Abstract

High-resolution, accurate quantitative precipitation estimation (QPE) is critical for monitoring and prediction of flash floods and is one of the most important drivers for hydrological forecasts. Rain gauges provide a direct measure of precipitation at a point, which is generally more accurate than remotely sensed observations from radar and satellite. However, high-quality, accurate precipitation gauges are expensive to maintain, and their distributions are too sparse to capture gradients of convective precipitation that may produce flash floods. Weather radars provide precipitation observations with significantly higher resolutions than rain gauge networks, although the radar reflectivity is an indirect measure of precipitation and radar-derived QPEs are subject to errors in reflectivity–rain rate (ZR) relationships. Further, radar observations are prone to blockages in complex terrain, which often result in a poor sampling of orographically enhanced precipitation. The current study aims at a synergistic approach to QPE by combining radar, rain gauge, and an orographic precipitation climatology. In the merged QPE, radar data depict high-resolution spatial distributions of the precipitation and rain gauges provide accurate precipitation measurements that correct potential biases in the radar QPE. The climatology provides a high-resolution background of the spatial precipitation distribution in the complex terrain where radar coverage is limited or nonexistent. The merging algorithm was tested on heavy precipitation events in different areas of the United States and provided a superior QPE to the individual components. The new QPE algorithm is fully automated and can be easily implemented in an operational system.

1. Introduction

High-resolution, accurate, real-time quantitative precipitation estimation (QPE) is one of the most important drivers for hydrological forecasts and for flash flood monitoring and prediction. Rain gauges provide a direct measure of precipitation at a point, which is generally more accurate than remote sensing observations from radar and satellite. However, high-quality, accurate rain gauges are expensive to maintain, and their distributions are often too sparse to capture gradients of convective precipitation that may produce flash floods. Weather radars provide precipitation observations with much higher resolutions than rain gauge networks, although the radar moment, reflectivity Z, is an indirect measure of precipitation, and radar QPEs are subject to errors associated with a number of factors, such as calibration biases and unrepresentative ZR (reflectivity–rain rate) relationships (e.g., Wilson and Brandes 1979; Zawadzki 1984; Austin 1987; Joss and Waldvogel 1969; Andrieu et al. 1997; Creutin et al. 1997). Further, radar QPEs are subject to range degradation and suffer from blockages in complex terrain, which often result in a poor sampling of orographically enhanced precipitation (e.g., Kitchen et al. 1994; Germann and Joss 2002; Germann et al. 2006; Zhang et al. 2012b).

The current study aims at a synergistic approach to a real-time hourly QPE over the conterminous United States (CONUS) by combining information from weather radar, rain gauges, and orographic precipitation climatology. It takes advantage of the merits from each component and provides a new QPE product that is potentially superior to each individual QPE. There have been many studies on the merging of radar and gauge QPEs, which include mean field bias (MFB) corrections of radar QPEs using gauge observations (e.g., Fulton et al. 1998; Tabary 2007), spatially interpolated radar–gauge bias corrections using inverse distance weighting (IDW)-type functions (e.g., Goudenhoofdt and Delobbe 2009; Zhang et al. 2011), and geostatistical (e.g., kriging) interpolations of rain gauge data using (semi)variograms derived from radar QPEs (e.g., Haberlandt 2007; Goudenhoofdt and Delobbe 2009; Velasco-Forero et al. 2009; Verworn and Haberlandt 2011; Schiemann et al. 2011; Sideris et al. 2013; Berndt et al. 2014). The MFB correction is most efficient in removing systematic biases in radar QPEs (e.g., those associated with calibration or ZR errors). It does not account for the spatial variability of QPE biases nor any range- or azimuth-dependent biases that may exist in the radar QPE. Spatially interpolated radar–gauge bias corrections can account for localized errors, although the IDW interpolations are usually isotropic and not adaptive to nonuniform bias distributions in the analysis domain. Geostatistical interpolation schemes with dynamically derived variograms can account for spatial variations of biases better than the other two approaches, although they are computationally expensive. Geostatistical approaches are also sensitive to the density and quality of the data used in the variogram calculations and may sometimes generate ill-fitted results (Goudenhoofdt and Delobbe 2009; Sideris et al. 2013; Berndt et al. 2014). Ly et al. (2013) reviewed a large number of methods for interpolations of rainfall data, although few studies were found on comparisons between deterministic (e.g., IDW) and geostatistical methods, especially on the hourly scale. Goudenhoofdt and Delobbe (2009) evaluated several radar–gauge merged QPEs on the daily scale over a 4-yr period in Belgium. The merging methods included an MFB, an IDW, and several kriging schemes. When compared to a radar-only QPE, a kriging interpolated QPE using radar-based variograms reduced the mean absolute error (MAE) by 40%. The local radar–gauge bias correction using a Brandes (1975)-type IDW scheme performed slightly worse than the kriging but still achieved ~36% reduction in the MAE (Goudenhoofdt and Delobbe 2009).

