322
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
and the hydrometeor classification system developed by Colorado State University
(Liu and Chandrasekar 2000; Lim et al. 2005). In general, these algorithms output
more than 10 distinct species of rain, snow, hail, and clutter. It is worth noting that
it is not easy to find accurate membership functions to discriminate those species.
In practice, the decision of membership function depends on experience. This is the
fundamental limitation of the fuzzy-logic approach. Nevertheless, the classification
algorithms improve our understanding of radar signals and guide rain estimation.
13.3.3.4 Attenuation Correction
Precipitation attenuation is one of the major problems for radar–rain estimation.
Attenuation cannot be ignored, especially for weather radars operating at very
high frequencies, for example, at C- and X-bands. Previous algorithms for singlepolarization radars are based mainly on the Hitschfeld–Bordan algorithm and its
revised version (e.g., Delrieu et al. 2000; Zhang et al. 2004; Berne and Uijlenhoet
2006), where the power-law relation between attenuation and radar reflectivity must
be assumed deterministically. When dual-polarization measurements became available, the phase term was extensively used to improve attenuation correction. Bringi et
al. (1990) proposed a direct correction method based on the deterministic power-law
relations between attenuation and phase term, that is, A
aK
b
H
DP
=
and A
cK
d
DP
DP
=
.
This kind of correction, which is based directly on phase term, is referred to as the
direct-phase approach (e.g., Matrosov et al. 2002). It was found that exponents and
coefficients of these relations are dependent on various factors such as temperature,
drop shape model, and DSD variation. Many algorithms, therefore, have focused on
the finding of optimal exponents or coefficients. For example, those parameters can
be fitted from either observations (Ryzhkov and Zrnić 1995; Carey et al. 2000) or
simulations [e.g., the ZPHI method proposed by Testud et al. (2000) and Gorgucci
and Chandrasekar (2005)]. Bringi et al. (2001) extended the ZPHI method and proposed the self-consistency (SC) approach to obtain optimal parameters for related
empirical relations. The SC method was further modified/improved by Park et
al. (2005), Vulpiani et al. (2005), Anagnostou et al. (2006), Gorgucci and Baldini
(2007), and Liu et al. (2006). The most promising method of attenuation correction is
through the variational approach (e.g., Hogan 2007; Xue et al. 2009; Cao and Zhang
2009). However, it is not as mature as phase-based algorithms. There are still issues,
which are beyond the scope of this book, to be addressed.
13.3.3.5 Model Error, System Bias, and Calibration
Even without the effects mentioned previously in this section, model errors would
still affect rain estimation. It is worth noting that radar measurements do not directly
represent rain variables. Some empirical models (e.g., R–Z h ) are derived through
comparing/fitting observations from radar with in situ instruments (e.g., rain gauge).
The more general way is the radar forward model, which is based on the scattering
theory and reasonable assumptions. For both approaches, model error is an inevitable
problem. Does the model error matter? What if radar measurements have a bias as
the radar–rain model predicts? Comparing radar observations with in situ measurements could be a practical way of evaluating the radar–rain model. This comparison
makes sense if in situ measurements are assumed to be the truth. Corresponding bias
Multiscale Hydrologic Remote Sensing: Perspectives and Applications
and the hydrometeor classification system developed by Colorado State University
(Liu and Chandrasekar 2000; Lim et al. 2005). In general, these algorithms output
more than 10 distinct species of rain, snow, hail, and clutter. It is worth noting that
it is not easy to find accurate membership functions to discriminate those species.
In practice, the decision of membership function depends on experience. This is the
fundamental limitation of the fuzzy-logic approach. Nevertheless, the classification
algorithms improve our understanding of radar signals and guide rain estimation.
13.3.3.4 Attenuation Correction
Precipitation attenuation is one of the major problems for radar–rain estimation.
Attenuation cannot be ignored, especially for weather radars operating at very
high frequencies, for example, at C- and X-bands. Previous algorithms for singlepolarization radars are based mainly on the Hitschfeld–Bordan algorithm and its
revised version (e.g., Delrieu et al. 2000; Zhang et al. 2004; Berne and Uijlenhoet
2006), where the power-law relation between attenuation and radar reflectivity must
be assumed deterministically. When dual-polarization measurements became available, the phase term was extensively used to improve attenuation correction. Bringi et
al. (1990) proposed a direct correction method based on the deterministic power-law
relations between attenuation and phase term, that is, A
aK
b
H
DP
=
and A
cK
d
DP
DP
=
.
This kind of correction, which is based directly on phase term, is referred to as the
direct-phase approach (e.g., Matrosov et al. 2002). It was found that exponents and
coefficients of these relations are dependent on various factors such as temperature,
drop shape model, and DSD variation. Many algorithms, therefore, have focused on
the finding of optimal exponents or coefficients. For example, those parameters can
be fitted from either observations (Ryzhkov and Zrnić 1995; Carey et al. 2000) or
simulations [e.g., the ZPHI method proposed by Testud et al. (2000) and Gorgucci
and Chandrasekar (2005)]. Bringi et al. (2001) extended the ZPHI method and proposed the self-consistency (SC) approach to obtain optimal parameters for related
empirical relations. The SC method was further modified/improved by Park et
al. (2005), Vulpiani et al. (2005), Anagnostou et al. (2006), Gorgucci and Baldini
(2007), and Liu et al. (2006). The most promising method of attenuation correction is
through the variational approach (e.g., Hogan 2007; Xue et al. 2009; Cao and Zhang
2009). However, it is not as mature as phase-based algorithms. There are still issues,
which are beyond the scope of this book, to be addressed.
13.3.3.5 Model Error, System Bias, and Calibration
Even without the effects mentioned previously in this section, model errors would
still affect rain estimation. It is worth noting that radar measurements do not directly
represent rain variables. Some empirical models (e.g., R–Z h ) are derived through
comparing/fitting observations from radar with in situ instruments (e.g., rain gauge).
The more general way is the radar forward model, which is based on the scattering
theory and reasonable assumptions. For both approaches, model error is an inevitable
problem. Does the model error matter? What if radar measurements have a bias as
the radar–rain model predicts? Comparing radar observations with in situ measurements could be a practical way of evaluating the radar–rain model. This comparison
makes sense if in situ measurements are assumed to be the truth. Corresponding bias