   = theta_vg(psi, theta_r_lu, theta_s_lu, alpha_lu, n_lu);
	
	% Clay:
	theta_r_tt = 0;
	theta_s_tt = 0.550541;
	alpha_tt   = 0.006812;
	n_tt       = 1.08155;
	theta_tt   = theta_vg(psi, theta_r_tt, theta_s_tt, alpha_tt, n_tt);
	
	% generate svg-file:
	fid        = fopen ("Wrc.svg","w");
	fprintf(fid,["<?xml version=\"1.0\" encoding=\"utf-8\"?>\n", ...
	             "<svg\n", ...
	             "xmlns=\"http://www.w3.org/2000/svg\"\n", ...
	             "width=\"600\" height=\"450\"\n", ...
	             ">\n",...
	             "\t<title>Water Retention Curves</title>\n"]);
	fprintf(fid,["\t<desc>\n",...
	             "\t\t* This is a corrected version of\n",...
	             "\t\t  https://commons.wikimedia.org/wiki/File:Wrc.svg\n",...
	             "\t\t  generated by DufterKunde\n",...
	             "\t\t  https://de.wikipedia.org/wiki/Benutzer:DufterKunde\n",...
	             "\t\t  on %i-%02i-%02i.\n",...
	             "\t\t* The plot shows the matric potential Psi_m\n",...
	             "\t\t  of different types of soil as a function of the\n",...
	             "\t\t  relative soil water content theta.\n",...
	             "\t\t  It is based on the equation and parameters from\n",...
	             "\t\t  {{cite web\n",...
	             "\t\t  | url=https://www.bgr.bund.de/DE/Themen/Boden/Netzwerke/Adhocag/Downloads/Ergaenzungsregel_1_18.pdf\n",...
	             "\t\t  | title=Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung\n",...
	             "\t\t  | accessdate=2015-07-29\n",...
	             "\t\t  | author=Ad-hoc-AG Boden\n",...
	             "\t\t  | coauthors=\n",...
	             "\t\t  | date=2004-09-17\n",...
	             "\t\t  | format=PDF, 242 KiB\n",...
	             "\t\t  | publisher=Staatlichen Geologischen Dienste und BGR\n",...
	             "\t\t  | language=German\n",...
	             "\t\t  }}\n",...
	             "\t\t  theta = theta_r + (theta_s - theta_r)/(1 + (alpha*(-psi))^n)^m\n",...
	             "\t\t  with\n",...
	             "\t\t  m     = 1 - 1/n .\n",...
	             "\t\t* Ss = Sand, Uu = Silt, Lu = Loam-Silt, Tt = Clay.\n",...
	             "\t\t* This svg-file has been generated line-by-line\n",...
	             "\t\t  by a GNU Octave function.\n",...
	             "\t\t* Compliance with the svg standard validated by:\n",...
	             "\t\t  https://validator.w3.org/\n",...
	             "\t\t  and practical functionality tested with\n",...
	             "\t\t  - Mozilla Firefox for Ubuntu 40.0,\n",...
	             "\t\t  - Chromium 43.0.2357.130 Ubuntu 15.04 (64-bit)\n",...
	             "\t\t  - eog (“Eye of Gnome”) 3.14.4,\n",...
	             "\t\t  - Inkscape 0.91 r13725, and\n",...
	             "\t\t  - SVG Check: https://tools.wmflabs.org/svgcheck/ (rsvg 2.36.1).\n",...
	             "\t</desc>\n"],today(1),today(2),today(3));
