gsw_entropy_second_derivatives function

Second Derivatives of Entropy

gsw_entropy_second_derivatives(SA, CT)

Arguments

• SA: Absolute Salinity [ g/kg ]. The valid range for most gsw functions is 0 to 42 g/kg.
• CT: Conservative Temperature [ degC ].

Returns

A list containing eta_SA_SA [ (J/(Kkg))/(g/kg)^2 ], the second derivative of entropy with respect to Absolute Salinity, eta_SA_CT [ (J/(Kkg))/(Kg/kg) ], the derivative of entropy with respect to Absolute Salinity and Conservative Temperature, and eta_CT_CT [ (J/(Kkg))/K^2 ], the second derivative of entropy 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.

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)
stopifnot(all.equal(r$eta_SA_SA, c(-0.007627718929669, -0.007591969960708, -0.007528186784540,
                                   -0.007455177590576, -0.007441108287466, -0.007414368396280)))
stopifnot(all.equal(r$eta_SA_CT, c(-0.001833104216751, -0.001819473824306, -0.001580843823414,
                                   -0.000930111408561, -0.000717011215195, -0.000548410546830)))
stopifnot(all.equal(r$eta_CT_CT, c(-0.043665023731109, -0.043781336189326, -0.045506114440888,
                                   -0.049708939454018, -0.050938690879443, -0.051875017843472)))

References

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