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stmt_fns.h
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stmt_fns.h
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!-----------------------------------------------------------------------------
integer, parameter :: &
#if defined (EOS_SIG0)
# if defined (EOS_7T)
sigver=1 !7-term sigma-0
# elif defined (EOS_9T)
sigver=3 !9-term sigma-0
# elif defined (EOS_12T)
sigver=7 !12-term sigma-0
# elif defined (EOS_17T)
sigver=5 !17-term sigma-0
# endif
#elif defined (EOS_SIG2)
# if defined (EOS_7T)
sigver=2 !7-term sigma-2
# elif defined (EOS_9T)
sigver=4 !9-term sigma-2
# elif defined (EOS_12T)
sigver=8 !12-term sigma-2
# elif defined (EOS_17T)
sigver=6 !17-term sigma-2
# endif
#endif
!
real sig,dsigdt,dsigds,tofsig,sofsig, &
sigloc,dsiglocdt,dsiglocds,tofsigloc
!
real sofsig_a,sofsig_b,sofsig_c
real a0,a1,a2,cubr,cubq,cuban,cubrl,cubim
real c1l,c2l,c3l,c4l,c5l,c6l,c7l
real sig_n,sig_d,sig_q, dsigdt_n,dsigdt_d, dsigds_n,dsigds_d
real tofsig_a,tofsig_b,tofsig_c
real sigloc_n,sigloc_d,sigloc_q, &
dsiglocdt_n,dsiglocdt_d, dsiglocds_n,dsiglocds_d
!
real r,s,t,pdb,prs
integer kkf
!
real, parameter :: &
aone =1.0, &
ahalf=1.0/2.0, &
a3rd =1.0/3.0, athird =a3rd, &
a4th =1.0/4.0, afourth=a4th
!
!
#if defined (EOS_7T)
# if defined (EOS_SIG0)
! --- coefficients for sigma-0 7-terms (based on Brydon & Sun fit)
real, parameter :: &
c1=-1.36471E-01, & !const. coefficent
c2= 4.68181E-02, & !T coefficent
c3= 8.07004E-01, & ! S coefficent
c4=-7.45353E-03, & !T^2 coefficent
c5=-2.94418E-03, & !T S coefficent
c6= 3.43570E-05, & !T^3 coefficent
rc6= 1.0/c6, &
c7= 3.48658E-05, & !T^2S coefficent
pref= 0.0 ! reference pressure, Pascals
# elif defined (EOS_SIG2)
! --- coefficients for sigma-2 (based on Brydon & Sun fit)
real, parameter :: &
c1= 9.77093E+00, & !const. coefficent
c2=-2.26493E-02, & !T coefficent
c3= 7.89879E-01, & ! S coefficent
c4=-6.43205E-03, & !T^2 coefficent
c5=-2.62983E-03, & !T S coefficent
c6= 2.75835E-05, & !T^3 coefficent
rc6= 1.0/c6, &
c7= 3.15235E-05, & !T^2S coefficent
pref= 2000.0e4 !reference pressure, Pascals
# endif
!
! --- HYCOM pressure to bar, for locally referenced equations
real, parameter :: prs2pb=1.e-5 !Pascals to bar
#elif defined (EOS_9T)
# if defined (EOS_SIG0)
! --- sigma-theta as a function of temp (deg c) and salinity (psu)
! --- (9-term polynomial fit to T:[-2:30],S:[18:38])
!
! --- coefficients for sigma-0.
real, parameter :: &
c1=-4.311829E-02, & !const. coefficent
c2= 5.429948E-02, & !T coefficent
c3= 8.011774E-01, & ! S coefficent
c4=-7.641336E-03, & !T^2 coefficent
c5=-3.258442E-03, & !T S coefficent
c6= 3.757643E-05, & !T^3 coefficent
rc6=1.0/c6, &
c7= 3.630361E-05, & !T^2S coefficent
c8= 8.675546E-05, & ! S^2 coefficent
c9= 3.995086E-06, & !T S^2 coefficent
pref= 0.0 ! reference pressure, Pascals
# elif defined (EOS_SIG2)
! --- coefficients for sigma-2.
real, parameter :: &
c1= 9.903308E+00, & !const. coefficent
c2=-1.618075E-02, & !T coefficent
c3= 7.819166E-01, & ! S coefficent
c4=-6.593939E-03, & !T^2 coefficent
c5=-2.896464E-03, & !T S coefficent
c6= 3.038697E-05, & !T^3 coefficent
rc6= 1.0/c6, &
c7= 3.266933E-05, & !T^2S coefficent
c8= 1.180109E-04, & ! S^2 coefficent
c9= 3.399511E-06, & !T S^2 coefficent
pref= 2000.0e4 ! reference pressure, Pascals
# endif
!
