Design of a High Resolution X-band Doppler
Polarimetric Weather Radar
Design of a High Resolution X-band Doppler
Polarimetric Weather Radar
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof.dr.ir. J.T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op 16 november 2009 om 15:00 uur
door
Jordi FIGUERAS I VENTURA
Enginyer Superior en Telecomunicaci´o Universitat Polit`ecnica de Catalunya
Dit proefschrift is goedgekeurd door de promotor: Prof.dr.ir. H.W.J. Russchenberg
Samenstelling promotiecomissie:
Rector Magnificus, voorzitter
Prof.dr.ir. H.W.J. Russchenberg, Technische Universiteit Delft, promotor Prof.dr.ir. F. Le Chevalier, Technische Universiteit Delft
Prof.ir. P. Hoogeboom, Technische Universiteit Delft
Prof.dr.ir. R. Uijlenhoet, Wageningen Universiteit en Researchcentrum Dr. I. Holleman, Koninklijk Nederlands Meteorologisch Instituut Prof.dr.rer.nat. M. Chandra, Technische Universit¨at Chemnitz
This research was supported by the Klimaat voor Ruimte Program
ISBN 978-90-9024759-5
Design of a High Resolution X-band Doppler Polarimetric Weather Radar Dissertation at Delft University of Technology.
Copyright c 2009 by J. Figueras i Ventura.
All rights reserved. No parts of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the author.
vii
Summary
The relation between anthropogenic greenhouse gases and global warming is currently well understood by the scientific community. However, other human activities impact as well the global climate. One poorly understood phenomenon is the effect that anthropogenic aerosols have on the climate and the hydrological cycle. It is hypothesized that an increase in aerosols leads to the creation of smaller droplets and therefore changes in the albedo of the clouds, their life cycle and the precipitation pattern. However, the relation between the aerosol com-position of the atmosphere and changes in the climate in general and in the precipitation pattern in particular is difficult to quantify. There are several reasons for that, among them: the non-homogeneity of the distribution of the aerosols in the atmosphere, which forces mea-surements to be taken at a local scale, and the lack of suitable instrumentation with the re-quired sensitivity and resolution. It is clear that a multi-sensor approach, combining several instruments and taking advantage of the synergies between them, is necessary to tackle the problem.
The Cabauw Experimental Site for Atmospheric Research (CESAR) in the Netherlands is in a unique position to get a better understanding of such complex relations thanks to the large range of instruments available. There are already instruments to measure to aerosol composition of the atmosphere. However, one problem that arose, is to design an instrument with sufficient sensitivity and resolution to permanently monitor the precipitation in the area surrounding the Site. Weather radar is a sound candidate for that due to the large area that can be covered and its capability to measure a wide range of precipitation events. However, com-mercial weather radars do not provide the adequate specifications to obtain high resolution measurements of phenomena as sensitive as light rain or drizzle. It is for this reason that it was decided at the International Research Centre for Telecommunication and Radar (IRCTR) to design and build a weather radar system in-house called IDRA (IRCTR Drizzle Radar).
The most challenging task is to obtain high quality measurements also for phenomena with low reflectivity like drizzle or light rain. Several techniques have been used in order to achieve that goal. The system is mounted on top of a 213 m high meteorological tower. This privileged position reduces the influence of ground clutter in the measurements. Moreover, it allows direct measurements of the spatial distribution of low level clouds and fog which are unique to this instrument.
In the hardware, state of the art techniques have been used to improve the sensitivity of the system. Among them, the use of direct digital synthesizers to perform the modulation,
quadrature receivers and, particularly, the use of polarimetry. Weather radars have tradition-ally used relatively low frequencies like S-band (3 GHz) or C-band (5 GHz). However, the antenna beamwidth is related to the wavelength and the dimensions of the antenna and there-fore, in order to obtain a high angular resolution, very bulky and heavy antennas would be required at such frequencies. Therefore a higher frequency, X-band (10 GHz) is used. A fre-quency modulated continuous wave (FMCW) architecture has been chosen in order to reduce the required transmitted power.
The signal processing chain implemented in real time makes extensive use of Doppler-polarimetry in order to reduce the impact of clutter and artefacts on the data. More traditional techniques to calculate the radar parameters, like the pulse-pair, have also been implemented for comparison with the non-standard Fourier transform processing. Other experimental pro-cessing techniques, like adaptive filtering propro-cessing, have also been implemented.
Being an experimental system, flexibility and easiness of use is desired. To this end, the use of direct digital synthesis allows the configuration of plenty of different modulation schemes, covering the needs of a wide range of users. The transmitted power can be con-trolled thanks to a digital attenuator, therefore allowing the radar to operate in a wide range of meteorological conditions. The data is time stamped using a GPS receiver and the position of the antennas is accurately measured with an angular encoder, facilitating the combination of radar data with other instruments data. The system can be operated remotely via Internet.
Overall the system gives satisfactory results. The measurements show the capability of monitoring a wide range of atmospheric phenomena, from clear air scattering to heavy storms. The importance of polarimetric data as both a means for clutter suppression and for a better identification of the scatterers has also been highlighted. Since X-band is not widely used in weather radar systems modelling of the expected radar parameters at this band have been performed, with particular interest in the effects of atmospheric attenuation and Mie scattering has been conducted. The results, corroborated with the analysis of an extensive dataset, show that these effects are minimal for the relatively small range covered by the system and the most frequent type of precipitation in the Netherlands.
A wide range of software tools are now available to further process, visualize and man-age the radar data and to combine it with other instruments. Several lines of research have been opened by the system. Data quality can still be improved, particularly the differential reflectivity. Automatic Gain control should be implemented in the software. The use of po-larimetry to obtain better quantitative precipitation estimation and precipitation classification should be studied in depth. Also application of the data in weather models, hydrology, etc. should be encouraged by disseminating and facilitating as much as possible the accessibility to the data and the system.
ix
Samenvatting
Wetenschappers hebben nu een goed begrip van het verband tussen antropogene emissies en het broeikaseffect. Er zijn echter ook andere menselijke activiteiten die het klimaat ben-vloeden waarover minder bekend is. Een hiervan is het effect van antropogene arosolen op het klimaat en de waterkringloop. We gaan hier uit van de aanname dat een toename van arosolen in de atmosfeer zorgt voor kleinere druppels en daardoor veranderingen in de albedo, levenscyclus en het neerslagpatroon van wolken. Het is echter moeilijk om het ver-band tussen de verschillende aerosolen in de atmosfeer en veranderingen van het klimaat in het algemeen te kwantificeren en van het neerslagpatroon in het bijzonder. Dit heeft een aan-tal oorzaken. Aerosolen zijn niet gelijkmatig verspreid in de atmosfeer, waardoor metingen op meerdere plaatsen moeten worden gedaan. Daarnaast zijn er geen geschikte instrumenten met de vereiste gevoeligheid en resolutie. Het is duidelijk dat er een multi-sensoraanpak nodig is voor dit probleem, een aanpak die verschillende instrumenten combineert.
Vanwege haar uitgebreide scala aan instrumenten is de Cabauw Experimental Site for At-mospheric Research (CESAR) in Nederland in de unieke positie om meer inzicht te verschaf-fen in de bovengenoemde complexe verbanden. Er zijn al verscheidene meetinstrumenten voor het bepalen van de hoeveelheid aerosolen in de atmosfeer. Een uitdaging die zich vo-ordeed was het ontwerpen van een instrument met voldoende gevoeligheid en resolutie om continu de neerslag in het gebied rond CESAR te bepalen. De weerradar was daar een goede kandidaat voor vanwege het grote gebied waar deze naar kan kijken en zijn vermogen om een groot scala aan neerslagsoorten te meten. Commercieel beschikbare weerradars geven echter niet de benodigde specificaties voor het doen van hoge-resolutie-metingen van neer-slagsoorten die grote gevoeligheid vereisen zoals lichte regen of motregen. Vanwege deze reden besloot het International Research Centre for Telecommunication and Radar (IRCTR) om zelf een weerradar te bouwen genaamd IDRA (IRCTR Drizzle Radar).