In the current study, an IDW-type approach is adapted for the merging of radar QPEs, gauge observations, and orographic precipitation climatologies because of its computational efficiency and fairly satisfactory performance (e.g., Tabios and Salas 1985; Dirks et al. 1998; Goudenhoofdt and Delobbe 2009). The computational efficiency is important for the real-time implementation given the large analysis domain (7000 × 3500 grid cells covering 20°–55°N and 130°–60°W at a 0.01° × 0.01° resolution) and the high volume of data (~148 radars and ~9000 hourly gauges) in the current study. Further, parameters of the IDW function are dynamically adjusted in the current study based on the surface precipitation type to account for the spatial variability of QPE biases. In the merged product, radar QPEs provide a high-resolution depiction of spatially distributed precipitation. The orographic precipitation climatology provides a background precipitation distribution in the western United States where radar coverage is poor and the orographic enhancement of precipitation is dominant. Real-time hourly rain gauge data provide in situ measurements of precipitation rates that can correct potential biases in the radar QPE. The merging algorithm is fully automated and can be easily implemented in an operational system.

A detailed description of the merging technique is provided in section 2, and section 3 presents the new merged QPE products for several precipitation events from different regions and seasons in the United States. A brief summary is provided in section 4.

2. Methodology

The radar, gauge, and precipitation climatology merged product is derived by combining two hourly precipitation products in the real-time National Mosaic and Multi-Sensor QPE (NMQ) system (Zhang et al. 2011), namely, the radar-based QPE (Q2rad) and the Mountain Mapper (Q2MM). Q2rad has an automated precipitation classification scheme based on a three-dimensional reflectivity structure and atmospheric environmental analyses. At each grid cell, precipitation is classified as one of five types: stratiform rain, convective rain, hail, tropical rain, and snow. Different ZR relationships are applied pixel by pixel (~1 km × 1 km) based on precipitation types to obtain an instantaneous precipitation rate field, and the rate fields are aggregated into hourly accumulations. In the current study, an enhanced version of Q2rad was used, in which a vertical profile of reflectivity (VPR) correction (Zhang and Qi 2010; Zhang et al. 2012b) was applied to mitigate errors associated with bright band and with the beam sampling above the melting layer. Such errors are most pronounced in cool season stratiform precipitation and include an overestimation bias in areas of melting snow aggregates (bright band) and an underestimation bias in areas near cloud tops. Brightband features associated with melting graupel/snow aggregates are also found in the trailing stratiform rain of mesoscale convective systems (Qi et al. 2013a,b) and can cause overestimations in the radar QPE.

The accuracy of the Q2rad product varies in space and in time because of a number of factors, which include 1) errors in measuring radar reflectivity, for example, the calibration bias; 2) contaminations from nonprecipitation echoes, for example, ground clutter due to anomalous propagations; 3) uncertainties in ZR relationships; and 4) variability in the VPR. The radar QPE error due to the first factor can be minimized through a close monitoring and routine calibrations of the radar network. Radar QPE errors due to the second factor may be minimized with dual-polarization capabilities (e.g., Ryzhkov et al. 2005a,b; Park et al. 2009). The uncertainty associated with ZR relationships can be significant, although quantifying this uncertainty requires a dense and high-accuracy rain gauge or disdrometer network across all precipitation regimes, which is impractical to maintain operationally. The error associated with ZR uncertainties is also expected to decrease with dual-polarization capabilities, since additional radar variables can be used for hydrometeor classifications (e.g., Ryzhkov et al. 2005b; Giangrande and Ryzhkov 2008). The radar QPE uncertainty associated with VPRs is another (if not the most) significant error source and cannot be reduced by the dual-polarization capabilities because the error is associated with the radar beam resolution and height. If the radar’s beamwidth and scan strategy stay the same, then the VPR uncertainties would stay the same.

