Correction of Radar QPE Errors Associated with Low and Partially Observed Brightband Layers

Youcun Qi Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma, and College of Atmospheric Science, Nanjing University of Information Science and Technology, Nanjing, China

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Jian Zhang NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Abstract

The melting of aggregated snow/crystals often results in an enhancement of the reflectivity observed by weather radars, and this is commonly referenced as the bright band (BB). The locally high reflectivity often causes overestimation in radar quantitative precipitation estimates (QPE) if no appropriate correction is applied. When the melting layer is high, a complete BB layer profile (including top, peak, and bottom) can be observed by the ground radar, and a vertical profile of reflectivity (VPR) correction can be made to reduce the BB impact. When a melting layer is near the ground and the bottom part of the bright band cannot be observed by the ground radar, a VPR correction cannot be made directly from the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar observations. This paper presents a new VPR correction method under this situation. From high-resolution precipitation profiler data, an empirical relationship between BB peak and BB bottom is developed. The empirical relationship is combined with the apparent BB peak observed by volume scan radars and the BB bottom is found. Radar QPEs are then corrected based on the estimated BB bottom. The new method was tested on 13 radars during seven low brightband events over different areas in the United States. It is shown to be effective in reducing the radar QPE overestimation under low brightband situations.

Corresponding author address: Youcun Qi, Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma and NOAA/OAR/National Severe Storms Laboratory, 120 David L Boren Blvd., Norman, OK 73072. E-mail: Youcun.Qi@noaa.gov

Abstract

The melting of aggregated snow/crystals often results in an enhancement of the reflectivity observed by weather radars, and this is commonly referenced as the bright band (BB). The locally high reflectivity often causes overestimation in radar quantitative precipitation estimates (QPE) if no appropriate correction is applied. When the melting layer is high, a complete BB layer profile (including top, peak, and bottom) can be observed by the ground radar, and a vertical profile of reflectivity (VPR) correction can be made to reduce the BB impact. When a melting layer is near the ground and the bottom part of the bright band cannot be observed by the ground radar, a VPR correction cannot be made directly from the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar observations. This paper presents a new VPR correction method under this situation. From high-resolution precipitation profiler data, an empirical relationship between BB peak and BB bottom is developed. The empirical relationship is combined with the apparent BB peak observed by volume scan radars and the BB bottom is found. Radar QPEs are then corrected based on the estimated BB bottom. The new method was tested on 13 radars during seven low brightband events over different areas in the United States. It is shown to be effective in reducing the radar QPE overestimation under low brightband situations.

Corresponding author address: Youcun Qi, Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma and NOAA/OAR/National Severe Storms Laboratory, 120 David L Boren Blvd., Norman, OK 73072. E-mail: Youcun.Qi@noaa.gov

1. Introduction

When icy crystals or snowflakes fell into warm surroundings below the freezing level, two consequent effects would impact the reflectivity of the particles (Ryde 1946): 1) the change from ice to water would result in an increase in the reflective properties of the particles so that the radar reflectivity intensity increases; and 2) the fall velocity of the flakes is less than that of the resulting water drops so that the number of particles per unit volume decreases continuously. These two effects formed the so-called bright band (BB) in the radar reflectivity field. Quantitative estimates (e.g., Austin and Bemis 1950; Wexler 1955; Wexler and Atlas 1956; Lhermitte and Atlas 1963) confirmed that the bright band associated with the freezing level was caused by the coalescence and melting of snowflakes and followed by breakup below. Battan (1973) proposed that the primary cause of the enhancement of weather targets reflectivity was a rapid increase in the dielectric constant of hydrometeors at the top of the melting layer followed by an increase of the fall velocities of particles toward the end of the melting process. Fabry and Zawadzki (1995) performed a detailed analysis of the bright band, and suggested that, in addition to changes in the refractive index of hydrometers during melting, shape effects (nonsphericity of melting hydrometeors) at drizzle rates and density effects (related to the way water is distributed within the melting snowflake) at stratiform rain rates are important causes of the bright band, while precipitation growth and the coupling of aggregation and breakup are relatively small contributors. Regardless, the locally high reflectivity causes significant overestimation in radar quantitative precipitation estimates if no appropriate correction is applied.

