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= Microwave remote sensing of the ocean =

== Exercises ==

PDF [[attachment:Brightness temperature of ocean surface.pdf]]

IPython notebook [[attachment:Brightness temperature of ocean surface.ipynb]] ([[https://wiki.zmaw.de/lehre/PythonQuickstart|see Python quick start]])

{{{#!python
def eps_water_func(T,S,f):

    """Complex dielectric constant of seawater by Klein and Swift (1977)"""
    T=T-273.15
    omega=2*pi*f
    eps_0=8.854*10**(-12)
    eps_inf=4.9

    eps_s_T=87.134-1.949*10**(-1)*T-1.276*10**(-2)*T**2+2.491*10**(-4)*T**3
    a_ST=1.+1.613*10**(-5)*S*T-3.656*10**(-3)*S+3.210*10**(-5)*S**2-4.232*10**(-7)*S**3
    eps_s=eps_s_T*a_ST

    tau_T0=1.768*10**(-11)-6.086*10**(-13)*T+1.104*10**(-14)*T**2-8.111*10**(-17)*T**3
    b_ST=1.+2.282*10**(-5)*S*T-7.638*10**(-4)*S-7.760*10**(-6)*S**2+1.105*10**(-8)*S**3
    tau=tau_T0*b_ST

    delta=25-T
    beta=2.0333*10**(-2)+1.266*10**(-4)*delta+2.464*10**(-6)*delta**2-S*(1.849*10**(-5)-2.551*10**(-7)*delta+2.551*10**(-8)*delta**2)
    sigma_25S=S*(0.182521-1.46192*10**(-3)*S+2.09324*10**(-5)*S**2-1.28205*10**(-7)*S**3)
    sigma=sigma_25S*exp(-delta*beta)

    eps_water=eps_inf+(eps_s-eps_inf)/(1+1j*omega*tau)-1j*sigma/(omega*eps_0)
    return eps_water
}}}