e£S.<3i&ZjL397~6i/&-*5p NOAA Technical Report ERL 397-WPL 52 ^V>X fr Basic Comparison of Lidar c X s S >*TES O* * J and Radar for Remote Sensing of Clouds V. E. Derr March 1978 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration Environmental Research Laboratories NOAA Technical Report ERL 397-WPL 52 '*^™of^ A Basic Comparison of Lidar and Radar for Remote Sensing of Clouds V. E. Derr Wave Propagation Laboratory Boulder, Colorado March 1978 % u o o. U.S. Department of Commerce o Juanita Kreps, Secretary National Oceanic and Atmospheric Administration Richard A. Frank, Administrator Environmental Research Laboratories Wilmot Hess, Director Digitized by the Internet Archive in 2013 http://archive.org/details/basiccomparisonoOOderr Contents Page ABSTRACT 1 1. INTRODUCTION 1 2. COHERENCE 2 3. SIGNAL-TO-NOISE RATIO EQUATION FOR PULSED LIDAR AND RADAR 3 4. COMPARISON OF RADAR AND LIDAR IN CLOUD OBSERVATIONS. . 4 5. LIMITATIONS OF LIDAR COHERENT DETECTION 12 6. COMPARISON OF COHERENT AND INCOHERENT LIDAR 13 7. CONCLUSIONS 13 8. ACKNOWLEDGMENTS 14 9. REFERENCES 14 Appendix: THE DEIRMENDJIAN MODIFIED GAMMA DISTRIBUTION 15 in A BASIC COMPARISON OF LIDAR AND RADAR FOR REMOTE SENSING OF CLOUDS V. E. Derr Abstract. Both radar and lidar have proved valuable in studying cloud microphysics and dynamics. Because of the large difference in wave- length, the two techniques have differing penetration capabilities and de- tection sensitivities. A "system-free" comparison of radar and lidar for several missions and many cloud types is presented to permit the optimum choice of technique for field studies of cloud formation, development, and precipitation. 1. INTRODUCTION The most obvious and most pressing of at- mospheric science problems are related to predic- tion and modification of atmospheric phenomena. Severe storm warning, regional and local forecast- ing (including effects of weather on pollution con- centrations), and climate prediction are among the most important of the meteorological services needed. A variety of observational, theoretical, and calculational techniques are required for study of atmospheric phenomena, which range widely over spatial and temporal scales. Until re- cently, with the notable exception of radar, obser- vation and measurement were primarily by in-situ instruments, either ground-based or aircraft- or balloon-borne. Increasingly, new satellite plat- forms and new forms of remote sensors play a role in atmospheric observations. Remote-sensing techniques provide essentially real-time three- dimensional measurements of conventional parameters of the atmosphere and new parameters not previously measurable. Clouds are important entities of the earth's at- mosphere, strongly affecting human activities by their optical properties and by their role in precipi- tation. The droplets and the interstitial water vapor even in clouds of slight thickness may absorb several watts of solar radiation per cubic meter, and may reflect back to space large por- tions of the solar radiation that would otherwise reach the earth's surface. Enormous amounts of heat, on the order of 2500 joules/gm, are absorbed or released when water vaporizes or condenses. Representative clouds contain approximately 1 g liquid water per m 2 . Thus, one cubic meter of cloud may release (or absorb) 2500 joules in change of state and may absorb on the order of 10,000 joules of solar radiation per hour. Varia- tions in cloud type, in cloud cover, and in precipi- tation may play an important long-range role in climate fluctuation in addition to their more im- mediate role in local weather processes. Changes in the temperature, water content, drop-size distribution, and spatial coverage, affect and are affected by the ambience of the clouds. The large spatial extent and the often rapid fluc- tuations of characteristics introduce grave diffi- culties into the in-situ study of cloud processes. Thus, clouds are an important example of atmos- pheric constituents that may be observed to ad- vantage with remote-sensing techniques, which provide essentially real-time measurements over large volumes. Radar and radiometry have been used to ob- serve cloud characteristics and processes for many years (Battan, 1973). More recently lidar has been used to observe clouds too thin to be "seen" with radar (Piatt, 1973). Backscatter coefficients may be obtained as a function of time and space, giving very exact measurements of the location of cloud bodies. Depolarization ratios give an estimate of ice to water content (Sassen, 1976; Derr, 1976). Multiple wavelengths have been used to obtain estimates of size distributions, and Doppler lidar gives promise of providing clear air velocity distri- butions around clouds. The most obvious differences between lidar and radar arise because of the large difference in wavelength. Because of this difference, lidar operating at a near-optical wavelength has greater sensitivity to small particles than microwave radar, but also suffers greater attenuation in dense clouds. This report provides a numerical analysis of these differences for a variety of cloud types and thus illustrates the proper choice of remote sensor for various observing missions. Because of the wide variety of radar and lidar systems existing (and the even greater list of potential systems) it is advisable, if possible, to avoid a discussion of particular systems and look instead at basic differences. To achieve a com- pletely "system-free" analysis is not possible, but one can be approached by considering only the characteristics of the medium ("clear" atmosphere and clouds) and the characteristics of typical de- tectors. The medium is described by