Help for package marelac

Version:

2.1.11

Title:

Tools for Aquatic Sciences

Author:

Karline Soetaert [aut, cre], Thomas Petzoldt [aut], Filip Meysman [cph], Lorenz Meire [cph]

Maintainer:

Karline Soetaert <karline.soetaert@nioz.nl>

Depends:

R (≥ 3.2), shape

Imports:

stats, seacarb

Description:

Datasets, constants, conversion factors, and utilities for 'MArine', 'Riverine', 'Estuarine', 'LAcustrine' and 'Coastal' science. The package contains among others: (1) chemical and physical constants and datasets, e.g. atomic weights, gas constants, the earths bathymetry; (2) conversion factors (e.g. gram to mol to liter, barometric units, temperature, salinity); (3) physical functions, e.g. to estimate concentrations of conservative substances, gas transfer and diffusion coefficients, the Coriolis force and gravity; (4) thermophysical properties of the seawater, as from the UNESCO polynomial or from the more recent derivation based on a Gibbs function.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

LazyData:

yes

NeedsCompilation:

yes

Packaged:

2023-09-25 10:04:59 UTC; karlines

Repository:

CRAN

Date/Publication:

2023-09-25 12:10:02 UTC

Tools for Aquatic Sciences

Description

R-package marelac has been designed as a tool for use by scientists working in the MArine, Riverine, Estuarine, LAcustrine and Coastal sciences.

It contains:

chemical and physical constants, e.g. atomic weights, gas constants.
conversion factors, e.g. from salinity to chlorinity, from mol to gram, etc.,
utility functions, e.g. to estimate concentrations of conservative substances as a function of salinity, ...

About the symbols used.

Here we adopt the symbolism as in McDougall et al., 2009:

S for practical (-) or absolute salinity, (g/kg)
P for absolute (total) pressure (bar)
p for sea pressure (also called gauge or applied pressure (bar), the pressure relative to P0, one standard atmosphere (=1.01325 bar)
t for temperature in ^\circC
T for absolute temperature, in ^\circK; T = t + 273.15

Many of the functions are from the UNESCO 1983 paper, or from Feistel, 2008. Note that in these papers, pressure is expressed in dbar.

Author(s)

Karline Soetaert (Maintainer)

Thomas Petzoldt

with contributions from Lorenz Meire and Filip Meysman

References

For solubilities, atmospheric composition, gas exchange coefficients:

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

For diffusion coefficients, viscosity

Boudreau BP, 1996. A method-of-lines code for carbon and nutrient diagenesis in aquatic sediments. Computers & Geosciences 22 (5), 479-496.

For many other fundamental properties of seawater, either the UNESCO report (1983):

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp. http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

or the more recent report and papers:

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

McDougall TJ, Feistel R, Millero FJ, Jackett DR, Wright DG, King BA, Marion GM, Chen C-T A and Spitzer P, 2009. Calculation of the Thermophysical Properties of Seawater, Global Ship-based Repeat Hydrography Manual, IOCCP Report No. 14, ICPO Publication Series no. 134.

Millero FJ, Feistel R, Wright DG, and McDougall TJ, 2008. The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.

Examples

## Not run: 
## show examples (see respective help pages for details)
example(Constants)
example(molvol)

## open the directory with documents
browseURL(paste(system.file(package="marelac"), "/doc", sep=""))


## End(Not run)

The Atomic Weights of Chemical Elements

Description

Atomic weights of chemical elements according to the IUPAC table.

Usage

AtomicWeight
atomicweight

Format

The capitalized version AtomicWeight is a data frame containing the IUPAC table of atomic weights. This data frame has following colums: Number, Name, Symbol, Weight, Footnotes.

Note that as in the IUPAC table, the Weight is given as a text rather than as numeric objects. It comprises the standard values and the uncertainties (in parentheses, following the last significant figure to which they are attributed). See IUPAC report for explanation of the Footnotes.

The lower case version atomicweight is a simplified list that only contains the weights (as numeric values) and allows symbolic computations with elements to arrive at molecular weights.

Details

Molecular weights of chemical elements may vary due to different isotope compositions, depending on geology, industrial processes or biological activity. Please consult the IUPAC Technical report about the details. The data set contains NA for elements that have no stable isotopes (except U, Th, Pa).

Author(s)

Thomas Petzoldt

References

Wieser ME, 2006. Atomic weights of the elements 2005 (IUPAC Technical Report). Pure Appl. Chem. 78 (11), 2051–2066., 2006. DOI: 10.1351/pac200678112051

Examples

## assess the data in the IUPAC table (with all footnotes)
AtomicWeight[1:20,]
AtomicWeight[AtomicWeight$Symbol == "C",]

## use the lower case version for simple calculations:
atomicweight$C
with(atomicweight, C)

## it can also be used to calculate molecular weights
## via symbolic computation
with(atomicweight, H * 2 + O)

World Bathymetric Data

Description

This dataset contains the elevation of sea (bathymetry) and land (hypsometry) across the globe at 1 degree intervals. Dataset as used by Andersson et al. (2004).

Usage

Bathymetry

Format

A list with the bathymetry (depth) and hypsometry (altitude) of the world. It contains:

x: the latitude,
y: the longitude,
z: the height (m).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Andersson H, Wijsman J, Herman PMJ, Middelburg J, Soetaert K and Heip C, 2004. Respiration patterns in the deep ocean. Geophysical Research Letters 31, LO3304.

Examples

par(mar = c(2,2,2,2))
image(Bathymetry$x, Bathymetry$y, Bathymetry$z, col = femmecol(100),
      asp = TRUE, xlab = "dg", ylab = "dg")
contour(Bathymetry$x, Bathymetry$y, Bathymetry$z, asp = TRUE, add = TRUE)


# remove land
zz       <- Bathymetry$z
zz[zz>0] <- 0

image(Bathymetry$x, Bathymetry$y, zz, col = c(femmecol(100), "black"),
      asp = TRUE)
contour(Bathymetry$x, Bathymetry$y, zz, asp = TRUE, add = TRUE)

Useful Physical and Chemical Constants

Description

Physical and chemical constants useful for aquatic sciences.

Usage

Constants

Format

A list specifying the value, the units, and a description for each physical constant.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Mohr PJ and Taylor BN, 2005. CODATA recommended values of the fundamental physical constants: 2002, Review of Modern Physics 77, 1 - 107.

Examples


data.frame(cbind(acronym = names(Constants),
           matrix(ncol = 3, byrow = TRUE, data = unlist(Constants),
           dimnames = list(NULL, c("value", "units", "description")))))

Useful Characteristics of the Oceans

Description

Surface area and volume of the world's oceans

Usage

Oceans

Format

A list specifying the value, units, and a description of each quantity.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

Examples


data.frame(cbind(acronym = names(Oceans),
           matrix(ncol = 3, byrow = TRUE, data = unlist(Oceans),
           dimnames = list(NULL, c("value", "units", "description")))))

Air Density

Description

The density of the air, in kg/m3

Usage

air_density(t = 25, P = 1.013253)

Arguments

t

Temperature, ^\circC.

P

True pressure, bar

Value

The air density, in kg/m3

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>, Lorenz Meire <lorenz.meire@nioz.nl>

References

http://www.cactus2000.de/uk/unit/masshum.shtml

Examples

air_density(t = 25) # 1.183894
plot(0:30, air_density(t = 0:30), xlab = "Temperature, dgC", ylab = "kg/m3")
plot(x= seq(0.8,1.2, 0.01), y = air_density(P = seq(0.8,1.2, 0.01)),
     xlab = "pressure, bar", ylab = "kg/m3")

Air specific humidity

Description

The specific humidity of air (mass mixing ratio in wet air), in kg/kg

Usage

air_spechum(t = 25, rh = 50, P = 1.013253)

Arguments

t

Temperature, ^\circC.

rh

Relative humidity, %

P

True pressure, bar

Value

The specific humidity, in kg/kg.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>, Lorenz Meire <lorenz.meire@nioz.nl>

References

Lowe, P.R. and J.M. Ficke, 1974: The computation of saturation vapor pressure. Tech. Paper No. 4-74, Environmental Prediction Research Facility, Naval Postgraduate School, Monterey, CA, 27 pp.

http://www.cactus2000.de/uk/unit/masshum.shtml

Examples

air_spechum(t = 25, rh = 50)*1000     # 9.7778
plot(0:30, air_spechum(t = 0:30), xlab = "Temperature, dgC", ylab = "kg/kg")
plot(0:100, air_spechum(rh = 0:100), xlab = "percent humidity", ylab = "kg/kg")

Atmospheric Gas Composition

Description

Provides the global average atmospheric composition at present day conditions (year 1998). The mixing ratio is generally defined as the ratio of the mass of an atmospheric constituent to the total mass of dry air. If not otherwise indicated, the term mixing ratio normally refers to water vapor. Here however the mixing ratio is provided for all constituents other than water. The mixing ratio is given as a mole fraction, i.e. the mass of each constituent gas (expressed in moles) divided by the total mass of dry air (also expressed in moles).

Usage

atmComp(species = c("He", "Ne", "N2", "O2", "Ar", "Kr", "CH4", "CO2",
  "N2O", "H2", "Xe", "CO", "O3"))

Arguments

species

character vector selecting the gases whose composition should be provided.

Value

A vector providing the mixing ratio of the selected gases.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>, Filip Meysman <filip.meysman@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

They cite Weast and Astle (1982) for all gasses except CO2, CH4 and N2O. For the latter three greenhouse gases, the 1998 concentrations are taken from Ramaswamy et al., 2001. Note that the sum of all mixing ratios is slightly larger than one, presumably due to the use of increased greenhouse gases values as compared to Weast and Astle (1982). In fact, the mixing ratio are changing slightly each year due to increases in greenhouse gas concentrations.

Examples

atmComp("O2")
atmComp(c("O2", "CH4", "CO2", "N2O"))
atmComp()
sum(atmComp()) # note this is not =1!

Conductivity-Salinity Conversion

Description

Estimates the salinity of seawater from conductivity, temperature and pressure. The equation is valid over ranges: temperature from -2 to 35 ^\circC, pressure from 0 to 1000 bar, and salinity from 2 to 42.

