R: Second Derivatives of Density

gsw_rho_second_derivatives {gsw} | R Documentation

## Second Derivatives of Density

### Description

Second Derivatives of Density

### Usage

    gsw_rho_second_derivatives(SA, CT, p)

### Arguments

`SA` | Absolute Salinity [ g/kg ]
`CT` | Conservative Temperature [ degC ]
`p` | sea pressure [dbar], i.e. absolute pressure [dbar] minus 10.1325 dbar

### Details

The present R function works with a wrapper to a C function contained within the GSW-C system (Version 3.05-4 dated 2017-08-07, available at https://github.com/TEOS-10/GSW-C, as git commit '5b4d959e54031f9e972f3e863f63e67fa4f5bfec'), which stems from the GSW-Fortran system (https://github.com/TEOS-10/GSW-Fortran) which in turn stems from the GSW-Matlab system (https://github.com/TEOS-10/GSW-Matlab). Consult http://www.teos-10.org to learn more about these software systems, their authorships, and the science behind it all.

### 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.

### 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)
    expect_equal(r$rho_SA_SA/1e-3, c(0.207364734477357, 0.207415414547223, 0.192903197286004,
                                   0.135809142211237, 0.122627562106076, 0.114042431905783))
    expect_equal(r$rho_SA_CT, c(-0.001832856561477, -0.001837354806146, -0.001988065808078,
                              -0.002560181494807, -0.002708939446458, -0.002798484050141))
    expect_equal(r$rho_CT_CT, c(-0.007241243828334, -0.007267807914635, -0.007964270843331,
                              -0.010008164822017, -0.010572200761984, -0.010939294762200))
    expect_equal(r$rho_SA_p/1e-8, c(-0.087202931942412, -0.087558612009845, -0.092549696987409,
                                  -0.106661486272630, -0.110022261844240, -0.112287954816717))
    expect_equal(r$rho_CT_p/1e-8, c(-0.116597992537549, -0.117744271236102, -0.141712549466964,
                                  -0.214414626736539, -0.237704139801551, -0.255296606034074))

[Package gsw version 1.0-5 Index]