Investigation of Weather Radar Quantitative Precipitation Estimation Methodologies in Complex Orography

Abstract

Near surface quantitative precipitation estimation (QPE) from weather radar measurements is an important task for feeding hydrological models, limiting the impact of severe rain events at the ground as well as aiding validation studies of satellite-based rain products. To date, several works have analyzed the performance of various QPE algorithms using actual and synthetic experiments, possibly trained by measurement of particle size distributions and electromagnetic models. Most of these studies support the use of dual polarization radar variables not only to ensure a good level of data quality but also as a direct input to rain estimation equations. One of the most important limiting factors in radar QPE accuracy is the vertical variability of particle size distribution, which affects all the acquired radar variables as well as estimated rain rates at different levels. This is particularly impactful in mountainous areas, where the sampled altitudes are likely several hundred meters above the surface. In this work, we analyze the impact of the vertical profile variations of rain precipitation on several dual polarization radar QPE algorithms when they are tested in a complex orography scenario. So far, in weather radar studies, more emphasis has been given to the extrapolation strategies that use the signature of the vertical profiles in terms of radar co-polar reflectivity. This may limit the use of the radar vertical profiles when dual polarization QPE algorithms are considered. In that case, all the radar variables used in the rain estimation process should be consistently extrapolated at the surface to try and maintain the correlations among them. To avoid facing such a complexity, especially with a view to operational implementation, we propose looking at the features of the vertical profile of rain (VPR), i.e., after performing the rain estimation. This procedure allows characterization of a single variable (i.e., rain) when dealing with vertical extrapolations. In this work, a definition of complex orography is also given, introducing a radar orography index to objectively quantify the degree of terrain complexity when dealing with radar QPE in heterogeneous environmental scenarios. Three case studies observed by the research C-band polarization agility Doppler radar named Polar 55C, managed by the Institute of Atmospheric Sciences and Climate (ISAC) at the National Research Council of Italy (CNR), were used to prove the concept of VPR. Our results indicate that the combined algorithm, which merges together differential phase shift (K_dp), single polarization reflectivity factor (Z_hh), and differential reflectivity (Z_dr), once accurately processed, in most cases performs better among those tested and those that make use of Z_hh alone, K_dp alone, and Z_hh, and Z_dr. Improvements greater than 25% are found for the total rain accumulations in terms of normalized bias when the VPR extrapolation is applied.

1. Introduction

In recent years, there has been increasing attention paid to developing new applications and planning missions to monitor and deliver quantitative information of near surface rain precipitation. The Global Precipitation Measurement (GPM) mission [1] is a recent valuable example of measuring precipitation using spaceborne active and passive sensors.

From the ground, measuring systems of rainfall are essential for providing a reference measure for the validation of the satellite rain products over land [2] as well as to prevent flood hazards (e.g., by using nowcasting algorithms [3] or assimilation into forecast models [4]), thus aiding civil protection actions. Ground-based measurements of rainfall can rely on rain gauges [5], disdrometers [6], weather radars [7], and profilers such as the micro rain radars [8] as well as the use of their combinations, merged with external information like lightning [9]. Typically, over land, weather radar and rain gauges are used most often as they are a conventional choice in the operational context at national weather service levels.

However, quantitative measurements of rain precipitation at the Earth’s surface using ground-based systems are typically affected by a number of limiting factors due to errors introduced both by the observation instruments used as well as the variability of rainfall in time and space compared to the sampling interval of the acquired measurements. In particular, weather radars can be affected by several error sources, including radar miscalibration [10], clutter contamination (originated by antenna side lobe contributions, surrounding orography, human-made obstacles, or anomalous propagation effects) [11], wet radome attenuation [12], rain-induced attenuation [13], non-uniform beam filling [14], radiofrequency interferences [15], and uncertainties related to the vertical variability of the particle size distribution (PSD) [16,17]. In addition, sampling differences in both time and space between radar measurements and reference observations at the surface add to the uncertainties of radar quantitative precipitation estimation [18] when multi-observation comparisons are carried out. In particular, the vertical variability of PSD directly impacts the variability of the measured radar quantities; for example, the reflectivity factor (Z_hh), the differential reflectivity (Z_dr), and the specific differential phase shift (K_dp) as well as the estimates of near-surface rain rate (R), which is usually obtained from the radar quantities measured aloft. In particular, in complex orography environments, when the radar antenna tilts have to be set higher than usual to limit beam blocking (say above 3 or 4 deg with respect to the horizon) or the radar is positioned at a high altitude (e.g., above 1500 m), the differences in the sampled radar quantities aloft with respect to those that would be observed close to the surface can be significant. Some past studies have focused on rain precipitation estimation in complex orography [19,20] while others have extensively addressed the issue of the vertical extrapolation of the reflectivity factor, Z_hh, down to the surface level to estimate the rain rate, R, taking into account, in particular, the distinct signatures of the vertical profile of reflectivity in stratiform and convective rain regimes [21,22,23]. However, as far as the authors have been able to ascertain, none of the works referenced above have addressed the issue of vertical extrapolation when dealing with weather radar dual polarization rain estimation formulas, although there is growing interest in the characterization of the signature of the vertical profile of K_dp and Z_dr [24].

The goal of this study is twofold: (i) test the variability of various radar quantitative precipitation estimation (QPE) algorithms in a complex orography environment, including those based on the R(Z_hh), R(K_dp), R(Z_hh,Z_dr) relationships, as well as those based on one of their combinations; (ii) show the impact of the use of quasi-vertical profiles of rain and K_dp filtering settings on QPE algorithms. In this work, the acronym VPR, often ambiguously referred to vertical profile of reflectivity, indicates the vertical profile of rain. The use of quasi-VPR, when dealing with dual polarization radar variables, is a key aspect of this study. The term “quasi-VPR” actually refers to the fact that we are not looking at vertical radar observations but instead we derive vertical information by exploiting slanted paths [25]. In this study, quasi-VPRs are used to overcome the complication that would result if we attempted to perform QPEs using dual polarization estimators (i.e., using Z_hh, Z_dr, and K_dp or a subset of them at the same time). Indeed, various QPE estimators exist based on several combinations of Z_hh, Z_dr, and K_dp, with estimation coefficients adapted as a function of rain regimens observed by radar (e.g., [26,27]). Those QPE estimators might benefit from the use of quasi-VPR as defined in this study because it allows near surface extrapolations after rain rate retrievals instead of performing them before the retrieval step.