Usage

convert_RtoS(R = 1, t = 25, p = max(0, P-1.013253), P = 1.013253)

Arguments

R

Conductivity ratio, the conductivity at (S, t, P) divided by the conductivity at S = 35, t = 15, p = 0 [-]

t

Temperature, ^\circC

p

Gauge (or applied) pressure, the pressure referenced against the local atmospheric pressure, bar

P

True pressure, bar

Value

The salinity.

Note

The conductivity ratio for Salinity = 40.0000, t = 40, p = 1000 is 1.888091.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

convert_RtoS(R = 1.888091, t = 40, p = 1000)

## Salinity = 40.0000, t = 40, p = 1000, cond = 1.888091
convert_RtoS(R = 1, t = 15, p = 0)

## Check values
convert_RtoS(R = 0.6990725, t = 10, p = 0)  # 26.8609
convert_RtoS(R = 0.6990725, t = 10, p = 100)  # 26.5072
convert_RtoS(R = 1.1651206, t = 20, p = 100)  # 36.3576

Salinity-Chlorinity Conversion

Description

Estimates the chlorinity concentration based on salinity

Usage

convert_StoCl(S = 35)

Arguments

S

salinity

Value

The chlorinity concentration, g/kg

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Cox RA, Culkin F, Riley JP, 1967. The electrical conductivity – chlorinity relationship in natural seawater. Deep–Sea Research 14, 203–220.

Examples

convert_StoCl(20)

Salinity-Conductivity Conversion

Description

Estimates the conductivity ratio from salinity, temperature and pressure.

The equation is valid over ranges of temperature from -2 to 35 ^\circC, pressure of 0 - 1000 bar and salinity 2-42 in the world ocean.

Usage

convert_StoR(S = 35, t = 25, p = max(0, P-1.013253), P = 1.013253)

Arguments

S

(practical) Salinity, -,

t

Temperature, ^\circC,

P

True Pressure, bar,

p

Gauge (or applied) pressure, the pressure referenced against the local atmospheric pressure, bar.

Value

The conductivity ratio (-), this is the conductivity at (S, t, p), divided by the conductivity at S = 35, t = 15, p = 0.

Note

Pressure here is true pressure, 1 bar (at sea surface), in contrast to hydrostatic pressure in dbar of original formula.

The conductivity ratio for Salinity = 40, t = 40, p = 1000 is 1.888091.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

convert_StoR(S = 40, t = 40, p = 1000)

convert_StoR(S = 35, t = 15, p = 0)

# Check values:
convert_StoR(S = 25, t = 10, p = 0)    #  0.654990
convert_StoR(S = 25, t = 10, p = 100)  #  0.662975
convert_StoR(S = 25, t = 10, p = 1000) #  0.712912

convert_StoR(S = 35, t = 10, p = 100) #  0.897778
convert_StoR(S = 40, t = 10, p = 100) #  1.011334

Conversion Between Different Temperature Units

Description

The function converts between different units of temperature.

Usage

convert_T(x, unit = c("K", "C", "F"))

Arguments

x

Vector of given temperature values,

unit

Measurement unit of the given value(s).

Value

A data frame with converted values.

References

Mangum BW and Furukawa GT, 1990. Guidelines for Realizing the International Temperature Scale of 1990 (ITS-90). NIST Technical Note 1265. and the url

http://www.cstl.nist.gov/div836/836.05/papers/magnum90ITS90guide.pdf

Examples

convert_T(0, "K")
convert_T(0, "C")
convert_T(0, "F")

convert_T(273.15, "K")
convert_T(-273.15, "C")
convert_T(c(-459.67, 0, 32), "F")

convert_T(32, "F")$C # 0 degrees C

Conversion Between Different Barometric Units

Description

The function converts between different units of pressure.

Usage

convert_p(x, unit = c("Pa", "bar", "at", "atm", "torr"))

Arguments

x

vector of given pressure values,

unit

measurement unit of the given value(s).

Value

A data frame with converted values.

References

https://en.wikipedia.org/wiki/Bar_(unit)

Examples

convert_p(1, "atm")
convert_p(c(2, 3, 4.5), "bar")

convert_p(1, "atm")$Pa

Practical - Absolute Salinity Conversions

Description

Conversion from practical to absolute salinity and vice versa.

Usage

convert_PStoAS(S = 35, p = max(0, P - 1.013253), P = 1.013253,
  lat = NULL, lon = NULL, DSi = NULL,
  Ocean = c("Global", "Atlantic", "Pacific", "Indian", "Southern"))

convert_AStoPS(S = 35, p = max(0, P - 1.013253), P = 1.013253,
  lat = NULL, lon = NULL, DSi = NULL,
   Ocean = c("Global","Atlantic","Pacific","Indian","Southern"))

Arguments

S

Salinity, either practical salinity (convert_PStoAS), dimensionless or absolute salinity (convert_AStoPS, g/kg)

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

lat

latitude (-90 to +90)

lon

longitude (0 to 360)

DSi

the silicate concentration, in micromol/kg

Ocean

the ocean in which the measurement was taken; only used if DSi is not NULL

Details

Absolute salinity (g kg-1) is estimated from Practical salinity as:

AS= 35.16504 /35 * PS + delt()

where delt is the absolute salinity anomaly. There are two ways in which to estimate the salinity anomaly

1. If DSi is not given a value, then the anomaly is estimated as a function of longitude lon, latitude lat and pressure p, using the lookup table as in sw_sfac.

2. If DSi is given a value, then a regression on it is used, based on the values of Ocean and -except for the "global" ocean- the latitute lat:

"Global"

a global estimate is used,

delt= 9.824e-5 *DSi,

"Southern"

the Southern Ocean (lat < -30),

delt= 7.4884e-5 *DSi,

"Pacific"

the Pacific Ocean ,

delt= 7.4884e-5 *(1 + 0.3622[lat/30 + 1])*DSi,

"Indian"

the Indian Ocean ,

delt= 7.4884e-5 *(1 + 0.3861[lat/30 + 1])*DSi,

"Atlantic"

the Atlantic Ocean ,

delt= 7.4884e-5 *(1 + 1.0028[lat/30 + 1])*DSi,

Note that for the Pacific, Indian and Atlantic Ocean regression, the latitude is needed. If lat is NULL then the Global regression will be used.

Value

The absolute salinity (convert_PStoAS) or practical salinity (convert_AStoPS).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Millero FJ, Feistel R, Wright DG and McDougall TJ, 2008. The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.

McDougall TJ, Jackett DR and Millero FJ, 2009. An algorithm for estimating Absolute Salinity in the global ocean. Ocean Science Discussions 6, 215-242. http://www.ocean-sci-discuss.net/6/215/2009/

Uses the Fortran code written by David Jackett. http://www.teos-10.org/

Examples

# check values: should be 35.7
convert_PStoAS(S = 35.52764437773386, p = 102.3, lon = 201, lat = -21)

# check values: should be 35.52764437773386
convert_AStoPS(S = 35.7, p = 102.3, lon = 201, lat = -21)

#
convert_PStoAS(S = 35)
convert_AStoPS(S = 35)
convert_PStoAS(S = 35, lat = 10, lon = 10, p = 0)

# Based on Si concentration
DSi <- seq(from = 0, to = 200, by = 10)
Global   <-  convert_PStoAS(30, DSi = DSi, Ocean = "Global")
Atlantic <-  convert_PStoAS(30, DSi = DSi, Ocean = "Atlantic", lat = 0)
Pacific  <-  convert_PStoAS(30, DSi = DSi, Ocean = "Pacific", lat = 0)
Indian   <-  convert_PStoAS(30, DSi = DSi, Ocean = "Indian", lat = 0)
Southern <-  convert_PStoAS(30, DSi = DSi, Ocean = "Southern")

matplot(x = DSi, y = cbind(Global, Atlantic, Pacific, Indian, Southern),
  pch = 1, xlab = "DSi, micromol/kg", ylab = "Absolute salinity (PS=30)")
legend("topleft",c("Global", "Atlantic", "Pacific", "Indian", "Southern"),
       col = 1:5, pch = 1)

The Coriolis Force as a Function of Latitude

Description

Estimates the coriolis factor, f (in s^{-1}), where f = 2 \cdot \omega \cdot sin(lat), where \omega = 7.292e^{-5} radians/sec, the rotation of the earth.

Usage

coriolis(lat)

Arguments

lat

latitude in degrees north (-90 to +90).

Value

The coriolis factor (s^{-1}).

Author(s)

Karline Soetaert < karline.soetaert@nioz.nl >

References

Pond S and Pickard G, 1986. Introductory Dynamical Oceanography, Pergamon Press, Sydney, 2nd Ed.

Griffies SM, 2004. Fundamentals of Ocean Climate Models. Princeton, NJ, Princeton University Press, 518 pp.

Examples

plot(-90:90, coriolis(-90:90), xlab = "latitude, dg North", 
  ylab = "/s", main = "coriolis factor", type = "l", lwd = 2)

Molecular Diffusion Coefficients

Description

Calculates the molecular and ionic diffusion coefficients in m^2 s^{-1}, for several inorganic species in seawater at a given salinity, temperature, and pressure.

Based on Chapter 4 in Boudreau (1997)

Usage

diffcoeff(S = 35, t = 25, P = 1.013253,
      species = c("H2O", "O2", "CO2", "H2", "CH4", "DMS",
      "He", "Ne", "Ar", "Kr", "Xe", "Rn",
      "N2", "H2S", "NH3", "NO", "N2O", "CO", "SO2",
      "OH", "F", "Cl", "Br", "I",
      "HCO3", "CO3", "H2PO4", "HPO4", "PO4",
      "HS", "HSO3", "SO3", "HSO4", "SO4", "IO3", "NO2", "NO3",
      "H", "Li", "Na", "K", "Cs","Ag","NH4",
      "Ca", "Mg", "Fe", "Mn", "Ba", "Be", "Cd", "Co",
      "Cu", "Hg", "Ni", "Sr", "Pb", "Ra", "Zn", "Al", "Ce",
      "La", "Pu", "H3PO4", "BOH3", "BOH4", "H4SiO4"))

Arguments

S

Salinity, -,

t

Temperature, ^\circC,

P

True pressure, bar,

species

character vector with the names of the chemical species whose diffusion coefficient should be calculated.