Zhang et al. (2012a) developed a real-time national Radar QPE Quality Index (RQI) as a function of the radar beam height and width and their relationships with the terrain (blockage) and the atmospheric freezing level. The RQI value ranges from 0 (poorest quality) to 1 (best quality), and the area of high RQI values increases with increasing freezing-level height (i.e., higher accuracy of Q2rad in the warm season than in the cold season). RQI values decrease with increasing radar beam blockages and with increasing beam height, especially when the beam height is at or above the freezing level. Figure 1 shows example RQI fields associated with a convective storm in Texas on 11 May 2012 (Fig. 1a) and a cool season stratiform rain in the Pacific Northwest on 11 March 2011 (Fig. 1b). For the Texas event, the RQI field showed a highest value of 1 for the whole domain. The high values indicated a very good sampling of the precipitation by the radars for this event—attributed to the flat terrain in the region and a high freezing level (~3.6 km above mean sea level) during the event. In contrast, the RQI field for the Pacific Northwest event (Fig. 1b) showed large areas of low values (<0.5). A significant portion of the domain had RQI < 0.1, indicating no effective radar coverage at all. The complex terrain and severe blockages contributed to the poor radar coverage. Further, the low freezing level (~1.6 km above mean sea level) caused the radar beams to sample above the melting layer in many areas [e.g., those southwest and northeast of KATX (Seattle, Washington) radar; Fig. 1b]. The RQI product has been implemented in the NMQ system for over 3 years and was shown to be a good indicator of the radar QPE accuracy in both space and time (Chen et al. 2013).

Fig. 1.

RQI fields in (a) southern Texas at 0000 UTC 11 May 2012 and (b) the Pacific Northwest at 0000 UTC 11 Mar 2011.

Fig. 1.

RQI fields in (a) southern Texas at 0000 UTC 11 May 2012 and (b) the Pacific Northwest at 0000 UTC 11 Mar 2011.

Q2MM interpolates hourly rain gauge observations using a monthly precipitation climatology as the background field. The gauges are from the Hydrometeorological Automated Data System (HADS; www.nws.noaa.gov/oh/hads/WhatIsHADS.html; Fig. 2). The precipitation climatology is a product of the Parameter–Elevation Regressions on Independent Slopes Model (PRISM; www.prism.oregonstate.edu/; Daly et al. 1994, 2008), which is derived using 30 years of gauge observations, atmospheric environmental data, and terrain elevation information.

Fig. 2.

The hourly HADS gauge network. The color represents the distance of each pixel (0.01° lat × 0.01° lon) in the CONUS analysis domain to the nearest HADS gauge.

Fig. 2.

The hourly HADS gauge network. The color represents the distance of each pixel (0.01° lat × 0.01° lon) in the CONUS analysis domain to the nearest HADS gauge.

A simple quality control (QC) process is applied to the HADS gauge hourly reports based on their consistency with the collocated hourly Q2rad (Q2rad_1h) that have an RQI value higher than 0.5. Radar observations provide reliable information on the precipitation/no-precipitation boundaries when the RQI is relatively high. If the Q2rad_1h indicates precipitation (≥0.01 in.) but the gauge report does not, or the other way around (i.e., Q2rad_1h = 0 but gauge report >0), then the gauge report is considered bad and removed. These simple quality checks can effectively remove “stuck” gauges that report constant zero and gauges that report false precipitation in a clear air environment (e.g., in a situation when unheated gauges report precipitation from the melting snow after the precipitation has ended). Additional censoring based on the surface temperature and radar QPEs in areas of low RQI will be tested to further remove problematic gauges during frozen precipitation events. Further, the area of RQI > 0.5 is relatively large in the warm season when the freezing level is high and may include regions where radar could potentially overshoot low stratus precipitation (especially when cloud tops are below 2 km above the ground level). Potential removal of correct nonzero gauge reports may occur in such situations and further refinements of the gauge QC may be necessary.

After the quality control, the gauge–climatology ratio is computed at each gauge station. The ratio is interpolated onto a regular ~1 km × 1 km grid via an inverse distance squared weighting function. The interpolated ratio field is multiplied by the PRISM climatology and a Q2MM hourly precipitation map is obtained. The U.S. National Weather Service River Forecast Centers in the west (i.e., Northwest, California–Nevada, and Colorado basin; see http://water.weather.gov/ahps/rfc/rfc.php) use a similar QPE for their operational river flow forecasts.

