PW Derivation Methodology
Theoretical analysis proposes an almost linear relationship between PW and ΔT, with slope and intercept being determined by the surface emissivity. As is has been shown in past studies the PW is proportional to the difference between the two AVHRR thermal channels brightness temperature.
This split-window technique is not a universal solution to PW retrieval due to the dependence of the difference ΔT on air temperature and surface characteristics. Linear relationships characterized by different coefficients are expected to hold in different locations. The coefficients of the linear relationship between PW and ΔT are site specific.
In this study, MODIS derived PW were used as an independent dataset, adjusted for the time lag between the time of Terra/MODIS and NOAA16/AVHRR overpasses. Radiosonde data were used for this adjustment. More specifically, if the AVHRR acquisition over the study area is performed at t = t0, the PW at this time, PW(t0), can be estimated as linear function of ΔΤ:
where, a and b are coefficients that need to be estimated for the study area, and ΔΤ = T4 – T5 is the brightness temperatures for channels 4 and 5 in the (x, y) cell.
By a Taylor's series expansion of PW about the time t0 we obtain:
Δt = t - t0 is the time difference between MODIS and AVHRR passes,
is the partial derivative of PW with respect to time, being evaluated at t=t0. It represents the rate of change of PW.
Therefore, the MODIS derived PW can be related to the AVHRR derived ΔT as:
The term represents an estimation of the actual precipitable water during the AVHRR acquisition time called the adjusted precipitable water (PW*). PW* was computed by combining MODIS derived PW with radiosonde derived PW rates of change over the study area. The latter was derived by spatial interpolation using the PW rates of change calculated at the synoptic stations of Athens, Thessaloniki, Heraklion and Izmir. Consequently, the Equation (3) can be written as:
The coefficients a and b in (4) were estimated by linear regressions of PW* vs ΔΤ. In this study, the estimation of the coefficients a and b was based on MODIS, AVHRR and radiosonde data acquired during 15 selected days of 2003 and 2004.
The selection criteria for these days were: a) As much cloud free land area as possible and b) near nadir NOAA16/AVHRR acquisitions over the study area. The aerosol concentration was low, since meteorological horizontal visibilities greater than 10 km are observed in all cases. Moreover, the values of horizontal visibilities, suggested that there was no Saharan dust episode, thus it was assumed that the aerosol haze had a small effect in observed radiances.
The estimated PW* – ΔΤ relationship was applied to AVHRR data to provide PW spatial distributions for the period 2001 – 2005 (for January, April, July and October).