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Beschreibung

Beschreibung
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
Quelle Eigenes Werk
Urheber FMoeckel, DufterKunde
Genehmigung
(Weiternutzung dieser Datei)		 http://de.wikipedia.org/wiki/Datei:Wrc.svg
Andere Versionen Wrc.jpg
 
W3C-validity not checked.

Van Genuchten model of soil water retention ( – relative soil water content, – soil matric potential):

with

Parameter List
Soil Soil
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

  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.

Lizenz

Public domain Ich, der Urheberrechtsinhaber dieses Werkes, veröffentliche es als gemeinfrei. Dies gilt weltweit.
In manchen Staaten könnte dies rechtlich nicht möglich sein. Sofern dies der Fall ist:
Ich gewähre jedem das bedingungslose Recht, dieses Werk für jedweden Zweck zu nutzen, es sei denn, Bedingungen sind gesetzlich erforderlich.

Kurzbeschreibungen

Ergänze eine einzeilige Erklärung, was diese Datei darstellt.

In dieser Datei abgebildete Objekte

Motiv

MIME-Typ

image/svg+xml

Dateiversionen

Klicke auf einen Zeitpunkt, um diese Version zu laden.

Version vomVorschaubildMaßeBenutzerKommentar
aktuell14:18, 17. Aug. 2015Vorschaubild der Version vom 14:18, 17. Aug. 2015600 × 450 (11 KB)DufterKundeMinor source code clean-up.
14:44, 14. Aug. 2015Vorschaubild der Version vom 14:44, 14. Aug. 2015600 × 450 (10 KB)DufterKundeRestricted to a more realistic range of matric potential / pF-values. (Unfortunately, the original source does not mention in which intervals the model is valid.)
16:17, 13. Aug. 2015Vorschaubild der Version vom 16:17, 13. Aug. 2015600 × 450 (14 KB)DufterKundeThe 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...
06:22, 7. Apr. 2011Vorschaubild der Version vom 06:22, 7. Apr. 2011512 × 405 (27 KB)Trex2001resized font
12:41, 6. Apr. 2011Vorschaubild der Version vom 12:41, 6. Apr. 2011512 × 404 (26 KB)Trex2001redone in SVG (was embedded bitmap before)
12:25, 6. Apr. 2011Vorschaubild der Version vom 12:25, 6. Apr. 2011512 × 724 (179 KB)Trex2001Reverted to version as of 16:07, 9 January 2010
12:16, 6. Apr. 2011Vorschaubild der Version vom 12:16, 6. Apr. 2011512 × 378 (180 KB)Trex2001cropped
17:07, 9. Jan. 2010Vorschaubild der Version vom 17:07, 9. Jan. 2010512 × 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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