Details

To correct for salinity, the Stokes-Einstein relationship is used. This is not quite accurate, but is at least consistent.

H_3PO_4 : Least (1984) determined D(H3PO4) at 25 deg C and 0 S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

B(OH)_3 : Mackin (1986) determined D(B(OH)3) at 25 deg C and about 29.2 S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

B(OH)_4 : No information on this species. Boudreau and Canfield (1988) assume it is 12.5% smaller than B(OH)3.

H_4SiO_4 : Wollast and Garrels (1971) found D(H4SiO4) at 25 deg C and 36.1 ppt S. Assume that this value can be scaled by the Stokes-Einstein relationship to any other temperature.

Arguments salinity, temperature or pressure can be vectors. In order to avoid confusion, S, t and P must have either same length or length 1. More flexible combinations are of course possible with expand.grid

Value

A data.frame with the diffusion coefficients m^2 s^{-1} of the selected chemical species.

Author(s)

Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>

References

Based on Chapter 4 in Boudreau (1997) :

Boudreau BP, 1997. Diagenetic Models and their Implementation. Modelling Transport and Reactions in Aquatic Sediments. Springer. Berlin.

who cites:

for self-diffusion coefficient H2O:

Cohen MH and Turnbull D. 1959. Molecular transport in liquids and glasses. Journal of chemical physics 31 (5): 1164-1169

Krynicki K, Green CD and Sawyer DW, 1978. Pressure and temperature-dependence of self-diffusion in water. Faraday discussions 66: 199-208

for gases O2 and CO2:

Novel relation by Boudreau (1997) based on new compilation of data

for gases He, Ne, Kr, Xe, Rn, H2, CH4:

Jahne B, Heinz G, and Dietrich W, 1987. Measurements of the diffusion coefficients of sparingly soluble gases in water. J. Geophys. Res., 92:10,767-10,776.

for Ar:

Ohsumi T and Horibe Y, 1984. Diffusivity of He and Ar in deep-sea sediments, Earth and Planetary Science Letters 70, 61-68.

for DMS:

Saltzman ES, King DB, Holmen K, and Leck C, 1993. Experimental Determination of the Diffusion Coefficient of Dimethylsulfide in Water, J. Geophys. Res., 98(C9), 16, 481-486.

for other gases (N2, H2S, NH3, NO, N2O, CO, SO2):

Wilke CR and Chang P, 1955. Correlation of diffusion coefficients in dilute solutions. Aiche journal 1 (2): 264-270

with the correction proposed by

Hayduk W and Laudie H, 1974. Prediction of diffusion-coefficients for nonelectrolytes in dilute aqueous-solutions. Aiche journal 20 (3): 611-615

for ions:

Hayduk W and Laudie H, 1974. Prediction of diffusion-coefficients for nonelectrolytes in dilute aqueous-solutions. Aiche journal 20 (3): 611-615

for H3PO4, B(OH)3, B(OH)4, H4SiO4 : see details

Examples

diffcoeff(S = 15, t = 15)*1e4*3600*24         # cm2/day
diffcoeff(t = 10, species = "O2")             # m2/s
difftemp <- diffcoeff(t = 0:30)[,1:13]
matplot(0:30, difftemp, xlab = "temperature", ylab = "m2/s",
        main = "Molecular/ionic diffusion", type = "l",
        col = 1:13, lty = 1:13)
legend("topleft", ncol = 2, cex = 0.8, title = "mean", 
       col = 1:13, lty = 1:13,
       legend = cbind(names(difftemp),
       format(colMeans(difftemp), digits = 4)))

## vector-valued salinity
select <- c("O2", "CO2", "NH3", "NH4", "NO3")
diffsal <- diffcoeff(S = 0:35, species = select)
matplot(0:35, diffsal, xlab = "salinity", ylab = "m2/s",
         main = "Molecular/ionic diffusion", type = "l",
         col = 1:length(select), lty = 1:length(select))
legend("topleft", ncol = 2, cex = 0.8, title = "mean",
       col = 1:length(select), lty = 1:length(select),
       legend = cbind(select, format(colMeans(diffsal), digits = 4)))

## vector-valued temperature
difftemp <- diffcoeff(S = 1, t=1:20, species = select)
matplot(1:20, difftemp, xlab = "temperature", ylab = "m2/s",
        main = "Molecular/ionic diffusion", type = "l",
        col = 1:length(select), lty = 1:length(select))
legend("topleft", ncol = 2, cex = 0.8, title = "mean",
       col = 1:length(select), lty = 1:length(select),
       legend = cbind(select, format(colMeans(difftemp), digits = 4)))

## combination of S and t
diffsaltemp <- diffcoeff(S = rep(c(1, 35), each = 20), 
                         t = rep(1:20, 2), species = select)

Surface of 1 dg by 1 dg Cells of the Earth

Description

earth_surf computes the surface of 1d by 1dg grid cells as a function of latitude.

Based on data that give the surface distance per 1 dg change in lat/lon from https://en.wikipedia.org/wiki/Latitude

earth_dist calculates the distance between two (lat, lon) points

Usage

earth_surf(lat = 0, lon = 0)
earth_dist(alat, alon, blat, blon, method = 1)

Arguments

lat

latitude (-90 - +90).

lon

longitude - not used.

alat

first latitude (-90 - +90).

alon

first longitude (-180, 180).

blat

second latitude (-90 - +90).

blon

second longitude (-180, 180).

method

an integer indicating the formula to use, either the spherical law of cosines (1) or the haversine formula (2)

Value

Surface of the grid cell, in m^2.

Distance between the points (alat, alon), (blat, blon), m.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

Examples


 earth_surf(seq(0, 90, by = 15))

 SURF <- outer(X = Bathymetry$x,
               Y = Bathymetry$y,
               FUN <- function(X, Y) earth_surf(Y, X))

 earth_dist(10, 80, 10, 81)
 earth_dist(20, 80, 20, 81)

 SURF <- outer(X = Bathymetry$x,
               Y = Bathymetry$y,
               FUN <- function(X, Y) earth_surf(Y, X))

 sum(SURF)                                   #is: 510,072,000  km2

# the surface of the Oceans, m2
 sum(SURF*(Bathymetry$z < 0))                  # is: 3.58e14

# the volume of the Oceans, m3
- sum(SURF*Bathymetry$z*(Bathymetry$z < 0))    # is: 1.34e+18

# the surface area at several depths
SurfDepth <- vector()

dseq <- seq(-7500, -250, by = 250)

for (i in 2:length(dseq)) {
  ii <- which (Bathymetry$z > dseq[i-1] & Bathymetry$z <= dseq[i])
  SurfDepth[i-1]<-sum(SURF[ii])
}

plot(dseq[-1], SurfDepth, xlab = "depth, m", log = "y",
     ylab = "m2", main = "Surface at ocean depths")

Saturation Concentration of Oxygen in Water

Description

Empirical formulae that can be used to compute saturation concentration of oxygen in water in mg/L

Usage

gas_O2sat(S = 35, t = 25, masl = 0, method = c("Weiss", "APHA", "Paul"))

Arguments

S

salinity (dimensionless, for method "Weiss" only),

t

Temperature in ^\circC,

masl

height above sea level (in m, for method "Paul" only),

method

formula to be used, see references for correct application.

Details

Method APHA is the standard formula in Limnology, method Weiss the standard formula in marine sciences. The method after Paul is a simple formula fitted on available tables. To avoid confusion between the arguments (S, t, masl) it is advisable to use named arguments in general, e.g. O2sat(t = 4).

Value

Vector with oxygen saturation concentration in mg L^{-1}.

References

American Public Health Association, Inc. (1985): Standard Methods for the Examination of Water and Wastewater. 18th edition, 1992.

Benson BB and Krause D, 1980. The concentration and isotopic fractionation of gases dissolved in freshwater in equilibrium with the atmosphere. I. Oxygen. Limnology and Oceanography 25, 662-671.

Brown LC and Barnwell TO Jr, 1987. The Enhanced Stream Water Quality Models QUAL2E and QUAL2E-UNCAS: Documentation and User Manual. U.S. Environmental Protection Agency, Athens, Georgia. EPA/600/3-87/007, p. 41. http://www.epa.gov)

DIN 38408-23, Ausgabe:1987-11: Deutsche Einheitsverfahren zur Wasser-, Abwasser- und Schlammuntersuchung; Gasf?rmige Bestandteile (Gruppe G); Bestimmung des Sauerstoffs?ttigungsindex (G 23).

Paul L, 1985. Das thermische Regime der Talsperre Saidenbach und einige Beziehungen zwischen abiotischen und biotischen Komponenten. Dissertation, TU Dresden, Fakult?t Bau-, Wasser- und Forstwesen. 84 pp.

Weiss R, 1970. The solubility of nitrogen, oxygen, and argon in water and seawater. Deep-Sea Research 17, 721-35.

Wagner R, 1979. Die Praxis der Bestimmung des biochemischen Sauerstoffbedarfs - Ergebnisse einer Umfrage (Berichtigung und Erg?nzung zur Ver?ffentlichung). Vom Wasser 53, S. 283-285.

Examples

gas_O2sat(S = 0, t = 20)                  # fresh water, Weiss formula
gas_O2sat(S = 0, t = 20, method = "APHA") # fresh water, APHA formula

## compare this with
gas_satconc(S = 0, t = 20, species = "O2") * molweight("O2") / 1000

T <- seq(0, 30, 0.1)
plot(T, gas_O2sat(S = 0, t = T, method = "APHA"),
  ylab="O2 sat (mg/L)", type = "l", ylim = c(0, 15))
lines(T, gas_O2sat(S = 0, t = T, method = "Weiss"),
  col = "blue", lwd = 2, lty = "dashed")
lines(T, gas_O2sat(S = 5, t = T, method = "Weiss"), col = "green")
lines(T, gas_O2sat(S = 10, t = T, method = "Weiss"), col = "yellow")
lines(T, gas_O2sat(S = 20, t = T, method = "Weiss"), col = "orange")
lines(T, gas_O2sat(S = 35, t = T, method = "Weiss"), col = "red")

legend("bottomleft", 
  col = c("black", "white", "blue", "green", "yellow", "orange", "red"),
  lty = c(1, 0, 2, 1, 1, 1, 1), lwd = c(1,0 ,2, 1, 1, 1, 1),
  legend=c("freshwater formula", "marine formula:", 
          "S = 0", "S = 5", "S = 10", "S = 20", "S = 35"))

Saturated Concentrations of Gases in Water

Description

Calculates the saturated concentration of several gases in water for a given temperature, salinity and pressure.