the radar backscatter coefficient /3, and the attenuation coef- ficient # ext . (The effects of atmospheric inhomo- geneities are discussed only briefly, in Section 5.) Detectors are characterized by their noise tem- peratures or, equivalently, by a noise figure. In this analysis we assume that the detector noise is the most important source of noise. In anticipa- tion of later discussion, the relative signal-to-noise ratio, S N(Rel) p e -0 ext (R-U R 2 T, eff and special cases of it, will be examined. R is the range to the cloud, h is the depth of cloud penetra- tion, and T e ff is the effective noise temperature of the detector. The relative signal-to-noise ratio is mission-dependent because of the range and depth of penetration. It is not completely "system-free" because of the detector characteristic 7 e ff. Both lidar and radar are, to some extent, limited by background as well as detector noise. The daytime use of lidar is severely limited in the wavelength range 0.2 to 3 /xm by solar radiation. The limitation, in the case of both background and detector noise, is partially removable by the use of superheterodyne receivers to limit the noise bandwidth. Such receivers are completely practic- able at some infrared wavelengths, e.g., 10.5 /*m, but are not yet field-worthy at visible wave- lengths. In the discussion to follow, we assume superheterodyne receivers are used for both radar and lidar. We begin with discussions of coherence and the radar-lidar equation before proceeding to a comparison of the uses of radar and lidar in cloud observations. 2. COHERENCE Coherent detection is fundamental to improv- ing laser probing techniques. It provides signifi- cant advantages to velocity measurement and sen- sitivity. The central parameters in the elementary theory of optical coherence are correlation func- tions; by means of these a precise theory can be given. It is both intuitively satisfying and mathe- matically productive to consider the correlation of an electromagnetic field at (possibly) two different times and two different points. However, we will not make much use of the "degree of coherence" that follows from such correlation functions (Mandel and Wolf, 1965), but will instead find it satisfactory to refer to intuitive concepts. Although such a concept of degree of co- herence shows the interdependence of time and space, it is often useful to make a distinction be- tween temporal and spatial coherence. The differ- ence, in terms relevant to this discussion, can be illustrated by heterodyne and interferometric ex- periments. To produce a set of interference fringes in space arising from two beams of light, the waves arriving at the "screen" must be in phase in order that the fringes remain visible. Sources that do not maintain phase coherence thus will not produce observable fringes. (Observable here implies persistence.) Consider a narrow frequency bandwidth light beam, in which component phases are drifting slowly (with respect to one cycle) but randomly, and are entering a Michelson interferometer. With the mirrors at equal spacing the zero order interference fringes are seen. As one plate is moved, we go through a series of construc- tive and destructive interference fringes. If the light is perfectly coherent and parallel (ignoring diffraction) the fringe system continues to be observable at wide separations. However, for any known light source the visibility (contrast, distinc- tiveness) of the fringes deteriorates with separation. This can be understood by the random rela- tionship of relative phases as the light beams re- unite at the "screen." Thus, the concept of "co- herence length" arises. A long difference in path lengths of a split non-monochromatic beam results in phase discrepancies that destroy fringe visi- bility. This effect is important, for example, in re- mote-sensing systems that utilize interference to detect Doppler shifts in Rayleigh backscatter. More relevant to the present problem is the effect noted when inhomogeneities of refractive index are introduced into one path. Some of the fringes would disappear because of the shift in phase caused by the change in optical path length; others would be displaced. The uniformity of fringes across the aperture would be destroyed. Thus one of the beams (thought of as a local oscillator) would have a random phase relationship to parts of the other beam (thought of as a signal travers- ing a turbulent atmosphere). Consider now the same beam of light incident on a detector together with a local oscillator that has similar spectral structure but is displaced in frequency by the amount A/. A short calculation shows that the difference is unaffected by phase for a square law detector. Thus the only require- ment for frequency mixing, or heterodyning, is a sufficiently narrow bandwidth. Coherence length or phase considerations are not required at a point. It is required, however, as indicated above, that the signal be relatively in phase across the mirror or antenna. Otherwise coherent mixing with a local oscillator signal cannot occur. Coherent detection involves a process of mix- ing of two frequencies at and near the carrier fre- quency and eliminates, by filtering, the noise and signal except near the frequency that is the differ- ence between the carrier and local oscillator. To illustrate these points we show how the signal-to- noise (S/N) ratio expression for both noncoherent and coherent detectors is derived and thereby the expected difference in S/N between video and superheterodyne receivers is calculated. 