Knudsen’s equation of state (1901)

Martin Knudsen, with Carl Forch and Søren Sørensen, measured seawater density against temperature and salinity and published the Hydrographical Tables used for the next 70 years. Near a reference state the density is linear in both: warming makes water lighter and salt makes it heavier, so lines of equal density in the temperature-salinity plane have slope alpha / beta.

import matplotlib.pyplot as plt
import numpy as np

from earthsciencekit.oceanography import linear_density

alpha, beta = 2e-4, 7.6e-4
temperature, salinity = np.meshgrid(np.linspace(-10, 15, 101), np.linspace(-3, 3, 101))
density = linear_density(1027, temperature, salinity, alpha, beta)
assert np.isclose(linear_density(1027, 1.0, alpha / beta, alpha, beta), 1027)

fig, ax = plt.subplots()
contours = ax.contour(salinity, temperature, density, levels=12, cmap="viridis")
ax.clabel(contours, fmt="%.1f", fontsize=7)
ax.set(xlabel="salinity anomaly [g/kg]", ylabel="temperature anomaly [K]", title="Isopycnals of the linear equation of state [kg/m^3]")

plt.show()