Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox

VERSION 3.0 May 2011

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Getting started with TEOS-10 3

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4 Getting Started with TEOS-10

2. Installing the GSW Oceanographic Toolbox in MATLAB

Step 1 Download the GSW Oceanographic Toolbox in MATLAB from www.TEOS-10.org.

Step 2 Unzip the Toolbox to a directory you name “GSW”. ENSURE THAT THE FOUR SUBFOLDERS (html, library, pdf, thermodynamics_from_t) HAVE ALSO BEEN EXTRACTED.

Step 3 (within MATLAB) Add the “GSW” directory to your MATLAB path using “Add with subfolders …” That is, use the menus as follows “File” → “Set Path…” → “Add with subfolders …”. (Alternatively, the “addpath” command could be used). ENSURE THAT THE FOUR SUBFOLDERS (html, library, pdf, thermodynamics_from_t) HAVE ALSO BEEN ADDED TO THE PATH.

Step 4 Run gsw_check_functions to check that the Toolbox is correctly installed and that there are no conflicts. (This function runs three stored vertical profiles through all of the GSW functions, and checks that the outputs are within pre-defined limits of the correct values. These pre-defined limits are a factor of approximately a hundred larger than the errors expected from the numerical precision of different computers, at the standard double precision of MATLAB).

If the MATLAB Desktop is running, Step 5 Run gsw_front_page to gain access to the front page of the GSW Oceanographic Toolbox, which describes all aspects of the Toolbox.

Having installed the GSW Oceanographic Toolbox, the command gsw_contents will show the contents list of the software functions. The software descriptions and the help files for the GSW functions can be accessed by clicking on the function names on this list.

In addition, we have included a short demonstration function, gsw_demo, to introduce the user to the GSW Oceanographic Toolbox. gsw_demo uses two stored (StpP ,, ) profiles from the North Pacific and demonstrates, in a step-by-step manner, how to convert these into (SpA,,Θ ) profiles. gsw_demo then demonstrates how to evaluate several water- column properties such as dynamic height, geostrophic streamfunction and geostrophic velocity, as well as forming potential density contours on the S −Θ diagram. A A user may want to run gsw_check_functions periodically to confirm that the software remains uncorrupted.

Getting started with TEOS-10 5

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6 Getting Started with TEOS-10

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8 Getting Started with TEOS-10

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Getting started with TEOS-10 9

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10 Getting Started with TEOS-10

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Getting started with TEOS-10 11

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12 Getting Started with TEOS-10

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Getting started with TEOS-10 13

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16 Getting Started with TEOS-10

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%$U*U SP −θ U (#@UU$U* )U SP −θ U (#U-U,U$U"U*%U(-U+(,U%$*%+()U %U&%*$* "U$) */U+) $US91@UUU $(US21U* )U&(* U)U$%-U$BSU$) */U$U&%*$* "U$) */UF$U""U */&)U %U %)*(%& U )*(#+$* %$U $"+ $U /$# U  *U $%#"/GU(U$%-U$%*U

+$* %$)U%U(* "U" $ */U SP U+*U(*(U(U+$* %$)U%U
)%"+*U" $ */U SA @UUU S21U")%U $)UU$-U*#&(*+(U,( "AU%$)(,* ,U#&(*+(U Θ AU- U *!)U *U &"U %U &%*$* "U *#&(*+(U θ U F)U )* %$U 6U %,G@U U &(* %$""/AU *U