3. SIGNAL-TO-NOISE RATIO EQUATION FOR PULSED LIDAR AND RADAR It is assumed that three separate electro- magnetic fields impinge on a photodetector: the signal from a distant target (A s cos co 5 f), the local oscillator (A r cos u3 r t), and the noise back- ground (LA bg cos o) bg .t). The sum, in the / background noise signal, is over the frequencies in the pass band, with or without heterodyning, as appropriate. The total field at the photodetector is then the sum of the amplitudes, £ = A r cos co r f + A s cos cj s f + E A bg cos cc hg t, i and the power incident on the photodetector is P = — E 2 =— (A r cos co r r + A s cos u> s t + LA t i cos <* bg ty. (Because of the coherence of the fields, we add the amplitudes of the signals.) The current produced in the detector by transduced radiation is z (f) = PP{t). To this must be added the "dark current," Id, of the detector to obtain the total current i = PPit) + l d . Using P, = — A, 2 to denote the power in the indi- vidual components, Pit) = P s + P r + P bg = 2\fl\P 5 cos (w r -w 5 )f + L2sJpK, cos(co 5 -o b „.)f + E2V PrPfee . cos(u) r -a) b „.)f UbgJ (The conclusions are unaffected by fixed relative phase shifts of the fields.) Factors such as cos(a> r + w 5 )f have been eliminated by averaging over a time that is long compared with the optical period l/w r , but short compared with the period of the difference frequency l/(a> r -a> s ). At this time I note two cases, depending on whether mixing is used. If there is no mixing, then ;. n = p P (t) +i d = pp s + P p bg + IP L>Jpj\.cos(u, s -cj bg )t + l d (the incoherent case), and i co = PP 5 +PP r + PP bg + 2Py/P r P 5 cos(u r -u s )t + 2P Ly/P s P bg .cos{o3 s -o) bg )t i + 2P E y/PrPbg. cos(w r -o) bg )t + l d , i when coherent mixing is used. The power at the output of the detector (neglecting amplifier noise and local oscillator noise) is proportional to the sum of the mean square currents from each com- ponent. Thus, the signal-to-noise ratios for the two cases is PP* - (in) = N 2eAf[p 5 + P bg + if] where the small effect of beats between the back- ground noise and the signal has been ignored, and PP s P r (co) = eAf[p r + P 5 + P bg +!^ (The mean square current noise power is equal to 2eAfP, where A/ is the receiver noise bandwidth and e is the electronic charge.) If P r > P s , P r > P bg , andP r > I d /P, then s , v pP s QPs — (CO) = = , , N eAf hpAf because Qe fiv = P, where Q = quantum effi- ciency, e = electronic charge, h — Planck's con- stant, and v = frequency. These formulas will be used in the following sections. For more details of this derivation, consult Biernson and Lucy (1963). It is important to note that increased local os- cillator power acts to negate the effect of the sky background noise, the shot noise of the signal, and the dark current noise. This is feasible in practice up to the saturation limit of the mixer. Signal-to-noise ratios for coherent and inco- herent detection may be compared by their ratio: s N (CO) [ 2 P 5 + P bg+ f\ S N (in) P s This expression shows that the S/N ratio for co- herent detection is always at least twice that for incoherent detection. When background noise dominates all other noise sources, as is frequently the case for daytime lidar use, the coherent S/N is independent of it if P r is sufficiently large. These equations will be used in the following section. 4. COMPARISON OF RADAR AND LIDAR IN CLOUD OBSERVATIONS A comparison of remote-sensing systems is difficult because the sensitivity, signal-to-noise ratio (S/N), and other characteristics depend on detailed design features. To avoid a system-de- pendent analysis to the fullest extent possible, per- formance will be compared for cases in which only fundamental shot noise limitations are present; subsequently, the effect of some essential system and mission parameters will be examined. Initially the signal-to-noise ratios of coherent detectors at microwave frequencies and coherent detectors at optical frequencies (using the S/N equation above), are compared in forms appropriate for each case: where k is the Boltzmann constant, and h is Planck's constant, where S/N(^X) is appropriate for microwave radar, and S/N(opt.) for optical lidar. Either the effective temperature T eff or the fre- quency v may be used to characterize the noise in systems described by these formulas. The noise in the optical case is often visualized as arising from the random arrival of photons. Pulse detection and ranging systems, either lidar or radar, will be compared by the effective temperatures of their detectors. Thus, the fundamental relation between coherent radar and optical lidar detectors is shown by the equality kT eff = hv/Q. We must distin- guish between T e , which arises from the funda- mental fluctuations of the signal, and T eff , which arises from the noise generated by detectors or amplifiers. The former will be called the essential noise temperature, T e = hv/k; the latter will be distinguished according to the specific type of de- tector or amplifier. At optical frequencies an im- portant characteristic is the quantum efficiency. At microwave frequencies, the noise character- istics of amplifiers (the most usual source of noise in microwave radar) are described by the effective temperature or the noise figure (NF), generally given in decibels. They are related by NF(dB) = 10log 10 [-^ £<*) kT. — , , and— opt.) = , —z rff A/ N MA/) The reference temperature T is generally taken as 290 K. Table 1 lists the essential noise tempera- tures for a number of wavelengths chosen as rep- resentative of existing radars, possible radar sys- tems, and existing lidar systems. This table shows that ultraviolet superheterodyne detector-mixers are inherently noisier than a 10-cm radar by a fac- tor of 2.96 x 10 5 . The reason for the lack of