When a melting layer is very high (e.g., melting layer A in Fig. 1), radar observations on the lowest elevation angle are not affected by the BB until at very far ranges. In a relatively dense radar network [e.g., the Weather Surveillance Radar-1988 Doppler (WSR-88D) radar network in the United States], a high BB does not significantly impact the radar rainfall estimates because data from far ranges are not used in the quantitative precipitation estimation (QPE) (Fig. 1) given the availability of lower level data from one or more neighboring radars. When a melting layer is moderately high (e.g., melting layer B in Fig. 1), a “complete” vertical BB structure including top, peak, and bottom can be observed by the radar such that a vertical profile of reflectivity (VPR) correction may be applied to mitigate the BB effects (e.g., Kitchen et al. 1994; Matrosov et al. 2007; Zhang and Qi 2010, hereafter ZQ10; Zhang et al. 2012; Qi et al. 2013a,b,c). When a melting layer is very low or near the ground (e.g., melting layer C in Fig. 1), the lower part of the BB structure cannot be observed by the radar and subsequently a VPR correction cannot be achieved. To mitigate the radar QPE overestimations under this condition, ZQ10 assumed a symmetric vertical BB structure with respect to the peak, and used empirical parameters, which are based on subjective analyses of WSR-88D radar observations, to determine the BB bottom height and intensity. For instance, a 28-dBZ reflectivity threshold is used as a lower bound for searching the BB bottom. Real-time assessments indicate that the ZQ10 VPR correction is insufficient for some low BB events because of this threshold. This paper presents an improvement made to the ZQ10 technique, where a relatively objective approach is developed to determine the BB bottom intensity and height for low BB events. The new approach is based on BB peak–BB bottom relationships developed from high-resolution precipitation profiler data.

Fig. 1.
Fig. 1.

Illustration of melting layer impacts on QPEs from two radars. Thin solid (dashed) lines indicate the center (top and bottom) of the lowest radar beams. Thick dotted line indicates the radar data used for generating QPEs. Melting layer A does not affect radar QPEs because it is well above the dotted line and has no impact on the data used in the QPEs. Melting layer B has an impact on the radar QPE, but the impact can be corrected because there is enough information observed by the radars below the melting layer. Melting layer C has an impact on radar QPEs and the impact cannot be corrected directly from the radar observations because no information below the bright band is observed.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

Fabry and Zawadzki (1995) conducted a comprehensive study on the radar bright band using more than 600 h of high-resolution data from vertically pointing radars in Montreal, Quebec, Canada. They showed that the brightband peak reflectivity Zpeak and the reflectivity of rainfall below the bright band Zbttm had an approximately linear relationship. A very similar ZpeakZbttm scatterplot was obtained from a different study by Kitchen et al. (1994) using data from a high-resolution scanning radar operated by the Rutherford Appleton Laboratory near Didcot in Oxfordshire, United Kingdom. These results suggested that reflectivities of the brightband peak and bottom have a close relationship, and the relationship has relatively small variations in space and time. If the brightband peak can be observed, then the brightband bottom can be estimated from the observed BB peak. This provides a way for VPR corrections of the radar QPE in low brightband situations.

In the current study, a large number of brightband profiles from high-resolution vertical pointing radars are analyzed, and a quantitative relationship between reflectivity factors at the BB peak (Zpeak) and BB bottom (Zbttm) is derived. The relationship is then applied to the WSR-88D radar data to correct for BB effects. The profiler data analysis and the new correction scheme are described in section 2. Assessments of the new scheme with seven heavy precipitation events in different regions of the United States are presented in section 3. A summary and discussion of future work follows in section 4.