"+"* %$U%U%$)(,* ,U#&(*+(U Θ U)UU+$* %$U%U ()StpA,, U+$(US21U )U$%U  ($*U $U &( $ &"U (%#U *U -/U &%*$* "U *#&(*+(U -)U "+"*U (%#U ()StpP ,, U +$(US91CU $U%*U))UU) #&"U%#&+*(U"%( *#U )U""@U U %$)(,* ,U #&(*+(U Θ U)U*U,$*U%,(Uθ U %U #%(U +(*"/U (&()$* $U *U L*U %$*$*MU %U )-*(AU $U )U ")%U #+U "%)(U F/U U *%(U %U U +$(GU *%U  $U U %$)(,* ,U,( "U*$U )U&%*$* "U*#&(*+(@UU*U )U.$U*-$U*U%$U $U *)U *#%)&(U $U U %+$( )U )U U "+.U %U &%*$* "U $*"&/U - U )U .*"/U 011−− cp ≡ 3991.867 957 119 63 J kg K U* #)U*U$) */U* #)U*U%(()&%$ $U"+.U%U Θ @UU 0 U*($)&%(*U%U&%*$* "U$*"&/U cpΘU $U*U%$AU$U $U&(* +"(U(%))U%$U)* %$)AU $UU((U)U*U*($)&%(*U%UL*MU (()&* ,U%U-*(U*(U(U$%$S0(%U"+.)U %U#))U$R%(U%U)"*U(%))U)+U%$U)* %$)UF U$2@AU3121G@UUU

$(U S21U )U $%*U &%)) "U *%U (-U )%" $)U %U &%*$* "U $) */U %$U U SP −θ U  (#@UU*(AU+)U%U*U)&* "U,( * %$)U%U)-*(U%#&%) * %$AUU ,$U,"+U%U

&%*$* "U$) */U $)U$U(U%$U*U SP −θ U (#AU$%*UU+(,U" $@UU$U%(U*U $"/) )U $U &+" * %$U %U %$U *U +$(U S21U -U $U *%U $U (%#U +) $U *U

SP −θ U (#U- U-)U&&(%&( *U+$(US91AU*%U+) $U*U SA −ΘU (#@UU *U )U%$U * )U SA −ΘU (#U**U*U )%" $)U%U&%*$* "U$) */U$UU(-$U+$(US21@UUU $) */U#/UU"+"*U(%#U*U)+#U%U*U )U+$* %$)U%U&+(U-*(UF
S 1:AU )*"UF3114GGU$U%U)"*UF
S19AU )*"UF3119GGU+) $U'+>&#>>,(F
AA&GU %(U (%#U *U 59S*(#U (* %$"U +$* %$U .&()) %$U '+>&#F
AA&G@U U U ((%()U $,%",U - *U+) $U*U59S*(#U.&()) %$U%(U$) */U(U#+U"))U*$U*U+$(* $*/U $U*U*U %U)-*(U%#&%) * %$U%$U$) */AU$U(U")%U#+U"))U*$U *U +$(* $*/U %U *U +$("/ $U"%(*%(/U$) */U*U*%U- U*US21U )U+$* %$U-)U **UF
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
AA&GU*%U,"+*U*U)'+(U%U*U+%/$/U('+$/AU '+>"( $-F
AA&GU*%U,"+*U*U)&  U$*"&/U%U)-*(AU$U),("U+$* %$)U *%U,"+*U,( %+)U%)*(%& U)*(#+$* %$)@UUU%)*(%& U)*(#+$* %$U*%UU+)U %(U "%-U $U $U )%( U )+(U )U '+>#>'(&>-">(U- "U**U*%UU+)U $U &&(%. #*"/U $+*("U )+()U F $"+ $U &%*$* "U $) */U )+()AU ω S)+()U $U

Getting started with TEOS-10 17

+*("U$) */UF γ n GU)+()GU )U'+>#>'(&>'#$-" @UU
")%AU *U )U* )U59S*(#U.&()) %$U %(U$) */U**U- ""UU*U) )U%(U+&*U"%( *#)U%(Uω S)+()UF "%!(U$2@UF3121GGU $U+*("U$) */U γ n UF !**U$U %+""UF2::8GG@UUU

$U)+##(/AU+$(US91U-U,U*%U*U+)U*U%)(,U,( ")U ()StpP ,, U*%U  ()*U%(#U&%*$* "U*#&(*+(U θ U$U*$U-U,U$"/0U-*(U#)))U%$U*U SP −θ U  (#AU$U-U,U$U"U*%U(-U+(,U%$*%+()U%U&%*$* "U$) */U%$U* )U)#U