To test the concept of quasi-VPR for QPE, three case studies from the area surrounding Rome, Italy, are considered. These studies include two particularly intense convective events on 15 October 2012 and 14 October 2015 and a stratiform event on 12 October 2012. The C-band Doppler dual polarization research radar Polar55C (hereafter P55C) operated by the National Research Council of Italy (CNR) at the Institute of Atmospheric Sciences and Climate (ISAC) in Tor Vergata, Rome, was used. An objective definition of complex orography is also given in this manuscript, introducing a radar orography index to better mark the boundary for those QPE applications performed in such adverse environments.

The work is organized in six sections. Section 2 describes the methodological aspects for QPE, Section 3 gives details on the experimental case studies as well as the radar and rain gauges specifications, Section 4 summarizes the results, while Section 5 discusses the results in the light of recent literature. Finally, Section 6 discusses the conclusions.

2. Methodology for Quantitative Precipitation Estimation

2.1. QPE from Radar Observables

Before applying QPE algorithms, an accurate processing of the acquired P55C radar variables involved in the rain estimation was carried out. All the processing steps were devoted to ensuring the maximum level of quality of the measurements above noise levels—that is, minimizing the contribution of system miscalibration, ground clutter returns, radio frequency interference, beam blocking effects, and path attenuation. All the processing steps are described in Appendix A. The QPE algorithms analyzed in this study make use of Z_hh, Z_dr, and K_dp, correctly processed. They are listed below for the reader’s convenience:

$$R_Z(p)=a_Z\cdot {\left[Z_{hh}(p)\right]}^{b_Z}$$

(1)

$$R_K(p)=a_K\cdot {\left[|K_{dp}(p)|\right]}^{b_K}\cdot \mathrm{sgn}\left[K_{dp}(p)\right]$$

(2)

$$R_{DR}(p)=a_{DR}\cdot {\left[Z_{hh}(p)\right]}^{b_{DR}}\cdot {\left[Z_{dr}(p)\right]}^{c_{DR}}$$

(3)

$$R_{KZ}(p)=(1-w)\cdot R_{DR}(p)+w\cdot R_K(p)$$

(4)

In Equations (1)–(4), the radar moments Z_hh and Z_dr are in linear units, respectively, whereas K_dp is in (deg·km⁻¹). All the variables are defined at longitude (x), latitude (y), altitude (h), and position p = (x,y,h) with respect to the radar location. The conversion coefficients a_q, b_q, and c_q are defined so that the resulting rain rate R_q is in (mm·h⁻¹), where the subscript q indicates one of the three estimation formulas through the labels “Z”, “K”, and “DR”. Finally, Equation (4) (with label q = KZ), adapted from the formulation proposed in [28], is a weighted combination of R_K and R_Z estimates from Equations (2) to (3) proposed by [29,30], respectively. In this case, the value of the weight (w) is set up so that the rain estimation that comes out using K_dp, i.e., R_K, weighs more for higher precipitation rates than that when making use of Z_hh and Z_dr only, i.e., R_DR. The values of filtered K_dp are used to discriminate high rain precipitation regimes from lower ones. In particular we fixed w = 1 for K_dp ≥ 0.5, w = 0 for K_dp ≤ 0.25, and w = 4·K_dp − 1 for 0.25 < K_dp < 0.5. The coefficients a_q, b_q, and c_q used are listed in

Table 1. Coefficients used for rain estimations in Equations (1)–(4).

Coefficient Symbols	Coefficients Values	Estimation Formulas	Reference Literature
aZ; bZ	0.0140; 0.728	$R_Z=a_Z·Z_{hh}^{bz}$	Adirosi et al., 2015 [31]
aK; bK	22.398; 0.813	$R_K=a_K·|K_{dp}{|}^{a_K}·sgn\left(K_{dp}\right)$	Adirosi et al., 2015 [31]
aDR; bDR; cDR	6.96 × 10−3; 0.934; −4.051	$R_{DR}=a_{DR}·Z_{hh}^{b_{DR}}·Z_{dr}^{c_{DR}}$	Adirosi et al., 2015 [31]
w	$\{\begin{array}{c}=1 for K_{dp}\ge 0.5\\ =0 for K_{dp}\le 0.25\\ =4·K_{dp}-1 for 0.25<K_{dp}<0.5\end{array}$	$R_{KZ}=\left(1-w\right)·R_{DR}+w·R_K$	Tested in this work

Values of Z_hh, Z_dr are in linear units. K_dp is in (deg·km⁻¹). The label “sgn” indicates the sign function.

. On the other hand, the estimation coefficients applied to implement the various estimation formulas can vary significantly depending on the way they are calculated and the assumptions made. We decided to fix those estimation coefficients using the results shown in [31] at C band (5.6 GHz), where the relations between the rain rate and the other radar variables are driven by experimental observations of drop size distribution obtained from a 2DVD disdrometer collected for two months in a field campaign in the Rome area, coupled with electromagnetic simulations of the propagating radar signal (i.e., using T-matrix routines). In these simulations an environmental temperature of 20 °C, the drop shape model of Beard and Chuang [32] and a Gaussian variation of the drop canting angle with a zero mean and a standard deviation of 7.5° are assumed. The choice of using the set of estimation coefficients derived by the same population of drop size distribution for the same geographical area for all the estimation formulas should help avoid inconsistencies that might arise when using parameterizations weighted by different approaches and measurement techniques.

