The way we estimate soil moisture from Sigma0

• Land surface is assumed to consist of soil surface and vegetation cover. Let f be the ratio of vegetation cover.
• Sigma0 is expressed as follows. Be careful the unit of Sigma0 is m²/m², not dB. Sigma0(soil) is a function of incident angle and soil moisture, while sigma0(veg) is a function of incident angle only.
  Sigma0(X%)=(1-f) Sigma0(soil,X%)+f Sigma0(veg)...(1)
  
  when soil moisture is 0%,
  Sigma0(0%)=(1-f) Sigma0(soil,0%)+f Sigma0(veg)...(1')
• Sigma0(soil, 0%) is set to be 2.671(dB), and Sigma0(veg0) is -8.534(dB) from the average value of Sahara Desert and Amazon Forests respectively.
• Histogram of Sigma0 is written for each site, and the value of 1% from minimum is assumed to be Sigma0(0%). Substituting Sigma0(0%) into (1'), f is calculated.
• For each time step, Sigma0(X%) are observed. Using (1) and (1'), Sigma0(soil, X%)-Sigma0(soil, 0%), that is the increase of Sigma0 in case of bare soil, is calculated.
• From IEM model, Sigma0(soil, X%)-Sigma0(soil, 0%) is converted into soil moisture X.