De grootste uitdaging bestond uit het verkrijgen van meetresultaten van een hoge kwaliteit, ook voor druppels met een slechte reflectie zoals die in motregen of lichte regen. Er zijn een aantal technieken gebruikt om dit doel te bereiken. Het systeem is op een 213-meter-hoge weertoren genstalleerd. Deze positie vermindert de invloed van grondreflecties in de metin-gen. Bovendien geeft deze het instrument het unieke vermogen om direct de ruimtelijke ver-spreiding van lage-reflectiewolken en mist vast te stellen. In de hardware zijn de allernieuwste technieken toegepast om het systeem gevoeliger te maken. Zo zijn digital synthesizers ge-bruikt voor de signaalopwekking, alsmede quadrature receivers en polarimetrie. Van oudsher
maken weerradars gebruik van relatief lage frequenties zoals de S-band (3 GHz) of C-band (5 GHz). Omdat de breedte van de bundel die de antenne uitzendt gerelateerd is aan de golflengte en de dimensies van de antenne zou men erg grote en zware antenne nodig hebben om een hoge hoekresolutie te behalen. Daarom hebben wij een hogere frequentie gebruikt, de X-band (10 GHz). Een FMCW architectuur is gekozen om het vereiste uitgezonden ver-mogen te bereiken.
Het signaalverwerkingssysteem dat onvertraagd wordt toegepast maakt gebruik van Doppler polarimetrie om de invloed van ruis en afwijkingen in de data te verminderen. Hiernaast is er ook gebruik gemaakt van traditionelere technieken om de parameters van de radar te bereke-nen zoals de pulse-pair om deze te vergelijken met de niet-standaard Fouriertransformatie verwerkingsmethode. Andere niet-standaard verwerkingsmethoden zoals adaptive filtering processing zijn ook toegepast.
Omdat dit een experimenteel systeem betreft, zijn flexibiliteit en gebruiksgemak belan-grijk. De directe digitale synthese laat het gebruik van een groot aantal verschillende modu-latieschemas toe, en voorziet zo in de behoeften van een groot scala aan gebruikers. Het uit-gezonden vermogen kan worden gecontroleerd met behulp van een digitale attenuator waar-door de radar onder een groot aantal verschillende weersomstandigheden kan functioneren. De signalen krijgen een tijdsaanduiding via een GPS ontvanger en de positie van de antennes wordt nauwkeurig gemeten met een hoekmeter, wat het makkelijk maakt om de data van de radar te combineren met data verkregen met andere instrumenten. Het systeem kan op afstand worden bediend via internet.
In het geheel genomen levert het systeem bevredigende resultaten op. De metingen laten zien dat er een grote verscheidenheid aan weersomstandigheden kan worden gemeten, van heldere lucht tot zware stormen. Ook is er aandacht besteed aan het belang van polarimetrie-data zowel als middel om ongewenste signalen te filteren als om de verstrooiers beter te identificeren. Omdat de X-band in weinig weerradartypen wordt gebruikt, hebben we de verwachte parameters voor deze band gemodelleerd, met speciale aandacht voor de effecten van atmosferische afzwakking en Mieverstrooiing. De resultaten, onderbouwd met analyse van een uitgebreide set data, laten zien dat deze effecten minimaal zijn bij het relatief kleine bereik van het systeem en de meest voorkomende soort neerslag in Nederland.
Er is nu een grote verscheidenheid aan software om de radardata verder te verwerken, visualiseren en te beheren en om deze met data van andere meetinstrumenten te combineren. Het systeem heeft de weg geopend naar verschillende nieuwe onderzoekspaden. De kwaliteit van de data kan worden verbeterd, de differential reflectivity in het bijzonder. Automatic Gain control zou moeten worden toegepast in de software. Het gebruik van polarimetrie om een betere kwantitatieve schatting van de neerslag te krijgen en een betere classificatie van het soort neerslag zou grondig moeten worden onderzocht. De toepassing van de data in weermodellen, hydrologie en dergelijke zou moeten worden aangemoedigd door de data en het systeem bekend te maken en de toegankelijkheid hiervan te vergroten.
CONTENTS xi
Contents
1 Introduction 1
1.1 Research motivation . . . 1
1.2 The need for a new weather radar . . . 3
1.3 Research Background and Objectives . . . 4
1.4 Chronology . . . 5
1.5 Outline of the dissertation . . . 6
2 Weather radar observables 9 2.1 Weather radar products . . . 9
2.1.1 Radar reflectivity . . . 10
2.1.2 Doppler moments . . . 14
2.1.3 Polarimetric products . . . 16
2.2 Precipitation and low level clouds and fog . . . 18
2.3 Clear air scattering . . . 21
2.4 Clutter, interferences and artefacts . . . 22
3 System description 23 3.1 Frequency Modulated Continuous Wave Radar . . . 23
3.1.1 FM-CW radar principles . . . 23
3.1.2 Antenna considerations . . . 26
3.2 Design considerations . . . 28
3.3 System overview and specifications . . . 29
3.4 The front end . . . 33
3.4.1 Transmitter . . . 33
3.4.2 Antennas . . . 35
3.4.3 Receiver . . . 36
3.4.4 Control and other circuitry . . . 36
3.5 Software and data storage structure . . . 38
4 Signal Processing 43 4.1 FM-CW signal analysis . . . 43
4.1.2 Atmospheric signal Doppler spectrum . . . 46
4.2 Doppler-polarimetric processing . . . 49
4.2.1 Computation of the Doppler polarimetric products . . . 49
4.2.2 Windowing . . . 50
4.2.3 Ground clutter suppression . . . 52
4.2.4 Smoothing . . . 53
4.2.5 Noise clipping . . . 54
4.2.6 Doppler-polarimetric filtering and aliasing correction . . . 55
4.2.7 Real time signal processing implemented in IDRA . . . 57
4.2.8 Alternative signal processing to minimize the effects of aliasing . . . 61
4.3 Time domain processing . . . 62
4.3.1 Computation of the Doppler polarimetric parameters . . . 62
4.3.2 Implementation of the time domain processing in IDRA . . . 64
4.3.3 Fourier transform based processing versus time domain processing . . 66
4.4 Adaptive filtering processing . . . 68
4.4.1 Signal model . . . 68
4.4.2 Adaptive filter estimation . . . 69
4.4.3 Implementation of the adaptive filtering processing in IDRA . . . 70
4.4.4 Fourier transform based processing versus adaptive filtering processing 71 5 System performance and calibration 75 5.1 Theoretical performance . . . 75 5.1.1 Sensitivity . . . 75 5.1.2 Dynamic Range . . . 80 5.1.3 Image Rejection . . . 81 5.1.4 Ground clutter . . . 82 5.2 System modelling . . . 83
5.2.1 Direct Digital Synthesizer modelling . . . 83
5.2.2 Quadrature deramping modelling . . . 86
5.3 Measurements of the system . . . 88
5.3.1 Transmitter . . . 89
5.3.2 Receiver . . . 92
5.3.3 Noise Measurements . . . 96
5.4 Calibration . . . 97
5.4.1 Calibration Techniques . . . 97
5.4.2 IDRA System Calibration . . . 99
6 Data analysis and applications 103 6.1 Radar observables modelling at X-band . . . 103
6.2 Radar observables analysis . . . 109
6.2.1 Impact of external phenomena . . . 109
CONTENTS xiii
6.2.3 Signal processing related issues . . . 114
6.3 Comparison with standard weather radars . . . 118
6.4 Rainfall rate measurements . . . 120
6.5 Fog and drizzle measurements . . . 129
6.6 Clear air scattering measurements . . . 134
7 Conclusions and recommendations 139 7.1 Major contributions of this research . . . 141
7.2 Recommendations . . . 142
List of Symbols and Acronyms 145
Bibliography 149
Author’s publications 157
LIST OF FIGURES xv
List of Figures
1.1 Level of scientific understanding of the different radiative forcing components. From
Solomon et al. [2007] . . . 2
1.2 Chronology of the IDRA project . . . 6
3.1 Time-frequency plot of a transmitted (solid) and received (dashed) chirp signal. The received signal is a delayed version of the transmitted one. The result of mixing the transmitted signal with the received is a signal the frequency of which is proportional to this delay. . . 24