2.2. Extrapolation of QPE at the Ground Using Quasi-Vertical Profiles

Rain estimations, R_q, performed using Equations (1)–(4) are in principle produced at any of the sampling positions, p, within the radar volume. Of course, R_q(p) is meaningful for p within areas of rain precipitation. This is likely if p describes positions below the bottom of the freezing band. However, this is not a condition that can be always met and depends on the radar position with respect to the surrounding orography (the terrain altitude variations). In such complex orography conditions, p can point to ice or mixed regions, making the values of estimated R_q agree less with the ground reality. Even when the radar antenna scan strategy and the surrounding orography allow for a sampling of rain below the bottom of the freezing band, i.e., in rain layers, modifications of the drop size distribution caused, for example, by spontaneous drop breakup, collision-induced breakup, coalescence, and/or evaporation redistribute the water mass contained in the raindrops across the size spectra. These modifications should lead to changes of the apparent trend of R_q with altitude. As a consequence, theoretically, the analysis of the vertical variations of R_q can be important for enhancing the QPE performance close to the ground level and may represent a smart way to deal with operational environments. To this goal, in this work we want to quantify the benefit, if any, of the use of quasi-vertical profiles of R_q (VPR_q^obs) extracted routinely by each of the radar volumes to perform rain rate extrapolations at the ground. To do that, a VPR_q^obs is primarily defined as an average “< · >” of R_q(p) within altitude intervals (∆h) centered at fixed altitudes h_j(x,y) = h_r(x,y) + j·∆h/2, where j is an index within [0, j_max] and h_r is the lowest altitude detected by the radar for each horizontal position (x,y):

$$VP{R}_q^{obs}(h_j)={\langle R_q(x,y,h_j)\rangle }_{\Delta h}$$

(5)

Of course, for those ∆h gaps with no data, a void value is assigned to VPR_q^obs. However, the spatial average in Equation (5) is not performed in the entire radar domain but the grid points (x,y) are selected using the criteria that comply with the following rule: Z_hh > 0 dBZ and Z_dr > −0.5 dB and |∆Z_hh/∆h| > 25 dBZ. This rule should avoid the inclusion of spikes and measurements too close to the signal-to-noise ratio level and guarantee good stability of the extracted profiles.

Note that conceptually, Equation (5) is similar to performing azimuthal averages as in [33], the only difference being that when performing azimuthal averages the altitudes h_j would not be regularly spaced due to the irregular radar spatial sampling along with the vertical direction. This should not be an issue when considering the VPR for QPE extrapolations, but in the case of visualization of the time series of VPR, azimuthal averages need to be interpolated in some way before displaying them.

After the computation of the observed VPR_q^obs we used it to correct R_q for the altitude effects by extrapolating the rain estimates at positions p = (x,y,h) up to the ground level (h_GRD); i.e., at positions p_GRD = (x,y,h_GRD). The extrapolation is performed by applying a regression on the values of VPR_q^obs(h_j) to obtain a modelled VPR_q^mod(h). Differently from past work, where it is a common practice to describe VPR_q^obs by stepwise linear models, in this study we propose the use of a non-linear regression model to keep the implementation as simple as possible:

$$VP{R}_q^{\mathrm{mod}}(h)=10{}^{0.1\left[p_1\cdot h+p_2\right]}$$

(6)

where p₁ and p₂ are regression coefficients in mm·h⁻¹·km⁻¹ and mm·h⁻¹, respectively and the subscript q can assume one of the labels “Z”, “K”, “DR”, and “KZ”, indicating the rain estimator used. It is worth noting that the regression model used in Equation (6) is unlikely to catch strong vertical variations of R_q but it is probably enough to correct for most of the bias in situations of particularly complex orography. Of course, Equation (6) can be updated with more accurate regression models driven by experimental evidence. The final correction on QPE estimates in Equations (1)–(4) is achieved by adding a correction quantity as formulated below:

$$R_q(p_{GRD})=R_q(p)+[VP{R}_q^{\mathrm{mod}}(h_m)-VP{R}_q^{\mathrm{mod}}(h)]$$

(7)

where Equation (7) is valid for altitudes, h, greater than h_m, and where p_GRD is a position at the ground level. The value of h_m can be set to h_r, the minimum altitude detected by the radar, or set to zero or set to the value below which R_q is constant. In the following sections we will apply the methodology just formalized to case studies that occurred in the inland area of Rome close to the Apennine chain acquired by the P55C radar. Then we will compare the outcomes of Equations (1)–(4) with those obtained by implementing Equation (7). It is worth remarking that VPR^obs and, as a consequence, VPR^mod, can be quite variable in space and time and a mean profile over a large area in space and time could be not representative of the vertical variation of precipitation at each position of the radar grid. One aspect we want to examine in this study is the level of improvement obtained when considering average vertical profiles, as in Equations (5) and (6), in estimating rain precipitation in complex orography using the dual polarization formulations in Equations (1)–(4) and (7).

3. Experimental Setup and Case Studies

3.1. Description of the Case Studies

The three cases studied occurred in Italy on 12 and 15 October 2012 and 14 October 2015 in the area surrounding Rome were analyzed. Some of these cases, and in particular those that occurred in 2012, were used in [9] to investigate the relation between the occurrences of lightning and the radar retrievals of integrated water content. For the sake of clarity, Figure 1 shows the interpolation of the rain accumulations registered on the Italian peninsula over a time interval of 24 h by local rain gauges for those three case studies. The P55C coverage is also shown to better highlight the studied area. In addition, Figure 2 and Figure 3 give a compact view of the rainy events seen by the P55C radar in terms of time series of quasi-vertical profiles of Z_hh, Z_dr, and K_dp and their temporal average, calculated using Equation (5), respectively. It follows a synthetic summary of the three events considered.