! --- HYCOM pressure to bar, for locally referenced equations
real, parameter :: prs2pb=1.e-5 !Pascals to bar
#elif (EOS_12T)
real, parameter :: &
c1= 1.0e-01, & !not used, required to compile mxkrtm.f
c2= 1.0e-02, & !not used, required to compile mxkrtm.f
c3= 1.0e-03, & !not used, required to compile mxkrtm.f
c4= 1.0e-04, & !not used, required to compile mxkrtm.f
c5= 1.0e-05, & !not used, required to compile mxkrtm.f
c6= 1.0e-06, & !not used, required to compile mxkrtm.f
c7= 1.0e-07 !not used, required to compile mxkrtm.f
!
! --- REFERENCE?
!
! --- coefficients for 18-term rational function sigloc().
real, parameter :: &
c001=-1.4627567840659594d-01, & !num. constant coefficent
c002= 6.4247392832635697d-02, & !num. T coefficent
c003= 8.1213979591704621d-01, & !num. S coefficent
c004=-8.1321489441909698d-03, & !num. T^2 coefficent
c005= 4.5199845091090296d-03, & !num. T S coefficent
c006= 4.6347888132781394d-04, & !num. S^2 coefficent
c007= 5.0879498675039621d-03, & !num. P coefficent
c008= 1.6333913018305079d-05, & !num. P T coefficent
c009= 4.3899924880543972d-06 !num. P S coefficent
real, parameter :: &
c011= 1.0000000000000000d+00, & !den. constant coefficent
c012= 1.0316374535350838d-02, & !den. T coefficent
c013= 8.9521792365142522d-04, & !den. S coefficent
c014=-2.8438341552142710d-05, & !den. T^2 coefficent
c015=-1.1887778959461776d-05, & !den. T S coefficent
c016=-4.0163964812921489d-06, & !den. S^2 coefficent
c017= 1.1995545126831476d-05, & !den. P coefficent
c018= 5.5234008384648383d-08, & !den. P T coefficent
c019= 8.4310335919950873d-09 !den. P S coefficent
real, parameter :: &
c004x2=c004*2.d0, & !for dsigdt and dsiglocdt
c014x2=c014*2.d0, & !for dsigdt and dsiglocdt
c006x2=c006*2.d0, & !for dsigds and dsiglocds
c016x2=c016*2.d0 !for dsigds and dsiglocds
real, parameter :: &
sqrmin=0.d0, & !sqrt arg can't be negative
sofmin=0.d0 !salinity can't be negative
! --- reference pressure.
real, parameter :: prs2pdb=1.d-4 !Pascals to dbar
# if defined (EOS_SIG0)
real, parameter :: pref= 0.d0 !ref. pressure in Pascals, sigma0
# elif defined (EOS_SIG2)
real, parameter :: pref=2000.d4 !ref. pressure in Pascals, sigma2
# endif
real, parameter :: rpdb=pref*prs2pdb !ref. pressure in dbar
! --- coefficients for 12-term rational function sig() at rpdb.
real, parameter :: &
c101=c001+rpdb*c007, & !num. constant coefficent
c102=c002+rpdb*c008, & !num. T coefficent
c103=c003+rpdb*c009 !num. S coefficent
real, parameter :: &
c111=c011+rpdb*c017, & !num. constant coefficent
c112=c012+rpdb*c018, & !num. T coefficent
c113=c013+rpdb*c019 !num. S coefficent
#elif (EOS_17T)
real, parameter :: &
c1= 1.0e-01, & !not used, required to compile mxkrtm.f
c2= 1.0e-02, & !not used, required to compile mxkrtm.f
c3= 1.0e-03, & !not used, required to compile mxkrtm.f
c4= 1.0e-04, & !not used, required to compile mxkrtm.f
c5= 1.0e-05, & !not used, required to compile mxkrtm.f
c6= 1.0e-06, & !not used, required to compile mxkrtm.f
c7= 1.0e-07 !not used, required to compile mxkrtm.f
!