SP −θ U (#@UU$(US21AU*U%)(,U,( ")U ()StpP ,, AU*%*(U- *U"%$ *+U $U"* *+AU(U+)U*%U ()*U%(#U
)%"+*U" $ */U SA U+) $U'+>
>&#!>AU$U*$U %$)(,* ,U #&(*+(U Θ U )U"+"*U+) $U'+>>&#!>(@U U $%(& U -*(U

#)))U(U*$U$"/0U%$U*U SA −ΘU (#UF+) $U'+>
>>$ #(GAU$U&%*$* "U $) */U%$*%+()U$UU(-$U%$U* )U SA −ΘU (#U+) $U'+>&#F
AA&P(G@UUU U ,( %+)U %$%(& U &(%&(* )U **U ("/U %$U *U '+* %$U %U )**U ,U $U

-( **$U $U *(#)U %U SA U$U Θ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Θ U )U *)U &(%&(* )U -()U &%*$* "U *#&(*+(U θ U%)U $%*@U U %(*+$*"/U *U )U ("* ,"/U )/U *%U $U %$U #%")U *%U ,U %$)(,* ,U #&(*+(U )U * (U *#&(*+(U ,( "@U U  *U *U .&()) %$U%(U$) */U $U)*U $U

*(#)U%U
)%"+*U" $ */U SA U$U%$)(,* ,U#&(*+(U ΘU)U ρˆ ()SpA,,Θ AU*U $*( %(U %U$U%$U#%"U$UU-( **$U*%*""/U $U*(#)U%U* )U%$U*#&(*+(U,( "AU Θ@UU $U*U  (S)U $*(* %$U#%+"U%U$U%$U#%"U*U)S)+(S*#&(*+(UFGU$)U*%UU ,"+*U %(U +)U $U +"!U  (S)U"+.U%(#+"AU$U* )U )U%$U /U "" $U *U +$* %$U '+>$(>&#!>@UU )U%$,() %$U(%#U Θ U*%UU$)U*%U%$U +)*U*U*U)U)+(U $U *U (S)U $*(* %$U#%+"@UUU U +(($*U &(* U $U $+#( "U #%")U )U *%U *(*U )" $ */U )U U &(*"/U %$)(,U '+$* */U $U*U $*( %(U%U*U%$@UU $U%((U*%U%$* $+U* )U&(* U*U&&(%&( *U#%"U

)" $ */U ,( "U )U (%(#U " $ */U S* @U U (%(#U " $ */U $U
)%"+*U " $ */U (U ("*U *%U SR U$U S* U ()&* ,"/U /U '$)@U F
@31@2GU $U F
@31@3GU %U *U S21U $+"AU (&*U(UU δ SS*R1= ()1 − rRAU F6GU δ SSFA*=+()1 AU F7GU -(UU atlas δ δ δ S []1+ rR1 R ≡ A UUUUUU$UUUUUU Fδ = @U F8AUGU S atlas δ R ()1 − rR1 U
)%"+*U " $ */U
$%#"/U * %AU Rδ ≡ δ S atlas S atlas AU )U*U(* %U%U*U,"+)U%U A R
)%"+*U" $ */U
$%#"/U$U($U" $ */U $U*U)*%(U/(%(& U*")@UUU