3.2 Frequency response of a single scatterer in the digital frequency domain. The sam-pling frequency isfs=2.5 MHz. The spectrum has been obtained using only the real signal in the deramping and therefore it consists in the response of the scatterer, situ-ated atfr=0.8 MHz, and its image at 1.7 MHz orfs− fr. It can be observed that the sidelobes of the response would mask any other scatterer with a power level 50 dB below this one. . . 25
3.3 Geometric configuration of two parallel located antennas. The percentage of area overlap between the beams of the two antennas increases with range. . . 26
3.4 Map of the area surrounding the radar. The two concentric circles represent the area covered by two of the most used modes of operation. It can be seen that the area surrounding the radar is flat and consisting mainly of farm fields. . . 28
3.5 The IDRA system on top of the Cabauw meteorological tower. The two antennas scan mechanically at a revolution rate of 1 rpm . . . 30
3.6 Resolution volume depth and minimum and maximum observed altitudes for an an-tenna of 1.8obeamwidth and 0.5oelevation angle. . . 31
3.7 Coverage by the two antennas . . . 32
3.8 IDRA Transmitter Block diagram . . . 34
3.9 Antenna measurements . . . 35
3.10 IDRA Receiver Block diagram. . . 37
3.11 Display . . . 39
4.1 Schematic representation of a scenario where the resolution volume is filled by droplets having the same reflectivity and velocity . . . 48
4.3 Reflectivity on a clear day with and without clutter suppression. . . 52
4.4 Effect of smoothing the Doppler spectrum. The grey solid line is the Doppler spec-trum before applying smoothing while the black dashed line is the same Doppler spectrum after applying smoothing. . . 54
4.5 resultant real part HH channel samples-sweeps matrix after multiplying by the two-dimensional Hamming window and suppressing the first 100 sweeps. The shaping of the data by the Hamming window is clearly visible . . . 58
4.6 Example of Doppler spectrum before and after filtering . . . 59
4.7 Examples of fields measured with IDRA . . . 61
4.8 Examples of fields measured with aliasing correction processing. . . 62
4.9 Polarimetric parameters . . . 67
4.10 Doppler parameters . . . 68
4.11 Examples of fields measured with adaptive filtering processing . . . 71
4.12 Comparison between the fields obtained using the Fourier transform based processing and those obtained by the adaptive filtering processing . . . 72
5.1 Background noise temperature as a function of frequency for different pointing angles. Obtained from Pozar [2005] . . . 76
5.2 Noise figure and gain of the receiver chain . . . 77
5.3 Residual phase noise at the output of the 1st down-converter . . . 80
5.4 Minimum reflectivity per Doppler cell considering that 512 sweeps are used and no clipping is applied. . . 81
5.5 Image rejection for different phase and gain imbalances . . . 82
5.6 Received ground clutter power as a function of range for different polarizations . . . 83
5.7 Schematic representation of a DDS. . . 84
5.8 Effect of phase truncation . . . 85
5.9 Effect of phase noise and DA converter resolution . . . 86
5.10 Effect of DA converter non-linearity . . . 86
5.11 Schematic representation of the deramping simulator . . . 87
5.12 Effect of harmonic distortion on the Doppler spectrum . . . 87
5.13 Effect of amplitude (0.1) and phase (5o) imbalances in the Doppler spectrum. The resultant image has a power of -23 dB with respect to the true signal . . . 88
5.14 Effect of a DC component. A 10 mV DC component has been added to the in-phase channel of the deramped signal . . . 88
5.15 Effect of a saturating the AD converter. The dynamic range of the AD converter is 16 dBm, while a signal of 22 dBm has been injected in each channel. . . 89
5.16 DDS output signal for a 5 MHz and 50 MHz frequency sweep . . . 90
5.17 DDS output signal for a 5 MHz and 50 MHz frequency sweep . . . 90
5.18 Deramping signal when transmitting a 5 MHz signal . . . 91
5.19 Deramping signal when transmitting a 50 MHz signal . . . 91
5.20 Transmitter output for different polarization and frequency sweeps . . . 92
LIST OF FIGURES xvii
5.22 Splitter signal when transmitting 5 MHz signal . . . 94
5.23 Splitter signal when transmitting 50 MHz signal . . . 94
5.24 receiver output signal when transmitting 5 MHz signal . . . 95
5.25 receiver output signal when transmitting 5 MHz signal . . . 95
5.26 Image rejection for the vertical and horizontal channels . . . 96
5.27 Noise profile . . . 97
5.28 Gain profile . . . 100
6.1 Axis ratio models found in literature . . . 104
6.2 Mie and Rayleigh backscattering cross-section for spherical water droplets at temper-ature 293 K . . . 105
6.3 Mie and Rayleigh reflectivity for Marshall-Palmer drop size distribution . . . 106
6.4 Extinction cross-section and attenuation at X-band for Marshall Palmer Drop-size distribution . . . 106
6.5 Differential reflectivity and differential attenuation at X-band . . . 108
6.6 Specific differential phase and backscattering differential phase at X-band . . . 109
6.7 Effect of suppressing the 0-Doppler bin into the reflectivity data. The arrows show areas where the reflectivity drops due to the suppression of the 0-Doppler bin and surrounding cells . . . 110
6.8 PPI of the reflectivity from the storm event measured the 1st of August 2008 at 01:00 UTC. . . 111
6.9 Range profile of reflectivity and differential reflectivity for a sector at 216o with re-spect to north measured the 1st of August 2008 at 01:00 UTC . . . 111
6.10 Effect of the surrounding fence on the differential reflectivity . . . 112
6.11 Effect of the residual high frequency signals in the receiver output. The marked area corresponds to the ringing signal that creates the distortion lines in the Doppler spectra.113 6.12 Effect of receiver saturation on the Doppler spectrum. The arrows show the replicas of the main atmospheric signal caused by the saturation . . . 113
6.13 Effect of sidelobes on the measurements . . . 114
6.14 Scattering plot of reflectivity calculated in the time domain versus reflectivity calcu-lated in the frequency domain . . . 115
6.15 Synthetically generated Gaussian Doppler spectrum. Plotted in grey the signal Gaus-sian atmospheric signal mixed with noise. In black the same signal after a 7 bin Gaussian smoothing to reduce the noise variance. The dashed line is the clipping level. 116 6.16 Linear depolarization ratio measured by IDRA . . . 117
6.17 Differential phase measured by IDRA and specific differential phase retrieved . . . . 117
6.18 Maximum and minimum altitude and volumetric resolution of the radar from KNMI . 118 6.19 Measured reflectivity by IDRA and by the KNMI radar . . . 119
6.20 Retrieved rainfall rate by IDRA and by the KNMI radar . . . 119
6.21 IDRA Reflectivity and rainfall rate when the resolution is downgraded to 990 m . . . 120
6.22 Rain gauge-radar rainfall rate comparison for rain gauge number 1 the 7th November. 122 6.23 Rainfall rate time series for radar and rain gauge number 6 . . . 123
6.24 Measured temperature at 200 m and 2 m . . . 124
6.25 Measured wind speed and direction at 200 m and 10 m . . . 124
6.26 Temperature as a function of height measured with radiosondes launched from De Bilt.125 6.27 Backscattered attenuation coefficient measured by the KNMI ceilometer the 16th of May 2008. . . 126
6.28 Backscattered attenuation coefficient measured by the KNMI ceilometer the 11th of November 2008. . . 126
6.29 Measurements by the 35 GHz KNMI cloud radar performed the 16th of May 2008. . . 127