! --- Jackett, McDougall, Feistel, Wright and Griffies (2006),
! --- Algorithms for Density, Potential Temperature, Conservative
! --- Temperature, and the Freezing Temperature of Seawater, JAOT
!
! --- coefficients for 25-term rational function sigloc().
real, parameter :: &
c001= 9.9984085444849347d+02, & !num. constant coefficent
c002= 7.3471625860981584d+00, & !num. T coefficent
c003=-5.3211231792841769d-02, & !num. T^2 coefficent
c004= 3.6492439109814549d-04, & !num. T^3 coefficent
c005= 2.5880571023991390d+00, & !num. S coefficent
c006= 6.7168282786692355d-03, & !num. T S coefficent
c007= 1.9203202055760151d-03, & !num. S^2 coefficent
c008= 1.0000000000000000d+00, & !den. constant coefficent
c009= 7.2815210113327091d-03, & !den. T coefficent
c010=-4.4787265461983921d-05, & !den. T^2 coefficent
c011= 3.3851002965802430d-07, & !den. T^3 coefficent
c012= 1.3651202389758572d-10, & !den. T^4 coefficent
c013= 1.7632126669040377d-03, & !den. S coefficent
c014= 8.8066583251206474d-06, & !den. T S coefficent
c015= 1.8832689434804897d-10, & !den. T^3S coefficent
c016= 5.7463776745432097d-06, & !den. T S^1.5 coefficent
c017= 1.4716275472242334d-09 !den. T^3S^1.5 coefficent
real, parameter :: &
c018= 1.1798263740430364d-02, & !num. P coefficent
c019= 9.8920219266399117d-08, & !num. P T^2 coefficent
c020= 4.6996642771754730d-06, & !num. P S coefficent
c021= 2.5862187075154352d-08, & !num. P^2 coefficent
c022= 3.2921414007960662d-12, & !num. P^2T^2 coefficent
c023= 6.7103246285651894d-06, & !den. P coefficent
c024= 2.4461698007024582d-17, & !den. P^2T^3 coefficent
c025= 9.1534417604289062d-18 !den. P^3T coefficent
! --- additional coefficients for dsiglocdt().
real, parameter :: &
c031= 7.3471625860981580d+00, & !num. constant coefficent
c032=-1.0642246358568354d-01, & !num. T coefficent
c033= 1.0947731732944364d-03, & !num. T^2 coefficent
c034= 6.7168282786692355d-03, & !num. S coefficent
c035= 7.2815210113327090d-03, & !den. constant coefficent
c036=-8.9574530923967840d-05, & !den. T coefficent
c037= 1.0155300889740728d-06, & !den. T^2 coefficent
c038= 5.4604809559034290d-10, & !den. T^3 coefficent
c039=-8.8066583251206470d-06, & !den. S coefficent
c040= 5.6498068304414700d-10, & !den. T^2S coefficent
c041= 2.9432550944484670d-09, & !den. T S^1.5 coefficent
c042= 1.9784043853279823d-07, & !num. P T coefficent
c043= 6.5842828015921320d-12, & !num. P^2T coefficent
c044= 7.3385094021073750d-17, & !den. P^2T^2 coefficent
c045= 9.1534417604289060d-18 !den. P^3 coefficent
! --- additional coefficients for dsiglocds().
real, parameter :: &
c051= 2.5880571023991390d+00, & !num. constant coefficent
c052= 6.7168282786692355d-03, & !num. T coefficent
c053= 3.8406404111520300d-03, & !num. S coefficent
c054= 1.7632126669040377d-03, & !den. constant coefficent
c055=-8.8066583251206470d-06, & !den. T coefficent
c056= 1.8832689434804897d-10, & !den. T^3 coefficent
c057= 8.6195665118148150d-06, & !den. S^0.5 coefficent
c058= 2.2074413208363504d-09, & !den. T^2S^0.5 coefficent
c059= 4.6996642771754730d-06 !num. P coefficent
!
