## Quantitative Precipitation Estimation (QPE) algorithms

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Traditional Z Algorithms
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Traditional reflectivity-based QPE algorithms, such as ones used by the WSR-88D network, relate radar reflectivity factor (Z) to
rain rate (R).
Unfortunately, the equation relating Z to R varies according to the drop sizes distribution (DSD) of the rain in the volume of
interest, which can vary widely from one event to another. Currently, WSR-88D radars use a variety of assumed DSDs, ranging from those
applicable to "tropical" air masses to those more suited for "continental" air masses. If the assumed DSD is not appropriate, the
rain fall rate error may exceed 300%.
In addition, this method does not correct for very high Z values found in hail, leading to the potential for gross over
estimation of rain totals where hail is present. False returns, such as found in side lobe contamination, ground clutter and
anomolous propagation, may also contaminate the rainfall estimates. Attenuation of the radar signal due to heavy rain
or partial beam blockage often leads to an underestimate of rainfall accumulation. Finally, Z-based algorithms are sensitive to
radar calibration.

The standard (non-tropical) Z-R relation used by the WSR-88D is Z = 300R^{1.4}. In addition, Z values above 53 dBZ are
assumed to be hail and are not considered. This assumption is not often valid and is another possible source of error.

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Z/Z___{DR} Algorithms

In high reflectivity regions, differential reflectivity (Z_{DR}) can provide an estimate
of the DSD, reducing errors from calculations using Z alone by a factor of two. However, the estimate is not precise enough
to yield an improvement for rates less than 20 mm h^{-1}. In addition, Z/Z_{DR} estimates can still suffer from
errors due to hail, non-precipitating echoes, attenuation, radar calibration, etc.

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K___{DP} Algorithms

Specific differential phase (K_{DP}) is much more directly related to the DSD and rain
rate than either Z or Z_{DR}, particularly in heavy rain. Analysis of experimental data suggests significant
improvement may be possible over Z-based algorithms, with errors as low as 10 to 15 percent for a well-calibrated radar.

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K___{DP}/Z_{DR} Algorithms

K_{DP} and Z_{DR} can be used in unison for another rainfall estimate. A complete evaluation of this
procedure and comparison with other procedures has not yet been made.

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