12 October 2012. This event, associated with a secondary trough over the central Mediterranean Sea, carried heavy precipitation mainly over the Lazio and Umbria regions on 11–12 October 2012. The storm started over the Tyrrhenian Sea, where several mesoscale convective systems developed during the night of 11 October. Convective systems reached central Italy in the early morning of 12 October, with heavy precipitation over the northern part of the Lazio and Umbria regions. The rain was not persistent, but the maximum cumulative rainfall registered exceeded 150 mm in 6 h (Figure 1a). The P55C radar was able to observe only part of the convective systems, mainly beyond 80 km from the radar site. In the last part of the event, the system moved to the south and farther away from the radar (100 km). The main activity developed between 03:15 UTC and 08:35 UTC, as shown in Figure 2, top left, where the time series of the quasi-vertical profile of Z_hh is shown. In terms of temporal averages of quasi-vertical profiles, Figure 3, top panels, shows the mixed nature of this event, with a stratiform rain regime at the beginning (labeled Time 1 in Figure 2 and Figure 3) with the typical pronounced peak of Z_hh just below the freezing level, lower values of Z_dr near zero close to the ground, and accompanied by low values of K_dp. Within the main phase (Time 2), the quasi-vertical profile of Z_hh moved to higher values with nearly constant behavior below the freezing level.

15 October 2012. This event took place on 14 and 15 October 2012 across a vast area in the western Mediterranean. The regional weather service issued a severe weather warning for central Italy and particularly for the city of Rome. The precipitation event was associated with a trough that deepened significantly over the northern Tyrrhenian Sea, pushed a frontal system eastward, and advected moist air from the Tyrrhenian Sea inland to fuel deep convection on the coast west of Rome. The synoptic scale system moved rapidly to the east and triggered a line of convection that crossed the western half of central Italy from north to south in a few hours. Most of the precipitation produced by this system occurred in the late afternoon of 15 October across the western part of central Italy and on the western slopes of the Apennines chain (Figure 1b). The main core of the event developed around 17:30 UTC, when a line of convective cells evolved quickly, then started to weaken after 19:00 UTC (Figure 2, middle left panel). The total rainfall amount recorded in Rome was less than had been predicted. The highest daily amount recorded within the historic area of Rome was modest and equal to 35 mm by operational rain gauge. This event is quite characteristic because it clearly shows a Z_dr tower during the core phase (Figure 3, middle center panel, “Time 2” curve). The time average profiles in Figure 3, middle panels, show the convective origin of this event and confirm the values of Z_dr larger than zero well above the freezing level.

14 October 2015. During October 14 and 15, 2015, strong thunderstorms accompanied by strong winds and heavy rain swept up several regions along central and southern Italy as well as the western and northwestern Balkans, causing floods and landslides across the affected areas. In central Italy, in the Lazio and Abruzzo regions, within the P55C radar coverage, authorities reported landslides and casualties caused by river overflow. In those regions, the extreme weather left three people dead and residents were evacuated for safety on 14 October 2015. A woman died in the town of Paliano near Frosinone after the car she was in fell into a crater that opened up due to flooding after torrential rainfall in the area. Closer to Rome, the Aniene River overflowed its banks at Tivoli, flooding homes and basements and driving some residents onto their roofs for safety. Official sources said 100 people were evacuated from the town of Canistro in the province of L’Aquila in the hills surrounding Rome after the Rio Spalto overflowed. The city of Rome was spared most of the bad weather, while surrounding towns and cities were mostly impacted. The single railway line connecting Rome and Cassino was taken out of action by a landslide. Local rain gauges registered peaks larger than 170 mm within 24 h (Figure 1c). This event was characterized by a severe convection phase with Z_hh maximum values up to 60 dBZ and vertical maximum extension up to 10–12 km, Z_dr values reaching 2 dB close to the surface and, at some times, extending with positive values over the zero temperature level and K_dp values around 2 deg/km (Figure 2 and Figure 3, bottom panels).

It is worth noting, as with all the case studies discussed here, that the shapes of the average vertical profiles were pretty similar to those found in [24] for convective and stratiform rain regimes. A particularly distinctive signature of such average profiles is noted for Z_dr and K_dp, which start sharply increasing just above the freezing level and below it, with different strengths probably depending on the degree of convection of the specific event. This characteristic shape can modify in the presence of Z_dr towers or ice crystal aggregation processes.

3.2. Radar System Specifications

The Polar 55C (P55C) is a research-grade C-band (working at 5.6-GHz carrier frequency, 5.35 cm wavelength) Doppler dual polarized coherent weather radar managed by the Italian CNR-ISAC. Differently from most commercial weather radar systems working with the transmission of simultaneous polarization, the P55C system was designed to operate with a polarization agility and single receiver scheme. This means that the total power is alternately transported by the horizontal and vertical polarized signals thanks to a fast switch that allows the transmitted polarization state to be changed on a pulse-pulse-basis. The reception of the horizontal and vertical polarized components alternate as well. This has a direct implication for the dual polarization variables (especially Z_dr), whose quality is expected to be higher than in the systems making use of simultaneous transmissions as the power transmitted is fully transferred to the two orthogonal polarization states.

Due to bus data transfer limitations in the signal processor compared with the number of bits used for encoding the radar variables and their required precision, the output quantities of P55C are only Z_hh, Z_dr, differential phase shift (φ_dp), and the Doppler velocity (V).

The P55C is located 15 km southeast of Rome (lat.: 41.8425 N deg, long.:12.6464 E deg, 102 m above sea level) on the roof of the ISAC-CNR. The receiver/transmitter apparatus is a fully coherent one. The transmitter is based on a klystron amplifier which allows for very high pulse-to-pulse and phase stability and uses a nominal peak power of 250 kW. For the data collected, considering PRF and antenna rotation speed, the radar measurements were obtained by averaging about 100 pulses transmitted with a 1250-Hz pulse repetition frequency in range bins spaced 75 m apart. The maximum unambiguous radar range was 120 km. The antenna geometry is a single offset type. This allows obtaining an increased radiation efficiency, avoiding beam blocking by stalls, which could both increase the cross-polarization level and cause differences in radiation patterns in the horizontal and vertical polarizations.