18 Getting Started with TEOS-10

+)U(%(#U" $ */U S* U )U) $U*%UUU%$)(,* ,U)" $ */U,( "AU" $U*%U *U *)U %U  %%# "U &(%)))AU *)U ,%"+* %$U '+* %$U )U $U*U%$)(,* ,U%(#U F)U&&$ .U
@32U%U U$2@UF3121GGAUU dSˆ ⎛ Sˆ ⎞ * −1 ˆ ∂ * = γ z∇n ⋅ γ z K∇nS* + ⎜ D ⎟ .UF9GU dt ()⎝ ∂z ⎠ z ˆ (U*U%,(S* "U%U S* U $ *)U **U * )U ,( "U )U *U * !$))S- *U ,(U (%(#U" $ */AU, $U$U,(U*-$UU& (U%U"%)"/S)&U$+*("U*$$*U &"$)@UUU#*( "U( ,* ,U%$U*U"*S$U) U%U'$@UF9GU )U- *U()&*U*%U*U)+#U%U *U+"( $U$U'+) S*%!)U,"% * )U%U *U%%( $*)UF'+ ,"$*U*%U*U)( &* %$U $U &&$ .U
@32U %U U $2 @U F3121GU $U *(#)U %U *U * !$))S- *U #$U %( 0%$*"U ,"% */U$U*U#$U $+*("U,"% */GAU- "U*U( *S$U) U%U* )U'+* %$U )U*U ˆ )*$(U$%** %$U $ * $U**U S* U )U $U +)U"%$U$+*("U*$$*U&"$)U- *U*U  +) , */U U$U $U*U,(* "U (* %$U- *U*U &/$"U +) , */UUF$Uγ −1 U )U*U z ,(U %U *U ( &(%"U %U *U ,(* "U ( $*U %U +*("U $) */U %(U "%""/S(($U &%*$* "U$) */G@UUU#%"U )U $ * " 0U- *U,"+)U%U(%(#U" $ */U+) $U'$@UF6GU )U%$U%)(,* %$)U%U(* "U" $ */U$U%$U*U $*(&%"*U"%"U%)(,U*U)U %U Rδ CU* )U )U)*U%$U/U"" $U'+>'(&>&#!>@UUU $U %((U *%U ,"+*U $) */U +( $U *U (+$$ $U %U $U %$U #%"AU
)%"+*U " $ */U #+)*UU,"+*U)U%$U*U#%"K)U&( #(/U)" $ */U,( "AU(%(#U" $ */AU$U '$@UF7G@UU )U$UU%$U/U((/ $U*U%""%- $U,%"+* %$U'+* %$U%(U Fδ UU

δ δ dF −1 δ ⎛ ∂F ⎞ −1 δ obs δ = γ z∇n ⋅ γ z K∇n F + ⎜ D ⎟ + τ F − F @U F:GU dt ()⎝ ∂z ⎠ () z δ δ U #%"U ,( "U F UF$%*U**U FSS= A * − 1GU )U $ * " 0U )U %$U %)(,* %$)U %U Rδ ≡ δ S atlas S atlas U$U*U+)U%U'$@UF8GCU* )U )U)*U%$U/U"" $U'+> (@UU'+* %$U A R F:GU)%-)U**U Fδ U )U,*U$U +)U" !U$/U%*(U*((AU+*U $U * %$AU*(U )UU $%$S%$)(,* ,U )%+(U *(#U τ −1()FFδδ obs − U- U)(,)U*%U()*%(U*U#%"U,( "U Fδ U*%-()U*U%)(,U,"+UF%+$U(%#U'+> (GU- *UU()*%( $U* #Uτ U**U$U U %)$U *%U )+ *U &(* +"(U #%" $U $)U F)U *U  )+)) %$U $U&&$ .U
@31U%U*U S21U $+"AU U$2@UF3121GG@UUU $U)+##(/AU*U&&(%U%(U$" $U)" $ */U $U%$U#%")U)+)*U $U U$2@U ˆ δ ˆ F3121GU$U)+##( 0U(U(( )U*U,%"+* %$U'$)@UF9GU$UF:GU%(U S* U$U F AU- "U SA U )U"+"*U(%#U*)U*-%U#%"U,( ")U*UU* #U)*&U%( $U*%UU ˆˆ δ SSFA*=+()1 @U F21GU ˆ *U )U* )U)" $ */AU SA AU- U )U+)U)U*U(+#$*U%(U*U#%"K)U.&()) %$U%(U$) */U*U U* #U)*&U%U*U#%"@UUU U"* UU )U)%#-*U%U$U.&* %$U+)U *)U%#&%) * %$"U,( * %$)U(U$%*U +U*%U %%# )*(/U+*U*%U$%#"%+)U ( ,( $U $&+*U %U  ))%",U )"*)U - U ,U

