R: Second Derivatives of Entropy

gsw_entropy_second_derivatives {gsw} | R Documentation

## Second Derivatives of Entropy

### Description

Second Derivatives of Entropy

### Usage

    gsw_entropy_second_derivatives(SA, CT)

### Arguments

`SA` | Absolute Salinity [ g/kg ]
`CT` | Conservative Temperature [ degC ]

### 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 `eta_SA_SA` [ (J/(K*kg))/(g/kg)^2 ], the second derivative of entropy with respect to Absolute Salinity, `eta_SA_CT` [ (J/(K*kg))/(K*g/kg) ], the derivative of entropy with respect to Absolute Salinity and Conservative Temperature, and `eta_CT_CT` [ (J/(K*kg))/K^2 ], the second derivative of entropy with respect to Conservative Temperature.

### Bugs

As of March 27, 2017, the test values listed in “Examples” do not match values provided at the TEOS-10 website listed in “References”, but they match with values given by the Matlab code that is provided on the TEOS-10 website. It is expected that the TEOS-10 website will be updated by May 2017. As those updates to the TEOS-10 website become available, the present comment will be revised or deleted.

### References

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

### See Also

Other functions with suspicious test values on the TEOS-10 website: `gsw_rho_second_derivatives_wrt_enthalpy`, `gsw_specvol_second_derivatives_wrt_enthalpy`, `gsw_t_freezing_first_derivatives_poly`

### Examples

    SA <- c(34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324)
    CT <- c(28.8099, 28.4392, 22.7862, 10.2262,  6.8272,  4.3236)
    r <- gsw_entropy_second_derivatives(SA, CT)
    expect_equal(r$eta_SA_SA, c(-0.007627718929669, -0.007591969960708, -0.007528186784540,
                              -0.007455177590576, -0.007441108287466, -0.007414368396280))
    expect_equal(r$eta_SA_CT, c(-0.001833104216751, -0.001819473824306, -0.001580843823414,
                              -0.000930111408561, -0.000717011215195, -0.000548410546830))
    expect_equal(r$eta_CT_CT, c(-0.043665023731109, -0.043781336189326, -0.045506114440888,
                              -0.049708939454018, -0.050938690879443, -0.051875017843472))

[Package gsw version 1.0-5 Index]