The paper is closed with concluding remarks in section 5. At hourly time steps, Q2 adjusts radar estimates with automated rain gauge networks using a spatially variable bias multiplicative factor. A radar quality index RQI is produced to represent the radar QPE uncertainty associated with reflectivity changes with height and near the melting layer Zhang et al. Many errors affect the estimation of rainfall from ground-based radars, such as nonweather echoes, NUBF, range dependency due to vertical profile of reflectivity VPR variability, conversion of Z to R , and calibration of the radar signal [see Villarini and Krajewski for a recent review].
While several procedures are already in place within the Q2 system to correct for these errors, additional postprocessing steps were taken to refine the reference dataset as much as possible. The original Q2 products utilized in this study are i the radar-only instantaneous rain-rate national mosaic updated every 5 min, ii the radar-only rain-rate national mosaic at hourly time steps, iii the hourly rain gauge—corrected national mosaic product, and iv the RQI.
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The reference rainfall is derived from an instantaneous bias-corrected Q2 product. Instantaneous Q2 products are adjusted using a spatially variable multiplicative bias field to minimize the aforementioned errors: pixel-by-pixel ratios between the hourly gauge-adjusted products and the hourly radar-only products are calculated and applied as multiplicative adjustment factors to the radar-only 5-min product. Extreme adjustment factors outside the 0. To eliminate overestimation in the bright band and mitigate range dependency caused by VPR effects, a filtering is finally applied using the RQI index so only Q2 estimates representing the best measurement conditions i.
One must keep in mind these improvements may not screen out all possible errors in ground-based radar estimates. The reference rainfall is computed from a block-Q2 rainfall pixel matching each PR pixel. All of the Q2 pixels rainy and nonrainy found within an approximate 2. The estimation reference quality is assessed using a standard error that is computed alongside the mean reference rainfall value. It represents the variability of the Q2 rainfall at its native resolution inside the PR footprint and is used to select the PR-Q2 reference pairs for which the is trustworthy [see Kirstetter et al.
Nonrobust reference values are discarded for quantitative comparison in this study. The current technique preserves the PR rainfall statistical characteristics the product remains free of undesirable impacts caused by resampling and increases the reliability and representativeness of our ground reference. The PR measures reflectivity profiles at K u band. The scan geometry and sampling rate of the PR lead to footprints spaced approximately 5.
The 2A25 algorithm relies on a hybrid attenuation correction method that combines the surface reference technique and Hitschfeld—Bordan method Iguchi et al. Retrieval errors of the algorithm have mainly been attributed to the uncertainty of the assumed drop size distribution DSD , incorrect physical assumptions freezing-level height, hydrometeor temperatures , and NUBF effects Iguchi et al. Some of the weaknesses previously reported in performance with V6 i. The case of PR having zero rainfall when it is raining according to the reference was addressed in Kirstetter et al. The major changes from version 6 to version 7 address rather the quantitative estimation of rainfall in 2A25 products than the detection of rainfall itself.
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Accordingly, we did not find any significant differences in performances in rainfall detection from the two versions, so we focus hereafter on specific cases when both PR and reference are nonzero. The PDF c represents the probability of rain-rate occurrence and tends to emphasize lighter rainfall rates. A possible explanation is the edges of rain areas might be only partially detected by PR because they are associated with low rain rates and intermittency Kirstetter et al.
The detectability issue is related to the sensitivity of PR and is thus not readily correctable with an update to the processing algorithm. Probability distributions of rain rates for the reference rainfall gray and for PR rainfall black using left V6 and right V7. Note that the x axis is in log scale. Density-colored scatterplots of PR versus reference rainfall are presented for the two versions of 2A25 in Fig. Better agreement with the reference i. We also provide common comparison metrics in Table 1.
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A rainy pixel is included in the statistics if both PR and the reference are nonzero. The V6 and V7 estimates are both subjected to the same discrepancies in spatiotemporal matching with the Q2 reference, which is a source for differences on a point-to-point comparison basis, so their relative differences can be directly attributed to algorithms themselves.
PR shows lower mean values than the reference rainfall in both versions. Note that Amitai et al. This shows a positive impact of the new processing i. The correlation coefficients between both versions of PR rainfall and Q2 reference estimates are moderate, but we note the correlation with V7 has improved slightly. Ciach et al. PR, version 7, shows improvements in both bias and MSE, which can be only obtained by a more accurate processing of the radar signal relative to version 6.
The correction of the largely underestimated rain rates in going from V6 to V7 see Fig.
The lines solid lines are displayed. Table 1. Only the reliable Q2 data are kept see section 2b for references. The uncertainties associated with satellite estimates of rainfall include systematic errors as well as random effects from several sources Yang et al. In a similar manner with Kirstetter et al.
With the true rainfall being unknown, the residuals are defined as the difference between the reference rainfall and the satellite estimates :. Only pairs for which and are both nonzero are considered in the calculations. The sets of distributions are studied using the generalized additive models for location, scale, and shape GAMLSS technique Rigby and Stasinopoulos , ; Akantziliotou et al.
We consider the main driving explanatory variable conditioning the departures of PR estimates from reference values, and we use the reverse Gumbel distribution to model the conditional residual distributions, where the location mean of the residual population is to be linked to systematic errors and the standard deviation is representative of random errors.
For a given conditional distribution of the response variable , the conditional quantiles can be expressed as a function of. The conditional PDFs of residuals present a high conditional shift from the zero line and a high conditional spread. The dotted lines represent the cumulative distribution function of the reference rainfall. Figure 4 shows the conditional biases and random errors of both versions of 2A25 relative to the Q2 reference dataset. The underestimation with V6 and V7 over a large range of rain rates induces a global negative bias, which was evident in Table 1.
The conditional biases of both versions relative to the reference are quite similar but with a slight improvement in V7. The random discrepancies increase consistently with for both products. The random discrepancies are greater for V7 than V6, suggesting that other factors in addition to could be considered to properly model the random error of V7 rain-rate estimates. Figures 5a,b show the residuals as a function of the NUBF and are segregated according to the PR-based rainfall type classification.
Q2 standard deviation values are greater for convective than for stratiform rainfall.
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In fact, convective rainfall generally presents higher rain rates and variability than stratiform rainfall, as expected. The residuals distribution is also very distinct according to the rainfall types with more spread in the convective case.
The c systematic part and d random part of error are represented for stratiform blue lines and convective red lines types and for 2A25, V6 dotted lines , and 2A25, V7 solid lines. Consistent with a theoretical study performed by Iguchi et al. Figures 5c,d show the systematic and random parts of error. The error features are confirmed to be very distinct according to the rainfall types.
The PR convective systematic biases present a shift toward higher values compared to stratiform biases. The random part of the error is consistently greater for convective rainfall. From version 6 to version 7, the systematic bias remains the same for stratiform but decreases significantly for convective rainfall.
The random error decreases for stratiform and convective echoes, illustrating the positive impact of the NUBF correction in version 7. The impacts of the NUBF and rainfall type classification, however, remain significant and motivate ongoing and future research. A quantification of the uncertainty of these rainfall estimates will be quite useful to users of the data, including hydrologists, which is the principal aim of this study.
V7 includes improvements in attenuation correction of the radar signal and a recalibrated Z — R equation for use over land areas, and a correction for NUBF effects was reintroduced. The former correction is most likely a result of the recalibration of the Z — R equation over land, while the latter is likely a result from the NUBF correction; NUBF is known to cause underestimation at high rain rates Iguchi et al.
A statistical error model was developed for both versions of PR algorithms to separate conditional biases and random discrepancies as a function of reference rainfall rate.
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