Rainfall radar observations in the U.S. VORTEX-SE campaign: VAM correction of Doppler spectra to improve data quality

Rainfall radar observations in the U.S. VORTEX-SE campaign: VAM correction of Doppler spectra to improve data quality. A Bachelor’s in Science Thesis Submitted to the Faculty of the Escola Tècnica d’Enginyeria de Telecomunicació de Barcelona, Universitat Politècnica de Catalunya by Paula Domínguez Pla In partial fulfillment of the requirements for the degree of Bachelor’s in Science in Engineering Physics Advisors: Sr. Andreu Salcedo Bosch Prof. Francesc Rocadenbosch Burillo CommSensLab Departament de Teoria del Senyal i Comunicacions Universitat Politècnica de Catalunya Barcelona, June 27, 2022 Acknowledgements This work was supported via Spanish Government–European Regional Development Funds project PGC2018-094132-B-I00 and H2020 ACTRIS-IMP (GA-871115). CommSensLab isa María-de-Maeztu Unit of Excellence funded by the Agencia Estatal de Investigación (Spanish National Science Foundation). VORTEX-SE project supported the measurement campaigns. VORTEX-SE project was supported by the NOAA grants NA1501R4590232 and NA16OAR4590209, and by the Purdue University Dept. of Earth, Atmospheric, and Planetary Sciences (EAPS). CommSensLab-UPC collaborated via the projects above. The University of Massachusetts, Microwave Remote Sensing Lab. and Purdue University, EAPS, deployed the mobile S-band radar, co-located Vaisala CL-31 ceilometer, and portable disdrometers. The NOAA National Severe Storms Lab. deployed the Collaborative Lower Atmosphere Mobile Profiling System during VORTEX-SE. iii I would like to manifest my deepest gratitude to Prof. Francesc Rocadenbosch for accepting to supervise this thesis and for dedicating part of his time to guide me through this journey. Above all, I would be delighted to thank Andreu Salcedo most sincerely for helping me whenever I needed it, no matter the time or the issue. Also for his supervision of my work. On the other hand, I would also like to thank my colleagues who have accompanied me throughout these four years, from whom I have learned both professionally and personally. And finally, to my family, who have helped me and encouraged me to keep on going and to be the best version of me. v Abstract This BSc thesis has been carried out as a part of CommSensLab-UPC research. We present research on two methods to estimate the Vertical Air Motion (VAM) velocity by comparing rainfall observations from two different sensing instruments: an S-band radar and a ground-based disdrometer during the Verification of the Origins of Rotation in Tornadoes Experiment-Southeast (VORTEX-SE). Different rain events are studied to assess the effects of unor mis-correcting the radarmeasured rainfall velocity for VAM. Once VAM effects are identified, the VAM velocity is estimated by means of two different approaches: The first approach is a rain-rate-matching method based on a constrained parametric solver that assumes high correlation between 5-min-averaged rain rates (RR) measured by the radar and the disdrometer. The grounds of the method is to compare the radarretrieved RR at different reference heights with the disdrometer-retrieved RR at ground level. Consistency of the method is discussed in terms of the collection of drops, their size distributions and height-time history. The second approach is an inverse method (so called ”forward” method) relying on parameterization of the drop size distribution (DSD) as a gamma distribution. This method estimates the VAM along with the shaping parameters of the raindrop distribution by using a non-linear least squares procedure. The radar-measured 2nd-order products obtained after VAM correction are crossexamined with those from the ground-level disdrometer in the framework of selected observations during Intense Observation Periods from VORTEX-SE conducted in northern Alabama. The advantages and disadvantages of each of the methods in terms of VAM estimation are discussed. In general terms, the quality of radar-retrieved 2nd-order products is improved after VAM correction, proving the validity of VAM estimations by both methods. vii Contents Acknowledgements iii Abstract vii Contents ix List of Acronyms xi List of Figures xiii List of Tables xv 1 Introduction 1 1.1 Rain Measurement and Vertical Air Motion ................. 1 1.2 Main Objectives ................................. 2 1.2.1 Objective 1: Identification and classification of rain events . . . . . 3 1.2.2 Objective 2: Rain-rate-matching method for VAM estimation. . . . 3 1.2.3 Objective 3: Forward method for VAM estimation. ......... 3 1.3 Organization of the Bachelor Thesis ...................... 3 2 Remote Sensing Instrument Foundations 5 2.1 Radar Foundations ............................... 5 2.2 Radar types and principles ........................... 5 2.2.1 FMCW radar fundamentals ...................... 7 2.3 FMCW radars in precipitation measurement ................. 9 2.3.1 Radar first and second order products ................ 9 2.3.2 Drop Size Distribution Characterization ............... 10 2.3.3 Vertical air motion influence on radar second order products . . . . 11 2.4 Disdrometer types and principles ....................... 13 2.4.1 Optical disdrometer fundamentals ................... 13 2.4.2 Optical disdrometer measurement of first and second order products 14 3 VORTEX-SE Campaign 15 3.1 Instruments ................................... 15 3.1.1 UMass FMCW Radar ......................... 15 3.1.2 OTT PARSIVEL2 Disdrometer .................... 16 ix Chapter 1 Introduction This chapter gives an overview of the state of the art of rain radar measurements and the correction of vertical air motion. Next, it motivates the BSc thesis and presents its organization and objectives. 