%$)(,* ,"/@UU(%(#U" $ */U S* U $U*U"* U )U'+"U*%U
)%"+*U" $ */U SA AU- U Fδ 0 #&" )U **U r1 = −1U$U = U $U*U"* U@UU$U $U*U"* AU$U%$U#%"U ) #&"/U&+*)U SSA = ∗ U$U*U,"+U%U
)%"+*U" $ */U
$%#"/Uδ SA U )U ##*( "U+( $U *U(+$$ $U%U*U#%"@UUU%+()U*U,"+)U%Uδ SA U $U*U"* U(U #&%(*$*U%(U ("* $U
)%"+*U " $ */U $U (%(#U " $ */U *%U #)+(U ,"+)U %U (* "U " $ */U *(@U U U  )()U F#))U "+.)GU %U ( ,(U -*(U $U %U
)%"+*U " $ */U )%+"U %*U &&(U)U)%+(U*(#)U*U*U)U%U*U"* UU $U*U#%"@UUU U$U%$U#%"U )U*%UU(+$U%(U%$"/UU)%(*U* #UF"))U*$UU$*+(/GU*$U *U#/UU

)+  $*"/U+(*U*%U((/U%$"/U%$U)" $ */U,( "AU$#"/U
)%"+*U" $ */U SA @UU%(U "%$(U $*(* %$)U*U$"*U%U*U$%$S%$)(,* ,U %%# "U)%+(U*(#U#$)U

**U*U#%"K)U)" $ */U,( "U SA U- ""U&(*U(%#U(" */@UU
U#%(U* "U )+)) %$U%U *)U&% $*)U )U, ""U $U&&$ .U
@31U%U*US21U $+"UF U$2@UF3121GG@UU

Getting started with TEOS-10 19

$U)+##(/AU*U$)U$U*%U#!U%$U#%")US21U%#&* "U(UU

F G +)U$U'+* %$U%U)**U $U*(#)U%U SA U$U Θ AU ρˆ ()SpA,,Θ AU)+U)U*U59S*(#U .&()) %$U*%UU%+$U $U'+>&#F
AA&GAUU F G ,U %$)(,* ,U #&(*+(U Θ U )U *U #%"K)U *#&(*+(U ,( "U F$%*U **UU$)U*%UU,"+*U $U*U#%"K)U (S)U"+.U#%+"U +) $U '+>$(>&#!>UU*U*U)U)+(U%$"/GAUU F G $%(&%(*U*U*)U%U*U)&* ""/U,( "U)-*(U%#&%) * %$U+) $U*U *$ '+)U%U&&$ .U
@31U%U U$2@UF3121GU)U)+##( 0U%,AUUU F ,G ()*%( $U %+$(/U %$ * %$)U %(U %$S%$"/U #%")U $U U #&%)U %$U *U

#%"U,( ")U S* U$U ΘAUU F,G #%"U%+*&+*U)" $ * )U$U*#&(*+()U(U)*U#U)U
)%"+*U" $ */U SA U $U %$)(,* ,U #&(*+(U Θ AU %$) )*$*U - *U *U ,( ")U - U - ""U U &+" )U $U%$%(& U %+($")@UUU U U /.8@
@)@(#@(@@ "#&$@## #,@@

U !/U **( +*)U %U *U *(U $-U %$%(& U ,( ")U SA AU S* U$U ΘU #/U U )+##( 0U )U %""%-)@U U (%(#U " $ */U S* U $U %$)(,* ,U #&(*+(U ΘU(U*U "U ,( ")U %(U (&()$* $U*UL)"*U%$*$*MU$UL*U%$*$*MU %U )-*(U $U *U )*$(U%$)(,* %$U'+* %$)U%U&/) "U%$%(&/@UU%-,(AU*U*(#%/$# U

&(%&(* )U %U )-*(U F $U &(* +"(AU$) */GU&$U$%*U%$U(%(#U " $ */U S* AU +*U (*(U %$U
)%"+*U " $ */U SA @U U  "U (* "U " $ */U SP U )U ("* ,"/U )/U *%U #)+(U +(*"/AU *U)%+"U$%-UU((U)UU)*&& $U)*%$U%$U*U-/U*%U"+"* $U*U*-%U

