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Summary

DescriptionWrc.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
Date	13 August 2015
Source	Own work
Author	FMoeckel, DufterKunde
Permission (Reusing this file)	http://de.wikipedia.org/wiki/Datei:Wrc.svg
Other versions	Wrc.jpg

W3C-validity not checked.Category:Unchecked SVG validity

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.

Licensing

I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Category:Self-published work#Wrc.svg Category:PD-self#Wrc.svg Category:Soil science diagrams Category:Hydrological diagrams Category:Images with Octave source code

[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.

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