1.1 Rain Measurement and Vertical Air Motion Radars and disdrometers have been widely used to measure precipitation processes in the atmospheric boundary layer [Rogers (1984); Doviak et al. (2006)]. Disdrometers are usually ground-based instruments that measure rain-related parameters based on a dropcounting procedure [Acharya (2017)]. They are able to retrieve the drop size distribution (DSD) and other rain-related parameters by recording the raindrop counts for different sizes and falling velocities. However, disdrometers are not able to give information on the vertical variations of precipitation and are limited to ground-level measurements. Microwave frequency radars are mostly unaffected during precipitation, and hence, they are an excellent candidate in order to reveal details regarding remote precipitation microphysical processes [Tanamachi et al. (2019)]. Depending on the carrier frequency, there is a compromise between attenuation at strong rain scenarios, and small hydrometeor detection [Kollias et al. (2007)]. Among the distinct radar technologies available, S-band (∼10 cm) Frequency-Modulated Continuous Wave (FMCW) radars have been used for more than 40 years as they are unaffected by rain attenuation and are able to monitor the atmospheric boundary layer in both clear air and precipitation scenarios [İnce et al. (2003); Tanamachi et al. (2019)]. Vertically-pointed S-band FMCW radars with high spatial and temporal resolution permit an accurate monitoring of precipitation vertical profiles [İnce et al. (2003)], offering excellent capabilities in precipitation remote sensing. Particularly, they allow the derivation of key rain second-order parameters such as the DSD, rain rate (RR) and reflectivity factor (Z), among others [Doviak et al. (2006)]. Second order parameters are estimated from the radar Doppler spectrum by assuming that rain drops are Rayleigh scatterers that fall at their terminal fall velocities, which are determined by the drop diameter. However, in practice, the Doppler spectrum is affected by the ambient vertical air motion (VAM) [Garcia-Benadi et al. (2020)], which arises as a radar-measured spectrum shift in the velocity axis. In presence of large VAM, such as in convective rain events, radar-derived DSD and 2nd order parameters may be corrupted [Lhermitte (1988)]. Therefore, given the Doppler spectrum as a function of height, it requires a height-dependent VAM correction. 1 The VAM estimation and correction from stand-alone Doppler radar measurements has been of interest since the beggining of radar usage in precipitation measurement [Hauser and Amayenc (1981)]. Lhermitte (1988) proposed a method to differentiate VAM and raindrops terminal velocity in W-band (λ= 3.2mm) radars by assuming Mie scattering. The VAM is determined by comparing the observed spectrum to a predicted spectrum assuming no VAM. However, this is only feasible for very-short wavelengths. Hauser and Amayenc (1981) proposed a fitting method in which the DSD was assumed to be with an exponential form characterised by two parameters (Marshall-Palmer distribution). This methodology optimised the best fit between the theoretical spectrum retrieved from the DSD model (shifted by VAM) with respect to the experimental spectrum observations. However, it required exponentially distributed size distributions and it is not suited for convective rain scenarios. More recently, Tridon et al. (2011) proposed a VAM-correction method by shifting the radar-measured spectrum to maximise the correlation with a noVAM scenario. Rocadenbosch et al. (2020) proposed a VAM estimation method based on the correspondence between Z-RR measurements with three different Z-RR models. It consisted on a trial-and-error procedure in which the radar-measured spectrum was shifted until Z-RR relationship matched theoretical models. A similar approach was proposed by Kim and Lee (2016), which resorted to radar reflectivity empirical relationships as well to estimate the VAM and then unshift the spectrum. However, they require user expertise in rain radar observations for an accurate correction. In contrast, here we explore two different methodologies based on numerical methods and cooperative measurements to estimate and correct for VAM. In order to test and validate the methods presented, experimental data measured during intensive observation periods (IOPs) in the context of Verification of the Origins of Rotation in Tornadoes Experiment-Southeast (VORTEX-SE) is used. Particularly, measurements from 2016 and 2017 by a vertically-pointed S-band FMCW radar and a ground-based disdrometer are used. 1.2 Main Objectives The aim of this thesis is to combine measurements from a radar and a disdrometer in order to estimate and correct for VAM in atmospheric boundary-layer radar measurements of rainfall events. The specific objectives of the project are: • Objective 1: Identification and classification of rain events. Identification of rain events on radar-measured data during IOPs from VORTEX-SE 2016 and 2017 campaigns. • Objective 2: Rain-rate-matching method for VAM estimation. Estimation of VAM at heights close to the ground by fitting radar-retrieved DSD measurements to ground-based disdrometer DSD measurements taken as reference. • Objective 3: Forward method for VAM estimation. Estimation of the VAM from stand-alone radar measurements relying on consistency of the forward-propagated DSD to the retrieved radar products. Ground-based disdrometer measurements are to be used as a reference. The methodologies presented in this manuscript have been tested and validated over experimental data gathered during IOPs from the VORTEX-SE 2016 and 2017 campaigns in the US. 2 1.2.1 Objective 1: Identification and classification of rain events The identification of rain events from radar measurements in VORTEX-SE campaigns is challenging due to the fine temporal and spatial resolution of the UMASS S-band radar. The huge amount of data gathered during IOPs is to be analyzed and filtered in order to spot relevant rain events. Moreover, the identified rain events are to be manually classified into VAM and no-VAM events in order to create a study database on which to test the different methods proposed. 1.2.2 Objective 2: Rain-rate-matching method for VAM estimation. In the absence of VAM, high correlation is observed between the RR measurements of a ground-based disdrometer and those from a FMCW radar at 500-m height when considering 5-min average ensembles. However, in the presence of VAM, the radar-measured Doppler velocity spectrum becomes shifted and, as a result, the radar-measured RR is corrupted and shows discrepancies as compated to ground-based RR measurements. Obj. 2 aims to find a method to solve for the necessary Doppler spectrum shift in order to match the radar-measured RR to the reference disdrometer RR. Towards this purpose, the rain-rate-matching method based on a non-linear least squares technique is used. 1.2.3 Objective 3: Forward method for VAM estimation. Usually, the DSD is characterised in the literature as a Gamma distribution Doviak et al. (2006), which is parameterised by three constitutive or shape parameters. At the same time, the measured radar reflectivity density can be derived from the DSD. Moreover, VAM effects (on average value) on the radar reflectivity density can essentially be easily modelled as velocity shift in the Doppler velocity spectrum. Obj. 3 aims at estimating the VAM velocity shift from stand-alone radar measurements by means of an inverse method: the so-called forward method. Towards this purpose, a forward model emulating the radar measurement process (DSD into rainfall data products) is presented. The results obtained with this method are cross-examined with ground-based disdrometer measurements. 