text: """
  ==========================================================================
    linear equation of state
    input is Salinity sa in g/kg,
    pot. temperature ct in deg C
  ==========================================================================
  """
  rho0 = 1024.0
  theta0 = 283.0 - 273.15
  S0 = 35.0
  betaT = 1.67e-4
  betaS = 0.78e-3
  grav = 9.81
  z0 = 0.0
  
  
  def linear_eq_of_state_rho(sa, ct):
      return - (betaT * (ct - theta0) - betaS * (sa - S0)) * rho0
  
  
  def linear_eq_of_state_dyn_enthalpy(sa, ct, p):
      zz = -p - z0
      thetas = ct - theta0
      return grav * zz * (-betaT * thetas + betaS * (sa - S0))
  
  
  def linear_eq_of_state_salt(rho, ct):
      return (rho + betaT * (ct - theta0) * rho0) / (betaS * rho0) + S0
  
  
  def linear_eq_of_state_drhodT():
      return - betaT * rho0
  
  
  def linear_eq_of_state_drhodS():
      return betaS * rho0
  
  
  def linear_eq_of_state_drhodp():
      return 0.0
  