Improved Observation of Transient Phenomena with Doppler Radars: a Common Framework for Oceanic and Atmospheric Sensing
IIMPROVED OBSERVATION OF TRANSIENT PHENOMENA WITH DOPPLER RADARS: ACOMMON FRAMEWORK FOR OCEANIC AND ATMOSPHERIC SENSING
Baptiste Domps, Julien Marmain
Degreane HorizonRadar DepartmentCuers, [email protected]
Charles-Antoine Gu´erin
Universit´e de Toulon, Aix-Marseille Univ.,CNRS, IRD, MIOToulon, [email protected]
ABSTRACT
Doppler radars are routinely used for the remote sensing ofoceanic surface currents and atmospheric wind profiles. Eventhough they operate at different frequencies and address dif-ferent media, they follow very similar processing for the ex-traction of measured velocities. In particular they both facethe challenging issue of capturing geophysical phenomenawhich vary rapidly with respect to the typical integration time.Recently, the authors applied a non-spectral formalism basedon autoregressive processes to model the backscattered timeseries obtained from High-Frequency oceanic radars. Theyshowed that it allows to calculate Doppler spectra for veryshort integration times without losing in frequency resolutionnor signal-to-noise ratio. We apply this technique to syntheticand experimental data within a common framework and showfor the first time the strong potential of the method for thestudy of transient atmospheric phenomena.
Index Terms — Doppler Radar, High-Frequency Radar,Wind Profiler, Bragg Scattering, Autoregressive Modeling
1. INTRODUCTION
Doppler radars have been customarily used for decades formeasuring wind profiles in the air column as well as oceaniccurrents at the sea surface (e.g [1, 2]). Even though the phys-ical mechanisms driving the backscattering from atmosphericand oceanic media are very different, there are many formalanalogies in the description of the received time signal andits conversion to geophysical variables. In both cases thederivation of a radial velocity, which can be further inter-preted in terms of wind speed or surface current, relies onmeasuring a Doppler shift with respect to some reference fre-quency, namely the zero Doppler in the atmospheric case andthe Bragg frequency in the oceanic case. In either situationthe accuracy of the measurement is limited by the coherentobservation time which is necessary to produce a Dopplerspectrum. As it is well known, the choice of the observa-tion time results from a trade-off between the required dura- tion for sufficient Doppler frequency resolution and Signal-to-Noise Ratio (SNR) and the maximum time scale over whichthe geophysical observables can be assumed stationary. Thetypically employed observation times are of the order of afew tens of seconds for VHF/UHF radar Wind Profilers (WP)and a few tens of minutes for oceanographic High-FrequencyRadars (HFR). This is satisfactory for the vast majority ofsituations where the main atmospheric and oceanic featuresare only slowly varying with respect to the temporal scaleof observation. However, there are some specific instanceswhich do not comply to this observation scheme. This is thecase whenever transient phenomena or rapidly evolving fieldsof velocities are involved, such as e.g. 1) wind gusts, stormsurges or tsunamis in the oceanic context; 2) landing planes,bird swarms and wake turbulence echoes in the atmosphericcontext. This calls for specific processing of the time echo toovercome the classical time-frequency dilemma.The authors recently applied a non-spectral, paramet-ric approach, referred to as the Time-Varying Autoregres-sive Maximum Entropy Method (TVAR-MEM) to processrapidly changing oceanic data [3, 4]. It is based on an Auto-Regressive (AR) representation of the received time seriesthat allows maintaining high Doppler resolution and ele-vated SNR even with short samples. Due to the similarity ofthe scattering formalism for oceanic and atmospheric sensing(Section 2), the method can be also employed for atmosphericsensing and we present here its first utilization in this context.We illustrate the performances of this analysis with synthetic(Section 3) as well as original experimental data (Section4). We provide high-resolution Time-Frequency imaging ofthe radar time series that can capture some hitherto hiddensignatures of birds and planes echoes.
