Datei:Wrc.svg
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Beschreibung
BeschreibungWrc.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 | |
Quelle | Eigenes Werk |
Urheber | FMoeckel, DufterKunde |
Genehmigung (Weiternutzung dieser Datei) |
http://de.wikipedia.org/wiki/Datei:Wrc.svg |
Andere Versionen | Wrc.jpg |
Van Genuchten model of soil water retention ( – relative soil water content, – soil matric potential):
with
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
- ↑ 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 domainPublic domainfalsefalse |
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. |
In dieser Datei abgebildete Objekte
Motiv
Urheber
Einige Werte ohne einen Wikidata-Eintrag
Urheberrechtsstatus
in die Gemeinfreiheit entlassen durch den Rechteinhaber
Lizenz
in die Gemeinfreiheit entlassen durch den Rechteinhaber
Datum der Gründung, Erstellung, Entstehung, Erbauung
13. August 2015
Quelle der Datei
durch Hochlader/in erstelltes Original
MIME-Typ
image/svg+xml
Dateiversionen
Klicke auf einen Zeitpunkt, um diese Version zu laden.
Version vom | Vorschaubild | Maße | Benutzer | Kommentar | |
---|---|---|---|---|---|
aktuell | 15:18, 17. Aug. 2015 | 600 × 450 (11 KB) | DufterKunde | Minor source code clean-up. | |
15:44, 14. Aug. 2015 | 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.) | ||
17:17, 13. Aug. 2015 | 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... | ||
07:22, 7. Apr. 2011 | 512 × 405 (27 KB) | Trex2001 | resized font | ||
13:41, 6. Apr. 2011 | 512 × 404 (26 KB) | Trex2001 | redone in SVG (was embedded bitmap before) | ||
13:25, 6. Apr. 2011 | 512 × 724 (179 KB) | Trex2001 | Reverted to version as of 16:07, 9 January 2010 | ||
13:16, 6. Apr. 2011 | 512 × 378 (180 KB) | Trex2001 | cropped | ||
18:07, 9. Jan. 2010 | 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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Diese Datei enthält weitere Informationen (beispielsweise Exif-Metadaten), die in der Regel von der Digitalkamera oder dem verwendeten Scanner stammen. Durch nachträgliche Bearbeitung der Originaldatei können einige Details verändert worden sein.
Kurztitel | Water Retention Curves |
---|---|
Bildtitel | * 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, abgerufen am 29. Juli 2015 (deutsch). 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). |
Breite | 600 |
Höhe | 450 |