	fprintf(fid,"\t<g shape-rendering=\"geometricPrecision\" stroke=\"black\" stroke-width=\"2\">\n");
	fprintf(fid,"\t\t<!-- horizontal grid lines: -->\n");
	fprintf(fid,"\t\t<g stroke=\"#c0c0c0\">\n");
	for k = (pF(1) + 1) : (pF(2) - 1)
		Y_grid = Y(1) + k * DY
		fprintf(fid,"\t\t\t<polyline points=\"%i,%i %i,%i\"/>\n",...
		        X(1),Y_grid,X(2),Y_grid);
	endfor
	fprintf(fid,"\t\t</g>\n");
	fprintf(fid,"\t\t<!-- actual graph data: -->\n");
	fprintf(fid,"\t\t<g fill=\"none\" stroke-width=\"3\">\n");
	write_svg_dat(fid,psi(1:end-10),theta_ss(1:end-10),x,y,X,Y,"0000ff","Ss = Sand");
	write_svg_dat(fid,psi,theta_uu,x,y,X,Y,"ff0000","Uu = Silt");
	write_svg_dat(fid,psi,theta_lu,x,y,X,Y,"00ff00","Lu = Loam-Silt");
	write_svg_dat(fid,psi,theta_tt,x,y,X,Y,"b000b0","Tt = Clay");
	fprintf(fid,"\t\t</g>\n");
	fprintf(fid,"\t\t<!-- ticks on x-axis: -->\n");
	for k = [0.1 : 0.1 : 0.5]
		X_grid = X(1) + k * diff(X)/diff(x)
		fprintf(fid,"\t\t<polyline points=\"%5.2f,%i %5.2f,%i\"/>\n",...
		        X_grid,Y(1),X_grid,Y(1)-Tick);
		fprintf(fid,"\t\t<polyline points=\"%5.2f,%i %5.2f,%i\"/>\n",...
		        X_grid,Y(2)+Tick,X_grid,Y(2));
	endfor
	fprintf(fid,"\t\t<!-- major ticks on y-axis: -->\n");
	for k = (pF(1) + 1) : (pF(2) - 1 )
		Y_grid = Y(1) + k * DY;
		fprintf(fid,"\t\t<polyline points=\"%i,%i %i,%i\"/>\n",...
		        X(1),Y_grid,X(1)+Tick,Y_grid);
		fprintf(fid,"\t\t<polyline points=\"%i,%i %i,%i\"/>\n",...
		        X(2)-Tick,Y_grid,X(2),Y_grid);
	endfor
	fprintf(fid,"\t\t<!-- minor log-ticks on left y-axis: -->\n");
	for k = pF(1) : (pF(2) - 1)
		for m = 2 : 9
			y_grid = Y(1) + ( k + log10(m) ) * DY;
			fprintf(fid,"\t\t<polyline points=\"%i,%5.2f %i,%5.2f\"/>\n",...
			        X(1),y_grid,X(1)+tick,y_grid);
		endfor
	endfor
	fprintf(fid,"\t\t<!-- legend: -->\n");
	fprintf(fid,["\t\t<rect x=\"%i\" y=\"%i\" width=\"%i\" " ,...
	             "height=\"%i\" stroke=\"black\" fill=\"white\"/>\n"],...
	        X(2)-lgnd_wdth-lgnd_Pad,Y(2)+lgnd_Pad,lgnd_wdth,lgnd_hght);
	Y_lgnd = Y(2)+1.5*Tick + [0.5 1.5 2.5 3.5]/4*lgnd_hght
	X_lgnd = [X(2)-lgnd_wdth-lgnd_pad X(2)-lgnd_wdth-lgnd_pad+lgnd_strk];
	fprintf(fid,"\t\t<g fill=\"none\" stroke-width=\"3\">\n");
	fprintf(fid,"\t\t\t<polyline stroke=\"#0000ff\" points=\"%i,%i %i,%i\"/>\n",...
	        X_lgnd(1),Y_lgnd(1),X_lgnd(2),Y_lgnd(1));
	fprintf(fid,"\t\t\t<polyline stroke=\"#ff0000\" points=\"%i,%i %i,%i\"/>\n",...
	        X_lgnd(1),Y_lgnd(2),X_lgnd(2),Y_lgnd(2));
	fprintf(fid,"\t\t\t<polyline stroke=\"#00ff00\" points=\"%i,%i %i,%i\"/>\n",...
	        X_lgnd(1),Y_lgnd(3),X_lgnd(2),Y_lgnd(3));
	fprintf(fid,"\t\t\t<polyline stroke=\"#b000b0\" points=\"%i,%i %i,%i\"/>\n",...
	        X_lgnd(1),Y_lgnd(4),X_lgnd(2),Y_lgnd(4));
	fprintf(fid,"\t\t</g>\n");
	fprintf(fid,"\t\t<!-- axis-box: -->\n");
	fprintf(fid,["\t\t<polygon points=\"%i,%i %i,%i %i,%i %i,%i\" ",...
