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Because they are based on a sparse number of actual in situ (balloon sonde) data taken every 12 hours and satellite measurements, the RUC data are not a perfect representation of the various meteorological parameters, especially water vapor. The model humidity at upper levels of the atmosphere is often too low, reflecting the current biases known to exist in our measurement system.
e_sat_w_Ta = (1.0007 + 0.00000346 * p)*6.1121*Math.exp((17.966*ta)/(247.15+ta));
e_sat_i_Ta = (1.0003 + 0.00000418 * p)*6.1115*Math.exp((22.452*ta)/(272.55+ta));
rhi = rh * (e_sat_w_Ta/e_sat_i_Ta);