2. Methodology

a. S-band precipitation profiler data analysis

The profiler data used in this study were obtained from two S-band precipitation profiler radars deployed during the National Oceanic and Atmospheric Administration (NOAA) Hydrometeorological Testbed (HMT, http://hmt.noaa.gov) in November 2005 to April 2006. The radars were located in Cazadero (CZC) near the west coast of California and in Alta (ATA) on the California Sierra. These profiler radars measure time evolutions of the reflectivity structure along a vertical column with high temporal (1 min) and spatial (60 m) resolution (e.g., White et al. 2000; Matrosov et al. 2006). The data used in the current study were 5-min averages of the 1-min observations.

A total of 6336 vertical reflectivity profiles (over 500 h of data) were analyzed in the current study. Among them, 2037 (605 from CZC and 1432 from ATA) were identified as to have a low but complete bright band. The criteria for having a low and complete bright band are as follows: 1) there was only one peak below the 0°C height, where the 0°C height was obtained from a nearby sounding; 2) the peak must be well defined in that an inflexion can be found both above and below the peak; 3) the inflexion points must be at least 100 m away from the peak (i.e., the brightband peak is at least 200 m wide); 4) the peak reflectivity must be at least 6 dBZ higher than the reflectivities of the top and bottom; and 5) the bottom of the BB must be less than 500 m above the radar height. From these profiles, the reflectivities of brightband peak (Zpeak) and bottom (Zbttm) were recorded. The BB bottom reflectivity is subjectively selected as the reflectivity at 100–300 m (depending on the VPR curvature) below the bottom inflexion point.

The manually identified BB bottom (Zbttm) and peak reflectivities (Zpeak) are plotted in Fig. 2, and a linear relationship is fitted to the data:
e1
This relationship has a slope larger than unity indicating that the BB peak intensity increases faster than the BB bottom intensity, which is consistent with the observations in Kitchen et al. (1994) and Fabry and Zawadzki (1995). The correlation coefficient is 0.93 suggesting that about 87% of the variability in the brightband bottom reflectivity can be explained by variations in the brightband peak reflectivity. This high correlation is significant at 99.999% confidence level based on a t test, which has passed 0.001 significance tests. This indicates that the peak and bottom relationship has relatively small spatial and temporal variations given the data were obtained from two profilers 290 km apart and over a time period of seven months. Further, subjective comparisons between the current and previous ZpeakZbttm scatterplots by Fabry and Zawadzki (1995) and Kitchen et al. (1994) showed high similarity. These provide a relatively high degree in confidence toward using the empirical relationship for the VPR correction.
Fig. 2.
Fig. 2.

Linear relationship between the brightband peak and bottom reflectivities measured by the S-band precipitation profilers. The data are from 2037 observed profiles recorded in widespread stratiform precipitation.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