	             "fill=\"none\" stroke=\"black\" stroke-width=\"2\"/>\n"],...
	        X(1),Y(2),X(2),Y(2),X(2),Y(1),X(1),Y(1));
	fprintf(fid,"\t\t<!-- text: -->\n");
	fprintf(fid,"\t\t<g stroke-width=\"0\" fill=\"black\" font-family=\"Helvetica\" font-size=\"24\">\n");
	fprintf(fid,"\t\t\t<!-- x-axis annotation: -->\n");
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"middle\" font-style=\"italic\">θ</text>\n",...
	        mean(X)-10,445);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"middle\">0</text>\n",...
	        X(1),420);
	for k = [0.1 : 0.1 : 0.5]
		X_grid = X(1) + k * diff(X)/diff(x);
		fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"middle\">%3.1f</text>\n",...
		X_grid,420,k);
	endfor
	fprintf(fid,"\t\t\t<!-- y-axis annotation: -->\n");
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" transform=\"rotate(-90)\" text-anchor=\"end\">p</text>\n",...
	        -mean(Y)+ 7,593);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" transform=\"rotate(-90)\" text-anchor=\"start\" font-style=\"italic\">F</text>\n",...
	        -mean(Y)+ 7,593);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" transform=\"rotate(-90)\" text-anchor=\"end\" font-style=\"italic\">–ψ</text>\n",...
	        -mean(Y)-20,19);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" transform=\"rotate(-90)\" text-anchor=\"start\" font-size=\"18\">m</text>\n",...
	        -mean(Y)-20,26);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" transform=\"rotate(-90)\" text-anchor=\"start\">/ hPa</text>\n",...
	        -mean(Y)   ,19);
	for k = pF(1) : pF(2)
		Y_grid = Y(1) + k * DY;
		if ( k < 0 )
			fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"end\">–</text>\n",...
			        X(2)+8,Y_grid+10);
		endif
		fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\">%i</text>\n",...
		        X(2)+8,Y_grid+10,abs(k));
		fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"end\">10</text>\n",...
		        X(1)-15,Y_grid+10);
		if ( k >= 0 )
			fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\" font-size=\"18\">%i</text>\n",...
			        X(1)-15,Y_grid-2,k);
		else
			fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\" font-size=\"18\">–%i</text>\n",...
			        X(1)-15,Y_grid-2,-k);
		endif
	endfor
	fprintf(fid,"\t\t\t<!-- legend: -->\n");
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\">Ss</text>\n",...
	        X_lgnd(2)+lgnd_Pad,Y_lgnd(1)+8);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\">Uu</text>\n",...
	        X_lgnd(2)+lgnd_Pad,Y_lgnd(2)+8);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\">Lu</text>\n",...
	        X_lgnd(2)+lgnd_Pad,Y_lgnd(3)+8);
	fprintf(fid,"\t\t\t<text x=\"%i\" y=\"%i\" text-anchor=\"start\">Tt</text>\n",...
	        X_lgnd(2)+lgnd_Pad,Y_lgnd(4)+8);
	fprintf(fid,["\t\t</g>\n",...
	             "\t</g>\n",...
	             "</svg>"]);
	fclose(fid);
	