The merged hourly precipitation, called Q2RM, is computed through the following three steps:

  1. At grid points that collocate with a gauge site, Q2RM is set to Q2MM.

  2. At grid points where RQI > 0.1 and Q2rad = 0, Q2RM is set to Q2rad (i.e., when RQI > 0.1 and radars “see” no precipitation, the merged product is set to “no precipitation”). This is based on the assumption that radar observations provide reliable spatial precipitation coverage if the beam is not too high (within ~1.5 km) above the freezing level.

  3. In the rest of the domain, Q2RM is computed based on the following equation:

 
formula

where

 
formula

Variables wm and wr are weighting functions representing confidence levels of the Q2MM and Q2rad hourly rainfall products, respectively.

The Q2MM weight wm is a function of three longitudinal zones: West Coast (125°–118°W), Rocky Mountains (118°–100°W), and eastern United States (100°–60°W). In the West Coast zone, most of the precipitation occurs in the cool season, with the heaviest associated with large moisture influx from the Pacific, a phenomena known as the “atmospheric river” (e.g., Ralph and Dettinger 2012; Ralph et al. 2004; Kingsmill et al. 2013). The complex topography in this zone plays an important role in modulating the precipitation distribution, and such orographic enhancement is captured well in the PRISM precipitation climatology. Gauge networks are much sparser in the west than in the east, although the density is relatively high in the lower elevations of central and northern California and in western Washington (Fig. 2). The radar coverage, on the other hand, suffers from severe blockages in a majority of the zone (e.g., Maddox et al. 2002). Some radars were placed on mountaintops to reduce blockages, and such siting choices resulted in radar beam frequently overshooting precipitation processes. A 3-yr comparison of root-mean-square errors (RMSEs; Fig. 3) of Q2rad and Q2MM 24-h with respect to the independent daily gauge observations from the Community Collaborative Rain, Hail & Snow Network (CoCoRaHS; www.cocorahs.org) showed a consistently better Q2MM performance (smaller RMSEs) than Q2rad in the West Coast zone. Based on the comparison results, Q2MM is given a constant weight of 1.0 (i.e., Q2RM = Q2MM) west of 118°W in the current merging scheme.

Fig. 3.

RMSE differences (diamonds) between Q2rad and Q2MM with respect to the CoCoRaHS 24-h rainfall observations (ending at 1400 UTC each day) from 1 Jun 2010 to 1 Jun 2013 for the West Coast zone. The domain-average CoCoRaHS rainfalls (circles) for the same time period are also shown.

Fig. 3.

RMSE differences (diamonds) between Q2rad and Q2MM with respect to the CoCoRaHS 24-h rainfall observations (ending at 1400 UTC each day) from 1 Jun 2010 to 1 Jun 2013 for the West Coast zone. The domain-average CoCoRaHS rainfalls (circles) for the same time period are also shown.

It is noted that the performance of Q2MM is largely dependent on the quality of its input gauges (i.e., HADS). During the 3-yr evaluation period, a few very large Q2MM RMSE outliers (not shown in Fig. 3) were found and each was associated with a single erroneous gauge. A new gauge quality control scheme is currently in development and will minimize the impact of such problematic gauges in the future.

In the longitude zone east of 100°W, the terrain is nearly flat (except for the Appalachian Mountains) and the radar coverage is much better in comparison to the western United States (Maddox et al. 2002). Further, precipitation patterns in this zone are largely variable with time. They range from isolated thunderstorms and mesoscale convective systems in warm season to frontal stratiform rain and snowstorms in cool season. Monthly climatologies are not as representative of the hourly precipitation distribution as they are in the West Coast zone. As a result, Q2MM performance varies from event to event and the associated QPE errors are generally large in areas where gauges are sparse. To reflect this error characteristic in the merged product, Q2MM is given a low background weight (default value = 0.1) in areas outside gauges’ influence radius Ri, and Ri is a function of the surface precipitation type. Surface precipitation type is a real-time NMQ product containing five categories (stratiform, convective, and tropical rain, hail, and snow; Zhang et al. 2011). Generally, a gauge report in convective rain or hail is representative of a smaller area than a gauge report from stratiform, tropical, and snow precipitation. Based on a number of case studies across the United States (Table 1), a default value of 10 km was chosen for Ri in convective rain and hail and 40 km in stratiform and tropical rain and snow. The new Q2RM product will be implemented in the real-time NMQ system and Ri will be further evaluated and refined.

Table 1.

List of the cases (all have a 24-h duration and ending times are indicated in the table).