radar systems in Table 1 between X = 0.0020(m) and X = 1.2 x 10" 5 (m) is the generally large molecular absorption by atmospheric water vapor in that region. In the troposphere, except for specially favored locations such as the terrestrial poles, attenuation is so great that transmission over useful distances may be im- practical. Figure 1 shows typical temperate mid- summer attenuation by water vapor as a function of wavelength. Returning to receiver noise considerations, it can be observed that neither microwave nor opti- cal receivers can achieve the limiting essential noise temperatures, T e . Optical receivers have a quantum efficiency that is less than unity; not every absorbed photon causes emission of a Table 1. Irreducible Noise Temperatures for Radar and Lidar Systems Wavelength -re System (m) (K) 1.00E-01 0.14 10-cm radar 3.21E-02 0.45 X-band radar 3.00E-02 0.48 2.00E-02 0.72 1.24E-02 1.16 K a -band radar 1.00E-02 1.44 6.20E-03 2.32 Possible radar 5.00E-03 2.88 Possible radar 3.20E-03 4.50 Possible radar 3.00E-03 4.80 2.00E-03 7.19 Possible radar 1.00E-03 14.39 7.00E-04 20.55 5.00E-04 28.78 3.37E-04 42.69 2.00E-04 71.94 1.40E-04 102.77 1.00E-04 143.88 6.00E-05 239.80 4.00E-05 359.70 2.80E-05 513.85 1.70E-05 846.34 1.20E-05 1198.98 Possible lidar 1.00E-05 1438.78 C0 2 lidar 7.0E-07 20554.0 6.94E-07 20731.7 Ruby lidar 3.471E-07 41451.5 3.470E-07 41463.4 Ruby (2nd harmonic) lidar photo-electron. Microwave receivers have effec- tive noise temperatures above the irreducible values shown in Table 1. The optical essential noise temperature T must be divided by the quan- tum efficiency Q to obtain eff "TV Q Microwaves offer several possibilities, de- pending on the frequency range. For example, we may utilize masers, traveling wave tubes, or para- metric amplifiers. The noise figures vary consider- ably for such choices. We make a representative performance choice as follows: 1) Assume masers are available at T e ff = 34.8 K for wavelengths from 0.10 to 0.0321(m) (S- and X- band radars). Assume traveling wave tubes are avail- able for wavelengths from 0.124 through 0.0020 m (possible mm-wave radar). Assume representative quantum efficien- cies (manufacturer's specifications) for wavelengths 1.2 x 10" 5 through 0.347 x 10" 6 (optical systems). 2) 3) 25 16.67 wmsm 1000 cm" 10 fj.rr\ Figure 1. Attenuation by water vapor: 0-12000 cm ' wave- length vs. attenuation (dB/km). The representative choices for microwave radar were taken from Skolnik (1962). More re- cent developments show some improvement in noise temperature, but will not affect our results significantly. The T e ff values resulting from these assumptions are shown in Table 2 and will be re- ferred to as "representative." With practical consideration given to repre- sentative detectors and amplifiers, the 10-cm radar is less noisy than the ultraviolet lidar receiver by a factor of 3956, and the noise of the red (ruby) lidar receiver exceeds the 10-cm radar by a factor of 14,836. In terms of noise temperature we note for future consideration that the 10-cm radar is less noisy, in terms of noise temperature, than the C0 2 lidar receiver by a factor of 82, in the representa- tive microwave case. Table 2. Effective Noise Temperatures for Radar and Lidar Systems Wavelength NT. Q.E. 1 T ef( (representative) 2 T eH (paramp) 3 T* (for comparison) (m) (dB) (K) (K) (K) .10 34.8 288 .14 .0321 34.8 627 .45 0124 4.6 546 2610 1.16 .0080 5.5 753 4658 1.80 .0062 5.0 838 5496 2.32 .0050 6.0 865 2.88 .0032 6.7 1066 4.50 .0020 8.0 1530 7.19 1.2 xicr 5 0.50 2398 1198.98 1.0 xlO' 5 0.50 2878 1438.78 .694X10"° 0.04 518293 20731.7 .347 XlO" 6 0.30 138211 41463.4 'Quantum efficiencies (Q.E.) are fractions between and 1. 2 T eff (representative) implies the assumptions in the text for medium-performance specifications. 3 Some representative values are given for parametric amplifiers, a commonly used device, under T efi (paramp). A major difference in the roles of radar and lidar may be clarified by examining atmospheric attenuation as a function of frequency. Only the attenuation due to hydrometeors is considered, leaving aside molecular absorption. That attenua- tion, or extinction coefficient /3 ext is composed of two parts, the absorption coefficient /3 a b s and the scattering coefficient, j8 sc . Thus, /3 ext = /3 a t, s + /3 SC . To provide examples of the wide range of at- tenuations found in the atmosphere, several sets of hydrometeor distributions will be considered; characteristics for various cloud types are listed in Table 3. The drop-size distributions, except for the continental cumulus and the cumulonimbus, are identical with those given by Deirmendjian (1969). Table 3a. Characteristics of Hydrometeor Distributions in Various Cloud Types Type Cloud Drop Density Density Minimum i radius Maximum radius Model radius (No./m 3 ) (kg/m 3 ) (/*m) (/art) (/im) Cloud C.3 (Light) 0.993 x 10 6 0.375 x 10" 7 0.5 4.3 2.0 Cloud C. 3 1.0 x 10" 0.379 x 10- 5 0.5 4.3 2.0 Cloud C. 2 1.0 x 10 8 0.302 x 10' 4 0.4 7.0 4.0 Cloud C.3 (Dense) 1.0 x 10" 0.379 x 10" 4 0.5 4.3 2.0 Cloud C.l 0.998 X 10 8 0.617 x 10~ 4 0.03 12.3 4.0 Rain L 1.0 x 10 3 0.113 x 10" J 4.0 1540.0 70.0 Continental cumulus 0.285 x 10 8 0.289 x 10"' 5.0 20.0 11.8 Cumulonimbus 0.130 x 10 8 0.537 x 10" 3 2.0 30.0 20.0 Table 3b. Parameters of Deirmendjian's Modified Gamma Distribution Type Cloud a 7 A B Cloud C.3 (Light) 8 3 5.5 X 10 58 3.3 X 10" Cloud C.3 8 3 5.6 X 10 60 3.3 X 10" Cloud C. 2 8 3 1.1 X 10 58 4.2 X 10 16 Cloud C.3 (Dense) 8 3 5.6 x 10" 3.3 X 10" Cloud C.l 6 1 2.4 X 10 48 1.5 X 10" Rain L 2 C.5 5.0 X 10 16 4.8 X 10 2 Continental Cumulus 8 1 2.4 X 10 55 6.8 X 10 5 Cumulonimbus 8 1 1.0 x 10 53 4.0 X 10 s