#%(U**(* ,U)" $ */U,( ")AU SA U$U S* @UUU U U +$* %$)U (U " )*U %$U *U $*("U *-%U &)U %U * )U %+#$*@U U U U +$* %$)U(U(%+&U+$(U),("U $)U%U+$* %$)U- *U) # "(U(*( )* )@UUU +$* %$U'+> >)"(#"'U%$ (#)U**U*UU$%(& U%%"%.U )U%((*"/U $)*""U $U **U *(U (U $%U %$" *)@U U  )U +$* %$U (+$)U *(U )*%(U ,(* "U &(% ")U *(%+U%U""U*U%*(UU+$* %$)AU$U!)U**U*U%+*&+*)U(U- * $U&( $U " # *)U%U*U%((*U$)-()@UU)U&(S $U" # *)U(UU*%(U %U &&(%. #*"/U U +$(U"((U*$U*U((%()U.&*U(%#U$+#( "U(%+$S%UF*U*U)*$(U%+"U &( ) %$U %U

G@UUU+)(U#/U-$*U*%U(+$U'+> >)"(#"'U &( % ""/U *%U %$ (#U**U*U)%*-(U(# $)U+$%((+&*@UU'+>!#U(+$)U$U )&"/)U()+"*)U(%#U ),("U%U*UU+$* %$)AU)%U $*(%+ $U*U+)(U*%U)%#U%U*U*+()U%U*U%%"%.@UUU U(%+&U%U+$* %$)UL(* "U" $ */UFGAUS89MU%$* $)U(%+* $)U%(U(* "U " $ */U $U *(#)U %U  *(U %$+* , */U U %(U %$+* , */U (* %U AU)U-""U)U* (U $,()U +$* %$)@UUU $&+*U*#&(*+(U*%U*)U+$* %$)U )U2#$%U*#&(*+(UF S:1GAU$U*U $,()U "%( *#)U (U *(*U +$* "U *U (* "U " $ */U )U '+"U *%U *U $&+*U ,"+U *%U - * $U3.10−14 AU**U )AU*%U# $U&( ) %$@UU)U+$* %$)U $%(&%(*UU#%  U%(#U%U *U.*$) %$U%U ""U$2@UF2:97GU*%U(* "U" $ * )U*-$U0(%U$U3@UUU#%  * %$U

$)+()U**U*U"%( *#U )U.*"/US89U%(U SP ≥ 2 U $U )U %$* $+%+)U *U SP = 2@UUU +$* %$U $U * )U (%+&AU '+>>' "#!(&AU "+"*)U (* "U " $ */U (%#U *U *-%U

%+*&+*)U%UU"%(*%(/U)" $%#*(AU$#"/U Rt U$U*U*U*#&(*+(@UUU U)%$U(%+&U" ,()U*U*(U$-U%$%(& U,( ")AU
)%"+*U" $ */U SA AU (%(#U " $ */U S* AU $U %$)(,* ,U #&(*+(U Θ @UUU ()*U*-%U+$* %$)U,U (* "U" $ */U SP AU&())+(AU"%$ *+U$U"* *+U)U $&+*U,( ")@UU%*U**U, (*+""/U ""U%U*U+$* %$)U- U%""%-U* )U)%$U(%+&U('+ (U
)%"+*U" $ */U SA U)U$U $&+*@UU $U *U )U "(U **U -$U $"/0 $U %$ U *AU *U ,(/U  ()*U +$* %$U ""U #+)*U U *%U '+>
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20 Getting Started with TEOS-10

" $ */U SR U F ,$U /U "" $U '+>>&#!>GU $U &"U %U SA @UUU+$* %$U '+>>&#!>(U,"+*)U%$)(,* ,U#&(*+(U Θ AU)UU+$* %$U%U
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Quantity Symbol Units Comments Chlorinity Cl g kg–1 Chlorinity is defined as the following mass fraction; it is 0.328 523 4 times the ratio of the mass of pure silver required to precipitate all dissolved chloride, bromide and iodide in seawater to the mass of seawater.

Standard Ocean g kg–1 –1 SSO 35.165 04 g kg being exactly 35 uPS , Reference Salinity corresponding to the standard ocean Practical Salinity of 35. freezing temperatures t f , Θf ºC in situ and conservative values, each as a function of SA and p. Absolute Pressure P Pa When Absolute Pressure is used it should always be in Pa, not in Mpa nor in dbar. sea pressure. Sea pressure p dbar Equal to PP− 0 and usually expressed in dbar not is the pressure argument Pa. to all the GSW Toolbox functions.