List of the cases (all have a 24-h duration and ending times are indicated in the table).
List of the cases (all have a 24-h duration and ending times are indicated in the table).

Inside gauges’ radius of influence, wm assumes the following form:

 
formula

Variable d is the distance from a grid point to the nearest gauge (Fig. 2) and β = 0.1 is the background weight for Q2MM when d > Ri.

The weighting function in the Rocky Mountains zone is the same as in the eastern United States since both cool season stratiform and warm season convective precipitation (e.g., those associated with the North America monsoon; Adams and Comrie 1997) occur in this region. However, the background weighting factor β changes linearly from 0.1 at the east bound (100°W) to 1.0 at the west bound of the zone (118°W). This weighting function assures a smooth transition in the merged precipitation field across the zonal boundaries.

3. Case studies

a. The eastern United States zone

Figure 4 shows a thunderstorm event that occurred on 9 October 2011 in southern Texas. The storm consisted of a heavy convective rainband in the leading edge to the east and a trailing stratiform area in the west (Fig. 4a). The hourly Q2rad, Q2MM, and Q2RM (Figs. 4a,d,g, respectively) are compared with in situ observations from the independent Lower Colorado River Authority (LCRA) gauge network (Figs. 4b,e,h). The domain average of the Q2rad hourly rainfall had a large overestimation of ~59% (Fig. 4c) with respect to the LCRA gauges. The overestimation was mainly caused by the contamination of melting snow aggregates/graupel in the trailing stratiform region (white circle in Fig. 4b). The correlation coefficient (CC) score was 0.89 and RMSE was 8.9 mm when compared with the hourly LCRA gauges. Q2MM had an underestimation of ~26% because the HADS gauges (black plus signs in Fig. 4d) did not capture the maximum rainfall in the heavy rainband (yellow circle in Fig. 4e). The CC score of Q2MM was lower than Q2rad at 0.60 and the RMSE was slightly larger at 9.9 mm (Fig. 4f). After merging the two products, all three scores were improved (bias ratio = 0.98, CC = 0.90, and RMSE = 5.6 mm; Fig. 4i). The improvement is attributed to the reduction of the Q2rad overestimation in the trailing stratiform area and the reduction of Q2MM underestimation in the leading convective rainband.

Fig. 4.

Hourly rainfall maps from (a) Q2rad, (d) Q2MM, and (g) Q2RM ending at 1100 UTC 9 Oct 2011 in southern Texas. (b), (e), (h) Bias ratios of the three QPEs over the LCRA hourly gauge observations are shown as bubble charts. The size of the bubbles represents the LCRA gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). (c), (f), (i) The scatterplots of the three QPEs vs LCRA data. The black plus signs indicate locations of the hourly HADS gauges. The white circle indicates the trailing stratiform rain area and yellow circle indicates the leading convective rainband.

Fig. 4.

Hourly rainfall maps from (a) Q2rad, (d) Q2MM, and (g) Q2RM ending at 1100 UTC 9 Oct 2011 in southern Texas. (b), (e), (h) Bias ratios of the three QPEs over the LCRA hourly gauge observations are shown as bubble charts. The size of the bubbles represents the LCRA gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). (c), (f), (i) The scatterplots of the three QPEs vs LCRA data. The black plus signs indicate locations of the hourly HADS gauges. The white circle indicates the trailing stratiform rain area and yellow circle indicates the leading convective rainband.

Figure 5 shows a heavy rain event that occurred on 7–8 September 2012 across Indiana, southern Illinois, and northeastern Ohio. Daily precipitation accumulations from Q2rad, Q2MM, and Q2RM are compared with independent 24-h rain gauge observations from CoCoRaHS. The rainfall distributions are remarkably different in the Q2rad (Fig. 5a) and Q2MM (Fig. 5d) daily accumulation fields, where the radar-based QPE showed larger areas of higher amounts than the gauge–climatology merged analysis. Q2MM had a large underestimation of ~36% (Fig. 5f) when compared to independent CoCoRaHS gauges. The CC score was 0.83 and RMSE was 17.04 mm. Q2rad had a small overestimation of 12% and a higher CC of 0.93 and lower RMSE of 9.74 mm (Fig. 5c) than Q2MM. The better performance of Q2rad than Q2MM was a result of good radar coverage in this region and very representative ZR relationships applied during this event. After merging the two products, all three scores were improved (bias ratio = 1.0, CC = 0.95, and RMSE = 7.5 mm; Fig. 5i).