b. VPR correction for a low bright band in radar reflectivity observations

The empirical relationship between BB peak and bottom intensities derived from the profiler data was used to refine the VPR correction method in ZQ10. The VPR correction in ZQ10 was based on a two-piece linear model fitted to the brightband layer in an apparent VPR (AVPR) (Fig. 3 in ZQ10). Such a profile automatically adapts to the WSR-88D radar beam broadening effect with increasing range, and simplifies the correction procedure. The word “apparent” signifies the beam broadening effects in the VPR. On a given tilt, the precipitation echoes are segregated into convective and stratiform precipitation regions based on a technique developed by Qi et al. (2013a). Then a first-guess brightband area (BBA) is delineated in the stratiform region on the given tilt based on the following three criteria (ZQ10): (i) the center of the radar bin is below 0°C height + D1 and above 0°C height + (D1 − 5 km); where D1 is the half beamwidth of the gate whose bottom intersects the 0°C level; (ii) composite reflectivity is greater than 30 dBZ; and (iii) the reflectivity of each radar scan tilt is higher than 15 dBZ. The AVPR of the tilt is computed by taking azimuthal average of reflectivities within the BBA, and the apparent BB peak (ABP) hp is identified as the maximum reflectivity closest to the 0°C height. The apparent BB top (ABT) ht and bottom (ABB) hb are identified as the first inflexion points in the AVPR above and below hp, respectively. A two-piece linear VPR model is fitted to the AVPR, one between ht and hp and another between hp and hb. And the first-guess BBA is refined to areas where the center of the radar bin is between ht and hb. Assuming that the reflectivity below hb is constant, the reflectivity in the brightband area can be corrected for surface precipitation estimation according to the following (Eq. [9] in ZQ10):
e2a
e2b
Here, r, ϕ, and h are the range, azimuth, and height of the beam axis at a given gate, respectively; dBZo(ϕ, h) and dBZc(ϕ, 0) are the raw and VPR corrected reflectivities, respectively; α and β are the slopes of the two-piece linear model above and below the BB peak respectively; dBza(h) is the reflectivity correction factor; and all reflectivity values are on the log scale.
When an apparent BB peak is identified while a bottom is not found from the apparent VPR [i.e., when the melting layer height is less than 1500 m above radar level (ARL) or the apparent BB peak is identified below 1000 m ARL], ZQ10 assumes a symmetric BB structure in the linear VPR model (i.e., α = −β), and the apparent BB bottom is derived through the following relationship:
e3
Here hb, hp, and α are described above; Zpeak is the reflectivity of apparent brightband peak; and 28 dBZ is an empirical constant for BB bottom reflectivity.
In the current study, a new BB bottom reflectivity is derived from the empirical ZpeakZbttm relationship [Eq. (1)] when the 0°C height is less than 1500 m ARL or the apparent BB peak is identified below 1000 m ARL, assuming that Zpeak is approximately the apparent BB peak reflectivity. The beam broadening effect was ignored given that the area to be corrected is very close to the radar and the broadening effect was relatively small. Further, an accurate beam broadening correction requires the knowledge of the true VPR, which is not available from the discrete WSR-88D scans. Figure 3 shows experiments of the beam broadening (at 0.5° elevation angle) effects on the relative bias of QPEs. The relative bias in Fig. 3 is defined by
e4
where Rtruth is the true precipitation rate at the ground, computed from the reflectivity (using ) at the BB bottom of the conceptual VPR model (Fig. 3a). Here, the conceptual BB VPR (Fig. 3a) is constituted by BB depth (the difference of height between BB top and bottom), ΔZr [the difference of reflectivity between BB peak and bottom (ZpZb)], and BB peak [height (Hp) and reflectivity (Zp) of BB peak]. The Rderived is the rate computed from the radar observed reflectivity at the lowest level without VPR correction (dark blue line), with VPR correction but not accounting for the beam broadening (red line, namely, no beam broadening affect), and with VPR correction that accounts for the beam broadening (green line, namely, with beam broadening affect). In Figs. 3b–e, the relative bias after VPR correction (accounting for beamwidth effect or not) is much lower than without VPR correction, where the peak of the VPR is appeared in an immovable range of the radar scan domain except in Fig. 3d. In Fig. 3d, the peak of VPR will appear in different ranges of the radar scan domain, and at far ranges, it will be largely influenced by the beam broadening affect. Overall, Figs. 3b–e show that the relative bias can be as high as 250% (overestimation) if no correction is applied. When a VPR correction is applied with the beam broadening effect accounted for, the relative bias can generally be reduced to less than 20%. If the beam broadening effect is ignored, the relative bias can still be largely reduced, although it is slightly higher (~10%–20% on the average) than the VPR correction with beam broadening effect considered.
Fig. 3.
Fig. 3.

(a) A conceptual BB VPR model, and (b)–(e) experiments of the beam broadening (at 0.5° elevation angle) effects on the relative bias of QPEs without VPR correction (dark blue line), with VPR correction but not accounting for the beam broadening (red line), and with VPR correction that accounts for the beam broadening (green line). (b) The brightband peak height (1.2 km, ARL), reflectivity (45 dBZ), and depth (0.7 km) are fixed, the relative bias is varied with ZpZb (the difference between brightband peak and bottom, dBZ). (c) The brightband peak height (1.2 km), reflectivity (45 dBZ), and ZpZb (11 dBZ) are fixed, the relative bias is varied with brightband depth. (d) The brightband peak reflectivity (45 dBZ), depth (0.7 km), and ZpZb (11 dBZ) are fixed, the relative bias is varied with brightband peak height. (e) The brightband peak height (1.2 km), depth (0.7 km), and ZpZb (11 dBZ) are fixed, the relative bias is varied with the brightband peak.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