real, parameter :: sqrmin=0.d0 !sqrt arg can't be negative
! --- reference pressure.
real, parameter :: prs2pdb=1.d-4 !Pascals to dbar
# if defined (EOS_SIG0)
real, parameter :: pref= 0.d0 !ref. pressure in Pascals, sigma0
# elif defined (EOS_SIG2)
real, parameter :: pref=2000.d4 !ref. pressure in Pascals, sigma2
# endif
real, parameter :: rpdb=pref*prs2pdb !ref. pressure in dbar
! --- coefficients for 17-term rational function sig() at rpdb.
real, parameter :: &
c101=c001+(c018-c021*rpdb)*rpdb, & !num. constant coefficent
c103=c003+(c019-c022*rpdb)*rpdb, & !num. T^2 coefficent
c105=c005+c020*rpdb, & !num. S coefficent
c108=c008+c023*rpdb, & !den. constant coefficent
c109=c009-c025*rpdb**3, & !den. T coefficent
c111=c011-c024*rpdb**2 !den. T^3 coefficent
! --- additional coefficients for dsigdt().
real, parameter :: &
c132=c032+(c042-c043*rpdb)*rpdb, & !num. T coefficent
c135=c035-c045*rpdb**3, & !den. constant coefficent
c137=c037-c044*rpdb**2 !den. T^2 coefficent
! --- additional coefficients for dsigds().
real, parameter :: &
c151=c051+c059*rpdb !num. constant coefficent
#endif
#if defined (EOS_7T) || (EOS_9T)
!
! --- sub-coefficients for locally referenced sigma
! --- a fit towards Jackett & McDougall (1995)
real, parameter, dimension(7) :: &
alphap = (/ -0.1364705627213484 , 0.04681812123458564, &
0.80700383913187 ,-0.007453530323180844, &
-0.002944183249153631 , 0.00003435702568990446, &
0.0000348657661057688 /) &
,betap = (/ 0.05064226654169138 ,-0.0003571087848996894, &
-0.0000876148051892879, 5.252431910751829e-6, &
1.579762259448864e-6 ,-3.466867400295792e-8, &
-1.687643078774232e-8 /) &
,gammap = (/ -5.526396144304812e-6 , 4.885838128243163e-8, &
9.96026931578033e-9 ,-7.251389796582352e-10, &
-3.987360250058777e-11, 4.006307891935698e-12, &
8.26367520608008e-13 /)
!
#endif
#if defined (EOS_7T)
! --- auxiliary statements for finding root of cubic polynomial
a0(s,r)=(c1+c3*s-r)*rc6 !constant coefficient
a1(s) =(c2+c5*s )*rc6 !linear coefficient
a2(s) =(c4+c7*s )*rc6 !quadratic coefficient
!cubic coefficient is c6*rc6=1.0
cubq(s)=a3rd*a1(s)-(a3rd*a2(s))**2
cubr(r,s)=a3rd*(0.5*a1(s)*a2(s)-1.5*a0(s,r))-(a3rd*a2(s))**3
! --- if q**3+r**2>0, water is too dense to yield real root at given
! --- salinitiy. setting q**3+r**2=0 in that case is equivalent to
! --- lowering sigma until a double real root is obtained.
cuban(r,s)=a3rd*atan2(sqrt(max(0.0,-(cubq(s)**3+cubr(r,s)**2))), &
cubr(r,s))
cubrl(r,s)=sqrt(-cubq(s))*cos(cuban(r,s))
cubim(r,s)=sqrt(-cubq(s))*sin(cuban(r,s))
!
! --- -----------------
! --- equation of state
! --- -----------------
!
! --- sigma-theta as a function of temp (deg c) and salinity (psu)
! --- (friedrich-levitus, polynomial fit that is cubic in T and linear in S)
!
sig(t,s)=(c1+c3*s+t*(c2+c5*s+t*(c4+c7*s+c6*t)))
!