Nominal half-power beam widths are 0.92 and 1.02 deg in azimuth and elevation, respectively. The antenna is not protected by a radome and a direct implication is that we do not have limitations due to radome-induced effects (e.g., wet radome attenuation, azimuthal inhomogeneity, cross-polarization couplings). On the other hand, strong winds can make the antenna operations difficult and the pointing might not be accurate in windy situations. However, for the present study the core of the events analyzed was far enough from the radar most of the time, and the wind on the radar site did not cause particular issues. It is worth highlighting that P55C is a weather radar for research, which gives it a larger flexibility with respect to operating systems. For example, during the rain events, the schedules and the scanning strategies can be changed to optimize the observation capabilities.

3.3. Available Measurements and Settings for the Analyzed Case of Study

For the analyzed events the radar antenna elevation sweeps with respect to the horizontal were set to 0.6, 1.59, 2.61, 4.40, 6.20, 8.28, and 11.00 deg. They built up a radar polar volume that was delivered every 5 min. For the case studies, observations covered time windows from 06:55 UTC to 23:55 UTC, from 00:00 UTC to 16:00 UTC, and from 00:00 to 23:55 for a total of 193, 249, and 197 polar volumes for each acquired radar variable on 12 October 2012, 15 October 2012, and 14 October 2015, respectively.

Some range height indicators (RHI) and vertical pointing scans were also scheduled during 14 October 2015 to allow insights into vertical structures of precipitating systems and to deal with Z_dr calibration issues. Three sequences of RHI were performed. Sequence 1 includes RHIs at 13:11, 13:17, and 13:21 UTC for the 66 deg azimuth; Sequence 2 includes RHIs at 13:30 and 13:31 UTC for the 190 deg azimuth, and sequence 3 includes RHIs at 13:34 and 13:36 UTC for the 90 deg azimuth. Useful vertical scans were available from 08:10 to 08:14 UTC, for a total of 2160 vertical profiles.

Reference rain gauges were used for comparison with radar QPE. We used rain gauges delivered from the DEWETRA platform, a real-time integrated system for hydro-meteorological and wildfire risk forecasting, monitoring, and prevention. DEWETRA is developed by the CIMA research foundation and is fully operational at the Italian National Department for Civil Protection [34].

Among other information, DEWETRA collects and stores, on an hourly basis, most of the rain gauges of the local weather services in Italy. A total of 293 rain gauges fall in the P55C radar domain after discarding those stations that show anomalous isolated spikes in terms of hourly rain accumulation greater than 300 mm.

3.4. Definition of Complex Orography

The area covered by the P55C, as shown in Figure 1, is situated in a diversified environment in terms of variation of terrain altitude. This is a situation often referred to as complex orography. As far as the authors were able to ascertain, there is not a unique and objective definition of complex orography, especially in weather radar studies. Indeed, this is a concept that is often more driven by common sense than by rigorous definition. In this section, we want to make a contribution regarding the definition of a complex orography environment for weather radar studies. The first goal in the analysis of the complex orography environment is to define a new parameter that takes into account both the features of the terrain altitudes and the radar geometry of view. For this reason, we define a radar orography index (ROI). ROI can be useful, for example, for comparing different works dealing with QPE in complex orography, fostering a quantitative categorization of previous and future studies by the degree of complex orography seen by the radar.

The complexity of the orography can be described by the gradient of the terrain altitude (G_TA). However, G_TA alone does not take into account the radar perspective. For example, a radar system positioned on the top of a mountain or in a valley nearby will likely have different QPE performance although the surrounding environment does not change (i.e., G_TA is the same within the radar coverage domain). For this reason, we consider an additional term, which is the gradient of the radar beam altitude (G_BA). In this way we can define the gradient of the radar orography G_RO as follows:

$$G_{RO}(p)={\left[{\left(G_{TA}(p)\right)}^2+{\left(G_{BA}(p)\right)}^2\right]}^{0.5}={\left[{\left(\frac{{\Delta }_r{h}_{TA}(p)}{{\delta }_r}\right)}^2+{\left(\frac{{\Delta }_r{h}_{BA}(p)}{{\delta }_r}\right)}^2\right]}^{0.5}$$

(8)

where at each position p the operator ∆_rh_X is the difference of the altitudes h_X along with the radial direction, and where δ_r is the radar radial resolution. The symbol “X” stands for “TA” or “BA”, indicating the terrain altitudes and sampled radar beams altitudes with respect to sea level. Note that in flat terrain and when considering PPI (plan position indicator) acquisitions, G_BA coincides with the local tangent of the antenna elevation angle. In that special case, sampling at higher elevations produces higher G_RO. In general, the term G_BA increases G_RO as a function of the radar position and the sampling strategy adopted, (e.g., PPI or LBM: lowest elevation beam or VMI: vertical maximum intensity, etc.). A practical example that will be discussed later on will help to clarify this aspect. So far, Equation (8) is not general enough for practical use in different contexts. In order to constrain the dynamic of G_RO to the interval [0, 1] we use an exponential compression formula that allows defining the ROI as follows:

$$ROI=1-\exp (-b\cdot G_{RO})$$

(9)

In Equation (9) the coefficient b is chosen so that when G_RO reaches its maximum value, ROI = 1 (b = 1/max(G_RO)). However, to avoid having the few peaks of G_RO corrupt the ROI, we considered the 90th percentile (prc₉₀) of G_RO instead of its maximum (b = 1/prc₉₀(G_RO)).