6.30 Measurements by the 35 GHz KNMI cloud radar performed the 11th of May 2008. . . 128
6.31 Scattering plot of the reflectivity against rainfall rate from disdrometer data obtained the 11th of November 2008. . . 129
6.32 Wind speed and direction measured on the Cabauw tower.. . . 130
6.33 Measured temperature on the Cabauw tower and by radiosondes launched in De Bilt. . 130
6.34 Rainfall rate measured by the KNMI rain gauge. . . 130
6.35 Backscattered attenuation coefficient measured by the KNMI ceilometer. . . 131
6.36 Differential reflectivity measured by IDRA . . . 131
6.37 Measurements by the 35 GHz KNMI cloud radar.. . . 132
6.38 Reflectivity measured by IDRA the 14th of November 2008. . . 133
6.39 Wind speed and direction measured on the Cabauw tower.. . . 134
6.40 Measured temperature on the Cabauw tower and by radiosonde launched in De Bilt. . 134
6.41 Backscattered attenuation coefficient measured by the KNMI ceilometer. . . 135
6.42 Measurements by the 35 GHz KNMI cloud radar.. . . 136
6.43 Mean Doppler velocity measured by IDRA . . . 137
6.44 Differential reflectivity measured by IDRA. . . 137
LIST OF TABLES xix
List of Tables
3.1 System specifications . . . 32
3.2 Block header for raw and processed data files. . . 40
4.1 Properties of several smoothing Windows. Extracted from Poularikas [1999]. . . 51
5.1 Noise figure and gain of the different devices in the receiver chain . . . 77
5.2 Phase noise from the different signal sources. The phase noise from the oscillators and the residual phase noise of the DDS has been obtained from the specifications provided by the manufacturers. The output phase noise of the DDS is the combination of the phase noise of the 300 MHz oscillator considering the effects of oversampling and the residual phase noise of the DDS. . . 79
5.3 Grasslands reflectivity as a function of incident angle for different polarizations . . . 82
5.4 DDS characteristics . . . 85
5.5 Delay line characteristics . . . 89
5.6 Calibration constant parameters . . . 100
6.1 average rainfall rate over the area covered by IDRA inmmh . . . 119
6.2 Coordinates of the rain gauges. The radar is located on top of the Cabauw tower. (Coordinates 51.970281N- 4.926263E) . . . 120
6.3 Rain gauge data availability . . . 121
6.4 Measured rainfall over 24 h by different instruments for the 16th of May and 11th of November 2008 . . . 122
1
Chapter 1
Introduction
1.1
Research motivation
Much research has been carried out on the impact of anthropogenic greenhouse gases emis-sions in the global climate. Its implications have reached now a high level of scientific un-derstanding and it can be confidently assessed that they have a significant global warming effect.
However, human activities may lead to other important mechanisms with a potentially huge impact in the radiation budget (Solomon et al. [2007]). The impact of these activities is yet far from being fully understood and could have effects greater than predicted by the report from the Intergovernmental Panel on Climate Change (IPCC) (Kabat et al. [2004]). Of particular impact are the changes of land use and the release of anthropogenic aerosols. The term anthropogenic aerosols refers here to all type of aerosols released due to human activity. These mechanisms may have a great influence in the global climate and even greater at a regional level. However, being a regional scale phenomena, they are much more difficult to study, due partially to the lack of worldwide sound data.
In concrete, the release of anthropogenic aerosols has implications not only in the radia-tion budget, but in the hydrological cycle as well. An increase in the concentraradia-tion of aerosols in the atmosphere causes the formation of smaller droplets in clouds. That causes changes in the albedo of the clouds in what is called the first indirect aerosol effect. The presence of smaller droplets also leads to a change in the life cycle of the clouds. Clouds may last longer and precipitation may be delayed. That is the second indirect aerosol effect. The precipitation pattern, when and if it finally occurs, is also different (Albrecht [1989]).
Both these two effects have a potentially huge cooling impact in the global radiation budget. However this phenomenon is still far from being completely understood and the uncertainty in the models is very large. Figure 1.1 shows the level of scientific understanding of this phenomenon.
One of the reasons for such poor understanding is that, unlike greenhouse gases, which are distributed homogeneously in the atmosphere, aerosol concentration and type varies at a local scale. This makes measurements at a global level much more difficult. Moreover, the
mechanisms and the implications of this phenomenon have revealed to be of a very complex nature. A multi-sensor approach is required, combining measurements of aerosols, clouds and precipitation, to get a better understanding of the subject.
Figure 1.1: Level of scientific understanding of the different radiative forcing components. From Solomon et al. [2007]
For these reasons, The International Research Centre for Telecommunications and Radar (IRCTR) considered the need of having a high resolution radar to obtain a detailed spatial distribution of precipitation that could be easily coupled with other sensors operational in the same meteorological site, the CESAR observatory located in Cabauw, The Netherlands. Russchenberg et al. [2005] provides an overview of the CESAR observatory. The purpose of the system is to have high spatial and temporal resolution measurements of precipitation and couple them with measurements of the presence of aerosols in the atmosphere in order to better understand the link between the changes in precipitation pattern and the presence of aerosols in the atmosphere.
It is important to understand better these relations in order to achieve a sustainable land use and industrial activity planning. As an example, understanding the relation between human activity and climate can lead to more efficient actions to slow down the desertification process.
1.2 The need for a new weather radar 3
1.2
The need for a new weather radar
In order to determine the influence of the release of anthropogenic aerosols in the precipita-tion cycle long term series of highly accurate measurements of both the aerosol composiprecipita-tion of the atmosphere and precipitation intensity with a high level of detail are required. In Cabauw there is instrumentation to classify and size aerosols like the MARGA (Instrument for Measuring AeRosols and GAses). Information on this instrument can be found in ten Brink et al. [2007]. However there was no instrument that could monitor the dynamics of precipitation in the surrounding area with sufficient level of detail and accuracy.
Measurements of precipitation can be performed by various instruments like rain gauges, disdrometers, etc. Radar technology though provides a good solution for several reasons. Among others:
• It offers a 24-7 autonomous monitoring capability.
• It can measure a wide range of phenomena, from very light rain to heavy storms. • Its measurements cover a wide area.
• Information on the composition of the precipitation can be automatically extracted. Weather radar is a mature technology which has been successfully applied for decades with an ever higher level of sophistication. There are numerous manufacturers and most gov-ernmental meteorological services operate a network of weather radars to monitor precipita-tion, with particular interest in phenomena like thunderstorms or hail which could potentially lead to hazardous situations and economical damage.