! --- d(sig)/dt
dsigdt(t,s)=(c2+c5*s+2.0*t*(c4+c7*s+1.5*c6*t))
!
! --- d(sig)/ds
dsigds(t,s)=(c3+t*(c5+t*c7))
!
! --- temp (deg c) as a function of sigma and salinity (psu)
! --- find a cubic polynominal root of t**3+a2*t**2+a1*t+a0=0
tofsig(r,s)=-cubrl(r,s)+sqrt(3.0)*cubim(r,s)-a3rd*a2(s)
!
! --- salinity (psu) as a function of sigma and temperature (deg c)
sofsig(r,t)=(r-c1-t*(c2+t*(c4+c6*t)))/(c3+t*(c5+c7*t))
!
! --- locally referenced sigma, a fit towards Jackett & McDougall (1995)
! --- t: potential temperature; s: psu; prs: pressure
c1l(prs)=alphap(1)+prs2pb*prs*(betap(1)+prs2pb*prs*gammap(1))
c2l(prs)=alphap(2)+prs2pb*prs*(betap(2)+prs2pb*prs*gammap(2))
c3l(prs)=alphap(3)+prs2pb*prs*(betap(3)+prs2pb*prs*gammap(3))
c4l(prs)=alphap(4)+prs2pb*prs*(betap(4)+prs2pb*prs*gammap(4))
c5l(prs)=alphap(5)+prs2pb*prs*(betap(5)+prs2pb*prs*gammap(5))
c6l(prs)=alphap(6)+prs2pb*prs*(betap(6)+prs2pb*prs*gammap(6))
c7l(prs)=alphap(7)+prs2pb*prs*(betap(7)+prs2pb*prs*gammap(7))
sigloc(t,s,prs)=c1l(prs)+c3l(prs)*s+ &
t*(c2l(prs)+c5l(prs)*s+t*(c4l(prs)+c7l(prs)*s+c6l(prs)*t))
dsiglocdt(t,s,prs)=(c2l(prs)+c5l(prs)*s+ &
2.0*t*(c4l(prs)+c7l(prs)*s+1.5*c6l(prs)*t))
dsiglocds(t,s,prs)=(c3l(prs)+t*(c5l(prs)+t*c7l(prs)))
#elif defined (EOS_9T)
! --- auxiliary statements for finding root of cubic polynomial
a0(s,r)=(c1+s*(c3+s*c8)-r)*rc6 !constant coefficient
a1(s) =(c2+s*(c5+s*c9) )*rc6 !linear coefficient
a2(s) =(c4+s* c7 )*rc6 !quadratic coefficient
!cubic coefficient is c6*rc6=1.0
cubq(s) =a3rd* a1(s) -(a3rd*a2(s))**2
cubr(r,s)=a3rd*(0.5*a1(s)*a2(s)-1.5*a0(s,r))-(a3rd*a2(s))**3
! --- if q**3+r**2>0, water is too dense to yield real root at given
! --- salinitiy. setting q**3+r**2=0 in that case is equivalent to
! --- lowering sigma until a double real root is obtained.
cuban(r,s)=a3rd*atan2(sqrt(max(0.0,-(cubq(s)**3+cubr(r,s)**2))), &
cubr(r,s))
cubrl(r,s)=sqrt(-cubq(s))*cos(cuban(r,s))
cubim(r,s)=sqrt(-cubq(s))*sin(cuban(r,s))
!
! --- -----------------
! --- equation of state
! --- -----------------
!
! --- sigma-theta as a function of temp (deg c) and salinity (psu)
! --- (polynomial fit that is cubic in T and quadratic in S)
!
sig(t,s)=(c1+s*(c3+s* c8)+ &
t*(c2+s*(c5+s*c9)+t*(c4+s*c7+t*c6)))
!
! --- d(sig)/dt
dsigdt(t,s)=(c2+s*(c5+s*c9)+2.0*t*(c4+s*c7+1.5*t*c6))
!
! --- d(sig)/ds
dsigds(t,s)=(c3+t*(c5+t*c7)+2.0*s* c8)
!