1.3 Organization of the Bachelor Thesis This thesis is divided into six chapters: • Chapter 1 provides the theoretical background and motivates the Bachelor thesis by presenting the state of the art on VAM correction on radar measurements. • Chapter 2 gives the radar and disdrometer foundations as well as the influence of VAM on radar measurements. • Chapter 3 presents VORTEX-SE 2016, and 2017 experimental campaigns sustaining the methods developed in this thesis. 3 • Chapter 4 addresses Obj. 1 on the identification and classification of rain events. Here, a series of selected rain events from VORTEX-SE campaigns are depicted and analyzed in qualitative terms. They are classified in stratiform and convective rain events. • Chapter 5 tackles Obj. 2 on the development of a direct method for VAM correction. The rain-rate-matching method for VAM estimation based on the fitting of radarmeasured RRs to disdrometer-measured RRs is presented. • Chapter 6 addresses Obj. 3 on the development of an inverse method for VAM estimation. The so-called forward method based on the assumption of the DSD as a gamma distribution is presented. Performance of the methodology presented is analysed by comparison to the ground-based disdrometer reference. • Chapter 7 gives concluding remarks and future lines. 4 Chapter 2 Remote Sensing Instrument Foundations This chapter gives the foundations of the remote sensing instruments used in this project: a radar and a ground-based disdrometer. Their types and functioning principles are presented as well as the rain products that they measure. 2.1 Radar Foundations ARAdio Detection And Ranging (RADAR) is a device employed to detect and locate a target by means of radio waves [Nature (1943)]. Radars transmit frequency-modulated electromagnetic (EM) beams in order to illuminate a target, and as a result, a fraction of the transmitted beam of energy bounces on the target and is received again by the radar with a delay. By comparing the received echo with the transmitted signal, significant information about the target such as its range and velocity can be extracted. They first appeared in the 20th century and experienced substantial changes with technical improvements in electronics and EM waves transmission. They were first used for atmospheric sounding and precipitation detection in the 1940s [Doviak et al. (2006)]. In the meteorology context they have a wide range of applications: from precipitation measurement/typing to temperature profiles measurement. 2.2 Radar types and principles Radars can be classified into different categories depending on its characteristics such as the carrier wavelength, the type of the transmitter and receiver antennas, the modulation used, etc. The main typing considered for radar typing is based on its wave-form and functioning principle: they can be pulsed radars (PR) or continuous wave radars(CW). PRs are based on the time-of-flight of EM pulses whereas CW radars emit continuously and are based in Doppler frequency shifts. Pulsed radars emit a train of frequency modulated pulses. They send high-power and high-frequency pulses towards the target object. Then, the echo signal from the target is received by the radar usually by the same transmitting antenna. The distance to the target (or range) can then be determined from the measurement of the pulse time-offlight by measuring the time span between the transmitted pulse and the echo. Moreover, the velocity of the illuminated target can be measured by means of the Doppler Effect. 5 This is, if the target is moving, the received signal will suffer a frequency shift due to the Doppler effect and by measuring the frequency shift between the transmitted and received signals, one may measure the target velocity. This is formulated as fd=−2f0 cvr,(2.1) where fdis the Doppler frequency shift due to motion between the received signal frequency, fr=f0+fd, and the carrier frequency, f0, and vris the radial velocity of the target relative to the radar (vrpositive when moving away from the radar) and cis the speed of light. Continuous wave radars emit a continuous EM wave and usually use separate antennas to transmit and receive the signals. CW radars do not measure the target range but rather the rate of change of the target range by measuring the Doppler shift of the return signal. If the received echo has the same frequency, the object is not moving. In case the target is moving, the receiving frequency will be different from the emitted frequency and, therefore, its velocity can be calculated by means of the Doppler effect equation, (see Equation 2.1). The main drawback of this type of radar is that it cannot measure distance, as it does not have a timing mark. CW radars without modulation can accurately measure target radial velocity (due to Doppler shift) and angular position. However, to extract range information, it is necessary some form of modulation due to the lack of pulses (Mahafza,2004). This is solved in frequency-modulated continuous-wave (FMCW) radars, where the lack of a timing mark issue is solved by adding a frequency modulation to the continuous wave. FMCW radars functioning principle is explained in detain in subsection 2.2.1. Additionally, radars can be divided into several different categories according to its operating frequency range. In Table 2.1 below, the main frequency bands are listed. Letter description Frequency Range (GHz) HF (High Frequency) 0.003 – 0.03 VHF (Very High Frequency) 0.03 – 0.3 UHF (Ultra High Frequency) 0.3 – 1.0 L-band 1.0 – 2.0 S-band 2.0 – 4.0 C-band 4.0 – 8.0 X-band 8.0 – 12.5 Ku-band 12.5 – 18.0 K-band 18.0 – 26.5 Ka-band 26.5 – 40.0 MWF (millimeter) >34.0 Table 2.1: Radar frequency band classification (Source: [(Mahafza,2004)]) The choice of frequency depends on the application requirements. Smaller antennas are suitable for higher operating frequency, and thus, lower wavelength. The range of the radar system is also influenced by the choice of frequency. Higher-frequency systems are able to measure smaller targets, but suffer higher atmospheric attenuation [Parker (2010)]. 