These radar systems, though, are mostly designed to cover wide areas of territory, cov-ering hundreds of kilometres. Consequently they have a moderate range resolution (in the order of tens or hundreds of metres). Moreover, they typically use relatively low frequencies. Traditionally most weather radars operate at S-band (3 GHz) or C-band (5 GHz). That is so because those frequencies suffer less from atmospheric attenuation, allowing the system to cover further ranges. However, as a consequence, they require large, bulky and heavy an-tennas to get a sufficiently high angular resolution. Such heavy and bulky equipment would hardly be placeable in the desired location on top of the 213 m high meteorological tower.
In recent times some manufacturers have started to offer more portable radar systems, mostly working at X-band (10 GHz). These systems are meant basically at detecting rainfall in situations where immediate weather awareness is necessary like for example military op-erations. In general terms what is favoured is the simplicity of use and robustness rather than sensitivity or accuracy and therefore they are not suit for the intended application.
Nevertheless the use of X-band radars for accurate quantitative precipitation estimation has enjoyed a revival recently because there is an increased requirement to not only detect precipitation but to accurately measure it with the highest resolution possible. X-band com-ponents are, in general terms, less bulky, cheaper and less power consumers and therefore they constitute good candidates for high density high resolution weather radar networks. The
interest in X-band weather radars has come together with the introduction of polarimetry in operational weather radar networks. Polarimetry offers several advantages but a crucial one is that it can successfully correct for atmospheric attenuation, thus improving the accuracy of the rainfall rate retrievals.
Yet, X-band systems with such characteristics are still far from being commercially ma-ture and there is still plenty of room for innovation. It is for this reason that it was decided by IRCTR to built its own X-band weather radar system. IRCTR has a history of successfully building radars for different applications and a large theoretical and practical knowledge on polarimetry. Moreover, building a system in-house would unleash the constrains imposed by commercial systems, i.e., complete adaptation of the design to the measurement require-ments, absolute flexibility of operation and the possibility to upgrade or modify the system whenever desired.
The new system makes use of the most advanced hardware (digital modulation, polarime-try, etc.) and signal processing techniques (Doppler-polarimetric processing) in order to achieve a high resolution and sensitivity. Moreover, it is placed on top of the Cabauw tower, at 213 m altitude, therefore minimizing the impact of ground clutter on the measurements. For reasons of economy the antennas have been taken from a previous radar system called SOLIDAR (Solid State Radar) which operated at X-band.
1.3
Research Background and Objectives
The research has been carried out within the framework of the ”Klimaat voor Ruimte-Climate Changes Spatial Planning” program funded by the Netherlands Organization for Scientific Research (NWO) . The main objectives of the ”Klimaat voor Ruimte” program are:
• To offer the Dutch government, the private sector and other stakeholders a clustered, high-quality and accessible knowledge infrastructure on the interface of climate change and spatial planning.
• To engage a dialogue between stakeholders and scientists in order to support the de-velopment of spatially explicit adaptation and mitigation strategies that anticipate for climate change and contribute to a safe, sustainable and resilient socio-economic in-frastructure in the Netherlands.
The ”Klimaat voor Ruimte” program is divided in several themes. One of them, called ”Climate Scenarios”, covers the role of terrestrial, atmospheric and oceanic processes in the climate system and the construction of specific, tailor-made climate change scenarios for dif-ferent sectors. One of the projects within ”Climate Scenarios” theme is ”The CESAR Obser-vatory climate monitoring and process studies”. The purpose of this project is to provide the essential infrastructure for the continuation, extension and maintenance of the Cabauw Ex-perimental Site for Atmospheric Research (CESAR) monitoring program. A sub project of the CESAR Observatory climate monitoring is the development of a high resolution weather
1.4 Chronology 5
radar for the observation of the detailed spatial and temporal distribution of rainfall and driz-zle in an area of 30 km2surrounding Cabauw. The project is named IDRA (IRCTR Drizzle Radar) .
The objectives of the project can be summarized as:
• The establishment of the correct radar system specifications in order to achieve the goal.
• The development of a radar system characterized by its high sensitivity and design flexibility.
• The development of signal processing algorithms for the retrieval of atmospheric in-formation.
• The assessment of the main problems considering the data quality at X-band. Namely calibration issues, Mie scattering, attenuation and differential attenuation.
• The creation of a long term dataset and the tools to exploit the atmospheric data.
1.4
Chronology
The development phase of the project lasted for 4 years: From June 2005 to June 2009. The summarized project schedule is shown in Figure 1.2. In the first phase the specifications of the system were established. This phase lasted 6 months, until the end of 2005. During the second phase the actual system design was established. This phase lasted for another 8 months, until August 2006. In the third, two activities ran in parallel. While the components for the system where ordered, tested and assembled, the real time signal processing routines were developed. That lasted until July 2007.
At the end of August 2007 the whole system was mounted on top of the Cabauw mete-orological tower. Unfortunately during the mounting process the rotary joint supplying the electrical power and the communication channels between the radar and the base of the tower was damaged. As a result the first scanning measurements were not obtained until January 2008. In the meanwhile the adjustment of the system and several programs for data interpre-tation were developed.
Shortly after the first scanning measurements were obtained the power supply of the high power amplifiers was damaged due to water condensation caused by high humidity. The radar was operational again by April 2008. From April to late November 2008 the radar was operating on a 24-7 basis. During this period, calibration was performed and the data compared with the standard weather radar from the Dutch Meteorological Service (KNMI) placed in De Bilt. Also, precipitation estimation algorithms were implemented. It was ob-served that the Doppler moments and the reflectivity was obtained with high quality but the differential reflectivity suffered from distortion. In order to exclude internal distortion and perform some quality checks of the system, the electronics were removed from the tower by the end of November 2008 and measurements were performed on the laboratory during
Figure 1.2:Chronology of the IDRA project
January and February 2009. By March 2009 the system was reinstalled in the tower and has been operational ever since.
1.5
Outline of the dissertation
The thesis is organized as follows:
Chapter 2 provides an overview of the weather radar. The weather radar primary
prod-ucts (reflectivity, Doppler moments and polarimetric parameters) are introduced. A brief description of common atmospheric observations namely precipitation, low level clouds and clear air scattering is provided. The chapter ends with a brief discussion on the concepts of clutter and artefacts.
Chapter 3 describes the X-band Doppler polarimetric radar IDRA developed at IRCTR.
Considering that the system architecture is frequency modulated continuous wave (FM-CW) , which is not widely known in the weather radar community, it has been consid-ered convenient to introduce some concepts specifically related to FM-CW. The design considerations are also discussed, as well as the resultant system specifications. A complete description of the radar front-end and the real time signal processing and data storage software are also provided in this chapter.
Chapter 4 describes different signal processing techniques implemented in the IDRA
soft-ware. The chapter starts with an analysis of the transmitted and received FM-CW radar signals and the expected atmospheric signal Doppler spectrum. Three different processing techniques are discussed in this chapter: Doppler-polarimetric processing,
1.5 Outline of the dissertation 7
adaptive signal processing and the pulse-pair estimate. Details about the actual imple-mentation of these processing techniques in the IDRA software are also provided.
Chapter 5 deals with the system performance and calibration. It provides a general
de-scription of the different phenomena that have to be taken into account to establish the theoretical performance of any radar system and uses the concepts introduced to calculate the theoretical performance of the IDRA system. In this chapter also, results from modelling of two of the main components of the radar system, the direct digital synthesizer and the quadrature deramping are discussed. It follows a description of the results of the measurements performed at different points of the transmitting and re-ceiving chains. The chapter ends with an overview of different calibration techniques.
