immune to attenuation. The coefficients of these algorithms can be obtained using
scattering simulations of the radar measurements assuming a wide range of DSDs.
Another algorithm of the form Z ¼ aR
1.5 has been proposed, where the parameter a is
a function of the DSD concentration, which can be calculated in real-time using DP
radar measurements [78]. A composite algorithm that uses an algorithm Z – R in light
rain, an algorithm R(Z, Z dr ) in moderate rain and an algorithm R(K dp ) in heavy rain
have shown to provide more accurate rainfall rates at C-band frequencies [79].
3 Adjusting Radar Rainfall with Raingauge Measurements
Weather radar provides precipitation estimates with good spatial and temporal
resolutions, but as discussed previously, the rainfall estimates can be affected by
different error sources. A raingauge network on the other hand may provide accurate
rainfall measurements, but at individual point locations. However, raingauge measurements are not always available in mountainous areas and the measurements are
also subject to several sources of errors. For instance, typical errors in tipping bucket
raingauges include blockages, wetting and evaporation in the funnel, condensation
errors, underestimation of high rain rates and wind effects [80]. Moreover, the
accuracy of the raingauge measurement is also affected by spatial and temporal
sampling uncertainties. The temporal sampling error is defined as the error resulting
from repeated temporal gaps during the measurements, whereas the spatial sampling
error is defined as the error resulting from approximating an areal estimate using
point measurements [79, 81]. A number of spatial interpolation methods,
geostatistical or non-geostatistical, are available for approximating an areal rainfall
estimate using raingauge point measurements. Geostatistical methods (i.e. kriging)
generally perform better than non-geostatistical methods [82–85]. Kriging for
instance takes into account the spatial correlation of precipitation through the
variogram (obtained from point rainfall observations) that helps to reconstruct the
two-dimensional precipitation field. However, even a high-density raingauge network is unable to fully capture the true rainfall field at short timescales [86–89]. In
order to exploit the strengths of both radar and raingauge measurement approaches, a
number of radar–raingauge merging techniques have been developed. The advantages of merging radar and raingauge rainfall measurements are to produce a rainfall
product that not only provides reliable distributed rainfall information, but also
provide accurate measurements that are in agreement with the raingauge measurements. These merging methods range from non-statistical methods, such as mean
field bias correction [90], spatial correction method [91] and range-dependent
adjustment [92], to more complex statistical techniques. These statistical methods
are based on univariate and multivariate geostatistical analysis, such as co-kriging
[14], kriging with radar-based error (KRE) [93, 94] and kriging with external drift
(KED) [83, 95]. For example, the mean field bias (MFB) correction is a simple and
effective method, which was developed by Smith and Krajewski [90] for adjusting
radar-based quantitative precipitation estimates based on raingauge information and
it is widely used in several studies [31, 96–98]. The assumption is that the radar
246
N. Nanding and M. A. Rico-Ramirez
scattering simulations of the radar measurements assuming a wide range of DSDs.
Another algorithm of the form Z ¼ aR
1.5 has been proposed, where the parameter a is
a function of the DSD concentration, which can be calculated in real-time using DP
radar measurements [78]. A composite algorithm that uses an algorithm Z – R in light
rain, an algorithm R(Z, Z dr ) in moderate rain and an algorithm R(K dp ) in heavy rain
have shown to provide more accurate rainfall rates at C-band frequencies [79].
3 Adjusting Radar Rainfall with Raingauge Measurements
Weather radar provides precipitation estimates with good spatial and temporal
resolutions, but as discussed previously, the rainfall estimates can be affected by
different error sources. A raingauge network on the other hand may provide accurate
rainfall measurements, but at individual point locations. However, raingauge measurements are not always available in mountainous areas and the measurements are
also subject to several sources of errors. For instance, typical errors in tipping bucket
raingauges include blockages, wetting and evaporation in the funnel, condensation
errors, underestimation of high rain rates and wind effects [80]. Moreover, the
accuracy of the raingauge measurement is also affected by spatial and temporal
sampling uncertainties. The temporal sampling error is defined as the error resulting
from repeated temporal gaps during the measurements, whereas the spatial sampling
error is defined as the error resulting from approximating an areal estimate using
point measurements [79, 81]. A number of spatial interpolation methods,
geostatistical or non-geostatistical, are available for approximating an areal rainfall
estimate using raingauge point measurements. Geostatistical methods (i.e. kriging)
generally perform better than non-geostatistical methods [82–85]. Kriging for
instance takes into account the spatial correlation of precipitation through the
variogram (obtained from point rainfall observations) that helps to reconstruct the
two-dimensional precipitation field. However, even a high-density raingauge network is unable to fully capture the true rainfall field at short timescales [86–89]. In
order to exploit the strengths of both radar and raingauge measurement approaches, a
number of radar–raingauge merging techniques have been developed. The advantages of merging radar and raingauge rainfall measurements are to produce a rainfall
product that not only provides reliable distributed rainfall information, but also
provide accurate measurements that are in agreement with the raingauge measurements. These merging methods range from non-statistical methods, such as mean
field bias correction [90], spatial correction method [91] and range-dependent
adjustment [92], to more complex statistical techniques. These statistical methods
are based on univariate and multivariate geostatistical analysis, such as co-kriging
[14], kriging with radar-based error (KRE) [93, 94] and kriging with external drift
(KED) [83, 95]. For example, the mean field bias (MFB) correction is a simple and
effective method, which was developed by Smith and Krajewski [90] for adjusting
radar-based quantitative precipitation estimates based on raingauge information and
it is widely used in several studies [31, 96–98]. The assumption is that the radar
246
N. Nanding and M. A. Rico-Ramirez