! --- temp (deg c) as a function of sigma and salinity (psu)
! --- find a cubic polynominal root of t**3+a2*t**2+a1*t+a0=0
tofsig(r,s)=-cubrl(r,s)+sqrt(3.0)*cubim(r,s)-a3rd*a2(s)
!
! --- salinity (psu) as a function of sigma and temperature (deg c)
! --- find a quadratic polynominal root of a*s**2+b*s+c=0
sofsig_a(r,t)=(c8+t* c9) !quadratic coefficient
sofsig_b(r,t)=(c3+t*(c5+t* c7)) !linear coefficient
sofsig_c(r,t)=(c1+t*(c2+t*(c4+t*c6))-r) !constant coefficient
sofsig(r,t)=(2.0*sofsig_c(r,t))/ &
(-sofsig_b(r,t) &
-sign(sqrt(sofsig_b(r,t)**2- &
4.0*sofsig_a(r,t)*sofsig_c(r,t)), &
sofsig_b(r,t)))
!
! --- locally referenced sigma, a fit towards Jackett & McDougall (1995)
! --- t: potential temperature; s: psu; prs: pressure
c1l(prs)=alphap(1)+prs2pb*prs*(betap(1)+prs2pb*prs*gammap(1))
c2l(prs)=alphap(2)+prs2pb*prs*(betap(2)+prs2pb*prs*gammap(2))
c3l(prs)=alphap(3)+prs2pb*prs*(betap(3)+prs2pb*prs*gammap(3))
c4l(prs)=alphap(4)+prs2pb*prs*(betap(4)+prs2pb*prs*gammap(4))
c5l(prs)=alphap(5)+prs2pb*prs*(betap(5)+prs2pb*prs*gammap(5))
c6l(prs)=alphap(6)+prs2pb*prs*(betap(6)+prs2pb*prs*gammap(6))
c7l(prs)=alphap(7)+prs2pb*prs*(betap(7)+prs2pb*prs*gammap(7))
sigloc(t,s,prs)=c1l(prs)+c3l(prs)*s+ &
t*(c2l(prs)+c5l(prs)*s+t*(c4l(prs)+c7l(prs)*s+c6l(prs)*t))
dsiglocdt(t,s,prs)=(c2l(prs)+c5l(prs)*s+ &
2.0*t*(c4l(prs)+c7l(prs)*s+1.5*c6l(prs)*t))
dsiglocds(t,s,prs)=(c3l(prs)+t*(c5l(prs)+t*c7l(prs)))
#elif (EOS_12T)
!
! --- -----------------
! --- equation of state
! --- -----------------
!
! --- sigma at rpdb (dbar) as a function of temp (deg c) and salinity (psu)
!
sig_n(t,s) = c101+(c102+c004*t+c005*s)*t + &
(c103+ c006*s)*s
sig_d(t,s) = c111+(c112+c014*t+c015*s)*t + &
(c113 +c016*s)*s
sig_q(t,s) = aone/sig_d(t,s)
sig( t,s) = sig_n(t,s)*sig_q(t,s)
!
! --- d(sig)/dt
dsigdt_n(t,s) = c102+c004x2*t+c005*s
dsigdt_d(t,s) = c112+c014x2*t+c015*s
dsigdt( t,s) = (dsigdt_n(t,s)- &
dsigdt_d(t,s)*sig_n(t,s)*sig_q(t,s))*sig_q(t,s)
!
! --- d(sig)/ds
dsigds_n(t,s) = c103+c005*t+c006x2*s
dsigds_d(t,s) = c113+c015*t+c016x2*s
dsigds( t,s) = (dsigds_n(t,s)- &
dsigds_d(t,s)*sig_n(t,s)*sig_q(t,s))*sig_q(t,s)
!
! --- temp (deg c) as a function of sigma and salinity (psu)
! --- find a quadratic polynominal root of a*t**2+b*t+c=0
tofsig_a(r,s)=( c004 - &
r* c014 ) !quadratic coefficient
tofsig_b(r,s)=( (c102+ c005*s) - &
r*(c112+ c015*s) ) !linear coefficient
tofsig_c(r,s)=( (c101+(c103+c006*s)*s) - &
r*(c111+(c113+c016*s)*s) ) !constant coefficient
tofsig(r,s)=( -tofsig_b(r,s) &
-sqrt(max(sqrmin, &
tofsig_b(r,s)**2 - &
4.0*tofsig_a(r,s)*tofsig_c(r,s))) ) / &
(2.0*tofsig_a(r,s))
!