Fig. 5.

Daily rainfall maps from (a) Q2rad, (d) Q2MM, and (g) Q2RM ending at 1100 UTC 8 Sep 2012 for a widespread heavy precipitation event across the northern and eastern United States. (b), (e), (h) Bias ratios of the three QPEs over the CoCoRaHS gauge observations are shown as bubble charts. The size of the bubbles represents the CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). (c), (f), (i) The scatterplots of the three QPEs vs CoCoRaHS data.

Fig. 5.

Daily rainfall maps from (a) Q2rad, (d) Q2MM, and (g) Q2RM ending at 1100 UTC 8 Sep 2012 for a widespread heavy precipitation event across the northern and eastern United States. (b), (e), (h) Bias ratios of the three QPEs over the CoCoRaHS gauge observations are shown as bubble charts. The size of the bubbles represents the CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). (c), (f), (i) The scatterplots of the three QPEs vs CoCoRaHS data.

b. The Rocky Mountains zone

Figure 6 shows a widespread storm event in Arizona on 21–22 August 2012. When compared with CoCoRaHS observations (Fig. 6c), Q2rad had a bias ratio of 1.3 (30% overestimation), a CC of 0.83, and an RMSE of 6 mm. Q2MM, on the other hand, had a bias ratio of 0.57 (43% underestimation), a CC of 0.6, and an RMSE of 7.71 mm (Fig. 6f). The merged product had a better agreement with the CoCoRaHS gauges (Figs. 6g,i) than the two individual QPEs (bias ratio = 1.03, CC = 0.85, and RMSE = 4.85 mm). The largest underestimation error in Q2MM came from an area west of Phoenix (yellow arrow in Fig. 6e), where there was only one HADS gauge (Fig. 7b) and PRISM indicated a relatively dry climatology (Fig. 7c). The single HADS gauge did not capture the storms to its west and resulted in a severe underestimation in Q2MM (Fig. 7a). In the merged product (Fig. 7e), the underestimation of Q2MM was significantly reduced by Q2rad (Fig. 7d) since this area was very close to KIWA (Phoenix, Arizona) radar and the storms were well captured in the radar observations.

Fig. 6.

As in Fig. 5, but for 24-h QPEs ending at 1300 UTC 22 Aug 2012 during a scattered convective storms event in Arizona.

Fig. 6.

As in Fig. 5, but for 24-h QPEs ending at 1300 UTC 22 Aug 2012 during a scattered convective storms event in Arizona.

Fig. 7.

Enlarged views of the bias ratio maps of (a) Q2MM, (d) Q2rad, and (e) Q2RM vs CoCoRaHS gauges in central Arizona (see yellow arrow in Fig. 6e) west of Phoenix. (b) Distributions of the hourly HADS gauge stations (plus signs). (c) The PRISM August monthly precipitation climatology (http://prism.oregonstate.edu).

Fig. 7.

Enlarged views of the bias ratio maps of (a) Q2MM, (d) Q2rad, and (e) Q2RM vs CoCoRaHS gauges in central Arizona (see yellow arrow in Fig. 6e) west of Phoenix. (b) Distributions of the hourly HADS gauge stations (plus signs). (c) The PRISM August monthly precipitation climatology (http://prism.oregonstate.edu).

Large overestimations of Q2rad with respect to CoCoRaHS gauges were found in an area northwest of Tucson (yellow arrow in Fig. 6b). An enlarged view of Q2rad in the area (Fig. 8d) shows a highly variable distribution of the precipitation because of scattered storms. There were only two HADS gauges (plus signs in Figs. 8a–c) in the area and they did not capture the storm cell ~20 km northwest of TUS. The radar–CoCoRaHS gauge discrepancy in the areas of white and yellow circles (Fig. 8a) was likely due to two factors: 1) the radar was sampling at 1 km or higher above the ground level in the region and the radar-observed rain (virga) partially or completely evaporated before it reached the ground, and 2) there was possible undercatch of rainfall by gauges because of high winds associated with the severe storms (based on storm reports from the Storm Prediction Center). The white circle area was relatively close to the two HADS gauges. Q2MM largely corrected the Q2rad overestimation and the merged QPE (Figs. 8c,f) agreed well with the CoCoRaHS observations. In the yellow circle area, the overestimation had little improvement in the merged product since the area was far away from any HADS gauges and the RQI (not shown) was high (>0.9).

Fig. 8.