The BB bottom height hb is computed from Eq. (3) by replacing 28 dBZ with the newly derived BB bottom reflectivity if the depth between apparent BB peak and the bottom of the AVPR is less than 250 m ARL or the difference between Zpeak and the reflectivity at the bottom of the VPR is less than 2 dBZ. Otherwise, the apparent VPR below the apparent BB peak is fitted to a linear model with a slope of β. The slope β and the new Zbttm are then used to compute a new BB bottom height by
e5
The final correction is then applied [Eqs. (2a) and (2b)] using the new BB bottom height.

Figure 4 shows three apparent VPRs (blue dots) with various low melting layer heights. The solid purple line is the old BB bottom derived from ZQ10, and the solid orange line is the new brightband bottom obtained using the current method (hereafter “NEW”). The dashed black line represents the 0°C height from the nearby sounding. In Fig. 4a, the bright band appeared to be complete. Since an inflexion point could not be found below the BB peak, the empirical BB bottom intensity constant (28 dBZ) was used in ZQ10 to derive the BB bottom (solid purple line in Fig. 4a). Figures 5b,c show the VPR correction of the bright band (Fig. 5a) with the VPR in Fig. 4a, but with different BB bottoms. The ZQ10 correction to the KABR reflectivity field (Fig. 5b) appeared to be overdone in the brightband area compared with the NEW correction in Fig. 5c. Even so, a comparison between the radar QPEs with gauge observations (Figs. 6a,b) showed that both ZQ10 and NEW VPR corrections provided better rainfall estimates than without any correction. ZQ10 seemed to overly reduce the radar rainfall for relatively heavier (>3 mm) amounts (Fig. 6a). The new BB bottom derived from the profiler-based ZpeakZbttm relationship resulted in a better comparison between the radar and gauge hourly rainfalls (Fig. 6b).

Fig. 4.
Fig. 4.

Apparent VPRs (blue dots) and associated linear VPR model (red lines) for (a) KABR at 1200 UTC 5 Oct 2009, (b) KABR at 1100 UTC 6 Oct 2009, and (c) KEAX at 1700 UTC 19 Feb 2010. Detailed discussions can be found in the text.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

Fig. 5.
Fig. 5.

Reflectivities from 0.50° elevation angle (a),(d),(g) before AVPR correction; (b),(e),(h) after the AVPR correction with ZQ10; and (c),(f),(i) after the AVPR correction with NEW. The three rows are images from (a)–(c) KABR at 1226 UTC 5 Oct 2009, (d)–(f) KABR at 1029 UTC 6 Oct 2009, and (g)–(i) KEAX at 1753 UTC 19 Feb 2010.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

Fig. 6.
Fig. 6.

Scatterplots of hourly radar precipitation estimates vs gauge observations before (red dots) and after (green triangles) a VPR correction using (a),(c),(e) the ZQ10 and (b),(d),(f) the NEW methods. The data are from (a),(b) KABR at 1300 UTC 5 Oct 2009; (c),(d) KABR at 1100 UTC 6 Oct 2009; (e),(f) KEAX at 1800 UTC 19 Feb 2010.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

Figure 4b shows a similar low BB structure as in Fig. 4a, but the new BB bottom derived using NEW method was much lower than that derived from ZQ10. Figures 5e,f also show the VPR correction of the bright band (Fig. 5d) with the VPR in Fig. 4b. The ZQ10 correction to the KABR reflectivity field (Fig. 5e) was insufficient in the brightband area compared to the NEW correction in Fig. 5f. As a result shown in Figs. 6c,d, the radar rainfall estimates with the NEW method (Fig. 6d) resulted in a less overestimation than the ZQ10 method (Fig. 6c) compared to gauges. The lower BB bottom in Fig. 5b yielded a lower Zbttm intensity and thus a more effective correction to the BB enhancement.