Note: a, y, A, B are adjusted to SI units. They have been chosen to illustrate a range of cloud types, from newly formed low-density clouds to dense cumulus and cumulonimbus. The characteristics of these distributions are briefly de- scribed in the Appendix. The parameters of the continental cumulus distribution are chosen to agree with the description given by Fletcher (1969, p. 115). By Mie scatter theory, the extinction (/3 ext ) and radar backscatter (/3) coefficients (defined in Van de Hulst, 1957) for these polydispersions may be calculated. The results of that calculation and the real (RFR) and imaginary (RFl) parts of the re- fractive indices used in the calculation for cloud C.l appear in Table 4. Note the very large varia- tion of these quantities over the wavelength ranges considered. The effect of the extinction coefficient may be expressed by determining the depth (of penetration) at which the signal-to-noise ratio is reduced to 1 from its value at entry into the cloud. Table 5a gives comparative depths of pene- tration for several radars and a ruby lidar. Table 5b gives the corresponding values of /3 ext for each. The depth of penetration (d) is calculated from -20 exi d (h + d) 2 We have assumed the base of the cloud h = 5000 m. The equation is obtained by assuming that the S/N at the entrance to the cloud is reduced to S/N = 1 at the penetration depth, d. The conclusion one must draw from these re- sults is obvious: the ruby lidar will penetrate denser clouds (e.g., cloud C.l or denser) only a few hundred meters. On the other hand, it is a common experience for lidar signals to penetrate several layers of clouds, which are together thick enough to prevent the sun's disk from showing. As an example of a less dense cloud, we consider a modified Deirmendjian cloud model C.3 (Light), which has the same number of drops per cubic meter, but which has a lower water content (4.6 x 10" 7 kg/m 3 ) and smaller drop sizes. For this cloud, 0c 3.02 x 10" 5 (m^sr -1 ), and the depth of (S/N) penetration is substantially increased. In addition, Table 5 shows penetration in a realistic "young" cloud C.3. The depth of penetration is a compli- cated function of the reciprocal of the backscatter coefficient. We cannot have both large backscatter and negligible extinction coefficients from spheres. Thus, increased penetration must be paid for by diminished sensitivity. The noise factors in the S/N equation are only part of the problem. To compare performance of lidar and radar, consider the signal power received Table 4. Extinction and Radar Backscatter Coefficients for a Set of Wavelengths Ranging from Micro- waves to Ultraviolet, for Cloud C.l Wavelength (/im) RFR RFI /W" 1 ) ,8(m"sr") 0.347 1.34 6.10x10-' 1.63 xlO" 2 1.05 xlO" 2 0.694 1.33 3.31 XlO" 8 1.67x10" 1.11 xlO" 2 10.0 1.218 5.08x10" 1.12x10" 2.36x10" 12.0 1.111 1.99 xlO" 1.02 xlO" 2 1.07 xlO" 17.0 1.376 4.29x10" 1.60 XlO" 2 5.76x10" 28.0 1.549 3.38x10" 1.22 xlO" 2 1.07x10" 40.0 1.519 3.85x10" 8.36 XlO" 3 1.17 xlO" 3 60.0 1.703 5.87x10"' 6.92 XlO" 3 1.15x10" 100 1.957 5.32x10"' 2.69 XlO" 3 2.94x10" 140 2.056 5.00 xlO"' 1.49 XlO" 3 8.71x10-" 200 2.130 5.04x10" 9.16 xlO" 2.28 xlO" 5 337 2.200 6.00x10" 5.73x10" 3.18 xlO" 6 500 2.220 7.40x10" 4.51x10" 7.28x10" 700 2.320 8.90 xlO" 3.43x10" 2.18X10" 1000 2.500 1.09x10° 2.40x10" 6.13 XlO" 8 2000= 2mm 2.510 9.00x10" 1.03x10" 3.40x10-" 3000 2.771 1.19 6.87 xlO" 5 8.30x10-'° 5000 3.192 1.77 3.76 xlO" 5 1.32x10-'° 8000 3.810 2.23 1.76 xlO" 5 2.21x10"" 10000 4.221 2.53 1.17 xlO" 5 9.37 xlO"' 2 20000 5.837 3.010 3.12 xlO" 6 6.08x10-" 30000 = 3cm 7.176 2.86 1.28x10-" 1.21 xlO" 3 100000 = 10cm 8.990 1.47 1.28 XlO" 7 9.86 XlO"' 6 Table 5a. Comparison of Depths of Penetration Into Five Cloud Types at Various Wavelengths Cloud S N Penetration Depths (m) 10-cm Radar 3-cm Radar 0.5-cm Radar Ruby Lidar 10 10598.5 10598.5 7104.7 68.1292 Cloud C.l 100 44714.7 42363.0 19247.5 136.269 1000 150105.0 129056.0 35937.8 204.420 10 10709.7 9896.73 3501.57 36.1828 Continental Cumulus 100 43700.1 35401.6 7723.38 72.3661 1000 140292.0 88051.8 12400.8 108.552 LO 10625.0 92519.15 2336.70 31.2942 Cumulonimbus 100 42674.6 30553.7 4921.77 62.5894 1000 131528 68563.4 7679.12 93.8857 10 7591.7 Cloud C. 3 (Light) 100 1000 10 21350.8 41090.4 357.192 Cloud C. 3 100 715.774 1000 --1075.59 Table 5b. Extinction Coefficients Used in Table 5a Wavelength Cloud C.l Cloud C. 3 Cloud C. 3 (Light) Continental Cumulus Cumulonimbus 10 cm 1.28 x 10" 7 3 cm 1.28 x 10" 6 0.5 cm 3.76 x 10" 5 0.694 M m 1.67 X IP' 2 3.03 X 10" J 3 X 10" 5 6.03 x 10" 7 6.02 x 10" 6 1.77 x 10" 4 3.16 X 10" 2 1.12 x 10" 1.12 x 10" 3.29 x 10" 3.67 x 10" as a function of wavelength. The transmitted power depends on the system used but we defer those considerations and instead examine the basic characteristics of the atmospheric targets and the transmission characteristics of the atmosphere. The targets include hydrometeors, lithometeors, and refractive index inhomogeneities. Only the first two types will be considered. The ratio 0/ T e a is calculated as a function of wavelength. Because no extinction is considered, the physical situation, or mission, is the detection of clouds (at least the leading edge) through an essentially clear at- mosphere. The ratio (3/T ei( is shown as a function of wavelength in Figure 2 for the clouds called Rain L, Cumulonimbus, Continental Cumulus and Cloud C.l, Cloud C.2, and Cloud C.3. Three ef- fective temperatures are considered, correspond- ing to the cases we have designated representative, irreducible (T e ff = T), and parametric amplifier cases. Results are presented only for the radar wavelengths for the parametric amplifier case. The larger drop-sizes