Second Derivatives of Density

Usage

gsw_rho_second_derivatives(SA, CT, p)

Arguments

SA: Absolute Salinity [ g/kg ]. The valid range for most `gsw` functions is 0 to 42 g/kg.
CT: Conservative Temperature [ degC ].
p: sea pressure [dbar], i.e. absolute pressure [dbar] minus 10.1325 dbar

Value

A list containing rho_SA_SA [ (kg/m^3)/(g/kg)^2 ], the second derivative of density with respect to Absolute Salinity, rho_SA_CT [ (g/kg)/(g/kg)/degC ], the derivative of density with respect to Absolute Salinity and Conservative Temperature, and rho_CT_CT [ (kg/m^3)/degC^2 ], the second derivative of density with respect to Conservative Temperature.

Implementation Note

This R function uses a wrapper to a C function contained within the GSW-C system as updated 2022-10-11 at https://github.com/TEOS-10/GSW-C with git commit `657216dd4f5ea079b5f0e021a4163e2d26893371`.

The C function uses data from the library/gsw_data_v3_0.mat file provided in the GSW-Matlab source code, version 3.06-11. Unfortunately, this version of the mat file is no longer displayed on the TEOS-10.org website. Therefore, in the interests of making GSW-R be self-contained, a copy was downloaded from http://www.teos-10.org/software/gsw_matlab_v3_06_11.zip on 2022-05-25, the .mat file was stored in the developer/create_data directory of https://github.com/TEOS-10/GSW-R, and then the dataset used in GSW-R was created based on that .mat file.

Please consult http://www.teos-10.org to learn more about the various TEOS-10 software systems.

References

http://www.teos-10.org/pubs/gsw/html/gsw_rho_second_derivatives.html

Examples

SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
CT <- c(28.7856, 28.4329, 22.8103, 10.2600,  6.8863,  4.4036)
p <- c(      10,      50,     125,     250,     600,    1000)

r <- gsw_rho_second_derivatives(SA, CT, p)

stopifnot(all.equal(r$rho_SA_SA/1e-3, c(0.207364734477357, 0.207415414547223,
            0.192903197286004, 0.135809142211237, 0.122627562106076,
            0.114042431905783)))

stopifnot(all.equal(r$rho_SA_CT, c(-0.001832856561477, -0.001837354806146,
            -0.001988065808078, -0.002560181494807, -0.002708939446458,
            -0.002798484050141)))

stopifnot(all.equal(r$rho_CT_CT, c(-0.007241243828334, -0.007267807914635,
           -0.007964270843331, -0.010008164822017, -0.010572200761984,
           -0.010939294762200)))

all.equal(r$rho_SA_p, 1e-9*c(-0.617330965378778, -0.618403843947729,
        -0.655302447133274, -0.764800777480716, -0.792168044875350,
        -0.810125648949170))
#> [1] TRUE

all.equal(r$rho_CT_p, 1e-8*c(-0.116597992537549, -0.117744271236102,
        -0.141712549466964, -0.214414626736539, -0.237704139801551,
        -0.255296606034074))
#> [1] TRUE