2. THEORETICAL BACKGROUND
As it is well known, the backscattered time series s ( t ) from anatmospheric turbulent layer and from the sea surface share thesame remarkable property, once resolved in direction: withina single-scattering approximation they are proportional to the a r X i v : . [ phy s i c s . a o - ph ] J a n patial Fourier Transform of the perturbating quantity X ( r , t ) in the medium: s ( t ) ∼ (cid:90) medium X ( r , t ) e − i K · r d r (1)In the former case, this is obtained with the Born approxima-tion for weak permittivity contrast (e.g. [5]), X is a contrastinduced by the atmospheric particles and K is the (three-dimensional) incident EM wave vector; in the latter case, thisresults from the perturbation theory for shallow rough sur-faces (e.g. [6]), X is the contrast of elevation induced bywaves at the sea surface and K is the (two-dimensional) hor-izontal projection of the incident EM wave vector. In bothcases, the backscattering echo is mainly caused by resonantstructures having a typical length comparable to half the radarwavelength, a result known as “Bragg law”. For clear-airscattering, such structures are “blobs” of turbulent air mov-ing with the wind. They are seen in the Doppler spectrumas a single broad peak around the central Doppler shift f c in-duced by the radial wind speed U r = − λf c / . For a cleansea surface observed with an coastal oceanographic radar, theresonant features are the so-called Bragg waves [7] which arethe gravity waves at half the radar wavelength. As they canbe possibly propagating in two opposite directions, the re-sulting Doppler spectrum generally exhibits 2 Doppler peaks f ± c = ± f B at the so-called Bragg frequency f B = (cid:112) g/ ( πλ ) and its opposite. Any additional surface current U r translatesthe 2 Bragg peaks by the same shift − U r /λ , so that the lattercan be inverted from the residual Doppler shift.Digital computation of the Doppler spectrum is routinelyachieved from the range-resolved complex voltage time series s ( t ) using a Fast Fourier Transform (FFT) algorithm. Bestfrequency resolution and SNR are thus obtained for “long” in-tegration times. Inversely, short integration times, such thoseneeded to observe transient phenomena, strongly deterioratesthe quality of the spectrum and eventually the Doppler esti-mate. Here, we use the TVAR-MEM approach [4] to modelthe backscattered Doppler spectrum at high temporal and fre-quency resolution. The full time series are splitted in se-quences of N samples, overlapping by half of their length.Each sequence is then modeled as an autoregressive (AR) pro-cess of order p [8]: s ( n ∆ t ) = − p (cid:88) k =1 a k s (cid:0) ( n − k )∆ t (cid:1) + ε n (2)where a k are the modeling AR coefficients and ε n is a whitenoise. In the context of oceanographic measurements, the au-thors experimentally demonstrated that the best choice for theAR order p is N/ [3], a criteria we extend to the contextof atmospheric analysis. The AR coefficients are here evalu-ated using the Maximum Entropy Method (MEM) or “Burgmethod” [9], which was found efficient for short integrationtimes. The Power Spectral Density (PSD) is finally computed from the AR coefficients: P AR ( ω ) = P ε (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) p (cid:88) k =1 a k e − ikω ∆ t (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) − (3)The fast updating of the AR coefficients makes them “time-varying” (TV) and we will refer to this method as TVAR-MEM. The temporal fluctuations of the backscattered Dopplerspectrum, evaluated at rapid scale with the TVAR-MEM, canvisually be assessed by representing the PSD in the Time-Doppler plane. We will further refer to this representation asthe “Time-Doppler spectrogram”. Despite being commonlyused in the radar community, this representation has foundlittle to none applications to HFR nor WP until now, be-cause of the “long” integration times usually required. TheTVAR-MEM approach alleviates this issue.