in Rain L provide suffi- ciently large backscatter at microwave frequencies that a microwave receiver equipped with only a parametric amplifier is clearly superior to the C0 2 laser at 10 /an and superior to any other optical laser (Figure 2e). (For other cases, the calculation of Rain L was not performed because of the ex- pense of computer time.) For all other clouds (Figures 2a, b, c, d), the lidar is clearly superior to all microwave radars. We must emphasize that the physical situation analyzed here does not require penetration, but only detection of the cloud's "leading edge." Consider now both attenuation and back- scatter. It is not possible to determine simply the effect of these quantities on a remote measurement system because the evaluation depends upon the mission, which depends on the range. Insight into the problem can be gained by graphing the relative S/N, (3e- 2 ^ {R - h) /R 2 T eff = S/N(Rel.), as a function of wavelength for a representative value of R (the range), where h is the cloud base height. (This quantity is not dimensionless. The graphs must be interpreted only in terms of the differences of the log(S/N), which is, of course, the 8 -5.0 -15.0 -20.0, Radar | Lidar i •Rain L 'Cumulonimbus Continental Cumulus oCloudC.l 1_J I I I L oo -5.0 u -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 log ( Wavelength) (M) -15.0 i i r Radar Lidar •Rain L •Cumulonimbus "Continental Cumulus °CloudC.l -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -70 log (WavelengthKM) -50 •RainL I I •Cumulonimbus "Continental Cumulus oCloud C.l -100 -150 -20.0 -1.0 -2.0 -3.0 log ( Wavelength) (M) -7.0 -15.0 -21.0 - b. 1 1 4 ! _ • <*> ° % o Radar | Lidar • • *» • • o * A O * ° o D • O A O • Cloud C.2 □ » Cloud C.3 (Dense) o Cloud C.3 t ° Cloud C.3 (Light) I 1 1 1 1 -5.0 -15.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 log ( Wavelength) (M) -20.0 Radar Lidar • Cloud C.2 • Cloud C.3 (Dense) ° Cloud C.3 ° Cloud C.3 (Light) J I L -1.0 -2.0 -3.0 -4.0 -5.0 -60 -7.0 log ( Wavelength) (M) -100 -150 -20.0 -25.0 • Cloud C.2 • Cloud C.3 (Dense) ° Cloud C.3 n Cloud C.3 (Light) -1.0 -2.0 -3.0 log ( Wavelength) (M) Figure 2. Relative signal-to-noise ratio ((3/T ef () considering radar backscatter coefficient and effective noise temperature, for radar and laser frequencies, (a, b) Representative cases; (c, d) Irreducible cases; (e, f) Parametric amplifier cases. same as considering dimensionless ratios of this quantity appropriate to the different cases con- sidered.) The physical situation is a cloud (1000 m thick), whose base is 5000 m above the observa- tion site. We calculate the signal-to-noise ratio for a sample cell in the vicinity of the top of the cloud. The results of the calculation are shown in Figure 3 for the same clouds and the same effective temperature cases as in Figure 2. We see in Fig- ure 3 a dramatic difference in signal-to-noise ratios for radar and lidar and a major dependence on cloud type. Consider clouds C.l and C.3, for example (Figures 3a and 3b). For cloud C.l, ap- propriate choices of microwave radar give greater signal-to-noise ratios than any lidar system. The situation is reversed for cloud C.3. C.3 is less dense than C.l; the average drop size of C.3 is half that of C.l and the water content of C.3 is less than that of C.l. Very much larger differences are seen in the case of the denser cumulonimbus and continental cumulus clouds. There the radar has much greater S/N by many orders of magnitude (Figures 3c and 3d). These results illustrate two facts that lead to an important conclusion and a suggested direction of study. The first fact is the sensitivity of the signal-to-noise ratio to the type of mission. A change from observing at a depth of 1000 m in a cloud to observing close to the surface of the cloud, or to observing in an atmosphere where cloud cover or rain extend from the antenna to the observation point would greatly change our re- sults. The second fact is the abrupt reversal in ap- plicability of radar and lidar when passing from cloud C.l to C.3. In the case of cloud C.3 (for the given mission) the radar is useless; for cloud C.l the lidar is useless. Cloud C.3 (Dense) has a water content of 6.2 x 10~ 5 kg/m 3 . On the other hand, continental cumulus has a water content of approximately 3.0 X 10" 4 kg/m 3 . For clouds of these densities and higher, lidar penetrates only a few hundred meters and radar is required to examine the cloud inte- rior. Table 6 summarizes the signal-to-noise ratios and provides a rule-of-thumb for estimating whether lidar or radar is most applicable for the mission described: the dividing line is somewhere between a water content of 1.17 X 10" 4 and 3.8 x 10" 5 (kg/m 3 ). The author's experience in analyzing ruby lidar and 24 GHz radar returns from clouds indicates the rule is generally a good approxi- mation. When observing a growing cloud with both lidar and radar, one can detect large changes abruptly. The apparent depth of the cloud as ob- served by lidar should shrink as the outline of the cloud begins to appear on the radar screen. If por- tions of the cloud are at distinct stages of develop- ment of drop-sizes, these stages may be distin- guishable by simultaneous radar and lidar obser- vations. Figure 4 illustrates such differentiation. Note that in the major portion of the cloud, the lidar and radar indicate the same relative back- scatter coefficient. However, the lower portion is detected by the lidar, but not by the radar. Simultaneous observations by radar and lidar are especially important for cloud systems' de- veloping into snow storms. Neither technique gives complete information on liquid water con- tent or glaciation