Chapter 6 discusses the use of weather radar data for different applications. The first section
shows the link between the physics of atmospheric phenomena and the radar param-eters. It also provides an overview of the expected radar parameter values at X-band, stressing the greater influence of attenuation and Mie scattering at that band. This is followed by a discussion of the issues affecting the radar data quality. In the next section, a comparison with a standard C-band weather radar is performed. The compar-ison highlights the advantage offered by the superior range resolution both in studies of the dynamics of precipitation and in quantitative precipitation estimation. The last three sections discuss examples of observations performed by IDRA of three different atmospheric phenomena: precipitation, fog and clear air scattering.
Chapter 7 summarizes the main results of the study which have led to this thesis. It also
offers recommendations for future work in terms of data analysis, system improvement and data availability for the scientific community.
9
Chapter 2
Weather radar observables
This chapter provides the reference mark of the thesis. Section one gives an overview of the products obtained by modern scanning weather radars, namely reflectivity, Doppler moments and polarimetric products. While discussing the reflectivity, the concepts of Mie and Rayleigh scattering are introduced. Section two discusses typical meteorological events observable by weather radar like precipitation in its various forms and fog and low level clouds. Section three covers a subject that in the past has been the source of much discussion: the origin of clear air scattering, i.e. radar echoes received when no optically visible scatterers are present. Finally, section four deals with the ”undesired” phenomena that can contaminate radar measurements, that is clutter (basically reflections of any non-meteorological scatterer), interferences by other emitting systems and artefacts (undesired signals caused by the radar itself)
2.1
Weather radar products
The term radar is the acronym of radio detection and ranging . A radar system transmits a radio wave. This signal is scattered in different directions by any object placed in the field of view of the radar. Part of the scattered signal is captured by the radar receiver. Typically the radar receiver is collocated with the radar transmitter although that is not fundamentally necessary. A careful analysis of the received signal reveals information about features of the object. The level of information obtained by radars depends on the waveform of the transmitted signal and the signal processing in the receiver. The simplest radars only detect and position the objects. More complex ones can provide information about the speed of the object, its shape, its material, etc. The most sophisticated radars can actually obtain an image of the environment.
The fact that radars can obtain non-invasive information of remote objects and cover ranges from a few centimetres to hundreds of kilometres have contributed to the use of radar technology in many applications ranging from sub-surface observation to air traffic control. It should be mentioned here that other active remote sensing techniques like lidar (light detection and ranging) and sonar are based on the same principle. The only difference between them is the nature of the wave that is transmitted. Radar uses radio waves with
wavelengths ranging from 20 km to fractions of a mm whereas lidar uses waves in the optical range, that is in the order of nm. Sonar transmits and receives acoustic waves.
The capability of radars to detect meteorological phenomena was acknowledged virtually from the beginning of radar history. In fact, atmospheric remote sensing can be considered one of the earliest operational applications of radar. The first parameter used in radar mete-orology was the reflectivity, which is proportional to the power of the signal scattered by an object and received by the radar system. In the 1950s parameters based on the Doppler effect were introduced. The Doppler effect refers to the frequency shift observable in a wave re-flected by a moving object, which is proportional to the radial velocity of the object respect to the radar system. Much more recently, the potential of polarimetry for a better discrimination between the different hydrometeors has been recognized and the most modern meteorological radars are slowly migrating towards polarimetric capability.
A distinction should be made here between atmospheric profilers and weather radars. At-mospheric profilers are radars, typically pointing towards the zenith or close to it, that observe the vertical structure of the troposphere. They are widely used in studies of the microphysics of clouds, the study of the melting layer, etc. Weather radars instead scan horizontally. They are mainly aimed at obtaining information of the horizontal spatial distribution of precipita-tion and its nature. The informaprecipita-tion contained in this dissertaprecipita-tion, unless stated otherwise, refers to weather radars.
This chapter does not intend to provide a comprehensive, detailed explanation of weather radar products and observables but rather to provide a general overview of the capabilities of weather radar. There is a wide literature covering the subjects of radar and weather radar in particular. Radar systems are discussed in Skolnik [2001]. On the topic of weather observa-tions with radar several books are available, among them Battan [1973] and Doviak and Zrnic [2006]. Bringi and Chandrasekar [2001] provides a comprehensive coverage of the topic of Polarimetric Doppler Weather Radar. For a short introduction to polarimetry the reader is referred to the paper by Zrnic and Ryzhkov [1999]. The information contained in this chapter is partially based on those references.
2.1.1 Radar reflectivity
A radar transmits a radio wave with peak power Pt. If the transmitting antenna were
omni-directional the transmitted power would spread out over a sphere. Thus, at a range r the power density P D would be:
P D(r) = Pt
4πr2Latm(r) (2.1)
where Latmaccounts for the losses due to the propagation in the atmosphere. Weather radars,
though, use directive antennas which favour a direction of propagation. The power density in the direction of maximum propagation becomes:
P D(r) = PtGt
2.1 Weather radar products 11
where Gtis the gain of the transmitting antenna. The power reflected by any scatterer is
proportional to the radar cross-section σ, which is defined as the effective area of an object that re-radiates isotropically. Therefore, if the radar receiver is collocated with the transmitter the power density at the receiver is:
P D(r) = PtGtσb
(4πr2Latm(r))2 (2.3)
Here the subindex b refers to the backscattered cross-section. The fraction of power collected by the receiver antenna depends on its effective area Ae. The received power Prcan therefore
be expressed: Pr(r) = PtGtAeσb (4πr2)2L2 atm(r) (2.4) The effective area of an antenna is related to its gain Grby the following formula:
Ae=
Grλ2
4π (2.5)
where λ is the central wavelength of the transmitted radio wave. Therefore, the received power can be re-written as a function of the receiver antenna gain as:
Pr(r) =
PtGtGrλ2σb
(4π)3r4L2
atm(r)
(2.6) This fundamental expression is known as the radar range equation. Here the radar cross-section refers to a point scatterer. However, meteorological phenomena are not point scatter-ers but a distribution of small particles within a volume. The radar cross-section is therefore given by the integration of the radar cross-section of the individual particles within the reso-lution volume of the radar. The resoreso-lution volume is related to the size of the antenna main beam and the range resolution Δr of the radar. Within the resolution volume the contribution of the point scatterers is not equal. Point scatterers in the direction of maximum antenna gain are going to contribute more. Assuming that the receiver and the transmitter antennas are observing the same resolution volume, assuming also that within the resolution volume the scatterers are randomly spaced and have the same radar cross-section and that the range resolution is much smaller compared to the actual range, the radar cross-section can be ap-proximated by (Probert-Jones [1962]):
σb= ηΔrr2
πθ2
8 ln 2 (2.7)
where θ is the minimum between the transmitter antenna half power beamwidth θtand the
receiver antenna half power beamwidth θr. η is the scattering cross-section per unit volume.