Enlarged bias ratio maps of 24-h (a) Q2rad, (b) Q2MM, and (c) Q2RM with respect to the CoCoRaHS gauge observations in the small area northwest of Tucson (indicated by the yellow arrow in Fig. 6b). The white plus signs in (a)–(c) indicate locations of the two HADS gauges used in Q2MM. (d)–(f) Q2rad, Q2MM, and Q2RM 24-h precipitation distributions, respectively.

Fig. 8.

Enlarged bias ratio maps of 24-h (a) Q2rad, (b) Q2MM, and (c) Q2RM with respect to the CoCoRaHS gauge observations in the small area northwest of Tucson (indicated by the yellow arrow in Fig. 6b). The white plus signs in (a)–(c) indicate locations of the two HADS gauges used in Q2MM. (d)–(f) Q2rad, Q2MM, and Q2RM 24-h precipitation distributions, respectively.

c. The West Coast zone

Figure 9 shows Q2rad and Q2MM products for a cool season stratiform event in the Pacific Northwest. Q2rad displayed significant blockage artifacts (Fig. 9a) and underestimated the precipitation by 25% (Fig. 9b) when comparing with the CoCoRaHS gauges. Q2MM produced a physically continuous precipitation field (Fig. 9c) and had much less underestimation (9%) and a higher correlation coefficient (0.9 versus 0.84) and lower RMSE (6.4 mm versus 8.9 mm) than Q2rad. Bias ratio maps of the two fields (Figs. 10a,b) versus CoCoRaHS gauges indicated major improvements in the Q2MM field in the southwest coastal region of Oregon (white circles in Fig. 10b). The radar QPE had the worst underestimation in the area (Fig. 10a) because of the radar beam overshooting precipitation processes (see Fig. 1b). The HADS hourly rain gauges are sparse in the region (Fig. 10c), but Q2MM was able to produce relatively accurate estimates because the PRISM monthly precipitation climatology (Fig. 10d) indicated heavy orographic precipitation in the area.

Fig. 9.

Daily rainfall maps of (a) Q2rad and (c) Q2MM for a heavy stratiform rainfall event in the Pacific Northwest during a 24-h period ending at 1500 UTC 10 Mar 2011. The scatterplots of (b) Q2rad and (d) Q2MM vs CoCoRaHS data are also shown.

Fig. 9.

Daily rainfall maps of (a) Q2rad and (c) Q2MM for a heavy stratiform rainfall event in the Pacific Northwest during a 24-h period ending at 1500 UTC 10 Mar 2011. The scatterplots of (b) Q2rad and (d) Q2MM vs CoCoRaHS data are also shown.

Fig. 10.

Bias ratio maps of (a) Q2rad and (b) Q2MM 24-h ending at 1500 UTC 10 Mar 2012 vs CoCoRaHS gauge observations. (c) Distributions of HADS gauges (white plus signs) in the region. (d) The PRISM March monthly precipitation climatology (http://prism.oregonstate.edu). The size of the solid circles in the bias ratio maps represents the 24-h CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation).

Fig. 10.

Bias ratio maps of (a) Q2rad and (b) Q2MM 24-h ending at 1500 UTC 10 Mar 2012 vs CoCoRaHS gauge observations. (c) Distributions of HADS gauges (white plus signs) in the region. (d) The PRISM March monthly precipitation climatology (http://prism.oregonstate.edu). The size of the solid circles in the bias ratio maps represents the 24-h CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation).

Figure 11 shows another heavy rain event in the West Coast zone (California). In this case, Q2rad had a significant underestimation of 64% with a CC of 0.68 and an RMSE of 21.11 mm. Q2MM, aided by a relatively dense HADS gauge network and the PRISM precipitation climatology, produced a 24-h accumulation with a much less underestimation bias of 26%, a higher CC of 0.88, and a lower RMSE of 11.37 mm. Q2rad performed better than Q2MM in very small areas near KMAX (Medford, California) and KBBX (Beale Air Force Base, California) radars (yellow arrows in Fig. 11b), but not so near KBHX (Eureka, California) and KMUX (San Francisco, California) radars (white arrows in Fig. 11b). With the recent polarimetric upgrade of the Weather Surveillance Radar-1988 Doppler (WSR-88D) network, areas of the radar QPE outperforming Q2MM may increase. Further studies are needed to understand the error distributions of the radar QPE and to make an effective use of the radar QPE in the West Coast zone.

Fig. 11.