Usage

gas_satconc(S = 35, t = 25, P = 1.013253,
        species =c("He","Ne","N2","O2","Ar","Kr","CH4","CO2","N2O"),
        atm = atmComp(species))

Arguments

S

Salinity (dimensionless),

t

Temperature, ^\circC,

P

True pressure, bar

species

character vector with gasses whose saturated concentration should be estimated.

atm

The number of moles of the gas per unit mole of air in the atmosphere, the "mixing ratio". When present, this overrules the species argument. When unspecified, the value from atmComp for the species is taken.

Value

The saturated concentration of the gas in mmol m^{-3}.

Note

Compared to the table in Sarmiento and Gruber, there is a slight deviation for N2O, and He.

CO2 is OK for temperature 0 only.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

who cite:

for He and Ne: Weiss R, 1971. Solubility of helium and neon in water and seawater. Journ. Chem. Eng. Data 16, 235-241.

N2, O2 and Ar: Weiss R, 1970. The solubility of nitrogen, oxygen, and argon in water and seawater. Deep-Sea Res. 17, 721-35.

Kr: Weiss R and Kyser TK, 1978. Solubility of Krypton in water and seawater. Journ. Chem. Eng. Data 23, 69-72.

Rn: Hackbusch 1979. Eine Methode zur Bestimmung der Diffusions-, L?slichkeits un Permeabilitats Konstanten von Radon-222 in Wasser und Meereswasser. Dissertation, University of Heidelberg, Germany.

CH4: Wiesenburg DA and Guinasso JNL, 1979. Equilibrium solubilities of methane, carbon monoxide and hydrogen in water and sea water. Journ. Chem. Eng. Data 24, 256-360.

CO2 and N2O: Weiss R and Price BA, 1980. Nitrous oxide solubility in wate and sewater. Mar. Chem. 8, 347-359.

CFC-11 and CFC-12: Warner MJ and Weiss R, 1985. Solubilities of chlorofluorocarbons 11 and 12 in water and sewater. Deep-Sea Res. 32, 1485-1497.

SF6: Bullister et al., 2002. The solubility of sulfur hexafluroide in water and sewater. Deep-Sea Res. I, 49, 175-188.

CCl4: Bullister JL and Wisegarver DP, 1998. The solubility of carbon tetrachloride in water and seawater. Deep-Sea Res. I, 1285-1302.

Examples

gas_satconc(species = "O2")
Temp <- seq(from = 0, to = 30, by = 0.1)
Sal  <- seq(from = 0, to = 35, by = 0.1)

mf  <- par(mfrow = c(1,2))

species <- c("N2", "CO2", "O2", "CH4", "N2O")
gsat  <- gas_satconc(t = Temp, species = species)

matplot(Temp, gsat, type = "l", xlab = "temperature", log = "y", lty = 1,
     ylab = "mmol/m3", main = "Saturated conc (S=35)", lwd = 2)
legend("right", col = 1:5, lwd = 2, legend = species)

gsat  <- gas_satconc(S = Sal, species = species)
matplot(Sal, gsat, type = "l", xlab = "salinity", log = "y", lty = 1,
     ylab = "mmol/m3", main = "Saturated conc (T=20)", lwd = 2)
legend("right", col = 1:5, lwd = 2, legend = species)


par(mfrow = mf)

## generate table 3.2.4 from Sarmiento and Gruber
Temp <- seq (0, 30, by = 5)
## saturated concentrations in mmol/m3, at 1 atm.
A <- data.frame(cbind( t = Temp,
            N2  = gas_satconc(t = Temp, species = "N2"),
            O2  = gas_satconc(t = Temp, species = "O2"),
            CO2 = gas_satconc(t = Temp, species = "CO2"),
            Ar  = gas_satconc(t = Temp, species = "Ar")))
format(A, digits = 4)
## table values
## at  0 dg C: 635.6   359.1  23.37  17.44
## at 20 dg C: 425.7   230.5  11.61  11.29
## note the deviations for CO2 (20dg)!

## saturated concentrations in micromol/m3, at 1 atm.
AA <- data.frame(cbind(t = Temp,
            N2O = gas_satconc(t = Temp, species = "N2O")*1000,
            Ne  = gas_satconc(t = Temp, species = "Ne" )*1000,
            Kr  = gas_satconc(t = Temp, species = "Kr" )*1000,
            CH4 = gas_satconc(t = Temp, species = "CH4")*1000,
            He  = gas_satconc(t = Temp, species = "He" )*1000))
format(AA, digits = 4)
## table values
## at  0 dgC: 14.84 8.11  4.33  3.44  1.81
## at 20 dgC: 7.16  6.94  2.50  2.12  1.70
## Note: different for N2O

The Schmidt Number for Gases in Seawater

Description

The Schmidt number as a function of temperature (0-30dgC) and for a salinity of 35.

Sc = v/D = Mu/(rho+D)

where v is the kinematic viscosity of the water and D is the mass diffusivity, rho is density and mu is the viscosity.

Schmidt numbers are used to estimate the gas transfer velocity.

Usage

gas_schmidt(t = 25, species = c("He", "Ne", "N2", "O2", "Ar",
        "Kr", "Rn", "CH4","CO2", "N2O", "CCl2F2", "CCL3F",
        "SF6", "CCl4"))

Arguments

t

Temperature in ^\circC,

species

character vector with gasses whose schmidt number should be estimated.

Value

The Schmidt number, a dimensionless quantity.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

who cite:

Wanninkhof R, 1992. Relationship between wind speed and gas exchange over the ocean. Journ. Geophys. Res. 97, 7373-7383.

except for O_2:

Keeling et al., 1998. Seasonal variation in the atmospheric O2/N2 ratio in relation to the kinetics of air-sea gas exchange. Global Biogeochemical Cycles 12, 141-164.

CFC-11 (CCl_2F_2), and CFC-12 (CCl_3F):

Zheng et al., 1998. Measurements of the diffusion coefficients of CF-11 and CF-12 in pure water and seawater. Journ. Geophys. Res. 103, 1375-1379.

and CCl_4 (Wanninkhof, pers.comm).

Examples

gas_schmidt(species = "CO2", t = 20) # about660

Solubility Parameters

Description

Solubility parameters SA, mmol m^{-3} bar^{-1}, calculated from the Bunsen solubility coefficients and the volumetric solubility coefficients.

Usage

gas_solubility(S = 35, t = 25, 
      species = c("He", "Ne", "N2", "O2", "Ar", "Kr", "Rn", "CH4", 
                  "CO2", "N2O", "CCl2F2", "CCl3F", "SF6", "CCl4"))

Arguments

S

salinity, -

t

temperature, ^\circC,

species

The gas

Value

The solubility, mmol/m3/bar.

Note

The molar volume used for the Bensen coefficient conversion is the ideal gas value of 22.4136 l/mol.

These coefficients are to be used with pAmoist, the partial pressure of the gas in moist air.

To convert them for use with partial pressure in dry air, divide by (1-vapor(S,t)).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

who cite:

for He and Ne: Weiss R, 1971. Solubility of helium and neon in water and seawater. Journ. Chem. Eng. Data 16, 235-241.

N2, O2 and Ar: Weiss R, 1970. The solubility of nitrogen, oxygen, and argon in water and seawater. Deep-Sea Res. 17, 721-35.

Kr: Weiss R and Kyser TK, 1978. Silubility of Krypton in water and seawater. Journ. Chem. Eng. Data 23, 69-72.

Rn: Hackbusch 1979. Eine Methode zur Bestimmung der Diffusions, Loeslichkeits un Permeabilitats Konstanten von Radon-222 in Wasser und Meereswasser. Dissertation, University of Heidelberg, Germany.

CH4: Wiesenburg DA and Guinasso JNL, 1979. Equilibrium solubilities of methane, carbon monoxide and hydrogen in water and sea water. Journ. Chem. Eng. Data 24, 256-360.

CO2 and N2O: Weiss R and Price BA, 1980. Nitrous oxide solubility in wate and sewater. Mar. Chem. 8, 347-359.

CFC-11 and CFC-12: Warner MJ and Weiss R, 1985. Solubilities of chlorofluorocarbons 11 and 12 in water and sewater. Deep-Sea Res. 32, 1485-1497.

SF6: Bullister et al., 2002. The solubility of sulfur hexafluroide in water and sewater. Deep-Sea Res. I, 49, 175-188.

CCl4: Bullister JL and Wisegarver DP, 1998. The solubility of carbon tetrachloride in water and seawater. Deep-Sea Res. I, 1285-1302.