6 2.2.1 FMCW radar fundamentals FMCW radars have been used to monitor the atmosphere for more than three decades due to their high spatial and temporal resolution (İnce et al.,2003). Particularly, they have been used in the detection of precipitation vertical profiles as well as clear-air echo. Figure 2.1 depicts the FMCW radar functioning principle. FMCW radars use a frequency-modulated signal with sweep period T(continuous trace in Figure 2.1 superior panels), and sweep frequency bandwidth B, which enable the measurement of distance and radial velocity of a target. Radiation is emitted vertically into the atmosphere where a small portion is scattered back to the antenna from meteorological targets. The backscattered signal (dashed trace in Figure 2.1 superior panels) will be delayed ∆t= 2r/c seconds, where cis the speed of light in meters per second and ris the range to target in meters. Due to the time delay of the echo, the frequency difference ∆fbetween the transmitted and received beams (Figure 2.1 inferior panels) is proportional to the range of the target. The frequency difference is obtained as ∆f= 2 B Tcr. (2.2) To measure the frequency difference, radar echoes are mixed with a copy of the transmitted signal and then are low-pass filtered, yielding a beat frequency that indicates the range of the target (see Equation 2.2). All targets can be sorted in range by applying a Fourier transform to the recorded beat data. As shown in Figure 2.1 a), with static targets, the frequency difference is ∆f. In case the target is not stationary, the echoed signal (dashed trace in 2.1 b) superior panel) will be both delayed and Doppler-shifted (due to the target velocity), being the frequency shift proportional to the velocity according to the Doppler effect (see Equation 2.1). Therefore, the frequency difference between the transmitted and received beams (Figure 2.1 b) inferior panel) consists of two contributions (METEK Meteorologische Messtechnik GmbH,2009), i.e., the range term and the velocity term, which can be formulated as ∆f= 2 B Tcr±fd,(2.3) where fdcorresponds to the Doppler frequency shift due to the target’s velocity (see Equation 2.1). As it can be observed in Figure 2.1 b), a small Doppler frequency shift is observed at the end of the frequency sweep with respect to the static case, i.e., ∆f−fd. On the other hand, a larger shift is observed at the begining of the frequency sweep, i.e., ∆f+fd. Therefore, in presence of moving targets, an ambiguity between range and velocity appears. To solve this ambiguity, Barrick (1973) proposed a method based on a double Fast Fourier Transformation (FFT) that can be used to produce a time-delay (range) and Doppler (velocity) display of the radar target data. This procedure is illustrated in Figure 2.2. First, the beat frequency signal as a result of one radar pulse (period T) is Fourier-transformed. Towards this purpose, the beat signal is sampled Mtimes during period T, leading to M/2complex samples in the frequency domain. These complex samples correspond to M/2range bins, with a frequency difference of 1/T between bins (see Figure 2.2 a)). Therefore, the range information is obtained, but the target velocity information is still to be retrieved. The radar repeats the same procedure for Nradar 7 (a) Stationary targets (b) Moving targets Figure 2.1: Working principle of FMCW radar. Time-series of the radar transmitted and received signals and the frequency shift between them. (Source: [Wang (2017)]). (a) 1st FFT of a single pulse of period T (b) 1st and 2nd FFT of a npulses of period T Figure 2.2: FMCW radar double FFT procedure. (Source: [METEK Meteorologische Messtechnik GmbH (2009)]). (a) First FFT of signal period Tto get the range. Arrows represent the phase. (b) Scheme of double FFT prodecure for a signal of duration nT. 8 pulses, obtaining a complex matrix of dimension M/2×N. Each complex vector stored in a matrix row mis then representative of the temporal evolution of the targets during an nT period at range m. Therefore, each row mcan be considered as a temporal series, with each complex sample nrepresenting a digital sample of the temporal series. As observed by Barrick (1973), there is virtually no amplitude change within a range gate, i.e., within a row. Therefore, velocity information is contained in the phase. In order to obtain the velocity component, a second FFT is carried out over each row m. The resultant spectrum corresponds to the Doppler shift spectrum at range gate m, from which the velocity spectrum can be derived by means of Doppler equation (Equation 2.1). In Figure 2.2 b) a radar measurement example is depicted, with M/2 = 10 range gates obtained for N= 8 different radar pulses. In this example, the radar observes targets at range gates 3 and 4, whose temporal evolution uncover a velocity component corresponding to a fn/4Doppler shift. 2.3 FMCW radars in precipitation measurement 2.3.1 Radar first and second order products In the context of meteorological radars, the transmitted wave is reflected by different meteorological targets. Here, we focus exclusively on raindrops, the sizes and shapes of which are diverse. Drops of small diameters (D<0.35 mm) are mainly spherical. Larger drops are progressively flattened, having the largest a high probability of breaking up into smaller fragments (Doviak et al.,2006). On the other hand, smaller droplets unite on collision when slightly electrified. The growth of big drops and the loss of small ones are balanced by drops breaking up when they reach a certain larger size. Thus, the approximate range of rain drop diameters existing in a rain event is approximately 0.1 ≤ D≤6 mm. These processes of coalescence and breakup determine the rain DSD. The DSD is of main importance in the determination of rain products such as the RR. It is defined as the number of drops per unit volume and diameter. Following (Rocadenbosch et al.,2020), the DSD is obtained as the ratio of the reflectivity density with respect to the drop diameter, η(D)[m−1/mm], to the single-particle backscattering cross section of a drop of diameter D, σ(D)[m2/drop]. It can be formulated as N(D) = η(D) σ(D).