In a recent study, (Tian et al 2010) introduced a real-time
bias adjustment method for correcting satellite data. In this paper, a similar methodology is adopted for creating a
consistent climatology. Having both GPCP (G) and real-time
satellite data (S) for the overlap period (2000–10), one
can derive the joint probability P.G; S/ using the Bayesian
theorem:
where G and S denote GPCP and real-time satellite
data (here, PERSIANN and TRMM-RT), respectively. The
conditional probability P.GjS/ indicates the likelihood of
the measurement G given the satellite observation S. For
more detail about this methodology, the reader is pointed
to Tian et al (2010). The right hand side of the equation (1)
can be computed for the overlap period (2000–10). Then,
one can derive G for any S by maximizing P.Gi; Sj/ using
the maximum likelihood method. Using this approach, for
the period for which GPCP (here, G) observations are not available (real-time data S), one can obtain the likely value
G given S. In other words, based on the overlap period, the
algorithm will estimate the likely value of G (here, GPCP
data) given an observed S from real-time satellite data. The
likely value of G, and hence the adjusted satellite data,
is derived based on historical values of G and S over the
same period of time (e.g., January, February) to account
for seasonality. Figure 2 displays example time series of
GPCP (solid blue), satellite data (here, PERSIANN) before
correction (dashed red), and satellite data after the Bayesian
correction (solid green) for two locations. One can see that
the differences between real-time satellite data and GPCP
observations reduce after applying the Bayesian correction
algorithm.