For the P55C we calculated ROI assuming an ideal LBM product. The outcome of this calculation is shown in Figure 4a. Figure 4b shows a mask buildup by applying a threshold to ROI; that is, assigning 0 to positions having ROI >0.6 and 1 otherwise. This mask can be of some practical use for selecting portions of the radar coverage having a reduced impact of complex orography. Figure 4c shows the distribution of the ROI values, whereas in Figure 4d we have drawn average ROIs in two cases: an ideal case where the P55C is positioned at a virtual altitude of 200 m in its actual longitude and latitude position and the actual case, where it is at the altitude of 102 m. In addition, we added the curve of the terrain altitude index (TAI), which is calculated using Equation (9) when G_TA is considered instead of G_RO. These three curves highlight the sensitivity of ROI to the altitude of the radar position with respect to the surrounding terrain orography. In addition, the separation between ROI curves and TAI highlights the contribution of G_RO with respect to G_TA. In the result sections below, the mask in Figure 4b is used to evaluate the performance of QPEs in different portions of the P55C coverage domain.

4. Results

Results are shown in the form of comparisons of radar rain estimates vs. rain gauge accumulations for the three events studied here. The rain intensities derived from P55C radar, available on average every 5 min, are accumulated on hourly time scales and then are further summed on larger time window to produce multi-hour accumulations. To make the radar-derived rain accumulations temporarily consistent, we considered only those hours where all the 5-min volume acquisitions were available. In doing so, all radar hourly accumulations were made up by considering 12 radar volumes.

Equations (1)–(4) were used to perform estimations of rain rate intensities, R_q, using single and dual polarization measurements sampled at the lowest elevation beam (LBM), i.e., at positions p = p_LBM. In addition, Equation (7) was coupled with the four rain estimations in Equations (1)–(4) to carry out the adjustments related to the vertical variability of the rain precipitation and produce estimations at the positions of the ground levels, p = p_GRD. Equation (7) was used in combination with Equation (6) where h_m = 0 and the coefficients p₁ and p₂ are dynamically calculated at each time step. In this respect, Figure 5a,d,g, show an example of quasi-vertical profiles of rain estimates and its regression model VPR^mod as formulated in Equations (5) and (6), respectively. Figure 5b,c,e,f,h,i, show the statistical distribution of the coefficients p₁ and p₂, respectively, for the entire event. It is worth noting that despite the variability of the events, the coefficients p₁ and p₂ are quite stable in terms of average and standard deviation. As a first approximation, the average values of p₁ and p₂ can be used as constant parameters in Equation (6) to adjust the rain estimates aloft and produce estimates closer to those registered at the surface.

To pair the radar estimates and gauge observations, we considered the median of the values of radar hourly accumulations within a circular domain around each rain gauge position. Such choice should smooth the effects due to the time delay needed for the water to fall to the ground as well as the area to point mismatches between the two measurements. The ray of the circular domain is set to 5 km, consistent with typical values of drop fall velocity and horizontal movements of storms. Note that the P55C did not cover the 24 h with a constant time sampling. We limited the rain accumulations only to the hours where the radar variables were available every 5 min, as previously specified.

For an immediate comparison of the performances of the various rain estimators considered for all the events simultaneously, Figure 6 shows the total rain accumulation of the events on 12, 14 October 2012 and 15 October 2015. Actually, to make the comparison more homogeneous and highlight the differences among the various QPE algorithms, we considered the values of the total rain accumulations from the radar at the positions of the rain gauges and then we interpolated them on the radar domain. The same was done for the total accumulations from rain gauges. As can been seen from the rain gauge accumulations (Figure 6a) the heaviest precipitation was accumulated mainly inland in the eastern area with respect to the radar position, where terrain altitude variations are more pronounced (Figure 6d). Over all, from this figure a qualitative ranking of the rain estimation algorithm can be done. Looking at the middle column of panels, where the total accumulations of R_q(p_LBM) are shown, we can see R_Z(p_LBM) behaves most poorly, with large underestimations (Figure 6i). A large improvement occurs when using R_K(p_LBM), which seems to correctly represent the area of heavy precipitation (Figure 6g). When introducing Z_dr; i.e., when using R_DR(p_LBM), (Figure 6e), we have a small improvement with respect to R_Z(p_LBM) but we still register an appreciable underestimation compared to R_K(p_LBM). Finally, when combining all R_K and R_DR into a single rain estimator, R_KZ(p_LBM), (Figure 6b), we have something that is more consistent with the rain gauges with respect to using R_K(p_LBM) alone. On the other hand, when applying the quasi-vertical profile adjustment (panels in the right columns of Figure 6) we have an increase of rain precipitation values for all the implemented estimates and a more qualitative agreement with rain gauges, especially in the tendency to represent the maxima of accumulated precipitation (compare, for example, Figure 6g,h with the reference Figure 6a). A confirmation of this is given in the example shown in Figure 7, where a zoomed version of R_KZ(p_LBM) and R_KZ(p_GRD) is displayed for the case of 14 October 2015. This figure can be particularly informative in the light of combined radar and rain gauge products. Indeed, in these merging approaches and in particular for those that make use of the Kriging methodology, the spatial structure of the rain field from radar, usually described in terms of spatial covariance or variogram, is used to train the interpolation algorithms [35]. As is evident in Figure 7, the spatial structure of rain precipitation fields changes depending on the effect of the spatial adjustment performed (quasi-vertical profile adjustment in our case), and this effect can cause variations in the final results of the combined radar vs. rain gauge products.

To complete the examination of the results, Figure 8 shows rain estimator comparisons in terms of total accumulations of radar vs. gauge scatter plots for all the events. Although we note the presence of a significant number of mis-detections (i.e., rain gauge registers rain whereas the radar does not register it), it seems that the use of K_dp is a key factor when estimating rain in complex orography environments, whereas the use of quasi-vertical profile adjustment is able to partially compensate for the overall bias, although the differences in this case can be subtle. For example, note the distribution of sample pairs around the reference 1:1 line and the error scores discussed below. On the other hand, the estimated precision (the variability of the estimates around the 1:1 line) seems to not get a strong benefit from the application of quasi-vertical profile adjustments.