Examples

gas_solubility(t = 1:20,S = 35, species = "CO2")
gas_solubility(t = 0:5,S = 35,species = "O2")

Temp <- seq(from = 0, to = 30, by = 0.1)
mf <- par(mfrow = c(1, 2))
gs  <- gas_solubility(t = Temp)
species   <- c("CCl4", "CO2", "N2O", "Rn", "CCl2F2")
matplot(Temp, gs[, species], type = "l", lty = 1, lwd = 2,
     xlab = "temperature", ylab = "mmol/m3", main = "solubility (S=35)")
legend("topright", col = 1:5, lwd = 2, legend = species)

species2 <- c("Kr", "CH4", "Ar", "O2", "N2", "Ne")
matplot(Temp, gs[, species2], type = "l", lty = 1, lwd = 2,
     xlab = "temperature", ylab = "mmol/m3", main = "solubility (S=35)")
legend("topright", col = 1:6, lwd = 2, legend = species2)




plot(Temp,gas_solubility(t = Temp, species = "CCl4"), xlab = "temperature",
     ylab = "mmol/m3/atm", main = "solubility (S=35)",
     type = "l", lwd = 2, ylim = c(0, 100000))
lines(Temp,gas_solubility(t = Temp, species = "CO2"), col = "red", lwd = 2)
lines(Temp,gas_solubility(t = Temp, species = "N2O"), col = "blue", lwd = 2)
lines(Temp,gas_solubility(t = Temp, species = "Rn"), col = "green", lwd = 2)
lines(Temp,gas_solubility(t = Temp, species = "CCl2F2"), col = "yellow", lwd = 2)

legend("topright", col = c("black", "red", "blue", "green", "yellow"), lwd = 2,
       legend = c("CCl4", "CO2", "N2O", "Rn", "CCl2F2"))

plot(Temp, gas_solubility(t = Temp, species = "Kr"), xlab = "temperature",
     ylab = "mmol/m3/atm", main = "solubility (S=35)", type = "l",
     lwd = 2, ylim = c(0, 4000))
lines(Temp, gas_solubility(t = Temp, species = "CH4"), col = "red", lwd = 2)
lines(Temp, gas_solubility(t = Temp, species = "Ar"), col = "blue", lwd = 2)
lines(Temp, gas_solubility(t = Temp, species = "O2"), col = "green", lwd = 2)
lines(Temp, gas_solubility(t = Temp, species = "N2"), col = "yellow", lwd = 2)
lines(Temp, gas_solubility(t = Temp, species = "Ne"), col = "grey", lwd = 2)

legend("topright",col = c("black", "red", "blue", "green", "yellow", "grey"),
       lwd = 2, legend = c("Kr", "CH4", "Ar", "O2", "N2", "Ne"))

par(mfrow = mf)

## generate table 3.2.3 from Sarmiento and Gruber
Temp <- seq (0,30,by = 5)

## saturated concentrations in mmol/m3 at at 1 atm;
# convert from /bar to /atm using 1.013253

A <- data.frame(cbind( t = Temp,
            He = gas_solubility(t = Temp,species = "He")*1.013253,
            Ne = gas_solubility(t = Temp,species = "Ne")*1.013253,
            N2 = gas_solubility(t = Temp,species = "N2")*1.013253,
            O2 = gas_solubility(t = Temp,species = "O2")*1.013253,
            Ar = gas_solubility(t = Temp,species = "Ar")*1.013253,
            Kr = gas_solubility(t = Temp,species = "Kr")*1.013253,
            Rn = gas_solubility(t = Temp,species = "Rn")*1.013253)  )
format(A,digits = 4)
## table values at
## 0   dgC:  349.4   448.6   818.8  1725  1879  3820  31150
## 20 dg C:  332.9   390.7   557.9  1126  1236  2241  14130
## note the (very) slight deviations for Rn

## saturated concentrations in micromol/m3 at 1 atm
AA <- data.frame(cbind( t = Temp,
            CH4    = gas_solubility(t = Temp,species = "CH4")   *1.013253,
            CO2    = gas_solubility(t = Temp,species = "CO2")   *1.013253,
            N2O    = gas_solubility(t = Temp,species = "N2O")   *1.013253,
            CCL2F2 = gas_solubility(t = Temp,species = "CCl2F2")*1.013253,
            CCL3F  = gas_solubility(t = Temp,species = "CCl3F") *1.013253,
            SF6    = gas_solubility(t = Temp,species = "SF6")   *1.013253,
            CCl4   = gas_solubility(t = Temp,species = "CCl4")  *1.013253))
format(AA,digits = 4)

## Table values at
##  0 dgC: 1984  64400 47840  6686 27380   425.2  97114
## 20 dgC: 1241  33110 23870  2566  9242   195.8  30307
## Note: there are slight deviations for CO2, and N2O!

The Gas Transfer Coefficient in m/sec

Description

The gas transfer coefficient, in m s^{-1}, for certain gases in seawater (S = 35).

Usage

gas_transfer(t = 25, u10 = 1, species = c("He", "Ne", "N2", "O2", "Ar",
        "Kr", "Rn", "CH4","CO2", "N2O", "CCl2F2", "CCL3F",
        "SF6", "CCl4"),
  method = c("Liss", "Nightingale", "Wanninkhof1", "Wanninkhof2"),
  Schmidt = gas_schmidt(t = t, species = species))

Arguments

t

Temperature in ^\circC,

u10

wind speed, in m/sec at a nominal height of 10 m above sea level,

species

character vector with gasses whose gas transfer coefficient should be estimated.

method

one of "Liss", for Liss and Merlivat, 1986; "Nightingale", for Nightingale et al., 2000; "Wanninkhof1", for Wanninkhof 1992, or "Wanninkhof2" for Wanninkhof and McGills 1999.

Schmidt

the Schmidt number, when given this overrules the arguments gas and t.

Value

The gas transfer velocity, for seawater, in m s^{-1}.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 85.

Liss PS and Merlivat L, 1986. Air-sea gas exchange rates: introduction and synthesis. In: the role of air-sea exchange in Geochemical cycling, edited by P. Buat-Menard, pp 113-127. D. Reidel, Dordrecht, the Netherlands.

Nightingale et al., 2000. In situ evaluation of air-sea gas exchange prameterizations using novel conservative and volatile tracers. Global biogeochemical cycles 14, 373-387.

Wanninkhof R, 1992. Relationship between wind speed and gas exchange over the ocean. Journ. Geophys. Res. 97, 7373-7383.

Wanninkhof R and McGillis W, 1999. A cubic relationshp between air-sea CO2 exchange and wind speed. Geophys. Res. Lett. 26, 1889-1892.

Examples

useq <- 0:15
plot(useq, gas_transfer(u10 = useq, species = "O2"), type = "l", lwd = 2, xlab = "u10, m/s",
     ylab = "m/s", main = "O2 gas transfer velocity", , ylim = c(0, 0.0003))
lines(useq, gas_transfer(u10 = useq, species = "O2", method = "Nightingale"), lwd = 2, lty = 2)
lines(useq, gas_transfer(u10 = useq, species = "O2", method = "Wanninkhof1"), lwd = 2, lty = 3)
lines(useq, gas_transfer(u10 = useq, species = "O2", method = "Wanninkhof2"), lwd = 2, lty = 4)

legend("topleft", lty = 1:4, lwd = 2,
  legend = c("Liss and Merlivat 1986", "Nightingale et al. 2000",
  "Wanninkhof 1992", "Wanninkhof and McGills 1999"))

Gravity on Earth

Description

Computes the gravity, based on latitude.

Usage

gravity(lat = 0, method = c("Moritz", "UNESCO"))

Arguments

lat

latitude (-90 - +90).

method

When "UNESCO", uses the UNESCO (1983) polynomial, else according to Moritz, 2000

Value

Gravity, in \rm m\,sec^{-2}.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

The UNESCO polynomial:

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Moritz H, 2000. Geodetic reference system 1980. Journal of Geodesy 74, 128-133.

Examples

gravity(lat = 30)

Internal Functions of the marelac Package

Description

Internal functions of package marelac.

Details

These are not to be called by the user.

Mol to Liter Conversion for a Gas

Description

Converts from liter to moles for a gas.

Usage

molvol(t = 25, P = 1.013253,
   species = c("ideal", "Ar", "CO2", "CS2", "CO", "CCl4", "Cl2",
         "C2H6S", "C2H5OH", "C6H5F", "CH3F", "CH4", "CH3OH", "C5H12",
          "C3H8", "H2O", "He", "H2", "HBr", "HCl", "H2S", "Hg",
          "Kr", "NH3", "Ne", "NO", "N2", "NO2", "N2O", "O2", "PH3",
          "SiH4", "SiF4", "SO2", "Xe"),
    quantity = 1, a = 0, b = 0)

Arguments

t

temperature, ^\circC

P

True pressure, bar.

species

character vector with gasses whose molecular volume should be estimated. if NULL then the coefficients a and b are used.

quantity

mol of the gas.

a

Van der Waals constant a, a species-specific coefficient, dm^6*bar/mol^2.

b

Van der Waals constant b, a species-specific coefficient, dm^3/mol.

Value

volume of the gas, liter

Note

The coefficients a and b are species-specific; values of 0 assume an ideal gas and in general give good estimates.

Use 1/molvol to convert from liter to moles.

The default calculates the molar volume of an ideal gas

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

The values of the van der Waals constants are from:

Weast RC (Ed.) 1972. Handbook of Chemistry and Physics (53rd Edn.), Cleveland:Chemical Rubber Co.

as found in: https://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page)

Examples

#molecular volume of an ideal gas.
molvol(species = "ideal", P = 1, t = 0)    # 22.710 980
molvol(species = "ideal", P = 1, t = 25)   # 24.789 598

plot(0:30, molvol(t = 0:30, species = NULL),
    xlab = "Temperature, dgC", ylab = "Molar volume")

#
molvol(a = 1.382, b = 0.03186, species = NULL, t = 0)

molvol(t = 0, species = "O2")

# the same but for all gasses
molvol(t = 0)

# table for different pressures
molvol(P = 1:5, species = "O2")

# the inverse function
1/molvol(species = "O2")

# contour plot
P    <- seq(1, 100, by = 1)
Temp <- seq(-5, 40, by = 1)

Val <- outer(X = P, Y = Temp,
      FUN = function(X, Y) molvol(P = X,  t = Y, species = "O2"))
contour(P, Temp, Val, xlab = "pressure", ylab = "temperature",
        main = "molvol", nlevel = 20, log = "x", axes = FALSE)
axis(1); axis(2); box()

Molecular Weight of a Chemical Species

Description

Calculates the molecular weight of chemical species.

Usage

molweight(species)

Arguments

species

character vector with chemical species whose molecular weight is requested.

Details

Molecular weights of chemical elements may vary due to different isotope compositions, depending on geology, industrial processes or biological activity. Please consult the IUPAC Technical report about the details. The function returns NA for elements (and their compounds) which have no stable isotopes (except U, Th, Pa).

Value

Vector with the molecular weights in g/mol.

Note

This function uses text parsing of chemical formulae, it is strictly case sensitive.

