source: issm/oecreview/Archive/12121-12140/ISSM-12125-12126.diff@ 12325

Index: /proj/ice/larour/issm-uci-clean/trunk-jpl/src/m/utils/Meca/paterson.py
===================================================================
--- /proj/ice/larour/issm-uci-clean/trunk-jpl/src/m/utils/Meca/paterson.py      (revision 0)
+++ /proj/ice/larour/issm-uci-clean/trunk-jpl/src/m/utils/Meca/paterson.py      (revision 12126)
@@ -0,0 +1,50 @@
+from numpy import *
+
+def paterson(temperature):
+
+    # Local Variables: pos11, pos5, pos10, temperature, pos, T, pos8, pos9, pos6, pos7, pos4, rigidity, pos2, pos3, pos1
+    # Function calls: length, zeros, argwhere, paterson, error
+    #PATERSON - figure out the rigidity of ice for a given temperature
+    #
+    #   rigidigty (in s^(1/3)Pa) is the flow law paramter in the flow law sigma=B*e(1/3) (Paterson, p97). 
+    #   temperature is in Kelvin degrees
+    #
+    #   Usage:
+    #      rigidity=paterson(temperature)
+    
+       pos=argwhere(temperature<0.)
+       if len(pos):
+               print 'input temperature should be in Kelvin (positive)'
+               return []
+    
+       T = temperature-273.15
+       #The routine below is equivalent to:
+       # n=3; T=temperature-273;
+       # %From paterson,
+       # Temp=[0;-2;-5;-10;-15;-20;-25;-30;-35;-40;-45;-50];
+       # A=[6.8*10^-15;2.4*10^-15;1.6*10^-15;4.9*10^-16;2.9*10^-16;1.7*10^-16;9.4*
+       # 10^-17;5.1*10^-17;2.7*10^-17;1.4*10^-17;7.3*10^-18;3.6*10^-18];;%s-1(kPa-3)
+       # %Convert into rigidity B
+       # B=A.^(-1/n)*10^3; %s^(1/3)Pa
+       # %Now, do a cubic fit between Temp and B: 
+       # fittedmodel=fit(Temp,B,'cubicspline');
+       # rigidity=fittedmodel(temperature);
+
+       rigidity=zeros(len(T))
+       pos1=argwhere(T<=-45);           rigidity[pos1]=10**8*(-0.000292866376675*(T[pos1]+50)**3+ 0.011672640664130*(T[pos1]+50)**2  -0.325004442485481*(T[pos1]+50)+  6.524779401948101)
+       pos2=argwhere(logical_and(-45<=T,T<-40));   rigidity[pos2]=10**8*(-0.000292866376675*(T[pos2]+45)**3+ 0.007279645014004*(T[pos2]+45)**2  -0.230243014094813*(T[pos2]+45)+  5.154964909039554)
+       pos3=argwhere(logical_and(-40<=T,T<-35));   rigidity[pos3]=10**8*(0.000072737147457*(T[pos3]+40)**3+  0.002886649363879*(T[pos3]+40)**2  -0.179411542205399*(T[pos3]+40)+  4.149132666831214)
+       pos4=argwhere(logical_and(-35<=T,T<-30));   rigidity[pos4]=10**8*(-0.000086144770023*(T[pos4]+35)**3+ 0.003977706575736*(T[pos4]+35)**2  -0.145089762507325*(T[pos4]+35)+  3.333333333333331)
+       pos5=argwhere(logical_and(-30<=T,T<-25));   rigidity[pos5]=10**8*(-0.000043984685769*(T[pos5]+30)**3+ 0.002685535025386*(T[pos5]+30)**2  -0.111773554501713*(T[pos5]+30)+  2.696559088937191)
+       pos6=argwhere(logical_and(-25<=T,T<-20));   rigidity[pos6]=10**8*(-0.000029799523463*(T[pos6]+25)**3+ 0.002025764738854*(T[pos6]+25)**2  -0.088217055680511*(T[pos6]+25)+  2.199331606342181)
+       pos7=argwhere(logical_and(-20<=T,T<-15));   rigidity[pos7]=10**8*(0.000136920904777*(T[pos7]+20)**3+  0.001578771886910*(T[pos7]+20)**2  -0.070194372551690*(T[pos7]+20)+  1.805165505978111)
+       pos8=argwhere(logical_and(-15<=T,T<-10));   rigidity[pos8]=10**8*(-0.000899763781026*(T[pos8]+15)**3+ 0.003632585458564*(T[pos8]+15)**2  -0.044137585824322*(T[pos8]+15)+  1.510778053489523)
+       pos9=argwhere(logical_and(-10<=T,T<-5));    rigidity[pos9]=10**8*(0.001676964325070*(T[pos9]+10)**3-  0.009863871256831*(T[pos9]+10)**2  -0.075294014815659*(T[pos9]+10)+  1.268434288203714)
+       pos10=argwhere(logical_and(-5<=T,T<-2));    rigidity[pos10]=10**8*(-0.003748937622487*(T[pos10]+5)**3+0.015290593619213*(T[pos10]+5)**2  -0.048160403003748*(T[pos10]+5)+  0.854987973338348)
+       pos11=argwhere(-2<=T);           rigidity[pos11]=10**8*(-0.003748937622488*(T[pos11]+2)**3-0.018449844983174*(T[pos11]+2)**2  -0.057638157095631*(T[pos11]+2)+  0.746900791092860)
+
+       #Now make sure that rigidity is positive
+       pos=argwhere(rigidity<0);        rigidity[pos]=1**6 
+
+       return rigidity
+