Getting started with TEOS-10 25

gauge pressure. Gauge pgauge dbar Equal to the Absolute Pressure P minus the local pressure (also called atmospheric pressure at the time of the instrument applied pressure) is calibration, and expressed in dbar not Pa. Sea sometimes reported from pressure p is preferred over gauge pressure pgauge , ship-born instruments. as p is the argument to the seawater Gibbs function. reference pressure pr dbar The value of the sea pressure p to which potential temperature and/or potential density are referenced. one standard atmosphere P0 Pa exactly 101 325 Pa (= 10.1325 dbar) isopycnal slope ratio r 1 αβΘΘpp r () () = ΘΘ αβ()pprr () Stability Ratio R 1 RSΘΘ θθ S. ρ ρ = αβΘ≈zz()AAzz αθβ() isopycnal temperature G Θ 1 GrRRrΘ = ⎡⎤⎡⎤−−1 ; ∇Θ= GΘ∇Θ gradient ratio ⎣⎦⎣⎦ρρ σ n S Practical Salinity P 1 Defined in the range 242<

Composition. At SP = 35, SR is exactly uSPS P . while in the range 242<

26 Getting Started with TEOS-10

temperature t ºC Absolute Temperature T K TT/ K≡ 0 / K+°= t /() C 273.15 +° t / () C temperature derivatives T K When a quantity is differentiated with respect to in situ temperature, the symbol T is used in order to distinguish this variable from time. Celsius zero point K T0 T0 ≡ 273.15 K potential temperature θ ºC Defined implicitly by Eqn. (3.1.3) Conservative Temperature Θ ºC Defined in Eqn. (3.3.1) as exactly potential 0 enthalpy divided by cp . –1 –1 the “specific heat”, for use 0 J kg K 011−− cp ≡ 3991.867 957 119 63 J kg K . This 15-digit cp 0 with Conservative number is defined to be the exact value of cp . 0 0 Temperature cp is the ratio of potential enthalpy h to Θ . combined standard uc Varies uncertainty enthalpy H J specific enthalpy h J kg–1 hu=+() pPv +0 .

Here p and P0 must be in Pa not dbar. 0 –1 specific potential enthalpy h J kg specific enthalpy referenced to zero sea pressure,

0 hhSSt===()AA,,,,0,0θ []pp r p r specific isobaric heat J kg–1 K–1 cp chTp = ∂∂ capacity SpA, internal energy U J specific internal energy u J kg–1 specific isochoric heat J kg–1 K–1 cv cuTv = ∂∂ capacity SvA,

Gibbs function G J (Gibbs energy) specific Gibbs function g J kg–1 (Gibbs energy) specific Helmholtz energy f J kg–1 –1 unit conversion factor for g kg −−11 uPS uPS ≡≈(35.16504 35) g kg 1.004 715... g kg salinities The first part of this expression is exact. This conversion factor is an important and invariant constant of the 2008 Reference-Salinity Scale (Millero et al. (2008a)). entropy Σ J K–1 specific entropy η J kg–1 K–1 In many other publications the symbol s is used for specific entropy. density ρ kg m–3 –3 density anomaly t kg m – 1000 kg m–3 σ ρ ()StA ,,0 –3 potential density anomaly kg m – 1000 kg m-3 where σ 2 ρθ()SStpppAA,,,,,[] rr referenced to a sea pressure of 2000 dbar pr = 2000 dbar –3 potential density anomaly kg m – 1000 kg m-3 where σ 4 ρθ()SStpppAA,,,,,[] rr referenced to a sea pressure of 4000 dbar pr = 4000 dbar thermal expansion t α K–1 vvT−−11∂∂//= −∂∂ρρ T coefficient with respect to SpAA,, Sp in situ temperature thermal expansion θ α K–1 vv−−11∂∂//θρρθ= −∂∂ coefficient with respect to SpAA,, Sp potential temperature θ

Getting started with TEOS-10 27

thermal expansion Θ α K–1 vv−−11∂∂Θ//= −∂∂Θρρ coefficient with respect to SpAA,, Sp Conservative Temperature Θ t saline contraction β kg g–1 −∂∂vvS−−11//= ρρ∂∂ S coefficient at constant in A,Tp A, Tp t situ temperature Note that the units for β are consistent with SA being in g kg-1.