Therefore the radar range equation for a volumetric scatterer can be written as: Pr(r) =
PtGtGrλ2θ2Δrη
π2r2L2atm(r)512 ln 2
This is a general expression for a volumetric scatterer. In the case of a precipitation event, particularly rain, the scattering volume is composed by a distribution of particles. If they are spherical with radius a and they have dielectric permittivity r, the scattering cross-section
can be computed exactly using the Mie solution, which is the following:
σb= π k02 ∞ n=1 (−1)n(2n + 1)(α o1n− βe1n) 2 (2.9)
where k0is the wave number defined as: k0= 2π λ (2.10) and: αo1n= ρjn(ρ)[ρ0jn(ρ0)]−√rρ0jn(ρ0)[ρjn(ρ)] √ rρ0h(2)n (ρ0)[ρjn(ρ)]− ρjn(ρ)[ρ0h(2)n (ρ0)] (2.11) and: βe1n = ρ0jn(ρ0)[ρjn(ρ)]− √rρjn(ρ)[ρ0jn(ρ0)] √ rρjn(ρ)[ρh(2)n (ρ0)]− ρ0h(2)n (ρ0)[ρjn(ρ)] (2.12)
where ρ0 = k0a; ρ = ρ0√r; [ρzn(ρ)]= d[ρzn(ρ)]/dρ. jnis the spherical Bessel function
of the first kind and h2n is the spherical Hankel function of the second kind. The spherical
Bessel function of the first kind is defined as:
jn(z) = 2nzn ∞ s=0 (−1)s(s + n)! s!(2s + 2n + 1)!z 2s (2.13)
whereas the Hankel function of the second kind is a complex magnitude defined as:
h(2)n (z) = jn(z) − ınn(z) (2.14)
where nn(z) is the spherical Bessel function of the second kind defined as:
nn(z) = (−1) n+1 2nzn+1 ∞ s=0 (−1)s(s − n)! s!(2s − 2n)! z 2s (2.15)
When ρ0and ρ are much smaller than unity the spherical Bessel and Hankel functions and their derivatives can be approximated by a simplified form and only the lowest order coefficients contribute significantly to the backscattering. Therefore it can be proved that the radar cross-section for a sphere can be approximated in such conditions as:
σb= 4π k02 r− 1 r+ 2 2ρ60= π 5 λ4|Kw| 2D6 (2.16)
2.1 Weather radar products 13
where|Kw|2is the dielectric factor of water:
|Kw|2= r− 1 r+ 2 2 (2.17)
and D = 2a is the diameter of the particle.
Since the total volumetric backscattering cross-section is a combination of the particles within the volume, the volumetric reflectivity is:
η =π 5 λ4|Kw| 2Z (2.18) where: Z ≡ 1 ΔV i D6i = ∞ 0 N(D, r)D6dD (2.19)
is the reflectivity factor. In the latest expression D is the droplet diameter and N (D, r) is the drop size distribution (DSD) at range r. The DSD has the general form of a Gamma distribution:
N(D) = NoDμe−ΛD (2.20)
where μ is a shape parameter which when it is 0 leads to an exponential distribution:
N(D) = Noe−ΛD (2.21)
A commonly used DSD is the Marshall-Palmer (Marshall and Palmer [1948]) where No =
8000 m−3mm and Λ is related to the rainfall rate as Λ = 4.1R−0.21with the rainfall rate
R in mmh−1. Thus, the reflectivity factor depends exclusively on the number and the size of droplets within the resolution volume. It is customary to express the reflectivity factor in units of mm6m−3.
The expression of volumetric reflectivity holds only for droplets small compared to the transmitted wavelength where the Rayleigh approximation can be used. For droplets with diameter comparable to, or bigger than, the wavelength the derived expression does not hold true any more since Mie scattering has to be applied. Moreover, particles other than droplets, like ice crystals, do not have the same reflectivity either. In such cases, particularly for high frequency radars where Mie scattering is more often encountered, it is customary to use the equivalent reflectivity factor Ze.
The radar range equation as a function of the equivalent reflectivity factor expressed in mm6m−3is therefore written as:
Pr(r) =
10−18P
tGtGrθ2Δr|Kw|2π3Ze(r)
r2λ2L2atm(r)512 ln 2
(2.22) This expression is true for a noiseless receiver. However in reality the received power is a mix of the scattered power Patmand additive noise Pn:
Also the power is measured after the received atmospheric signal has gone through the re-ceiver chain, which has a gain Grec. The measured equivalent reflectivity factor finally takes
the form: Ze(r) =
λ2r2L2atm(r)512 ln 2 · 1018(Pr(r) − Pn)
PtGtGrGrecΔrθ2|Kw|2π3
(2.24) In this expression there are various parameters that are exclusively dependent on the radar system. Grouping those:
Ze(r) = C(Pr(r) − Pn)
L2atm(r) |Kw|2
r2 (2.25)
where C is the radar calibration constant. This is a fundamental equation since it provides a relation between the system received power and a parameter that characterizes precipitation. It is evident that for an accurate measurement of the reflectivity a good characterization of the radar system and a good characterization of the atmospheric propagation losses if any is required. Due to the large dynamic range of Zeit is customary to express this radar observable
in decibels.
2.1.2 Doppler moments
The Doppler effect refers to the frequency shift observable by a wave reflected by moving object. The shift is proportional to the radial velocity of the object with respect to the radar system, i.e.:
fD=
2vr
λ (2.26)
where fDis the Doppler frequency and vris the radial velocity. Within the resolution volume
of a weather radar many particles are moving. Eventually, each one of them has its own velocity vector. Therefore the backscattered signal is a combination of signals with different Doppler velocities corresponding to the different particles. Since each particle has also its own reflectivity value, a relation can be established between the measured Doppler velocities and reflectivities. That is the Doppler spectrum.
The physical mechanisms of the Doppler velocity are variable. In atmospheric profilers the Doppler velocity is primarily related to the fall velocity of the particles and therefore to their size and state. On the contrary, the main contributor to Doppler velocity in weather radars is the horizontal wind and its variations within the resolution volume.
It can be proved (Doviak and Zrnic [2006]) that for weather radars, in the case of uniform wind shear and reflectivity, the shape of the Doppler spectrum is dependent exclusively on the shape of the antenna pattern. Therefore the Doppler spectrum can be well approximated by a Gaussian shape. Since a Gaussian function can be fully characterized by its mean and variance for most applications the computation of the mean Doppler velocity and Doppler spectrum width σvis sufficient.
2.1 Weather radar products 15
The mean Doppler velocity is related to the mean wind speed within the volume. The mechanisms that contribute to the enhancement of the Doppler spectrum width have been the subject of much investigation. Classically, the Doppler spectrum width has been considered the sum of various independent contributions, both related to the radar and the environmental conditions. Thus, the Doppler spectrum width can be expressed as (Doviak and Zrnic [2006]):
σ2v= σ2s+ σ2ω+ σd2+ σo2+ σt2 (2.27)
where σ2s is the broadening of the spectrum due to wind shear, σω2 is caused by antenna
motion, σ2dis due to the fall speed of the different hydrometeors, σ2ocorresponds to changes in orientation or vibration of the hydrometeors and σt2is due to turbulence. Since σ2dis related to the elevation angle θeof the radar antennas:
σ2d= (σdosin θe)2 (2.28)
This term is negligible for horizontally scanning radars. It can be proved that σω2 can be
expressed as: σ2ω= ωλθe 2π 2 ln 2 θtθr (2.29) where ω is the angular velocity of the antenna. The wind shear term is composed of three contributions:
σ2s= σ2sθ+ σ2sφ+ σsr2 (2.30)
The terms are related to the radial velocity shear along the three orthogonal directions through the resolution volume. It is assumed that wind shear is uniform and the weighting function due to the antenna pattern and the reflectivity are product separable along the orthogonal directions. If kθ, kφ, kr are the wind shears in the directions θ, φ and r then σ2s can be
approximated by:
σ2s= (rσθkθ)2+ (rσφkφ)2+ (rσrkr)2 (2.31)
where σθ and σφ are defined as the second central moments of the two-way antenna power
pattern in the indicated directions and σris the second central moment of the contribution of
the range resolution. For a circularly symmetric Gaussian pattern: σ2θ= σ2φ= θtθr
16 ln 2 (2.32)
while:
σ2r= (0.35Δr)2 (2.33)
The spectral broadening σo due to changes in orientation or vibration of hydrometeors is
Frisch and Clifford [1974] establish a connection between the eddy dissipation rate and σt
for homogeneous and isotropic turbulence.