In terms of spatial averages of rain accumulations over time, a clear performance evaluation is shown in Figure 9 for each case study. Figure 9a,c confirms the best performance of R_KZ(p_GRD) (red dashed line, which shows the results closest to the blue curve of the rain gauge total accumulation). On the contrary, for the case on 15 October 2012 (Figure 9b) we have a different outcome, with quite a large overestimation of R_DR(p_GRD) and R_KZ(p_GRD) and the best performance obtained when considering R_Z(p_GRD) or R_K(p_GRD). Finally, it is worth noting that the performance of the K_dp-based rain estimator depends to some extent on how it is retrieved. In particular, Figure 9d, shows the performance of R_KZ(p_LBM) as a function of four thresholds used (K_{dp_min}) for the retrieval of K_dp as specified in the figure legend for the case study on 14 October 2015. See Appendix A and Figure A3 for more details on the filtering of the differential phase shift (φ_dp) and K_dp estimation. For the analyzed cases we used K_{dp_min} = −1.5 deg/km, which seems to be a reasonable choice in terms of φ_dp filtering.

Looking at more quantitative results,

Table 2. Scores of the radar vs. rain gauge daily accumulations on 12 October 2012. K_dp__min = −1.5 deg/km. The best value in each row is in boldface. The error scores are defined in Appendix B *.

Score s, Alg. q	RqLBM = R(pLBM)				RqGRD = R(pGRD)				RqAF = AF×RqLBM				<100×[sGRD − sLBM]/sLBM>
	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	ROI ≤ 0.6	ROI > 0.6
RMSE	18.32	16.31	18.30	12.55	15.82	13.41	15.83	12.08	27.90	17.89	23.06	15.12	−9.85	−21.07
NSE	0.82	0.73	0.82	0.56	0.71	0.60	0.71	0.52	1.25	0.80	1.03	0.68	−8.48	−21.06
NB	−0.37	−0.40	−0.34	−0.03	0.03	−0.12	0.03	0.04	0.57	−0.01	0.42	0.19	−146.26	−52.50
CC	0.65	0.77	0.65	0.81	0.69	0.79	0.69	0.79	0.80	0.78	0.79	0.84	+1.80	+1.60

* Root Mean Square Error (RMSE) is in (mm), the last two columns are in (%) whereas the other values of Normalized standard Error, Normalized Bias and Correlation coefficient, indicated by NSE, NB and CC, respectively, are dimensionless. The last two columns list the average score variation of R(p_GRD) with respect to R(p_LBM) when the radar scene is partitioned using the radar orography index (ROI). The label “s” indicates one of the score index in the first column.

,

Table 3. As in Table 2 but for 15 October 2012.

Score s, Alg. q	RqLBM = R(pLBM)				RqGRD = R(pGRD)				RqAF = AF×RqLBM				<100×[sGRD − sLBM]/sLBM>
	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	ROI ≤ 0.6	ROI > 0.6
RMSE	16.24	14.67	16.23	14.57	15.65	14.63	15.91	18.84	17.39	15.81	16.47	15.04	1.82	−14.33
NSE	0.87	0.78	0.87	0.78	0.83	0.78	0.85	1.01	0.93	0.84	0.88	0.80	2.48	−14.18
NB	−0.52	−0.32	−0.52	−0.15	−0.13	0.03	0.07	0.39	0.02	0.03	−0.06	−0.05	−124.00	−42.61
CC	0.31	0.32	0.31	0.30	0.26	0.32	0.27	0.29	0.34	0.32	0.34	0.31	−7.0	−14.01

and

Table 4. As in Table 2 but for 14 October 2015.

Score s, Alg. q	RqLBM = R(pLBM)				RqGRD = R(pGRD)				RqAF = AF×RqLBM				<100×[sGRD − sLBM]/sLBM>
	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	RZ	RK	RDR	RKZ	ROI ≤ 0.6	ROI > 0.6
RMSE	28.07	19.07	22.11	17.60	23.79	18.26	19.37	17.22	22.45	19.31	23.02	18.26	−9.00	−12.20
NSE	1.12	0.76	0.88	0.70	0.95	0.73	0.77	0.68	0.89	0.77	0.92	0.73	−8.90	−11.40
NB	−0.69	−0.32	−0.49	−0.23	−0.52	−0.19	−0.30	−0.04	−0.45	−0.04	−0.49	−0.31	−57.18	−14.92
CC	0.73	0.81	0.79	0.84	0.77	0.82	0.80	0.84	0.76	0.82	0.76	0.83	+1.85	+3.65

list the root mean square error, the normalized standard error, the normalized bias, and the correlation coefficient, labeled as RMSE, NSE, NB, and CC, respectively, and defined in Appendix B, for the various rain estimators implemented for the three case studies. In these tables we also included the error scores obtained when applying a gauge-bias adjustment factor (AF) to R_q(p_LBM) since many operational QPE algorithms use a gauge-bias correction procedure to fold all of the error sources that compromise the QPEs. Basically, AF is an average ratio of rain gauge accumulations with respect to those from radar estimates as a function of the distance from the radar. We described AF using an exponential law and derived its regression parameters for each of the R_q(p_LBM) algorithms in Equations (1)–(4) by considering the three case studies together. In addition, the right column in each table lists the average relative improvement between R_q(p_LBM) and R_q(p_GRD) when they are evaluated for two distinct parts of the radar domain: the domain where ROI ≤ 0.6 (lower degree of complex orography) and ROI > 0.6 (higher degree of complex orography).

From the tables, we note that there is a maximum improvement of approximately 20% in terms of root mean square error (RMSE) when applying a quasi-vertical profile adjustment on an R_Z estimator (i.e., when moving from R_Z(p_LBM) to R_Z(p_GRD)), although the increment was as low as 4% in the case on 15 October 2012 (Table 3). The biggest improvement, as noted previously, is made when using R_K. In this case, the improvement from R_Z(p_GRD) to R_K(p_GRD) is between 18% and 30%, with the exception of 15 October 2012, where the improvement reaches only 7%. The combined rain estimator, R_KZ, gives a further small improvement between 6% and 10% with respect to R_K(p_GRD) and between 30% and 38% compared to R_Z(p_GRD). Even in this case, the only exception is given by the performance obtained on 15 October 2012 that register a deterioration of R_KZ(p_GRD) with respect to the other estimators when quasi-vertical profiles are used. Actually, the strongest improvement brought by the use of quasi-vertical profile adjustment seems to be in terms of normalized bias, with results significantly reduced by a factor larger than 25% when moving from R_Z(p_LBM) to R_Z(p_GRD) and from R_KZ(p_LBM) to R_KZ(p_GRD) on 12 and 15 October 2012.