endfunction

function theta = theta_vg(psi, theta_r, theta_s, alpha, n)
	% van Genuchten equation
	m = 1 - 1/n
	theta = theta_r + (theta_s - theta_r)./(1 + (alpha*(-psi)).^n).^m;
endfunction

function write_svg_dat(fid,psi,theta,x,y,X,Y,cl,name)
	Y_dat = ( log10(-psi) - y(1) )*diff(Y)/diff(y) + Y(1);
	X_dat = ( theta       - x(1) )*diff(X)/diff(x) + X(1);
	fprintf(fid,"\t\t\t<polyline stroke=\"#%s\" points=\"",cl);
	for	k = 1 : (length(psi) - 1)
		fprintf(fid,"%4.2f,%i ",X_dat(k),Y_dat(k));
	endfor
	fprintf(fid,["%4.2f,%i\">\n",...
	             "\t\t\t\t<title>%s</title>\n",...
	             "\t\t\t</polyline>\n"],X_dat(end),Y_dat(end),name);
endfunction

Reference

↑ Ad-hoc-AG Boden (2004-09-17). Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung (in German) (PDF, 242 KiB). Staatlichen Geologischen Dienste und BGR. Archived from the original on 2016-03-04. Retrieved on 2015-07-29.

Licentie

Ik, de auteursrechthebbende van dit werk, geef dit werk vrij in het publieke domein. Dit is wereldwijd van toepassing.
In sommige landen is dit wettelijk niet mogelijk; in die gevallen geldt:
Ik sta iedereen toe dit werk voor eender welk doel te gebruiken, zonder enige voorwaarden, tenzij zulke voorwaarden door de wet worden voorgeschreven.

Bestandsgeschiedenis

Klik op een datum/tijd om het bestand te zien zoals het destijds was.

	Datum/tijd	Afmetingen	Gebruiker	Opmerking
huidige versie	17 aug 2015 15:18	600 × 450 (11 kB)	DufterKunde	Minor source code clean-up.
	14 aug 2015 15:44	600 × 450 (10 kB)	DufterKunde	Restricted to a more realistic range of matric potential / pF-values. (Unfortunately, the original source does not mention in which intervals the model is valid.)
	13 aug 2015 17:17	600 × 450 (14 kB)	DufterKunde	The original file was based on a wrong equation due to a typo (see File talk:Wrc.svg#Plots seem to be based on wrong equation). This has been discussed with and confirmed by the original author User:FMoeckel~commonswiki via e-mail. The new SVG...
	7 apr 2011 07:22	512 × 405 (27 kB)	Trex2001	resized font
	6 apr 2011 13:41	512 × 404 (26 kB)	Trex2001	redone in SVG (was embedded bitmap before)
	6 apr 2011 13:25	512 × 724 (179 kB)	Trex2001	Reverted to version as of 16:07, 9 January 2010
	6 apr 2011 13:16	512 × 378 (180 kB)	Trex2001	cropped
	9 jan 2010 18:07	512 × 724 (179 kB)	FMoeckel~commonswiki	{{Information \|Description={{en\|1=calculated diagram of soil with model formula (van Genuchten, 1980) <ref>[www.bgr.de/saf_boden/adhocag/Ergaenzungsregel_1_18.pdf]</ref>}} {{de\|1=neu berechnetes Diagramm verschiedener Bodenarten mit Modelldaten gemäß va

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Dit bestand wordt op de volgende 2 pagina's gebruikt:

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De volgende andere wiki's gebruiken dit bestand:

Gebruikt op de.wikipedia.org
Gebruikt op en.wikipedia.org
- Water retention curve
Gebruikt op ja.wikipedia.org
- 水分保持曲線
Gebruikt op pl.wikipedia.org
- Roztwór glebowy
Gebruikt op ru.wikipedia.org
- Основная гидрофизическая характеристика
Gebruikt op sv.wikipedia.org
- Vattenbindningskurva
Gebruikt op zh.wikipedia.org
- 水分持留曲线
- Talk:水分持留曲线

Metadata

Dit bestand bevat metadata met EXIF-informatie, die door een fotocamera, scanner of fotobewerkingsprogramma toegevoegd kan zijn.

Korte naam	Water Retention Curves
Omschrijving afbeelding	* This is a corrected version of https://commons.wikimedia.org/wiki/File:Wrc.svg generated by DufterKunde https://de.wikipedia.org/wiki/Benutzer:DufterKunde on 2015-08-17. * The plot shows the matric potential Psi_m of different types of soil as a function of the relative soil water content theta. It is based on the equation and parameters from Ad-hoc-AG Boden, Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung (PDF, 242 KiB). Staatlichen Geologischen Dienste und BGR (17 september 2004). Geraadpleegd op 29 juli 2015. theta = theta_r + (theta_s - theta_r)/(1 + (alpha(-psi))^n)^m with m = 1 - 1/n . Ss = Sand, Uu = Silt, Lu = Loam-Silt, Tt = Clay. * This svg-file has been generated line-by-line by a GNU Octave function. * Compliance with the svg standard validated by: https://validator.w3.org/ and practical functionality tested with - Mozilla Firefox for Ubuntu 40.0, - Chromium 43.0.2357.130 Ubuntu 15.04 (64-bit) - eog (“Eye of Gnome”) 3.14.4, - Inkscape 0.91 r13725, and - SVG Check: https://tools.wmflabs.org/svgcheck/ (rsvg 2.36.1).
Breedte	600
Hoogte	450

[1] Ad-hoc-AG Boden (2004-09-17). Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung (in German) (PDF, 242 KiB). Staatlichen Geologischen Dienste und BGR. Archived from the original on 2016-03-04. Retrieved on 2015-07-29.

[1]

Bestand:Wrc.svg

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