estimates are affected by a uniform systematic error. This error may be due to a poor
electronic calibration or an erroneous coefficient in the Z – R relationship due to
variations of the DSD [9, 14, 99]. This systematic bias between radar and raingauge
rainfall can be adjusted using raingauge information. The bias adjustment is based on
estimation of a single multiplicative factor as the ratio of the accumulated raingauge
rainfall and the radar rainfall. This simple MFB correction improves radar rainfall
estimation considerably [100] and it is often used operationally [101, 102]. However,
bias adjustment of radar rainfall may be subjected to sampling errors due to the fact
that the raingauge network cannot represent the areal precipitation accurately especially during high variability of precipitation (e.g. during convective precipitation).
There are however some techniques that account for the sampling errors to estimate
the real-time mean field bias using a Kalman filter technique [90, 96, 97, 103]. Merging radar rainfall with raingauge measurement using KED is an effective method to
combine both measurements. In KED, the rainfall predictions are modelled as a drift
term plus a residual term. The drift term is an unknown linear function defined
externally through an auxiliary variable (e.g. radar rainfall). A full description of the
KED method is presented in Wackernagel [104], Haberlandt [83], and Verworn and
Haberlandt [105]. The variogram is an important function in geostatistical interpolation [106–108]. The spatial characteristic of the rainfall field contained in the
variogram is influenced by the characteristics of the storm, density of raingauge
network and rainfall accumulation period. The variogram used in kriging methods
can either be parametric or non-parametric and it is calculated independently for
each time step. The predefined model variogram represent the spatial variability of
the rainfall distribution, and therefore the suitability of the model function and
parameter values used to estimate the variogram has impact on the quality of the
final merged rainfall product. However, a non-parametric automatic procedure for
estimating a spatial variability model does not require any prior assumption about
the correlation of the observations. This non-parametric automatic methodology
based on Fast Fourier Transform (FFT) was initially proposed in Yao and Journel
[109] to estimate spatial variability models and further developed by Velasco-Forero
et al. [110] to estimate rainfall fields by merging radar and raingauge data. It is
worth to note that the variogram is a function of both distance and direction
(e.g. anisotropic) in the non-parametric method. This non-parametric spatial variability model is particularly appropriate for real-time applications of radar observations for operational purpose.
The performance of any rainfall interpolation method highly relies on the density
of the raingauge network [96, 97, 111, 112]. An accurate estimation of the true
rainfall field often requires a high density raingauge network [81, 113, 114]. Simple
adjustment methods (such as mean field bias correction) are less sensitive to the
raingauge network density, while the improvement by geostatistical methods
(e.g. KED) increases with a more dense raingauge network [115]. Moreover, the
improvement of rainfall estimation by the different radar–raingauge merging techniques may vary between different accumulation timescales. For instance, Berndt
et al. [116] examined the effect of accumulation timescales on the performance of
different merging techniques at different accumulation timescales from 10 min to
6 h. Their results showed that the performance of the radar–raingauge merging
Precipitation Measurement with Weather Radars
247
electronic calibration or an erroneous coefficient in the Z – R relationship due to
variations of the DSD [9, 14, 99]. This systematic bias between radar and raingauge
rainfall can be adjusted using raingauge information. The bias adjustment is based on
estimation of a single multiplicative factor as the ratio of the accumulated raingauge
rainfall and the radar rainfall. This simple MFB correction improves radar rainfall
estimation considerably [100] and it is often used operationally [101, 102]. However,
bias adjustment of radar rainfall may be subjected to sampling errors due to the fact
that the raingauge network cannot represent the areal precipitation accurately especially during high variability of precipitation (e.g. during convective precipitation).
There are however some techniques that account for the sampling errors to estimate
the real-time mean field bias using a Kalman filter technique [90, 96, 97, 103]. Merging radar rainfall with raingauge measurement using KED is an effective method to
combine both measurements. In KED, the rainfall predictions are modelled as a drift
term plus a residual term. The drift term is an unknown linear function defined
externally through an auxiliary variable (e.g. radar rainfall). A full description of the
KED method is presented in Wackernagel [104], Haberlandt [83], and Verworn and
Haberlandt [105]. The variogram is an important function in geostatistical interpolation [106–108]. The spatial characteristic of the rainfall field contained in the
variogram is influenced by the characteristics of the storm, density of raingauge
network and rainfall accumulation period. The variogram used in kriging methods
can either be parametric or non-parametric and it is calculated independently for
each time step. The predefined model variogram represent the spatial variability of
the rainfall distribution, and therefore the suitability of the model function and
parameter values used to estimate the variogram has impact on the quality of the
final merged rainfall product. However, a non-parametric automatic procedure for
estimating a spatial variability model does not require any prior assumption about
the correlation of the observations. This non-parametric automatic methodology
based on Fast Fourier Transform (FFT) was initially proposed in Yao and Journel
[109] to estimate spatial variability models and further developed by Velasco-Forero
et al. [110] to estimate rainfall fields by merging radar and raingauge data. It is
worth to note that the variogram is a function of both distance and direction
(e.g. anisotropic) in the non-parametric method. This non-parametric spatial variability model is particularly appropriate for real-time applications of radar observations for operational purpose.
The performance of any rainfall interpolation method highly relies on the density
of the raingauge network [96, 97, 111, 112]. An accurate estimation of the true
rainfall field often requires a high density raingauge network [81, 113, 114]. Simple
adjustment methods (such as mean field bias correction) are less sensitive to the
raingauge network density, while the improvement by geostatistical methods
(e.g. KED) increases with a more dense raingauge network [115]. Moreover, the
improvement of rainfall estimation by the different radar–raingauge merging techniques may vary between different accumulation timescales. For instance, Berndt
et al. [116] examined the effect of accumulation timescales on the performance of
different merging techniques at different accumulation timescales from 10 min to
6 h. Their results showed that the performance of the radar–raingauge merging
Precipitation Measurement with Weather Radars
247