Figure 4c shows a situation where only a partial brightband structure can be observed by the apparent radar VPR, and the corresponding VPR corrected fields are shown in Figs. 5h,i. The ZQ10 VPR correction to the KEAX reflectivity field (Fig. 5h) appeared to be overcorrected in the brightband area compared to the NEW method in Fig. 5i. For this event, the new BB bottom provided slight improvements in the VPR corrected radar rainfall estimates for the hourly amounts around 1.5 mm (Figs. 6e.f). For the three events discussed above, the improvements with NEW VPR correction algorithm have passed 0.01 significance tests compared with ZQ10 except KABR at 1300 UTC 5 October 2009, which has passed 0.05 significance tests.

3. Case study results

The NEW VPR correction scheme was evaluated using seven wide spread rainfall events that had a low and partial bright band. A summary of the events and associated data is provided in Table 1. Three statistic scores, namely root-mean-square error (RMSE), relative mean absolute error (RMAE), and relative mean bias (RMB), were calculated for hourly radar QPEs with respect to gauge observations using the following equations:
e6
Here and represent a matching pair of the radar-derived and gauge observed rainfall, respectively; and represents the total number of matching gauge and radar pixel pairs in the BBA. A matching pair of radar-gauge is found if 1) the gauge location is within the boundary of a 1° × 1 km radar pixel and 2) both the radar estimate and the gauge observation are greater than zero. In addition, is an averaged radar rainfall in 5° × 5 km box centered at the corresponding gauge:
e7a
e7b
Here is the averaged hourly gauge precipitation:
e8
Table 1.

Summary of the events.

Table 1.

In the current study, the corrected reflectivity field is converted into rain rate using one ZR relationships: . The rain rates are aggregated into hourly rainfalls and compared to the surface gauge observations. The gauge data were from the Hydrometeorological Automated Data System (HADS, http://www.nws.noaa.gov/oh/hads) and were manually quality controlled before the statistics calculation. The quality control was based on subjective assessments of temporal and spatial consistencies of the gauge observations, and only gauges with very high confidence were retained for the evaluation of radar QPEs.

Figure 7 shows the three scores of radar hourly rainfall estimates with respect to the HADS observations for 13 radars during the 7 events. Both ZQ10 and the current VPR correction techniques significantly reduced the radar overestimation errors due to brightband effects. The NEW technique performed consistently better than the ZQ10 in all three statistic scores. The most significant improvements are for KFDR20091224 and KAMA20100315, where the hourly RMSE error was reduced more than 2 mm (Fig. 7a) and the relative mean bias was reduced more than 75% (Fig. 7c). The results indicated that the empirical ZpeakZbttm relationship derived from the profiler data is more representative of the brightband structure than the simple empirical parameters in ZQ10. Almost all the events show that the improvements with the NEW VPR correction algorithm have passed 0.01 significance tests compared to ZQ10 as shown in Table 2, except KEAX20091224, KTWX 20100219, and KLBB20100315.

Fig. 7.
Fig. 7.

(a) The RMSE, (b) relative MAE, and (c) the relative mean bias scores for radar precipitation estimates before (red) and after VPR corrections using the ZQ10 (green) and the NEW (blue) methods.

Citation: Journal of Hydrometeorology 14, 6; 10.1175/JHM-D-13-040.1

Table 2.

The results of the t significant tests on 13 radars between the ZQ10 and NEW method.

Table 2.

4. Summary

A new method of finding the brightband bottom intensity and height was developed based on precipitation profiler data. High temporal and spatial (vertical) resolution profiler data from two sites were analyzed and an empirical BB peak and BB bottom relationship was obtained. The empirical relationship was combined with the apparent vertical profile of reflectivity (VPR) from volume scan radars to find the BB bottom height and intensity. The new BB bottom information was used to improve the VPR correction scheme developed by ZQ10 for situations where a BB bottom cannot be identified from the apparent VPR. Previously an empirical constant was used for the BB bottom intensity. The modified VPR correction resulted in consistently better radar QPEs than the old method, indicating that the profiler-based BB peak–bottom relationship could provide more representative BB bottom information than the empirical constant. This method can be easily expanded for using high-resolution vertical reflectivity profiles from satellite precipitation radar (e.g., the Tropical Rainfall Measuring Mission and the future Global Precipitation Measurement) as well as additional ground based precipitation profilers in different geographical regions. A more comprehensive study of VPR parameters based on high-resolution profiler radar data is ongoing. The parameters include slopes above the BB top and below the BB bottom and their relationships to other VPR parameters as well as to the atmospheric environment. These relationships are critical for effective VPR corrections of radar QPEs.