(2.4) Assuming spherical droplets of much smaller size than the beam wavelength, the backscattering cross section can be obtained as σ(D) = π5 λ4|Kw|2D6,(2.5) where Kw= (m2−1)/(m2+ 2), and mis the complex refractive index of water. FMCW radars are able to measure the volume spectral reflectivity,η(fn), which is the ratio of the light reflected to the Doppler frequency fn. This spectra can be defined as a function of either the Doppler frequency fnor the vertical velocity vn, given the relationship between the two (Equation 2.1). In practice, the conversion between frequency and vertical velocity is carried out by the radar as vn=fn λ 2,(2.6) 9 where the sub-index nis the index of the Doppler spectrum, fn=ni∆fis the discrete frequency, with ithe range index and ∆fthe frequency resolution of the Doppler spectrum. In order to retrieve the DSD from radar measurements (see Equation 2.4 above), we need to express the reflectivity density as a function of drop diameter. To do so, the relationship η(D)∂D =η(v)∂v is used. Therefore, it is necessary to find the relationship between the velocity vand the droplet diameter D, which was found empirically by Gunn and Kintzer (1949), and was put expressed analytically by Atlas et al. (1973) as vn(D)[m/s] = (9.65 −10.3e−0.6·D[mm])δv(h)for 0.109 ≤Dn≤6mm,(2.7) where δv(h)is the height-dependent density correction for the terminal fall velocity, which is formulated as δv(h) = 1 + 3.68 ·10−5h+ 1.71 ·10−9h2,(2.8) where his the measurement height. From the DSD, second order products such as the reflectivity factor Zand the RR can be derived. The radar reflectivity factor can be obtained as the sixth power of the DSD as Z=∫∞ 0 N(D)D6dD, (2.9) or, may also be computed as the equivalent reflectivity factor,Ze, Ze=λ4 π5 1 |Kw|2∫∞ 0 η(D)dD, (2.10) from which the reflectivity factor density can be related to the volume reflectivity density as dZ =λ4 π5 1 |Kw|2η(v),(2.11) where dZ is in units of [mm6/m3]. On the other hand, the RR can be estimated from the DSD third moment as a function of drop terminal fall velocity RR =π 6∫∞ 0 N(D)D3v(D)dD. (2.12) Figure 2.3 depicts radar data products measured by a vertically-pointed FMCW radar during a rain-event period of 1 hour in the context of VORTEX-SE campaign. The DSD, N(D), as well as the integrands N(D)D3and N(D)D6used for the derivation of the radar reflectivity factor and the RR (2.9 and 2.12, respectively) are displayed. From the figure it can be observed that even though the most numerous size of droplets are the smallest (blue trace), the sixth power of its diameter reduces its importance in the contribution of Z (black dashed trace). On the other hand, the red trace represents the integrand term of the RR, which, as shown in the figure, results in a value of 0.11 mm/h. 2.3.2 Drop Size Distribution Characterization The DSD is characterised by multiple models in the literature. Marshall and Palmer (1948) (M-P) modelled the DSD as an exponential function defined by parameters N0 and Λ. The M-P model is formulated as N(D) = N0e−ΛD,(2.13) 10 2017. The pips are instrumented metal-framed probes designed to be quickly deployed in rapidly evolving convective weather scenarios (Figure 3.2). Each PIPS, in addition to the optical disdrometer, has sensors that measure temperature, pressure, humidity, wind speed and direction. Data from the conventional meteorological instruments, along with compass heading, GPS data, and other diagnostic information, are recorded at 1s intervals. A new data file containing the 1-s data is created every 10 min. A separate series of files (binned every 10 min) records the Parsivel derived parameters. Those included in the data files include precipitation intensity, total precipitation accumulation, and radar reflectivity. Figure 3.2: Photograph of the Purdue PIPS with instrumentation identified. (Source: [(Dawson,2017)]) Parameter Value Units Manufacturer OTT - Model Parsivel2 - Location Scottsboro,AL Municipal Airport - Laser wavelength 780 nm Laser output power 0.5 mW Beam size (W x L) 180 x 30 mm Measurement surface 54 cm2 Measuring size range 0.2... 5 mm Measuring speed range 0.2... 20 m/s Rain rate minimum intensity 0.001 mm·h−1 Rain rate maximum intensity 1200 mm·h−1 Rain rate accuracy ±5% Averaging period 10 s Table 3.2: Main characteristics of the OTT Parsivel2 disdrometer. (Source: [(Dawson, 2017)]) 17 Chapter 4 Selected Rain Events: Stratiform versus Convective This chapter introduces the characteristics of stratiform and convective rain regimes. Next, it presents and discusses radar and disdrometer measurements of different rain events from VORTEX-SE 2017 campaign and classifies them as stratiform or convective. The contents of this chapter are aligned with Obj. 1 of the thesis. 4.1 Rain event cases In this section, different FMCW-radar measurements from VORTEX-SE 2017 are presented and discussed: Figures 4.1,4.3,4.2 and 4.4 show four different rain events from the measurement campaign. Left panels show the radar-measured volume reflectivity density. Recall that the reflectivity density is related to the reflectivity factor density by means of Equation 2.11. The reflectivity density is represented as a function of Doppler velocity (X axis) and the radar measurement height (Y axis) assuming stagnant air (VAM=0 m/s), i.e., the measured volume reflectivity density is not VAM-corrected. Therefore, in the presence of significant VAM, the reflectivity density would be shifted along the velocity axis (X axis). To illustrate this, the red dashed trace represents the threshold for which the droplets terminal fall velocity is not physically feasible (corresponding to a negative argument in the logarithm of Equation 2.17). If the reflectivity density exceeds this threshold, the retrieved second-order products become corrupt, and thus, the radar-derived products differ from those from the disdrometer. This can easily be identified in the right panels. Right panels compare the second-order products measured by the radar at 500 m and the disdrometer at ground level, namely, the DSD and the RR. The radar-measured RR at 500 m (grey trace) is compared with the disdrometer-measured RR at ground level (0 m, black trace). In the background, the radar-measured DSD is represented in colormap fashion. In case of stagnant air (VAM=0 m/s), the RRs measured by both instruments should be quite similar (as observed in Figure 4.1 b), for example). In contrast, in convective rain, radar-measured RR values become corrupted by VAM, leading to disparate RR values in comparison to the disdrometer-retrieved RR (as seen in Figure 4.3). Following this criterion for identifying stratiform and convective rain events, the four rain events under analysis were classified into these two categories: stratiform rain or convective rain. Next, these events are analyzed in detail: 19 4.1.1 Stratiform rain events Two selected experimental measurements from VORTEX-SE 2017 were essentially identified as stratiform rain events: March 26 from 01:30 to 01:40 UTC (Figure 4.1), and March 31 from 07:40 to 07:50 UTC (Figure 4.2). In both cases it can be observed that the volume spectral reflectivity vertical profiles (left panels) do not exceed the maximum terminal fall velocity threshold (see above). The spectra remain more or less homogeneous vertically, meaning that there is no relevant VAM during these periods. Moreover, it can be seen that the maximum terminal fall velocity observed for the first case is far from the maximum physical limit, as expected from light stratiform rain [Steiner and Smith (1998)]. 