processes because of the very large fluctuations of the signal strengths caused by inhomogeneities of content and thermodynamic state. It is a common experience in such simul- taneous observations to observe rapid fades in the radar signal, of duration from several seconds to several minutes. Concurrently, the lidar signal often changes from penetration of a few hundred meters to many times that amount, sometimes as great as a few kilometers. The lidar signal from the cloud base to a few hundred meters into the cloud is always very strong. Table 6. Signal-to-Noise Ratios* for Radar and Lidar for Representative Clouds Wavelength Technique Cloud Type (m) C.Cu Rain L C.3 (Dense) C.3 CuNb 10 Radar (s) -22 -18 -26 -27 -22 .03? Radar (x) -20 -16 -24 -24 -20 1.0 x 10" 5 Lidar -51 -17 -18 -16 -52 .347 x 10"" Lidar (Ruby X 2) -40 ? -39 -17 -46 Water Content (kg/m 3 ) 4.1x10' 4 1.17X10-" 3.8 xlO" 5 3.8 XlO" 6 5.4X10- 4 Note: Signal is from top of cloud 1 km above its base which is 5 km above the observer. The algebraically larger numbers indicate greater signal-to-noise ratios. 10 -2.0 -3.0 -4.0 -5.0 -6.0 log ( Wavelength) (M) -14.0 -200 -30.0 -32.0 1 b. 1 1 1 1 A a o .1* • »* o • ° D ° j 'Cloud C.2 * D * Cloud C.3 (Dense) A Cloud C.3 ° Cloud C.3 (Light) 1 1 ! 1 1 -\cv d f *-. o cP 1 1 -20.0 □ D •Roin L ° Cloud C.l °o -?nn 1 -15.0 -20.0 -10 -20 -3.0 -4.0 -5.0 -60 log ( Wavelength) (M) -30.0 -10 -2.0 -30 -4.0 -50 log (WavelengthHM) -6.0 -17.0 -20.0 -30.0 -400 -500 -53.0 'Cumulonimbus 'Continental Cumulus ± IM.U I I 1 1 J ] e .:: CD 20.0 — • * o * • * • D° ♦Cloud C.2 * cP ♦Cloud C.3 (Dense) D "Cloud C.3 inn D °Cloud C.3 (Light) 1 1 -400 -1.0 -2.0 -3.0 -4.0 -5.0 log (Wavelength) (M) -10.0 -60 -50.0 -530 f. > TT^n — r ♦Cumulonimbus "Continental Cumulus J L -2.0 -3.0 -4.0 -5.0 log (Wavelength)(M) -60 -20.0 -2.0 -3.0 -40 -5.0 -6.0 log (Wavelength) (M) -300 •Rain L ♦Cumulonimbus "Continental Cumulus = Cloud C.l -100 -200 -10 -2.0 log ( Wavelength) (M) -30.0 ♦Cloud C.2 ♦Cloud C.3 (Dense) "Cloud C.3 a Cloud C.3 (Light) -1.0 -2.0 log (WavelengthHM) Figure 3. Relative signal-to-noise ratio, considering backscatter and extinction coefficients, and effective noise temperature, (a, b, c) Representative cases; (d, e, f) Irreducible cases; (g, h) Parametric ampli- fier cases. 11 6000 Range (m) Range (m) Figure 4. Oscilloscope traces of simultaneous radar and lidar observation of a cloud, (a) Lidar (dual channel polarized receiver); (b) Radar. 5. LIMITATIONS OF LIDAR COHERENT DETECTION The experience cited and the calculations shown lead to the inevitable conclusion that for scientific studies of developing clouds from initial formation to precipitation both radar and lidar are required. However, the decision to use lidar or radar cannot be finally made until system param- eters such as power, average versus peak power, antenna size and gain, and especially the attenua- tion of the "clear" atmosphere are considered. Steering away from system-dependent conclusions helps to establish principles, but cannot eliminate the need for detailed design procedures. An additional advantage of coherent systems is the possibility of coding the signal to increase sensitivity without degrading resolution. In some cases the signal-to-noise ratio can be multiplied by the time-bandwidth product of the signal. These advantages can be found in continuous-wave fre- quency-modulated devices. It is clear that such techniques can improve radar, but the extent to which they can be applied in laser systems is still unknown. Some of the principal deterrents to optical co- herent detection are aperture limitations arising from the decohering effect of atmospheric turbu- lence. Because of atmospheric inhornogeneities the signals returning from each particle in the scatter- ing volume may not arrive at the energy collector (mirror, antenna) with a uniform phase across the aperture, and thus cannot heterodyne construc- tively, as discussed in the remarks on coherence. The practical result is that aperture sizes are re- stricted in coherent optical systems. A lidar sys- tem at wavelength 0.7 /im, pointed vertically, would be limited to a receiving aperture of ap- proximately 10 cm. These effects are frequency- dependent and limit performance much more at visible wavelengths than at 10.6 /xm. To some ex- tent such a limitation may be partially mitigated by the use of multiple apertures. However, the author has not seen a serious attempt to design such a system. The signal outputs from the various mixers would have to be added inco- herently — that is, after demodulation — and would thereby lose some of the advantage of coherent detection. 12 6. COMPARISON OF COHERENT AND INCOHERENT LID AR We have argued that coherent lidar has an in- herently greater signal-to-noise ratio than inco- herent lidar. This may be illustrated by the rela- tionship S/N(in) = 2(1 + — ) P< ' J S/N(coh). (This assumes that background noise dominates other noise sources, which is generally true during daytime.) The S/N ratio of coherent lidar systems is at least twice that of incoherent lidar, achieving that minimum when Py g /P s is zero. As the ratio Pb g /P s increases (for example, as the range in- creases) the coherent advantage can increase. Be- cause the magnitude of the advantage is both sys- tem- and mission-dependent, a detailed analysis is beyond the scope of this paper. However, as an example, we may assume that the sky background noise B is that of reflecting clouds (one of the noisiest situations), i.e., B = 1CT 2 W m" 2 sr -1 A _1 . A short calculation shows that at a range of ap- proximately 9000 m, the ratio fin p. Vbsia\~ \[ r 2 "I results in S/N(in) = 10" 4 S/N(co), which gives a substantial advantage to a coherent system, suffi- cient in many cases to overcome the effect of a re- duced aperture. Here it is assumed that fi = 16 X 10" 6 (sr), AX = 5( A ), P (the peak transmitted power) = 150 (Mw), and (3 = 4xl0" 3 (m^sr -1 ). The range increment is AR = l(m), and a = is chosen for simplicity. At this range, even under daylight conditions, the relative advantages, shown in Figures 2 and 3, of radar and lidar re- main. However, as the range increases or the transmitted power decreases, the superiority of coherent systems rapidly becomes evident. 