Acknowledgments

The authors are grateful to Dr. Pengfei Zhang for many insightful comments that greatly improved this manuscript. Major funding for this research was provided under NOAA’s Hydro-Meteorological Testbed (HMT) program and partial funding was provided under NOAA–University of Oklahoma Cooperative Agreement NA17RJ1227.

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  • Fig. 1.

    Illustration of melting layer impacts on QPEs from two radars. Thin solid (dashed) lines indicate the center (top and bottom) of the lowest radar beams. Thick dotted line indicates the radar data used for generating QPEs. Melting layer A does not affect radar QPEs because it is well above the dotted line and has no impact on the data used in the QPEs. Melting layer B has an impact on the radar QPE, but the impact can be corrected because there is enough information observed by the radars below the melting layer. Melting layer C has an impact on radar QPEs and the impact cannot be corrected directly from the radar observations because no information below the bright band is observed.

  • Fig. 2.

    Linear relationship between the brightband peak and bottom reflectivities measured by the S-band precipitation profilers. The data are from 2037 observed profiles recorded in widespread stratiform precipitation.

  • Fig. 3.

    (a) A conceptual BB VPR model, and (b)–(e) experiments of the beam broadening (at 0.5° elevation angle) effects on the relative bias of QPEs without VPR correction (dark blue line), with VPR correction but not accounting for the beam broadening (red line), and with VPR correction that accounts for the beam broadening (green line). (b) The brightband peak height (1.2 km, ARL), reflectivity (45 dBZ), and depth (0.7 km) are fixed, the relative bias is varied with ZpZb (the difference between brightband peak and bottom, dBZ). (c) The brightband peak height (1.2 km), reflectivity (45 dBZ), and ZpZb (11 dBZ) are fixed, the relative bias is varied with brightband depth. (d) The brightband peak reflectivity (45 dBZ), depth (0.7 km), and ZpZb (11 dBZ) are fixed, the relative bias is varied with brightband peak height. (e) The brightband peak height (1.2 km), depth (0.7 km), and ZpZb (11 dBZ) are fixed, the relative bias is varied with the brightband peak.

  • Fig. 4.

    Apparent VPRs (blue dots) and associated linear VPR model (red lines) for (a) KABR at 1200 UTC 5 Oct 2009, (b) KABR at 1100 UTC 6 Oct 2009, and (c) KEAX at 1700 UTC 19 Feb 2010. Detailed discussions can be found in the text.

  • Fig. 5.

    Reflectivities from 0.50° elevation angle (a),(d),(g) before AVPR correction; (b),(e),(h) after the AVPR correction with ZQ10; and (c),(f),(i) after the AVPR correction with NEW. The three rows are images from (a)–(c) KABR at 1226 UTC 5 Oct 2009, (d)–(f) KABR at 1029 UTC 6 Oct 2009, and (g)–(i) KEAX at 1753 UTC 19 Feb 2010.

  • Fig. 6.

    Scatterplots of hourly radar precipitation estimates vs gauge observations before (red dots) and after (green triangles) a VPR correction using (a),(c),(e) the ZQ10 and (b),(d),(f) the NEW methods. The data are from (a),(b) KABR at 1300 UTC 5 Oct 2009; (c),(d) KABR at 1100 UTC 6 Oct 2009; (e),(f) KEAX at 1800 UTC 19 Feb 2010.

  • Fig. 7.

    (a) The RMSE, (b) relative MAE, and (c) the relative mean bias scores for radar precipitation estimates before (red) and after VPR corrections using the ZQ10 (green) and the NEW (blue) methods.

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