01:30:00 01:35:00 01:40:00 UTC Time 0 1 2 3 4 5 6 D[mm] 0 5 10 15 20 25 30 Rain Rate [mm h-1] 26-Mar-2017 0 0.5 1 1.5 2 2.5 3 log(N [m-3mm-1]) Radar Disdrometer b) Figure 4.1: Statiform rain event of March 26 2017 from 01:30 to 01:40 h UTC in Alabama, USA. Left panel: Radar volume reflectivity density with respect to velocity as a function of height. Right panel: Time series representing the radar-measured RR and the disdrometer-measured RR. The radar-retrieved DSD is represented in the background. The right panel of Figure 4.1 shows that the radar-retrieved RR at 500 m in height virtually matches the disdrometer-measured RR, further corroborating the stratiform hypothesis. It can be observed that RR values remain more or less constant during all the observation period, showing RR values between 2 and 3 mm ·h−1, i.e., light rain. Similar behaviour is observed for the DSDs, remaining homogeneous for all the observation period. 4.1.2 Convective rain events Two selected experimental measurements from VORTEX-SE 2017 were also identified as convective rain events: March 28 from 04:44 to 04:54 (Figure 4.3), and April 03 from 07:40 to 07:50 (Figure 4.4). In contrast to the stratiform rain events (see subsection 4.1.1 above), here it can be clearly observed how the radar-retrieved volume reflectivity density exceeds the maximum terminal velocity threshold. It is hypothesized that this is due to a positive (verticallydown) VAM. High variability is observed for the reflectivity density vertical profile, probably due to a convective atmosphere generating updrafts and downdrafts that affect the hydrometeors terminal fall velocity Houze (1997). The presence of VAM can be further corroborated in Figure 4.3 and 4.4 right panels when comparing the RRs retrieved by the radar and the disdrometer. Here it can be 20 07:45:00 07:50:00 UTC Time 0 1 2 3 4 5 6 D[mm] 0 2 4 6 8 10 Rain Rate [mm h-1] 31-Mar-2017 0 0.5 1 1.5 2 2.5 3 log(N [m-3mm-1]) Radar Disdrometer b) Figure 4.2: Statiform rain event of March 31 2017 from 07:40 to 07:50 h UTC in Alabama, USA. Left panel: Radar volume reflectivity density with respect to velocity as a function of height. Right panel: Time series representing the radar-measured RR and the disdrometer-measured RR. The DSD product of the radar is represented on the background. 04:45:00 04:50:00 UTC Time 0 1 2 3 4 5 6 D[mm] 0 5 10 15 20 25 30 Rain Rate [mm h-1] 28-Mar-2017 0 0.5 1 1.5 2 2.5 3 log(N [m-3mm-1]) Radar Disdrometer b) Figure 4.3: Convective rain event of March 28 2017 from 04:44 to 04:54 UTC in Alabama, USA. Left panel: Volume reflectivity density with respect to the velocity as a function of height without VAM correction. Right panel: Time series representing the radar-measured RR, without VAM correction and the disdrometer-measured RR. The DSD product of the radar is represented on the background. 21 clearly seen how radar and disdrometer retrievals of the RR highly disagree. In general terms, in the presence of VAM, lower RR values are retrieved by the radar. Regarding the RR values, heavy rain is observed for both scenarios, specially for the 3rd of April, with RR values higher than 10 mm ·h−1. This corroborates the assumption of convective rain [Houze (1997)]. 11:10:00 11:15:00 UTC Time 0 1 2 3 4 5 6 D[mm] 0 5 10 15 20 25 30 Rain Rate [mm h-1] 03-Apr-2017 0 0.5 1 1.5 2 2.5 3 log(N [m-3mm-1]) Radar Disdrometer b) Figure 4.4: Convective rain event of April 03 2017 from 11:30 to 11:50 UTC in Alabama, USA. Left panel: Volume reflectivity density with respect to the velocity as a function of height without VAM correction. Right panel: Time series representing the radar-measured RR, without VAM correction and the disdrometer-measured RR. The DSD product of the radar is represented on the background. 4.1.3 Melting Layer Regarding the volume reflectivity density vertical profiles above (left panels), it is possible to observe a horizontal layer in which the reflectivity is maximum. This is usually identified as the bright band (BB). The BB is the radar signature of the layer in which the ice crystals coalesce and melt, namely, the melting layer [Li and Moisseev (2020)]. In the rain events analyzed here, the melting layer is found between 2000 and 3500 m height. A clear Doppler velocity increment is clearly seen as crystals melt and coalesce into droplets. The melting layer is also indicative of the type of rain. Usually, a more flat melting layer is indicative of stratiform rain, as atmosphere layers are more stratified [Houze (1997)]. In contrast, in a convective rain scenario, melting layers extend in height. This can be clearly observed in the stratiform and convective reflectivity profiles of March 26 and April 3, Figure 4.1 and Figure 4.4, respectively. The first shows a flat melting layer at 2700 m in height, and the latter a wider melting layer extending from 3000 m up to 4000 m. 22 Chapter 5 Rain-Rate-Matching Method For Vertical Air Motion Estimation The contents of this Chapter are part of the co-authored work Salcedo-Bosch, A., DomínguezPla P., Rocadenbosh, F. and Frasier, S.J., (2022a), which has been accepted at the The International Geoscience and Remote Sensing Symposium, IGARSS 2022, Kuala Lumpur, Malaysia (https://www.igarss2022.org/, indexed as ”notable conference UPC”). 5.1 Introduction As exposed in section 2.3, the RR and the DSD are key parameters that can be retrieved from vertically pointed radar observations. RR estimation is influenced by the assumed DSD. In turn, the DSD can be computed from the vertically pointed radar Doppler spectrum with the assumption that the drops are Rayleigh scatterers falling at their terminal velocities. However, in practice, the Doppler spectrum is affected by the ambient VAM (see Chapter 4). Thus, given the Doppler spectrum as a function of height, RR and DSD retrievals require height-dependent VAM correction. While raw velocity bins in the radar observations represent a shifted, and possibly aliased, version of the mean Doppler radial velocity, velocity bins after VAM correction are expected to represent the true terminal fall velocity of the raindrops. Different approaches to estimate VAM have been carried out in the literature: Kim and Lee (2016) obtained VAM estimations using Doppler spectra derived from a 1290-MHz wind profiler, which showed good agreement in comparison with the VAM derived at 300 m in height from a K-band micro-rain radar and at surface from a disdrometer. They used the Sans Air Motion (SAM) gamma-size hydrometeor distribution model introduced by Williams (2002), who proposed a method to estimate VAM based on iterative fitting the DSD retrieved from the velocity-shifted observed spectrum and the SAM-DSD model. In contrast, this chapter tackles VAM estimation relying on RR measurements by a groundbased disdrometer, assuming high RR correlation between different measurement heights considering 5-min average ensembles. Although collision and coallescence processes limit radarand disdrometer-DSD coincidence, correlation coefficients of ρ≃0.75 are found for the RR between disdrometer and radar at 500 m in Rocadenbosch et al. (2020). 