Author(s)

Thomas Petzoldt

References

Wieser ME, 2006. Atomic weights of the elements 2005 (IUPAC Technical Report). Pure Appl. Chem. 78(11), 2051–2066. doi:10.1351/pac200678112051

Examples

molweight("CO2")
molweight("HCO3")
molweight("H")
molweight("H3PO4")

## eicosapentaenoic acid (EPA)
molweight("CH3CH2CHCHCH2CHCHCH2CHCHCH2CHCHCH2CHCH(CH2)3COOH")
molweight("C20H30O2")

## works also with vectors
molweight(c("C2H5OH", "CO2", "H2O"))
molweight(c("SiOH4", "NaHCO3", "C6H12O6", "Ca(HCO3)2", "Pb(NO3)2", "(NH4)2SO4"))

## note that chemical formulae are case-sensitive
molweight("Co") # cobalt
molweight("CO") # carbon monoxide


## from gram to mol
1/molweight("CO3")

Redfield Ratio Calculator

Description

Estimate elemental composition of biomass (or media) according to the Redfield ratio.

Usage

redfield(q, species, method = c("mol", "mass"), 
         ratio = c(C=106, H=263, O=110, N=16, P=1))

Arguments

q

amount of substance of that element (in mol or mass units),

species

The element that is given ("C", "H", "O", "N", "P"),

method

measurement unit ("mol" or "mass"),

ratio

average elemental composition.

Details

The average elemental composition of marine plankton (Redfield ratio) is traditionally assumed to be \mathrm {C_{106}H_{263}O_{110}N_{16}P_{1}} (Redfield 1934, 1963, Richards 1965). Note that while the C:N:P ratio is widely agreed there is still discussion about the average of O and H, e.g. \mathrm{C_{106}H_{180}O_{45}N_{16}P_{1}} (Stumm, 1964).

Note also that there are, of course, large differences depending on species and physiological state.

Value

A data frame with the estimated ratio of the main elements.

References

Redfield AC, 1934. On the proportions of organic derivations in sea water and their relation to the composition of plankton. In: James Johnstone Memorial Volume. (ed. R.J. Daniel). University Press of Liverpool, 177-192.

Redfield, AC, Ketchum, BH and Richards FA, 1963. The influence of organisms on the composition of seawater. In: Hill, MN, Editor, The Sea vol. 2, Interscience, New York (1963), pp.26-77.

Richards FA, 1965. Anoxic basins and fjords. In: Riley JP, Skirrow D. (Eds.), Chemical Oceanography, vol. 1. Academic Press, New York, 611-645. (cited in Hedges et al, 2002).

Stumm W, 1964. Discussion (Methods for the removal of phosphorus and nitrogen from sewage plant effluents by G. A. Rohlich). In Eckenfelder, WW (ed.), Advances in water pollution research. Proc. 1st Int. Conf. London 1962, volume 2, pp. 216-229. Pergamon.

Vollenweider RA, 1985. Elemental and biochemical composition of plankton biomass: some comments and explorations. Arch. Hydrobiol. 105, 11-29.

Anderson LA, 1995. On the hydrogen and oxygen content of marine plankton. Deep-Sea Res. 42, 1675-1680.

Hedges JI., Baldock JA, Gelinas Y, Lee C, Peterson ML and Wakeham SG, 2002. The biochemical and elemental compositions of marine plankton: A NMR perspective. Marine Chemistry 78, 47-63.

Examples

## Redfield ratio
redfield(1, "P")
## returns the molar Redfield ratio, rescaled to nitrogen
redfield(1, "N")
## how many mass units are related to 2 mass units (e.g. mg) P
redfield(2, "P", "mass")
redfield(c(1, 2, 3), "N", "mass")

## mass percentage of elements
x <- redfield(1, "P", "mass")
x / sum(x)

## with alternative elemental composition (Stumm, 1964)
x <- redfield(1, "P", "mass", 
              ratio = c(C = 106, H = 180, O = 45, N = 16, P = 1))
x / sum(x)

## rule of thumb for fresh mass (in mg) formed by 1 microgram P
redfield(1, "P", "mass")$C * 2 * 10 / 1000
sum(redfield(1, "P", "mass",
  ratio = c(C = 106, H = 180, O = 45, N = 16, P = 1))) * 10 / 1000

Estimate Global Radiation from Measured Sunshine Duration Time

Description

The function converts values of sunshine duration (in hours) to global radiation (in J m^{-2} s^{-1}).

Usage

ssd2rad(S, doy, a = 0.25, b = 0.5, rho = 50.29)

Arguments

S

Sunshine duration (hours)

doy

Julian day (for northern hemisphere only)

a, b, rho

site specific conversion parameters, must be fitted to measured data.

Value

Estimated value of global radiaton in J m^{-2} s^{-1}.

Note

Don't forget to fit the function parameters to site specific values!

References

Dyck S and Peschke G., 1995. Grundlagen der Hydrologie. 3. Auflage. Verlag f?r Bauwesen, Berlin 1995, ISBN 3-345-00586-7.

Examples

ssd2rad(8, 120)

Adiabatic Temperature Gradient in Seawater

Description

Computes the adiabatic temperature gradient in seawater, using the UNESCO 1983 polynomial.

Also known as the adiabatic lapse rate, the change of temperature per unit pressure for an adiabatic change of pressure of an element of seawater. It is assumed that no heat or salt is exchanged with the surroundings.

Usage

sw_adtgrad(S = 35, t = 25, p = P-1.013253, P = 1.013253 )

Arguments

S

Practical salinity (-),

t

Temperature, ^\circC

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

adiabatic temperature gradient, in dg K / bar

Note

Note: in the original formula, the units of sw_adtgrad are dg K/dbar (here: dg K/bar).

sw_adtgrad for S = 40, t = 40, p = 1000 is 3.255976e-3

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

sw_adtgrad(t = 40, S = 40, p = 1000)  #3.255976e-4

## Check values
sw_adtgrad(S = 25, t = 10, p = 0)    # 0.1002e-3
sw_adtgrad(S = 25, t = 10, p = 100)  # 0.1135e-3
sw_adtgrad(S = 25, t = 10, p = 1000) # 0.2069e-3

sw_adtgrad(S = 25, t = 30, p = 0)    # 0.2417e-3
sw_adtgrad(S = 40, t = 30, p = 0)    # 0.2510e-3
sw_adtgrad(S = 40, t = 0,  p = 100)  # 0.0630e-3

Thermal Expansion Coefficient of Seawater

Description

Computes the seawater thermal expansion coefficient with respect to in situ temperature, 1/K

Usage

sw_alpha(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Thermal expansion coefficient, 1/K.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_alpha(35.7, 25.5, 102.3)#0.000309837839319264

Haline Contraction Coefficient of Seawater

Description

Computes the seawater haline contraction coefficient with respect to constant, in situ temperature, kg/g

Usage

sw_beta(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Haline contraction coefficient, kg/g.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_beta(35.7, 25.5, 102.3)    #0.000725729797838666

Reference Sea Salt Composition

Description

The sea salt composition definition for reference salinity of the standard ocean at 25 dgC and 1.01325 bar (atmospheric pressure), given in mass fractions).

Usage

sw_comp(species = c("Na", "Mg", "Ca", "K", "Sr", "Cl", "SO4", "HCO3",
                    "Br", "CO3", "BOH4", "F", "OH", "BOH3", "CO2"))

Arguments

species

character vector with components whose composition should be estimated.

Value

A vector with the mass fractions.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Millero FJ, Waters J, Woosley R, Huang F and Chanson M, 2008. The effect of composition of the density of Indian Ocean waters, Deep-Sea Res. I, 55, 960-470.

Examples

sw_comp("CO2")
sw_comp()
sum(sw_comp())

Concentrations of (Conservative) Species in Seawater

Description

Estimates the concentration of Borate,Calcite, Sulphate and Fluoride in seawater, as a function of salinity.

Usage

sw_conserv(S = 35)

Arguments

S

Practical salinity, (-).

Details

The borate and calcite concentration as in Millero (1995),

Sulphate as in Morris and Riley, 1966,

Fluoride as in Riley, 1965.

Value

A data frame with the concentrations in micromol/kg.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Millero FJ, 1995. Thermodynamics of the carbon dioxide system in the oceans. Geochim. Cosmochim. Acta 59, 661 677.

Riley JP, 1965. The occurrence of anomalously high fluoride concentrations in the North Atlantic. Deep-Sea Res. 12, 219 220.

Morris AW, Riley JP, 1966. The bromide- chlorinity and sulphate- chlorinity ratio in seawater. Deep-Sea Res. 13, 699 706.

Examples

data.frame(salinity = 1:35, sw_conserv(1:35) )

Heat Capacity of Sea Water

Description

Estimates the heat capacity of seawater.

Valid for S = 0 to 40, T = 0 to 35 dg C

Usage

sw_cp(S = 35, t = 25, p = P-1.013253, P = 1.013253,
      method = c("Gibbs", "UNESCO"))

Arguments

S

Salinity, when method = "UNESCO": practical salinity (-) else absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

method

When "UNESCO", uses the UNESCO (1983) polynomial, when "Gibbs", based on the gibbs functions as in Feistel, 2008

Value

Heat capacity, in J kg^{-1} dgC^{-1}

Note

p is applied pressure, 0 bar at sea surface.

when using UNESCO polynomial, cp for S = 40, T = 40, P = 1000 is 3849.5 J/(kg dg C).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_cp(S = 40, t = 40, p = 1000, method="UNESCO")  # 3849.5

# Check value Gibbs function
sw_cp(35.7,25.5,102.3)#3974.42541259729

# Check values UNESCO
sw_cp(S = 25, t = 10, p = 0,    method = "UNESCO")  # 4041.8
sw_cp(S = 25, t = 10, p = 1000, method = "UNESCO")  # 3842.3
sw_cp(S = 25, t = 30, p = 0,    method = "UNESCO")  # 4049.1

sw_cp(S = 40, t = 10, p = 0, method = "UNESCO")  # 3959.3

Density of Sea Water

Description

Density of sea water in kg m^{-3}

Usage

sw_dens(S = 35, t = 25, p = max(0, P-1.013253), P = 1.013253,
        method=c("Gibbs","UNESCO","Chen"))

Arguments

S

Salinity, when method = "UNESCO": practical salinity (-) else absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

method

When "UNESCO", uses the UNESCO (1983) polynomial, when "Gibbs", based on the Gibbs functions as in Feistel, 2008 "Chen" for the limnological range (i.e. fresh water systems).

Details

To avoid confusion between the arguments (S, t, p) it is advisable to use named arguments in general (e.g. rho(t = 4). The UNESCO formula is imported from package seacarb.

Value

Density of water in kg m^{-3}.