In a more recent paper, Fang and Doviak [2008] argue that equation 2.27 may only be valid for non-scanning radars. The reason for that being that, if the beam scans, some terms in the equation are not independent variables but dependent on the scanning rate of the antennas.
2.1.3 Polarimetric products
At far range the transmitted electromagnetic field is a planar wave. Polarization refers to the orientation of the electric field in this plane. If the variation of orientation in time does not form any particular shape the electromagnetic wave is not polarized. However if it takes an elliptic shape it is polarized. If the form of the ellipse changes in time the electromagnetic field is partially polarized. A particular case of polarized electromagnetic wave is linear polarization where the orientation of the electromagnetic field lies on a line.
Polarization is a very useful source of information to determine the shape and orientation of a scatterer. For example, if a linearly polarized wave interacts with an elongated object the size of which is much smaller than the wavelength the backscattered power will be much larger if the object is oriented along the polarization direction than if it is perpendicular to it. By transmitting and receiving two orthogonal polarizations, the polarization matrix describ-ing the polarimetric properties of the object can be fully determined.
The two most widely used polarimetric bases in radar meteorology have been the circular and linear polarization bases. It can be proved (see Jameson and Dav´e [1988]) that it is possible to change from one base to another and both bases provide equivalent information. However, the way to obtain the polarimetric parameters operationally can lead to significant differences between the two polarizations and the direct information retrievable from each polarization is not the same. For operational weather radars, scanning towards the horizon, the linear polarization base has been favoured because it has the advantage to provide a direct relation between the shape and orientation of the observed hydrometeors and the measured backscattered electromagnetic fields. The linearly polarized radars transmit consecutively horizontal and vertical polarization and receive, either simultaneously or consecutively, both polarizations.
Polarization has multiple applications in weather radar. In the first place, since the po-larimetric properties of precipitation are well known, it can be used to identify clutter (i.e. undesired echoes) like ground clutter, birds, insects, etc. Secondly, the type of precipitation, (hail, snow, rain, etc.) can be discriminated. Moreover, it can improve greatly the quantitative precipitation estimation. The relation between reflectivity and rain intensity is not trivial due to the influence of the droplet size on the reflectivity. Bigger droplets reflect more but at the same time the water content is smaller than in an ensemble of smaller droplets because they are less concentrated. However, small droplets have a spherical shape, whereas they tend to become more oblate when they grow in size. Therefore polarimetry can be used to determine the size of the droplets and consequently improve the precipitation estimates.
fol-2.1 Weather radar products 17
lowing the most widely used ones in the linear polarization base will be described.
The differential reflectivity ZDRis the ratio between the measured reflectivity factor for
co-polar vertical and co-polar horizontal, commonly expressed in dB. i.e: ZDR= 10 log
Zhh
Zvv
(2.34) The linear depolarization ratio LDR is the ratio between the measured reflectivity factor for cross-polar and co-polar horizontal, i.e.:
LDR= 10 logZhv Zhh
= 10 logZvh
Zhh
(2.35) By antenna reciprocity Zhv= Zvh. In practice, if simultaneous measurements of the received
horizontal and vertical polarization can be performed, Zhhand Zhvare simultaneously
ob-tained to avoid decorrelation.
The co-polar correlation coefficient ρhvis defined as:
ρhv= |ρhv|ejδ (2.36) where |ρhv| = |S hhSvv∗ | |Shh|2|Svv|2 (2.37)
where Sxx is the backscattered electromagnetic field, with the first subindex denoting the
transmitted polarization and the second the received polarization. h stands for horizontal polarization and v for vertical polarization. δ is the backscatter differential phase, i.e. the difference in phase between the horizontal and vertical fields caused by backscattering. The backscattering differential phase tends to 0 for objects much smaller than the wavelength (Bringi and Chandrasekar [2001]).
Propagation effects strongly influence the polarimetric measurements. The two most im-portant are the differential attenuation and differential phase shift φDP . Differential
attenu-ation refers to the fact that the vertical and horizontal components are not equally attenuated. That poses a serious difficulty for the correct estimation of the differential reflectivity partic-ularly at far ranges and in situations of heavy precipitation. Differential phase shift refers to the fact that in rainy media the horizontally polarized waves propagate slower than the verti-cal ones. The measured differential phase ψDP is actually a combination of the backscattered
differential phase and the propagation differential phase shift:
ψDP = φDP+ δ (2.38)
As mentioned before δ tends to 0 for objects much smaller than the wavelength. Therefore it is generally negligible for large wavelengths but has to be taken into account for smaller wavelengths, particularly in heavy rain situations.
The specific differential phase KDP is a range derivative of the differential propagation
phase:
KDP(r2) =
φDP(r2) − φDP(r1)
2(r2− r1) (2.39)
This observable is useful, either alone or combined with others, for quantitative precipitation estimation, particularly because it is not affected by differential attenuation (Ryzhkov and Zrnic [1995]).
2.2
Precipitation and low level clouds and fog
The most common precipitation phenomena in the Netherlands are rain and drizzle. In winter time snow is not infrequent whereas in summer episodes of hail can occur. During the cold season low level clouds and fog are usual.
The two most common types of precipitation in the Netherlands are, in this order, frontal and convective rainfall respectively. Frontal rainfall is produced when a mass of cold air meets a warmer one. Being lighter, the warm air mass is forced to rise above the cold air. As it rises it gets cooler. When this warm, moist air reaches the dew point temperature, water condenses forming clouds that eventually precipitate. This type of rainfall is widespread and it can last several hours. The rainfall intensity tends to be moderate. Convectional rainfall is most likely produced during a hot period. During the day the sun warms the surface of the earth. The air above the surface gets heated and therefore it rises since it becomes lighter. As the air rises it cools and the water content condenses, initially forming clouds called cumulus. If the atmosphere in the region is not stable, i.e. there is turbulence, and there is sufficient moisture the droplets collide forming bigger droplets. Eventually, the cumulus clouds may grow, forming deep clouds named cumulonimbus, which may lead to locally intensive precipitation of a relatively short duration. Convective-like precipitation caused by instabilities of the atmosphere can be encountered within frontal rainfall events.
Generally speaking, air temperature decreases with height. The height with temperature 0oC is called the 0oC isotherm. Above the 0oC isotherm the water content is usually in the form of ice crystals, although liquid water in the form of supercooled droplets can be present in stratiform or cumulus clouds. As ice crystals grow they fall. During their fall they may collide with other ice crystals producing snowflakes by aggregation. When the falling snowflakes pass below the 0oC isotherm they start to melt, turning into raindrops. If the 0oC is located close to the surface precipitation is in the form of snow. This stratified structure of the precipitation is typical of frontal phenomena. Because convective rainfall tends to occur in a much more turbulent atmosphere, different types of particles can appear at the same altitude due to the influence of up and down drafts. If raindrops are lifted above the 0oC isotherm due to a strong updraft they may freeze and turn into hailstones.
Another common type of precipitation is drizzle. Drizzle is defined as a fairly uniform precipitation composed exclusively of fine drops of diameter less than 0.5 mm which are very close together. Drizzle appears to float while following air currents, although unlike fog