23 5.2 Methods 5.2.1 Data products and Vertical Air Motion correction Data products.- The steps to estimate the RR and DSD from radar-measured volume reflectivity η(v)as a function of velocity are presented in detail in subsection 5.2.1. As exposed, the derivation of RR and DSD must include the correction for the VAM in the velocity-to-diameter relationship (see Equation 2.16). Depending on the VAM correction value, different RR values will be obtained (see Equation 2.12). Therefore, in practice, the RR product can be defined as a function of the VAM velocity correction as RR(vV AM ). Taking this into account, Equation 2.12 can be reformulated into RR(vV AM ) = π 6∫∞ 0 N(D)D3[v(D)−vV AM ]dD, (5.1) where vV AM is the VAM correction value. VAM estimation.- The VAM estimation method consists on an optimisation problem by solving Equation 5.1 as a function of the VAM velocity correction. The optimization problem can be formulated as vV AM =arg min vV AM ||RRdisdro −RR(vV AM )||2,(5.2) where RR(vV AM )is the RR radar product obtained as a function of the vV AM velocity correction solving Equation 5.1.Equation 5.2 above is posed assuming that RRdisdro and RR(vV AM )are correlated in height (at altitudes considerably lower than the melting layer) when considering 5-min averages. The VAM optimization is carried out by means of a constrained non-linear Least-Squares algorithm, minimizing the squared error between RRdisdro and RR(vV AM ). 5.3 Results and Discussion The algorithm presented in subsection 5.2.1 has been applied to radar and disdrometer measurements (5-min averaged) taken during April 30, 2016 00:00-01:00 UTC in the context of VORTEX-SE measurement campaign. The algorithm estimated VAM values that, when used to correct the radar reflectivity measurements at 500 m height, provided RR values virtually identical to RRdisdro (||RRdisdro −RR(vV AM )||2<0.002mm ·h−1). Figure 5.1 compares the radar-measured RR at 500 m, with and without VAM correction (solid black and gray traces, respectively), to RRdisdro (dashed blue). It can be observed that without correction, radar-derived RR shows considerably lower values (≃0.1 mm · h−1) compared to RRdisdro (≃0.4 - 0.8 mm ·h−1) mainly due to VAM-velocity-induced error (Rajopadhyaya et al.,1998). With VAM correction, the radar-derived RR trace overlaps RRdisdro time series, and the estimated VAM time series is obtained (dashed brown trace), showing a nearly constant value of ≃4m·s−1. The background color map depicts the 5-min averaged DSD measured by the FMCW radar after VAM correction. In order to validate the VAM-corrected DSDs obtained for each 5-min average, and thus, the estimated RRs and VAM velocities, the gamma distribution parameterization of DSD was derived by means of the method of moments (Tokay and Short,1996). Figure 5.2 shows a DSD parameterization example in which the average DSD measured by the radar 24 00:10:00 00:20:00 00:30:00 00:40:00 00:50:00 0.2 0.4 0.6 0.8 1 1.2 1.4 D[mm] 0 2 4 6 8 10 Rain Rate [mm h-1]; VAM [m/s] 0 1 2 3 4 5 log(N [m-3mm-1]) Radar VAM corrected Radar uncorrected Disdrometer VAM Figure 5.1: Time series representing the radar-measured RR, with and without VAM correction, the disdrometer-measured RR and the VAM estimation results. The DSD is represented on the background. between 00:00 UTC and 00:05 UTC, with and without VAM correction (solid trace, b) and a) panels, respectively), is plotted along its gamma parameterization (dashed trace). It can be observed that without VAM correction (Figure 5.2 a)) the measured DSD is poorly fitted to a gamma distribution, showing a great bias between the modelled and measured DSDs. This is further evidenced by the gamma distribution parameters obtained, with µ=−3.574 which is out of the accepted range in the literature for µvalues (µ∈[−3,8]) (Doviak et al.,2006). On the other hand, after VAM correction (Figure 5.2 b)), the obtained DSD can be nicely fitted to a gamma distribution. This result is quantitatively validated as well by the gamma distribution parameters obtained, now with µ=−2.185 within the expected ranges. 0 0.2 0.4 0.6 0.8 1 1.2 D [mm] 102 104 106 N(D) [m-3 mm-1] Measured N(D) N(D)=N0D e-D N0 = 97 = -3.574 = 1.9958 a) 0 0.5 1 1.5 D [mm] 102 104 106 N(D) [m-3 mm-1] Corrected N(D) N(D)=N0D e-D N0 = 1.47e+04 = -2.1854 = 3.875 b) Figure 5.2: Case example showing the gamma distribution fitting to a radar-measured DSD without (panel a)) and with (panel b)) VAM correction. Table 5.1 depicts the gamma distribution parameters obtained for each of the 5-min averaged DSD measurements after VAM correction. N0values range from a minimum of 5.94 ·103at 00:35 UTC, corresponding to the lowest RR within the measurement period under study, to a maximum of 6.66 ·104.µvalues remain approximately constant around µ=−2, and finally, Λranges from a minimum of 3.87 at 00:05 UTC to a maximum of 7.44 at 00:55 UTC. The obtained values are in accordance with the ranges found in the 25 Time (UTC+2) N0 N0 N0µ µ µΛ Λ Λ 00:05:00 1.47 ·104-2.19 3.87 00:10:00 3.15 ·104-2.19 4.50 00:15:00 2.33 ·104-2.12 4.49 00:20:00 5.76 ·104-1.91 5.07 00:25:00 3.95 ·104-1.97 4.78 00:30:00 1.43 ·104-2.19 4.58 00:35:00 5.94 ·103-1.99 4.58 00:40:00 8.85 ·103-2.01 4.5 00:45:00 1.45 ·104-2.33 4.53 00:50:00 2.35 ·104-1.53 5.45 00:55:00 6.66 ·104-1.99 7.44 Table 5.1: Gamma distribution N0,µ, and Λfit parameters found for the VAM-corrected radar-measured DSDs for the measurement period under study (April 30, 2016 00:0001:00 UTC) in the context of VORTEX-SE campaign. Each row corresponds to a DSD 5-minute average. literature (Doviak et al.,2006) and their temporal correlation seem to validate the VAM estimations obtained. However, all we have shown is that the radar-derived RR can be made to match the disdrometer-derived RR, and that the resulting radar-derived DSD seems realistic. The Gamma distribution parameters obtained still need to be validated according to the rain type present in the scenario under study, and the DSDs from the two instruments should be compared in light of their respective sensitivities. The rather substantial apparent VAM over the course of 1 hour also deserves further investigation. 