Note

Pressure used here is 1 bar (true pressure), in contrast to hydrostatic pressure (0 bar at surface) in original formula.

The coefficients from McDougall et al., 2009 were used. For temperature, they differ slightly from Feistel 2003 and Feistel 2008, which is why, for temparatures different from 0, there is a slight offset from the estimates as from table 22 or 21 from Feistel (2008).

References

Chen Ch.-T. and Millero FJ, 1986. Thermodynamic properties of natural waters covering only the limnological range. Limnol. Oceanogr. 31 No. 3, 657 - 662. doi:10.4319/lo.1986.31.3.0657

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

# table 22 Feistel 2008
sw_dens(0, 0, 0)               #0.999843086e3
sw_dens(0, 79.85, 0)           #0.97188383e3   - deviates
sw_dens(0, 0,998.98675)        #0.104527796e4

# table 21 Feistel 2008
sw_dens(35.16504, 0, 0)        #0.10281072e4
sw_dens(100, 79.85, 0)         #0.102985888e4
sw_dens(35.16504, 0,998.98675) #0.10709264e4

sw_dens(35.7, 25.5, 102.3)     #1027.95249315662

S <- 0:40
plot(S, sw_dens(S = S, t = 4, method = "UNESCO"))

lines(S, sw_dens(S = S, t = 4, method = "Gibbs"), col = "red")

lines(S, sw_dens(S = S, t = 4, method = "Chen"), col = "blue")

Water Depth

Description

Computes the water depth for water of salinity 35, and temperature 0 dg C, based on latitude and hydrostatic pressure, using the UNESCO 1983 polynomial.

Usage

sw_depth(p = P-1.013253, P = 1.013253, lat = 0)

Arguments

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

lat

latitude (-90 to +90), -,

Value

Water depth in m.

Note

sw_depth for p = 1000, lat = 30 is 9712.653 m.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

sw_depth(p = 1000, lat = 30:40)

## Check values
sw_depth(p = 1000, lat = 30)     #9712.65
sw_depth(p = 50,   lat = 30)     #496.00
sw_depth(p = 50,   lat = 60)     #494.69
sw_depth(p = 500,  lat = 60)     #4895.60

Specific Enthalpy of Seawater

Description

Computes the seawater specific enthalpy, J/kg

Usage

sw_enthalpy(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Specific enthalpy, J/kg.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_enthalpy(35.7,25.5,102.3) #110776.712408975

Specific Entropy of Seawater

Description

Computes the seawater specific entropy, J/(kg*K)

Usage

sw_entropy(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Specific entropy, J/(kg*K).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_entropy(35.7, 25.5, 102.3) #352.81879771528

Gibbs Function of Seawater

Description

Calculates the seawater specific gibbs free energy, including derivatives up to order 2, for a given temperature, salinity and pressure.

The Gibbs function of seawater g(S,t,p) is related to the specific enthalpy h and entropy s, by g = h - (273.15 K + t) s

Usage

sw_gibbs(S = 35, t = 25, p = P-1.013253, 
         P = 1.013253, dS = 0, dt = 0, dp = 0)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

dS

order of the S derivative

dt

order of the t derivative

dp

order of the p derivative

Value

The Gibbs function, J/kg, or its derivative

Note

The gibbs function is defined as the sum of a pure water part and the saline part (IAPWS-08)

The coefficients from McDougall et al., 2009 were used. For temperature, they differ slightly from Feistel 2003 and Feistel 2008, which is why, for temperatures different from 0, there is a slight offset from the estimates as from table 22 or 21 from Feistel (2008).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

# table 22 Feistel 2008
sw_gibbs(0, 0, 0)                             #= 101.34274
sw_gibbs(0, 0, 0, dS = 1)                     # 0
sw_gibbs(0, 0, 0, dt = 1)                     #0.147643376
sw_gibbs(0, 0, 0, dp = 1)                     #0.1000015694e-2
sw_gibbs(0, 0, 0, dS = 1, dp = 1)             #0
sw_gibbs(0, 0, 0, dt = 1, dp = 1)             #-0.677700318e-7

sw_gibbs(0, 79.85, 0)                         #-0.446114969e5 differs (see note)
sw_gibbs(0, 79.85, 0, dt = 1)                 #-0.107375993e4 differs
sw_gibbs(0, 79.85, 0, dp = 1)                 #0.102892956e-2 differs
sw_gibbs(0, 79.85, 0, dS = 1, dp = 1)         #0
sw_gibbs(0, 79.85, 0, dt = 1, dp = 1)         #0.659051552e-6


sw_gibbs(0, 0, 998.98675)                     #0.977303862e5
sw_gibbs(0, 0, 998.98675, dt = 1)             #0.851466502e1
sw_gibbs(0, 0, 998.98675, dp = 1)             #0.956683329e-3
sw_gibbs(0, 0, 998.98675, dS = 1, dp = 1)     #0
sw_gibbs(0, 0, 998.98675, dt = 1, dp = 1)     #0.199079571e-6

# table 21 Feistel 2008
sw_gibbs(35.16504, 0, 0)                      #=0
sw_gibbs(35.16504, 0, 0, dS = 1)              #0.639974067e2      differs
sw_gibbs(35.16504, 0, 0, dt = 1)              #=0
sw_gibbs(35.16504, 0, 0, dp = 1)              #0.972661217e-3
sw_gibbs(35.16504, 0, 0, dS = 1, dp = 1)      #-0.759615412e-6
sw_gibbs(35.16504, 0, 0, dt = 1, dp = 1)      #0.515167556e-7    !!!

sw_gibbs(100, 79.85, 0)                       #=-0.295243229e5   differs
sw_gibbs(100, 79.85, 0, dS = 1)               #0.251957276e3
sw_gibbs(100, 79.85, 0, dt = 1)               #-0.917529024e3    differs
sw_gibbs(100, 79.85, 0, dp = 1)               #0.971006828e-3    differs
sw_gibbs(100, 79.85, 0, dS = 1, dp = 1)       #-0.305957802e-6
sw_gibbs(100, 79.85, 0, dt = 1, dp = 1)       #0.146211315e-5

sw_gibbs(35.16504, 0, 998.98675)                 #=0.951294557e5
sw_gibbs(35.16504, 0, 998.98675, dS = 1)         #-0.545861581e1
sw_gibbs(35.16504, 0, 998.98675, dt = 1)         #0.160551219e2
sw_gibbs(35.16504, 0, 998.98675, dp = 1)         #0.933770945e-3
sw_gibbs(35.16504, 0, 998.98675, dS = 1, dp = 1) #-0.640757619e-6
sw_gibbs(35.16504, 0, 998.98675, dt = 1, dp = 1) #0.245708012e-6

Isentropic Compressibility of Seawater

Description

Computes the seawater isentropic compressibility, 1/bar

Usage

sw_kappa(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Salinity (dimensionless),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Isentropic compressibility, 1/bar

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_kappa(35.7, 25.5, 102.3) #4.03386268546478e-6

Isothermal Compressibility of Seawater

Description

Computes the seawater isothermal compressibility, 1/Pa

Usage

sw_kappa_t(S = 35, t = 25, p = P-1.013253, P = 1.013253)

Arguments

S

Absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

isothermal compressibility, 1/Pa.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_kappa_t(35.7, 25.5, 102.3) #4.10403794615135e-6

Salinity conversion factors

Description

Factors to convert from practical to absolute salinity and vice versa.

Usage

sw_sfac

Format

A list with the following:

longs: the longitude, a vector with 91 elements, range (0,360), third dimension in del_sa,
lats: the latitude, second dimension in del_sa, a vector with 44 elements, range (-82,90),
p: dbar , the first dimension in del_sa, a vector with 45 elements, range(0,6131),
ndepth: the number of depth intervals at a certain lat,long, a matrix of dimension (4,91),
del_sa: the salinity anomaly, an array with dimension (45,44,91), i.e. for (p, lats, longs) values.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Millero FJ, Feistel R, Wright DG and McDougall TJ, 2008. The composition of Standard Seawater and the definition of the Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.

McDougall TJ, Jackett DR and Millero FJ, 2009. An algorithm for estimating Absolute Salinity in the global ocean. Ocean Science Discussions 6, 215-242. http://www.ocean-sci-discuss.net/6/215/2009/

Uses the Fortran code written by David Jackett http://www.teos-10.org/

Examples


mf <- par(mfrow = c(2, 1))
ma <- par(mar = c(3, 5, 2, 5))

dsal <- t(sw_sfac$del_sa[1, , ])
dsal [dsal < -90] <- NA
image(sw_sfac$longs, sw_sfac$lats, dsal, col = femmecol(100),
      asp = TRUE, xlab = "dg", ylab = "dg",
      main = "salinity conversion - p = 0 bar")
contour(sw_sfac$longs, sw_sfac$lats, dsal, asp = TRUE, add = TRUE)

dsal <- t(sw_sfac$del_sa[5,,])  # 5th depth level sw_sfac$p[5]
dsal [dsal < -90]<-NA
image(sw_sfac$longs, sw_sfac$lats, dsal, col = femmecol(100),
      asp = TRUE, xlab = "dg", ylab = "dg",
      main = "salinity conversion - p = 4 bar")
contour(sw_sfac$longs, sw_sfac$lats, dsal, asp = TRUE, add = TRUE)

par("mfrow" = mf)
par("mar" = ma)

Velocity of the Sound in Seawater

Description

Computes the velocity of the sound in seawater, using the UNESCO 1983 polynomial or based on the Gibbs function.

Valid for salinity from 0 to 40, temperature from 0 to 40 dgC, pressure from 1 to 1000 bars.

Usage

sw_svel(S = 35, t = 25, p = P-1.013253, P = 1.013253,
  method = c("Gibbs", "UNESCO"))

Arguments

S

Salinity, when method = "UNESCO": practical salinity (-) else absolute salinity (g/kg),

t

Temperature, ^\circC,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

method

When "UNESCO", uses the UNESCO (1983) polynomial, when "Gibbs", based on the gibbs functions as in Feistel, 2008

Value

Sound velocity, in m / sec.

Note

Sound velocity for S = 40, t = 40, p = 1000 is 1731.995 using UNESCO polynomial.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Feistel R, 2008. A Gibbs function for seawater thermodynamics for -6 to 80 dgC and salinity up to 120 g/kg. Deep-Sea Research I, 55, 1639-1671.