In terms of the adjustment factor (AF), its impact is to increase the correlation coefficient a little bit and in some cases to reduce the bias, but at the same time to produce larger RMSEs. On the other hand, when partitioning the radar scene in the regions most affected by the complex orography (ROI > 0.6) by those with lower complexity (ROI ≤ 0.6), we find that the impact of quasi-vertical profile adjustment is, in most of cases, larger (i.e., more negative) than that in the areas with lower complex orography, as expected. Note that ROI is correlated with QPE; that is, larger ROI corresponds, in most of cases, to larger RMSE. However, to maintain a reasonable size for Table 2, Table 3 and Table 4 we did not list all the error scores as a function of ROI. To have an idea of the correlation of ROI with the RMSE when all the QPE algorithms with no correction are considered, we list the average, standard deviation, and maximum RMSE for ROI ≤ 0.6 and ROI > 0.6, (18.37, 3.80, 27.41) and (25.92, 14.41, 53.67), respectively.

5. Discussion

From the results just presented one notable aspect is an ambiguity in the interpretation of the results regarding the identification of the best robust rain estimator among the various case studies. In most of the analyzed cases in this study, the combined R_KZ with the use of quasi-vertical profile adjustment seems to perform better than the others, although an exception exists. Recent literature on QPE studies seems to be more oriented toward a combination of various QPE algorithms whose choice can guided by information related to the type of precipitation [22,26,27]. In this respect, the concept of adjusting rain estimates using quasi-vertical profiles of rain, VPR, as introduced in this work can add to the existing techniques. The advantage of using quasi-VPR is that it allows adjusting rain estimates from its vertical variability in a direct and self-consistent way. However, complications in using quasi-VPR can arise because its variability reflects that of the QPE algorithm used. In other words, the shape of the VPRs depends on the specific QPE algorithm used, and a characterization of the VPR for each QPE algorithm would be needed. For example, we expect that a VPR obtained considering R_K will have a lower negative slope than R_Z in the ice part given the typical values of Z_hh and K_dp in the ice region. Then, an ideal procedure that used VPRs and a combination of several QPE algorithms should address this issue. On top of this, the co-existence of different types of precipitation in different radar domains adds complexity to the procedure because a single VPR is unlikely to represent the entire radar scene. Thus, a more sophisticated VPR retrieval would require the separation of the observed radar scene in areas of different precipitation types. Then, for each of those areas we should identify a characteristic VPR and apply the adjustment separately. This lack of further sophistication is probably responsible for the larger errors found when applying the VPR adjustment for the event on 15 October 2012. In that case, another aspect to highlight is the fact that the QPE algorithms we are using do not take into account peculiar situations such as, for example, Z_dr columns. For this reason, in general, caution is needed when dealing with QPE algorithms that are based on Z_dr. A last issue that would need to be addressed when dealing with quasi-vertical profiles is that they are “apparent” (i.e., they are the result of the antenna pattern convolution with the actual unknown measured quantity) and obtained using slant observations. This consideration is open to the possibility of further refinement, which should include the identification of the actual VPR using deconvolution techniques [36] and estimation theory e.g., [37].

6. Conclusions

This work analyzed three case studies of heavy rain precipitation in Italy that affected the Roman area and caused damage and three casualties, as reported by local news. The C-band dual polarization radar Polar 55 C (P55C), managed by the Institute of Atmospheric Sciences and Climate (ISAC) at the National Research Council of Italy (CNR), tracked the events. The work focused on two aspects scarcely considered by past studies on radar rain estimation: (i) a proposal to objectively define the complexity of an orography scenario with respect to the radar standpoint; and (ii) an evaluation of the benefit brought by the vertical profile extrapolation when using dual polarization QPE algorithms. P55C coverage is well suited to pursue these goals because it includes quite flat regions as well as a part of the Apennine chain with terrain peak altitudes higher than 1500 m and a difference in the P55C radar lowest available bin altitudes and gauge stations of 1240 m on average, with maximum values up to 6 km.

The comparison of radar QPE with rain gauge accumulations indicates that the combined algorithm, which merges together, through a weight factor, the differential phase shift K_dp, the single polarization reflectivity factor Z_hh, and the differential reflectivity Z_dr, once accurately post-processed, performs better in most of the cases tested than those that make use of Z_hh alone, K_dp alone, and Z_hh and Z_dr. An improvement larger than 25% is found in terms of normalized bias when applying VPR extrapolations to Z_hh-based QPE and to the combined QPE algorithm. Many limited improvements are registered in terms of root mean square errors because the error standard deviation probably accounts for most of the discrepancies registered between radar QPE and reference rain gauge.

An additional aspect that emerges from the analysis is that the quality of the K_dp estimates, through its filtering, has an impact on the performance of the QPE algorithms, although this impact is less significant when the combined algorithm is considered. In addition, in one case analyzed, where we observed Z_dr columns we found that the VPR adjustment produced quite large overestimations, leading us to conclude that methods based on Z_dr can worsen the final results if we do not apply any special care in the preprocessing step as well as in the QPE algorithms.

Although further and more robust analysis in terms of statistical significance will be needed to corroborate our findings and validate our methodology, the results of this work point to a possible operational way to improve the radar QPE algorithms based on dual polarization variables in complex terrain. Future work could be focused on the systematic collection of a considerable number of case studies with different precipitation types from other radar systems in Italy to validate the VPR approach.