! --- salinity (psu) as a function of sigma and temperature (deg c)
! --- find a quadratic polynominal root of a*s**2+b*s+c=0
sofsig_a(r,t)=( c006 - &
r* c016 ) !quadratic coefficient
sofsig_b(r,t)=( (c103+ c005*t) - &
r*(c113+ c015*t) ) !linear coefficient
sofsig_c(r,t)=( (c101+(c102+c004*t)*t) - &
r*(c111+(c112+c014*t)*t) ) !constant coefficient
sofsig(r,s)=max(sofmin, &
( -sofsig_b(r,s) &
+sqrt(max(sqrmin, &
sofsig_b(r,s)**2 - &
4.0*sofsig_a(r,s)*sofsig_c(r,s))) ) / &
(2.0*sofsig_a(r,s)) )
!
! --- locally referenced sigma, using the 18-term equation of state.
! --- t: potential temperature; s: psu; prs: pressure
!
sigloc_n(t,s,pdb) = c001+(c002+c004*t+c005*s)*t + &
(c003+ c006*s)*s + &
(c007+c008*t+c009*s)*pdb
sigloc_d(t,s,pdb) = c011+(c012+c014*t+c015*s)*t + &
(c013 +c016*s)*s + &
(c017+c018*t+c019*s)*pdb
sigloc_q(t,s,pdb) = aone/sigloc_d(t,s,pdb)
sigloc( t,s,prs)=sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb)
!
! --- d(sig)/dt
dsiglocdt_n(t,s,pdb) = c002+c004x2*t+c005*s+c008*pdb
dsiglocdt_d(t,s,pdb) = c012+c014x2*t+c015*s+c018*pdb
dsiglocdt( t,s,prs)=(dsiglocdt_n(t,s,prs*prs2pdb)- &
dsiglocdt_d(t,s,prs*prs2pdb)* &
sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb) ) * &
sigloc_q(t,s,prs*prs2pdb)
!
! --- d(sig)/ds
dsiglocds_n(t,s,pdb) = c003+c005*t+c006x2*s+c009*pdb
dsiglocds_d(t,s,pdb) = c013+c015*t+c016x2*s+c019*pdb
dsiglocds( t,s,prs)=(dsiglocds_n(t,s,prs*prs2pdb)- &
dsiglocds_d(t,s,prs*prs2pdb)* &
sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb) ) * &
sigloc_q(t,s,prs*prs2pdb)
!
#elif defined (EOS_17T)
!
! --- -----------------
! --- equation of state
! --- -----------------
!
! --- sigma at rpdb (dbar) as a function of pot.temp (deg c) and salinity (psu)
!
sig_n(t,s) = c101 + t*(c002+t*(c103+t*c004)) + &
s*(c105-t*c006+s*c007)
sig_d(t,s) = c108 + t*(c109+t*(c010+t*(c111+t*c012))) + &
s*(c013-t*(c014+t*t*c015) + &
sqrt(max(sqrmin,s))*(c016+t*t*c017))
sig_q(t,s) = aone/sig_d(t,s)
sig( t,s) = sig_n(t,s)*sig_q(t,s) - 1000.0
!
! --- d(sig)/dt
dsigdt_n(t,s) = c031 + t*(c132+t*c033) - &
s* c034
dsigdt_d(t,s) = c135 + t*(c036+t*(c137+t*c038)) + &
s*(c039-t*t*c040+ &
sqrt(max(sqrmin,s))*t*c041 )
dsigdt( t,s) = (dsigdt_n(t,s)- &
dsigdt_d(t,s)*sig_n(t,s)*sig_q(t,s))*sig_q(t,s)
!
! --- d(sig)/ds
! --- additional coefficients for dsigds().
dsigds_n(t,s) = c151 - t*c052 + s*c053
dsigds_d(t,s) = c054 + t*(c055-t*t*c056) + &
sqrt(max(sqrmin,s))*(c057+t*t*c058)
dsigds( t,s) = (dsigds_n(t,s)- &
dsigds_d(t,s)*sig_n(t,s)*sig_q(t,s))*sig_q(t,s)
!