7. CONCLUSIONS The results illustrated in Figures 2 and 3 per- mit us to describe suitable missions for radar and lidar and reinforce a conclusion many have arrived at intuitively: a simultaneous use of these instruments can extend our ability to study cloud growth from early formation to precipitation. Simultaneous observations by calibrated systems will allow some estimates of drop-size distribution and the observation of droplet growth. If both can be polarization-sensitive, glaciation processes can be studied from early stages through precipitation stages. In general, roles that are essentially of equal importance can be assigned to lidar and radar in basic studies of cloud processes. However, it is clear that radar will predominate in observations required for weather forecasting because of its range and sensitivity in all weather conditions. Figures 2 and 3 provide an interesting lead. The C0 2 lidar shows excellent capability for cloud studies, according to our system-independent method of analysis. In addition, the technological capabilities of C0 2 lasers, including coherence, high peak power, high pulse rates, and reliability, are developing rapidly. (For details of extinction by the atmosphere at 10.6 fim see Calfee and Derr, 1977.) Further advantages include eye safety and lack of sky background noise. Coherent C0 2 Doppler lidar and microwave Doppler radar will probably be combined in atmospheric studies of clear air dynamics and cloud development. It may be advisable to emphasize an obvious fact. Neither the microwave radar nor the C0 2 lidar is the best candidate for study of small at- mospheric particles, the dusts and aerosols with radii below 1 /xm. For these, visible and ultraviolet lidars must be used and may be constrained to incoherent devices, because of the decohering effect of the atmosphere. 13 8. ACKNOWLEDGMENTS The author wishes to thank Margot Ackley for devoted and skillful mathematical analysis and computational results. The author has benefitted greatly from the knowledge and integrity of R. Strauch, and from discussions with R. Chadwick, R. Schwiesow, G. T. McNice, and E. R. West- water. T. Larison aided in computer program- ming. J. Cooney must be thanked for his profes- sional advice. Patient and skillful manuscript preparation was performed by J. Thompson, T. Drey, and K. Lykins. Special thanks are due to K. Umemoto for careful numerical verification and graphing. 9. REFERENCES Battan, L. J. (1973): Radar Observation of the Atmos- phere, University of Chicago Press, Chicago, Illinois. Biernson, G. and R. F. Lucy (1963): Requirements of a coherent laser pulse-Doppler radar, Proc. IEEE, 51, 202. Calfee, R. F. and V. E. Derr (1977): Molecular and par- ticulate extinction in the atmosphere between 8 and 15 fim wavelength, NOAA Data Report ERL WPL- 1. Deirmendjian, D. (1969): Electromagnetic Scattering on Spherical Poly dispersions, American Elsevier, New York. Derr, V. E., N. L. Abshire, R. E. Cupp and G. T. McNice (1976): Depolarization of lidar returns from Virga and source cloud, /. Appl. Meteor., 15, 1200-1203. Fletcher, N. H. (1969): The Physics of Clouds, Cam- bridge University Press, England. Mandel, L. and E. Wolf (1965): Coherence properties of optical fields, Rev. Mod. Phys., 37, 231-287. Piatt, C. M. R. (1973): Lidar and radiometric observa- tions of cirrus clouds, /. Atmos. Sci., 30, 1191. Sassen, K. (1976): An Evaluation of Polarization Diver- sity Lidar for Cloud Physics Research, Ph.D. the- sis, Department of Atmospheric Sciences, Univer- sity of Wyoming, Laramie, Wyoming. Skolnik, M. I. (1962): Introduction to Radar Systems, McGraw-Hill, New York. Van de Hulst, H. C. (1957): Light Scattering by Small Particles, Wiley, New York. 14 APPENDIX The Deirmendjian Modified Gamma Distribution The convenience, for Mie scattering calculations, of an analytical drop-size dis- tribution function is so great that the relatively small unreality in a multiparameter representation can be tolerated. Deirmendjian (1969) uses a drop-size distribution function n(r) = /4r a exp(-6r 7 ), where n{r)dr is the number of drops between r and r + dr. The number of drops per unit volume is N = Ay- l B- {a + 1)/y T (- 9L ^). The modal radius (r c ) is given by r < = { Yb ] The volume occupied by the drops per unit volume of space is V = 4 A*7 1 B- ( « +4)/ 'T(^-). H 3 7 By a suitable choice of A, B, a and 7, a cloud distribution can have characteristics that closely match measured unimodal distributions. Figure A-l gives examples of Deirmendjian distributions used in this report. I0 14 !0 13 I0 12 10' I I lllllll — TTTTT 7 = 3 a = A=I.085E58 = B = 4.I667EI6" 1 I lllllll I I M il A=5.556E60 B=3.3333EJ7; a ' i imiii i i [ i n n 10 Radius (r) f 7 I0" 6 I0" 5 Radius (r) !0 G A=5.56E6I | B = 3.33EI7 : - a = 8 X =3 I I I lllllll I I nun r 7 I0" 6 I0" 5 Radius (r) Radius (r Figure A-l. Examples of Deirmendjian distributions used in this report: (a) Cloud type C.l, (b) Cumulonimbus, (c) Conti- nental Cumulus, (d) Cloud type C.2, (e) Cloud type C.3, (f) Cloud type C.3 (dense). ■ftu.S. 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