File:Wrc.svg

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原始檔案（SVG 檔案，表面大小：600 × 450 像素，檔案大小：11 KB）

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摘要

描述Wrc.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
日期	2015年8月13日
來源	自己的作品
作者	FMoeckel, DufterKunde
授權許可 (重用此檔案)	http://de.wikipedia.org/wiki/Datei:Wrc.svg
其他版本	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.

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我，此作品的版權所有人，釋出此作品至公共領域。此授權條款在全世界均適用。
這可能在某些國家不合法，如果是的話：
我授予任何人有權利使用此作品於任何用途，除受法律約束外，不受任何限制。

檔案歷史

點選日期/時間以檢視該時間的檔案版本。

	日期/時間	尺寸	使用者	備⁠註
目前	2015年8月17日 (一) 13:18	600 × 450（11 KB）	DufterKunde	Minor source code clean-up.
	2015年8月14日 (五) 13:44	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.)
	2015年8月13日 (四) 15:17	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...
	2011年4月7日 (四) 05:22	512 × 405（27 KB）	Trex2001	resized font
	2011年4月6日 (三) 11:41	512 × 404（26 KB）	Trex2001	redone in SVG (was embedded bitmap before)
	2011年4月6日 (三) 11:25	512 × 724（179 KB）	Trex2001	Reverted to version as of 16:07, 9 January 2010
	2011年4月6日 (三) 11:16	512 × 378（180 KB）	Trex2001	cropped
	2010年1月9日 (六) 16:07	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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以下其他 wiki 使用了這個檔案：

de.wikipedia.org 的使用狀況
en.wikipedia.org 的使用狀況
- Water retention curve
ja.wikipedia.org 的使用狀況
- 水分保持曲線
nl.wikipedia.org 的使用狀況
- Veldcapaciteit
- Zuigspanning
pl.wikipedia.org 的使用狀況
- Roztwór glebowy
ru.wikipedia.org 的使用狀況
- Основная гидрофизическая характеристика
sv.wikipedia.org 的使用狀況
- Vattenbindningskurva
www.wikidata.org 的使用狀況
- Q889790

詮釋資料

此檔案中包含其他資訊，這些資訊可能是由數位相機或掃描器在建立或數位化過程中所新增的。若檔案自原始狀態已被修改，一些詳細資料可能無法完整反映出已修改的檔案。

簡稱	Water Retention Curves
影像標題	* 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. -{R\|Verknüpfungsregel 1.18 – Parameter für das Modell einer stetigen Funktion der θ(ψ)-Beziehung}- (PDF, 242 KiB). Staatlichen Geologischen Dienste und BGR. 2004-09-17 [2015-07-29] （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. * 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).
寬度	600
高度	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]

File:Wrc.svg

摘要

Reference

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說明

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沒有維基數據項目的某些值

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成立或建立時間

13 8 2015

檔案來源 ^{Chinese (Taiwan) (已轉換拼寫)}

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13 8 2015

檔案來源 Chinese (Taiwan) (已轉換拼寫)

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檔案來源 ^{Chinese (Taiwan) (已轉換拼寫)}