! --- temp (deg c) as a function of sigma and salinity (psu)
! --- NOT AVAILABLE AS AN EXPRESSION - DO NOT USE
tofsig(r,s)=99.0
!
! --- salinity (psu) as a function of sigma and temperature (deg c)
! --- NOT AVAILABLE AS AN EXPRESSION - DO NOT USE
sofsig(r,t)=99.0
!
! --- locally referenced sigma, using the 25-term equation of state.
! --- t: potential temperature (degC); s: salinity (psu); prs: pressure (dbar)
sigloc_n(t,s,pdb) = c001 + &
t*(c002 + &
t*(c003 + &
t* c004 )) + &
s*(c005 - &
t* c006 + &
s* c007 ) + &
pdb*(c018 + &
t*t* c019 + &
s* c020 - &
pdb*(c021 + &
t*t* c022 ))
sigloc_d(t,s,pdb) = c008 + &
t*(c009 + &
t*(c010 + &
t*(c011 + &
t* c012 ))) + &
s*(c013 - &
t*(c014 + &
t*t* c015 ) + &
sqrt(max(sqrmin,s))*(c016 + &
t*t* c017 )) + &
pdb*(c023 - &
pdb*t*(t*t* c024 + &
pdb* c025 ))
sigloc_q(t,s,pdb) = aone/sigloc_d(t,s,pdb)
sigloc(t,s,prs)=sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb) - 1000.0
!
! --- d(sig)/dt
dsiglocdt_n(t,s,pdb) = c031 + &
t*(c032 + &
t* c033 ) - &
s* c034 + &
pdb*t*(c042 - &
pdb* c043 )
dsiglocdt_d(t,s,pdb) = c035 + &
t*(c036 + &
t*(c037 + &
t* c038 )) + &
s*(c039 - &
t*t* c040 + &
sqrt(max(sqrmin,s))*t* c041 ) - &
pdb*pdb*(t*t* c044 + &
pdb* c045 )
dsiglocdt(t,s,prs)=(dsiglocdt_n(t,s,prs*prs2pdb)- &
dsiglocdt_d(t,s,prs*prs2pdb)* &
sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb) ) * &
sigloc_q(t,s,prs*prs2pdb)
!
! --- d(sig)/ds
dsiglocds_n(t,s,pdb) = c051 - &
t* c052 + &
s* c053 + &
pdb* c059
dsiglocds_d(t,s,pdb) = c054 + &
t*(c055 - &
t*t* c056 ) + &
sqrt(max(sqrmin,s))*(c057 + &
t*t* c058 )
dsiglocds(t,s,prs)=(dsiglocds_n(t,s,prs*prs2pdb)- &
dsiglocds_d(t,s,prs*prs2pdb)* &
sigloc_n(t,s,prs*prs2pdb)* &
sigloc_q(t,s,prs*prs2pdb) ) * &
sigloc_q(t,s,prs*prs2pdb)
!
#endif
!
!> Revision history
!>
!> May 2000 - conversion to SI units
!> Jul 2000 - removed rarely used functions, constants via parameter
!> Jan 2002 - removed geometery functions
!> Dec 2002 - new thermobaricity fit with toff=0.0,soff=34.0
!> Jun 2003 - removed sigma4
!> Jun 2003 - added locally referenced sigma
!> Sep 2004 - added kkf to kappaf, select one of three reference states
!> Aug 2006 - more restrictive kappaf1 offset limits
!> Sep 2006 - 9-term polynominal fit to T:[-2:30],S:[18:38]
!> May 2007 - added sigver
!> Mar 2009 - modified limits in kappaf
!> Mar 2009 - more accurate kappaf, with potential density
!> Oct 2010 - 17-term rational function equation of state
!> Aug 2017 - moved kappaf to internal_kappaf.h
!> Jan 2019 - define MACRO to choose EOS at compile time (EOS_SIGX; EOS_XXT)
!-----------------------------------------------------------------------------