Daily rainfall maps of (a) Q2rad and (d) Q2MM ending at 1500 UTC 22 Dec 2012 for a winter stratiform precipitation event. Bias ratios of the 24-hr (b) Q2rad and (e) Q2MM over the CoCoRaHS gauge observations are shown as bubble charts. The size of the bubbles represents the CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). The scatterplots of (c) Q2rad and (f) Q2MM vs CoCoRaHS data are also shown.

Fig. 11.

Daily rainfall maps of (a) Q2rad and (d) Q2MM ending at 1500 UTC 22 Dec 2012 for a winter stratiform precipitation event. Bias ratios of the 24-hr (b) Q2rad and (e) Q2MM over the CoCoRaHS gauge observations are shown as bubble charts. The size of the bubbles represents the CoCoRaHS gauge amounts and the color represents the QPE bias (red means underestimation and blue means overestimation). The scatterplots of (c) Q2rad and (f) Q2MM vs CoCoRaHS data are also shown.

The new merged QPE algorithm was tested on 16 heavy rain events (Table 1) from different seasons and different regions across CONUS. Figure 12 shows the bias ratio, RMSE, and CC scores of Q2rad, Q2MM, and Q2RM 24-h for all the events when compared with CoCoRaHS gauges. The Q2rad showed overestimation biases for warm season convective storms and underestimation for cool season precipitation, especially in the mountainous west. The Q2MM, on the other hand, had large underestimation for the warm season convective storms and less so for the cool season stratiform-type precipitation. The Q2RM was able to reduce the biases and moved the bias ratio closer to unity than Q2rad and Q2MM for the majority of the cases. Additionally, Q2RM reduced the RMSEs and increased the correlation coefficients. When averaged for all events, Q2RM has an RMSE of 9.25 mm (versus 14.79 mm for Q2rad and 12.77 mm for Q2MM) and a CC of 0.90 (versus 0.82 for both Q2rad and Q2MM).

Fig. 12.

Statistical scores of (a) bias ratio, (b) RMSE, and (c) CC of Q2rad, Q2MM, and Q2RM 24-h with respect to CoCoRaHS observations for the 16 events listed in Table 1.

Fig. 12.

Statistical scores of (a) bias ratio, (b) RMSE, and (c) CC of Q2rad, Q2MM, and Q2RM 24-h with respect to CoCoRaHS observations for the 16 events listed in Table 1.

4. Summary

A new QPE product was developed using a synergistic approach to combine radar, gauge, and monthly orographic precipitation climatologies. The new QPE merges the NMQ hourly radar-based and the Mountain Mapper precipitation estimates using heuristic rules and weighting functions that are based on error characteristics of radar and gauge observations. The merged QPE retains high-resolution spatial structure of precipitation observed by radars and minimizes the bias in the radar precipitation estimates using gauge observations. In the complex terrain where rain gauge distributions are sparse and radars have relatively poor coverage, a monthly precipitation climatology is used to provide a physically reasonable and spatially continuous precipitation map.

The new algorithm was tested for 16 heavy precipitation events from different areas of CONUS, and the merged product showed consistent improvements over the individual QPE components. In the Pacific Northwest, the merged product reduced underestimations in the radar QPE and provided a spatially continuous precipitation map without blockage discontinuities. In the central United States and Arizona, the merged product reduced radar QPE overestimations because of inaccurate ZR relationships and mitigated false precipitation estimates derived from virga. The merged product still has limitations with transient precipitation in areas where both radar and gauge coverage are poor. Additional observations from local mesonets, gap-filling radars, or spaceborne radars may help further increase the QPE accuracy in such areas. The new QPE algorithm is fully automated and computationally efficient and will be implemented in the real-time NMQ system for further evaluations.

Currently, the radar QPE plays little role in the West Coast mountainous area because of its significantly poorer performance than the Mountain Mapper. With the polarimetric upgrade to the WSR-88D network, the radar QPE quality may improve for the Intermountain West. The research and development of a national polarimetric radar QPE is ongoing in the NMQ system. The new polarimetric radar QPE and a local gauge bias–corrected radar QPE will be tested for the merged QPE in the future.

Acknowledgments

Major funding for this research was provided under the agreement between the National Oceanic and Atmospheric Administration (NOAA) and the American Institute in Taiwan (AIT) and the agreement between NOAA and the Salt River Project. Partial funding was provided under NOAA–University of Oklahoma Cooperative Agreement NA17RJ1227.

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