3. ASSESSMENT WITH SYNTHETIC DATA
We will first assess the performances of the TVAR approachin a common formalism including both atmospheric andoceanic remote sensing. For this, we simulate radar timeseries following the approach proposed by [10]. A typ-ical backscattered Doppler spectrum P can be written as P ( ω ) = − (cid:0) S ( ω ) + N (cid:1) X ( ω ) where S is the signal PSD, N is the uniform PSD of white noise and X is an exponentiallydistributed random variable. The complex voltage time seriescan then be obtained (up to a scaling factor) with a DiscreteFourier Transform of the complex spectral components: s ( t ) ∼ (cid:88) j (cid:113) P ( ω j ) e i (cid:0) ω j t + ϕ j (cid:1) e iΦ D ( t ) (4)where ϕ j are uniform independent random phases. By con-struction, the amplitudes (cid:112) P ( ω j ) are Rayleigh distributedand the individual frequency components are complex Gaus-sian variables. The deterministic varying phase Φ D ( t ) repre-sents the phase shift induced by the velocity of perturbations, Φ D ( t ) = (cid:82) t U r ( τ ) dτ . In the oceanic context, U r ( τ ) is theinstantaneous radial surface current and the integral Φ D ( t ) isreferred to as the “Memory Term”, see e.g. [11]; in the atmo-spheric context, U r ( τ ) is the radial wind speed. The mem-ory term accounts for the possible fluctuations of the veloc-ity U r during the integration time and reduces to the classi-cal Doppler shift, Φ D ( t ) = 4 π/λU r t = ω D t , whenever thevelocity can be assumed constant over the integration time.The resonant frequency peaks in the signal PSD S are mod-eled with a pair of Gaussian functions centered at plus or mi-nus the Bragg frequency (HFR) or a single Gaussian shapecentered at the null Doppler frequency (WP). As a genericexample we have generated a backscattered time series cor-responding to 20 MHz radar carrier frequency at a samplingrate ∆ t =
100 ms. A single positive Bragg line of width σ = × −3 m.s −1 has been assumed with rapidly varyingelocity U r ( t ) = U cos ( ω t ) where U = −1 and ω = × −2 rad.s −1 . The instantaneous PSD has been re-calculated from the time series using either the TVAR-MEMor the classical FFT approach by processing half overlappingseries of N =
128 samples (i.e. 33 s). The chosen valuescorrespond to the typical case of a HFR observing surfacecurrents but could be simply rescaled to be consistent withthe case of a WP sensing wind velocity. Figure 1 shows theTime-Doppler spectrograms obtained with the two methods.The temporal variations of the Bragg line are accurately ren-dered with the TVAR-MEM, while barely visible using FFT. − . . . (a) . . . . . . . Time (min) − . . . (b) − − − − −
10 0 dB D opp l e rfr e qu e n c y ( H z ) Fig. 1 : Simulation of the normalized PSD (colorscale; dB)that would obtained with a HFR. The representation is in theTime-Doppler plane, where the vertical axis is the residualDoppler frequency. The instantaneous PSD is computed fromoverlapping synthetic time series of N =
128 points (33 s) inpresence of a rapidly-varying radial surface current U r ( t ) andlimited to the positive Bragg line: (a) TVAR-MEM; (b) FFT.Simulated Doppler shift f D is superimposed as dashed line.
4. APPLICATION TO EXPERIMENTAL DATA
Next we present an application of the TVAR-MEM approachto two experimental data sets. The first has been routinelyacquired by the WERA HFR (Helzel GmbH) of Tofino, onthe Pacific Coast of Vancouver Island, British Columbia; theselected time series has been recorded during the passage ofa an abnormal transitory oceanic and atmospheric event. Thesecond has been acquired with the Degreane Horizon PCL-1300 WP during the SESAR experiment that took place nearthe landing runways of Paris Charles de Gaulle Airport.