Examples

sw_svel(t = 40, S = 40, p = 10:20, method = "UNESCO")

# Check value UNESCO
sw_svel(t = 40, S = 40, p = 1000, method = "UNESCO")  # 1731.995
sw_svel(t = 0, S = 40, p = 0, method = "UNESCO")      # 1455.8

sw_svel(t = 40, S = 25, p = 1000, method = "UNESCO")  # 1719.2
sw_svel(t = 40, S = 25, p = 0, method = "UNESCO")     # 1553.4
sw_svel(t = 0, S = 25, p = 0, method = "UNESCO")      # 1435.8


# Check value Gibbs
sw_svel(S = 35.7, t = 25.5, p = 102.3)              # 1552.93372863425

Freezing Temperature of Seawater

Description

Estimates the freezing temperature of seawater, using the UNESCO 1983 polynomial.

Valid for salinity 4-40

Usage

sw_tfreeze(S=35, p = P-1.013253, P = 1.013253 )

Arguments

S

practical salinity, -,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

P

true pressure, bar

Value

Temperature, ^\circC

Note

freezing temperature for S = 40, p = 50 is -2.588567 dgC.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

sw_tfreeze(S = 40,p = 50)

## Check values
sw_tfreeze(S = 10,p = 0)  #-0.542
sw_tfreeze(S = 10,p = 10) #-0.618
sw_tfreeze(S = 30,p = 0)  #-1.638
sw_tfreeze(S = 40,p = 50) #-2.589

Potential Temperature of Seawater

Description

Estimates the potential temperature of seawater, using the UNESCO 1983 polynomial.

It is the temperature an element of seawater would have if raised adiabatically with no change of salinity, to atmospheric pressure.

Usage

sw_tpot(S = 35, t = 25, p, pref = 0)

Arguments

t

temperature, ^\circC,

S

practical salinity, -,

p

gauge or applied pressure, pressure referenced against the local atmospheric pressure, bar

pref

reference hydrostatic pressure, bar.

Value

Temperature, ^\circC.

Note

sw_tpot for S = 40, t = 40, p = 1000 is 36.89073 dgC

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Fofonoff NP and Millard RC Jr, 1983. Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science, 44, 53 pp.
http://unesdoc.unesco.org/images/0005/000598/059832EB.pdf

Examples

sw_tpot(S = 40, t = 40:45, p = 1000)

## check values
sw_tpot(S = 25, t = 40, p = 0)      #40
sw_tpot(S = 25, t = 40, p = 100)    #36.6921
sw_tpot(S = 25, t = 10, p = 1000)   #8.4684
sw_tpot(S = 25, t = 0, p = 100)     #-0.0265

sw_tpot(S = 40, t = 40, p = 1000)  #36.89073

Saturation Water Vapor Pressure

Description

The partial pressure of water in saturated air (pH20/P), as in Weiss and Price (1980), where P is the total atmospheric pressure, (1 atmosphere), and pH2O is the partial pressure of the water vapor.

Usage

vapor(S = 35, t = 25)

Arguments

S

Salinity (-),

t

Temperature, ^\circC.

Value

The saturation vapor pressure (-).

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Sarmiento JL and Gruber N, 2006. Ocean Biogeochemical Dynamics. Princeton University Press, Princeton. p 74

Weiss R and Price BA, 1980. Nitrous oxide solubility in water and seawater. Mar. Chem. 8, 347-359.

Examples

plot(0:30, vapor(t = 0:30), xlab = "Temperature, dgC", ylab = "pH2O/P")

Vapor Pressure

Description

The vapor pressure of water, in hPa.

Usage

vapor.hPa(t = 25)

Arguments

t

Temperature, ^\circC.

Value

The vapor pressure of water, in hecto Pascal; valid for temperature of [-50,100] dgC.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>, Lorenz Meire <lorenz.meire@nioz.nl>

References

Lowe, P.R. and J.M. Ficke, 1974: The computation of saturation vapor pressure. Tech. Paper No. 4-74, Environmental Prediction Research Facility, Naval Postgraduate School, Monterey, CA, 27 pp.

http://www.cactus2000.de/uk/unit/masshum.shtml

Examples

vapor.hPa(t = 25)
plot(0:30, vapor.hPa(t = 0:30), xlab = "Temperature, dgC", ylab = "hPa")

Vertical Volume Weighted Mean of Matter Concentrations in Water Bodies

Description

Calculate vertical mean values which respect to depths of different layers or lake morphometry.

Usage

vertmean(depth, vari, level, top, bot, vol, total=FALSE)

Arguments

depth

sorted vector of sampled depths,

vari

measurements corresponding to depth (concentration, temperature, ...),

level

surface water level (above ground or above sea level (m a.s.l.), depending on bathymetric function used,

top

top water level of requested layer over which to average or integrate,

bot

bottom water level of requested layer over which to average or intgrate,

vol

hypsographic function to be used (e.g. vol.depth),

total

if TRUE the total sum over the water body is returned (integrated value), instead of the volumetric mean.

Value

Volumetric average respectively total value (for total =TRUE) for a given quantity (concentration, energy, temperature) in the requested layer between depths top and bottom.

Author(s)

Thomas Petzoldt

Examples


## define a bathymetric formula for a given lake or basin
## z:     water depth  (m below surface)
## zz:    water column (m above ground)
## level: total water depth (m above ground or above reference level)
weight.vol <- function(z, level) {
  zz  <- level - z
  if (any(zz < 0)) stop("depth > maximum depth")
  vol <- 175947 * zz^2 + 2686 * zz^3 # m^3
}

## area is first derivative
area <- function(z, level) {
  zz  <- level - z
  A   <-   0.5 * 175947 * zz + 1/3 * 2686 * zz^2 # m^2
}

## dummy formula for depth-weighted averaging
## (water column, instead of bathymetric curve)
weight.column <- function(z, level) {z}

## Plot of lake volume (bathymetric curve)
par(mfrow = c(1, 2))
z <- 0:12
V <- weight.vol(z, 12)
plot(V, z, type = "l", ylim = c(12, 0), xlab = "Volume (m3)",
  ylab = "Depth (m)")
polygon(c(V, 0), c(z, 0), col = "cyan")

## Test Data
level <- 12
depth <- c(0, 1, 3.5, 5, 7, 10, 10.5, 11.5)
pconc <- c(3.7, 4.2, 6.1, 8.9, 7.8, 9.7, 11.4, 11.4)

## Plot test data
plot(pconc, depth, xlim=range(c(0, pconc)), ylim=c(12,0), type="n",
  xlab="P concentration (mu g / L)", ylab="Depth (m)")
segments(rep(0, 13), depth, pconc, depth, lwd=3)

## simple means
m <- mean(pconc[depth <= 4])
lines(c(m, m), c(0, 4), col="blue", lwd=2)

m <- mean(pconc[depth >= 4])
lines(c(m, m), c(4, 12), col="blue", lwd=2)

## depth weighted
m <- vertmean(depth, pconc, level, top=0, bot=4, weight.column)
lines(c(m, m), c(0, 4), col="red", lwd=2)

m <- vertmean(depth, pconc, level, top=4, bot=12, weight.column)
lines(c(m, m), c(4, 12), col="red", lwd=2)

## volume weighted
m <- vertmean(depth, pconc, level, top=0, bot=4, weight.vol)
lines(c(m, m), c(0, 4), col="green", lwd=2)

m <- vertmean(depth, pconc, level, top=4, bot=12, weight.vol)
lines(c(m, m), c(4, 12), col="green", lwd=2)

m <- vertmean(depth, pconc, level, top=4, bot=12, weight.vol)
lines(c(m, m), c(4, 12), col="green", lwd=2)

legend("topright", col=c("blue", "red", "green"), lwd=2, cex=0.7,
  legend=c("non weighted", "depth weighted", "volume weighted"))

## total sum over the whole water column
vertmean(depth, pconc, level, top=0, bot=12, weight.vol, total=TRUE)

Shear Viscosity of Water

Description

Calculates the shear viscosity of water, in centipoise (g/m/sec). Valid for 0 < t < 30 ^\circC, 0 < S < 36, 1 < P < 1000 bars.

Based on the code "CANDI" by B.P. Boudreau

Usage

viscosity(S = 35, t = 25, P = 1.013253)

Arguments

S

salinity, -,

t

temperature, ^\circC,

P

True pressure, bar.

Details

The details given in the original code by B. Boudreau are repeated here:

Uses the equation given by Kukulka et al. (1987).

Value

Shear visocisity in centipoise.

Author(s)

Karline Soetaert <karline.soetaert@nioz.nl>

References

Based on the FORTRAN implementation of the diagenetic model "CANDI" of B.P. Boudreau:

Boudreau BP, 1996. A method-of-lines code for carbon and nutrient diagenesis in aquatic sediments. Computers & Geosciences 22 (5), 479-496.

Kulkula DJ, Gebhart B and Mollendorf JC, 1987. Thermodynamic and transport properties of pure and saline water. Adv. Heat transfer 18, 325-363.

Examples

plot(0:30, viscosity(t = 0:30, S = 35, P = 1),
      xlab = "temperature", ylab = "g/m/s",
      main = "shear viscosity of water", type = "l")
lines(0:30, viscosity(t = 0:30, S = 0, P = 1), col = "red")
lines(0:30, viscosity(t = 0:30, S = 35, P = 100), col = "blue")
legend("topright", col = c("black","red","blue"), lty = 1,
        legend = c("S=35, P=1", "S=0, P=1", "S=35, P=100"))

Tools for Aquatic Sciences

Description

Author(s)

References

See Also

Examples

The Atomic Weights of Chemical Elements

Description

Usage

Format

Details

Author(s)

References

See Also

Examples

World Bathymetric Data

Description

Usage

Format

Author(s)

References

Examples

Useful Physical and Chemical Constants

Description

Usage

Format

Author(s)

References

See Also

Examples

Useful Characteristics of the Oceans

Description

Usage

Format

Author(s)

References

See Also

Examples

Air Density

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Air specific humidity

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Atmospheric Gas Composition

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Conductivity-Salinity Conversion

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

Salinity-Chlorinity Conversion

Description

Usage

Arguments

Value