5.4 Conclusions A methodology to estimate VAM velocity from radar and disdrometer RR measurements has been presented. The method consists on fitting the radar-retrieved RR, as a function of VAM velocity correction, to the disdrometer-measured RR using constrained non-linear Least-Squares optimization. The methodology was tested over experimental data captured during a 1-hour period by an S-band FMCW radar and an OTT Parsivel2 disdrometer in the context of VORTEX-SE measurement campaign. The estimation results found a nearly constant VAM velocity of ≃4 m/s during the observation period. After VAM correction, the radar-measured RR was found to match almost ideally the disdrometer-measured RR. In order to validate these results, the gamma distribution parameterization was derived for each of the estimated DSD. It was found that without VAM correction, the gamma distribution parameters showed unrealistic values, outside of the accepted bounds for a precipitation process. On the other hand, after VAM-correction, realistic values for all parameters were found with a coherent temporal continuity, showing the methodology improvement of the radar measurements. Although good performance of the algorithm has been observed, it needs to be tested over different experimental data, validating the VAM estimations by means of radar wind profilers. Moreover, the effect of reflectivity density aliasing needs to be studied as well. 26 Chapter 7 Conclusions 7.1 Conclusions This Bachelor thesis aimed to study the effects of VAM on S-band FMCW radar measurements, and how to correct them. To do so, data from VORTEX-SE 2016 and 2017 campaigns was screened in order to identify VAM-corrupted radar measurements. Two methods to estimate and correct for VAM influence, the rain-rate-matching method and the DSD forward method, were presented. Three objectives were tackled in this project: • Obj. 1: Identification and classification of rain events. Radar and disdrometer measurements from VORTEX-SE 2017 experimental campaign were analyzed. Different rain events were identified VORTEX-SE and classified as a function of the rain type: stratiform or convective. Different radar-reflectivity-density vertical profiles were presented along with temporal series comparing radar (at 500 m) and disdrometer measurements of the RR (see, Figure 4.1,4.2,4.3, and 4.4). It could be observed that in convective rain scenarios, the reflectivity density exceeded the maximum fall velocity limit and, as a result, high discrepancies were found between the RRs measured by both instruments. In stratiform rain, the reflectivity density showed typical values, and the radar-measured RR matched ideally the disdrometer. Moreover, the ML characteristics were presented and identified for both rain types. • Obj. 2: Rain-rate-matching method for VAM estimation.. A numerical method to estimate VAM velocities from cooperative radar and disdrometer measurements was presented. This method relies on the assumption of high vertical correlation of the rain process: ρ= 0.75 between radar-measured RR at 500 m and disdrometer. The method relied on expressing the radar-retrieved RR as a function of the VAM correction, and optimizing its value to fit the disdrometer-measured RR. The method was tested over experimental data from VORTEX-SE 2016 campaign. VAM values of ≃4m/s were found. After correcting the radar measurements for the VAM values found, the RRs matched the reference with an error lower than 0.002 mm ·h−1 (see Figure 5.1). The obtained results were further validated by fitting the DSDs to a gamma distribution (see Figure 5.2). • Obj. 3: Forward method for VAM estimation. An inverse method to estimate the VAM from stand-alone radar measurements was presented. By expressing the DSD as a gamma distribution, the radar volume reflectivity density could be expressed as a function of the Gamma distribution constitutive parameters (N0,µ, and Λ) and 33 the VAM. The inverse method performance was tested over radar measurements from VORTEX-SE 2017 campaign, leading to VAM estimations between -1 and 1.5 m/s. The results were validated in terms of RR by considering the disdrometer as a reference. After correcting for the VAM, the radar-measured RRs showed a much higher agreement with the disdrometer than without correction (see Figure 6.2). However, an over-estimation of negative VAM values was found. These results were further corroborated in terms of DSD (see Figure 6.3). In general terms, the VAM estimation and correction resulted in improved quality of radar rain measurements with both methods. However, no final conclusions on which method is better can be given, as their performance is still to be tested under different rain scenarios. Moreover, the VAM estimations need to be validated by external instrumentation such as radar wind profilers. Nevertheless, the results obtained in this thesis project permitted to summarise their performance by a series of strengths and weaknesses. They are presented in Table 7.1 next: Method Strengths Weaknesses Rain-RateMatching Method • High temporal & spatial resolution. • Reliable VAM estimation at low heights. • Simple estimation: only VAM to be optimised. • The higher the measurement height, the worst the VAM estimation. • Requires a disdrometer co-located to the radar. • Does not take into account precipitation vertical evolution. Forward Method • High temporal & spatial resolution. • Estimations from stand-alone radar measurements. • Performance independent of measurement height. • Optimization in terms of radar 1st order products. • Higher computational effort. • Overestimation of negative VAMs. Table 7.1: Summary of strengths and weaknesses for each VAM retrieval method. . 34 Appendix A List of Publications A.1 International Conferences • Salcedo-Bosch, A., Domínguez-Pla, P., Rocadenbosch, F., Frasier, S.J., ”Numerical Solver For Vertical Air Motion Estimation” in 2022 IEEE Int. Geosci. Remote. Se. (IGARSS-2022). IEEE, accepted. • Salcedo-Bosch, A., Domínguez-Pla, P., Rocadenbosch, F., Frasier, S.J., ”Forward Method for Verical Air Motion Estimation from Frequency Modulated Continuous Wave Radar Rain Measurements” in 2022 European Conference on Radar in Meteorology and Hydrology (ERAD-2022). EPFL, accepted. 35 References Acharya, R., 2017: Chapter 7 - Tropospheric impairments: Measurements and mitigation. 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