On October 14, 2016, the HFR of Tofino raised a tsunamialert based on the measurements of strong abnormal surface currents. Due to the absence of any recorded seismic activity,this event was related to the family of atmospheric-inducedtsunamis [11, 4] and can be used as benchmark for tsunamidetection algorithms. Here, we apply the TVAR-MEM tomodel the backscattered Doppler spectrum at high temporalscale. The time series s ( t ) were processed by half overlappingblocks of N =
128 samples (i.e. 33 s). Figure 2 is the result-ing Time-Doppler spectrogram centered on the positive Braggline. The fine frequency resolution reveals a micro-Dopplerjump of 2.5 × −2 Hz (i.e. 25 cm.s −1 ) at 05:40 UTC, corre-sponding to a sudden surge of surface current. Furthermore,the increase of the positive Bragg line amplitude correspondsto a strengthening of the Bragg waves advancing towards theradar, confirmed by a sudden 20 cm rise in sea level measuredby coastal tide gauges. :
00 05 :
15 05 :
30 05 :
45 06 :
00 06 :
15 06 :
30 06 : Time (UTC) . . D opp l e rfr e q . ( H z ) Fig. 2 : Normalized HFR PSD (same colorscale as Figure 1;dB) in the Time-Doppler plane, computed from overlap-ping synthetic time series of N =
128 points (33 s) every τ = f B ± × −3 Hz window (i.e. ±
75 cm.s −1 ). Vertical baris an interruption in acquisition for quality control. The SESAR P12.2.2 XP1 campaign was conducted in autumn2012 on the Paris CDG airport. The Degreane Horizon PCL-1300 WP was installed vertically below the “Outer Marker”of the landing runway 26L, which is located about 10 km Eastof the runway and marks the begin of the final approach seg-ment. We have analyzed the complex voltage time series re-ceived on an antenna pointed towards the landing axis at a73° site angle. The time series were processed using TVAR-MEM from overlapping blocks of N =
32 points (0.15 s) andupdated every τ =
75 ms. We selected for the illustration 3specific events, acquired on September 24, 2012 at range gate3 (altitudes 720 to 1075 m). Figure 3 shows the TVAR-MEMcorresponding Time-Doppler spectrograms and time series. (a) Wind Echoes:
Typical steady wind echoes are seenin Figure 3a as the horizontal strip around the frequency f D =
45 Hz (i.e. U r = −1 ). The instantaneous PSD(vertical slices in the Time-Doppler representation) have a − D opp l e rfr e qu e n c y ( H z ) Ground Clutter EchoesWind Echoes (a)
Time (s), starting at 05:36:00 UTC − R e (cid:0) s ( t ) (cid:1) ( a . u . ) Flapping Bird (b)
Time (s), starting at 19:03:27 UTC − P l a n e Wake Turbulences (c)
Time (s), starting at 05:30:46 UTC − − − −
25 0 dB
Fig. 3 : Data acquired with the PCL-1300 WP during the SESAR experiment.
Top:
Normalized PSD (colorscale; dB) inthe Time-Doppler plane, computed with TVAR-MEM from overlapping samples of N =
32 points (0.15 s) every τ =
75 ms.
Bottom:
Real part of the radar time series s ( t ) showing the “contamination” by transient phenomena.Gaussian shape around this central frequency. The markedhorizontal line around the zero Doppler frequency corre-sponds to the dominant echo of fixed target. (b) Flapping Bird: Clear-air echoes are contaminated byavian echoes starting at 19:03:37 UTC (Figure 3b). A bird isflying towards the radar at a radial speed varying from 4.7 to0 m.s −1 . The wingbeat frequency can be extracted from themicro-Doppler oscillations and is here close to 3 Hz. (c) Plane and Wake Turbulences: Strong echo of an air-plane is located in the the first 10 s. Note that the airplanespeed exceeds the Nyquist frequency leading to aliased echo.Assuming constant speed and altitude during the record, onecan infer a Doppler rate of change of 66 Hz.s −1 , correspondingto an average plane radial speed of 75 m.s −1 which is consis-tent with the typical landing speed of commercial aircrafts.The echo is followed by multiple oscillating echoes which weattribute to wake vortex turbulence.
5. CONCLUSION
We have presented the first application of the TV-AR-MEMin the double context of ocean and atmospheric sensing. It hasbeen applied for the first time to an experimental WP dataset.The resulting Time-Doppler maps unveil details of rapid at-mospheric variations at the scale of one second, such as birdflapping or turbulence in the wake of a plane. Further work isin progress to confirm the strong potential of this technique.
Acknowledgments:
First author was supported by the DirectionG´en´erale de l’Armement (DGA). We are grateful to Ocean NetworksCanada for providing HFR data and to Dr Philipp Currier for count-less discussions on WP.
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