θ saline contraction β kg g–1 −∂∂vvS−−11//= ρρ∂∂ S coefficient at constant A,θθpp A, θ potential temperature Note that the units for β are consistent with SA being in g kg-1. saline contraction Θ –1 −−11 β kg g −∂∂vvS//A,ΘΘpp=+ρρ∂∂ S A, coefficient at constant Θ Conservative Temperature Note that the units for β are consistent with SA being in g kg-1. –1 isothermal compressibility κ t Pa isentropic and isohaline κ Pa–1 compressibility –1 chemical potential of μ W J g water in seawater –1 chemical potential of sea μS J g salt in seawater relative chemical potential μ J g–1 gS SW of (sea salt and water in) ()∂∂A tp, = μμ− seawater dissipation rate of kinetic ε J kg–1 s–1 energy per unit mass = m2 s–3 adiabatic lapse rate Γ K Pa–1 ∂t ∂t ∂t ∂v ()T0 +θ ∂v Γ = = = = = ∂P ∂P ∂P ∂η c0 ∂Θ SA ,θ SA ,Θ SA ,η SA , p p SA , p sound speed c m s–1 3 –1 specific volume v m kg v = ρ −1 specific volume anomaly δ m3 kg–1 thermobaric coefficient θ KPa−−11 TPθθθθ Tb b = βαβ∂∂() based on θ SA ,θ thermobaric coefficient Θ KPa−−11 TPΘΘΘΘ= βαβ∂∂ Tb b () based on Θ SA ,Θ 2 cabbeling coefficient θ −2 θθ⎛⎞ Cb K CSSθθ2 αα θ θ bAA= ∂∂αθ+ θθ∂∂ α −⎜⎟ ∂∂ β based on θ SpA,,ββθθ p⎝⎠ , p 2 cabbeling coefficient Θ −2 ΘΘ C K CSSΘΘ2 αα Θ⎛⎞ Θ b bAA= ∂∂Θαα+ ΘΘ∂∂ −⎜⎟ ∂∂ β based on Θ SpA,,ββΘΘ p⎝⎠ , p buoyancy frequency N −1 Ng2 = αβΘΘΘ− S= g αθβθθ− S s ()()zzAAzz neutral helicity H n m−3 defined by Eqns. (3.13.1) and (3.13.2) n a density variable whose iso-surfaces are designed Neutral Density γ kg m–3 to be approximately neutral, i. e. ΘΘ αβ∇Θ≈γγ ∇SA. Neutral-Surface-Potential- −3 −1nwhere f is the Coriolis NSPV s NSPV= − gργ f z Vorticity parameter. dynamic height anomaly Ψ ms22− Pa m31 kg−−= m 22 s 22 31 22 Montgomery geostrophic ΨM ms− Pa m kg−−= m s streamfunction

28 Getting Started with TEOS-10

streamfunction for f times the depth-integrated PISH (Pressure-Integrated Ψ′ kg s-2 Steric Height) relative mass flux, see Eqns. (3.31.1) – (3.31.5). Coriolis parameter f s−1 1.458 42x 10−−41 sinφ s , where φ is latitude

1 SA –1 mm== where M is the molality mol kg SW ∑i i S mSW MSSA()1−

mole-weighted average atomic weight of the

elements of sea salt, −1 MS = 0.031 403 821 8
kg mol 22 ImZ==11 mz ionic strength I mol kg–1 22SW ∑i ii

= 0.622 644 9 mSW 622.644 9 S ≈ mol kg−1 A 31.403 821 8() 1− SA

gtp0, ,W Stp , , ()− μ (A ) osmotic coefficient φ 1 φ ()STpA ,, = mRTtSW() 0 + where the molar gas constant, R = 8.314 472 J mol–1 K–1. See also Eqns. (2.14.1) and (3.40.9) for an equivalent definition of φ.

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