I have calculated the required scaling for bandpass quantities:
w:rh2o (wq in EVE) in units of m/s gm/kg
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Latent heat flux (W) = LE = rho*L*w:rh2o
w:rh2o = LE/(rho*L) = (J/m^2-s)/(1 kg/m^3 * 2.5e6 J/kg)
= LE*4e-7 m/s * 1e3 gm/kg
= LE*4e-4 m/s gm/kg
Thus a range of +- 1000 W/m^2 for LE requires a range
of +- 0.4 m/s gm/kg for w:rh20;
a resolution of 0.1 W/m^2 for LE requires a resolution
of 4e-5 m/s gm/kg for w:rh2o
Similar requirements would apply to "a" in wq = a + b*wt
w:t (wt in EVE) in units of m/s degC
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Sensible heat flux (W) = S = rho*Cp*w:t
w:t = S/(rho*Cp) = (J/m^2-s)/(1 kg/m^3 * 1e3 J/kg-degC)
= S*1e-3 m/s degC
Thus a range of +- 1000 W/m^2 for S requires a range
of +- 1 m/s degC for w:t;
a resolution of 0.1 W/m^2 for S requires a resolution
of 1e-3 m/s degC for w:t
b = w:rh2o/w:t in units of gm/kg-degC
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Bowen ratio = B = S/LE = rho*Cp*w:t/(rho*L*w:rh2o)
b = Cp/(L*B)*1e3 gm/kg = (1e3 J/kg-degC)/(2.5e6 J/kg)*(1e3 gm/kg)
= 0.4/B gm/kg-degC
We might want a resolution of +- 0.01 for B and a range of +- 100
to cover circumstances where either heat flux is more than 1% of
their sum. Thus a similar range and resolution is required for b,
since 0.4 ~ 1.