Observations of precipitation associated with a cold front using

Transcription

1 JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 103, NO. D10, PAGES 11,401-11,409, MAY 27, 1998 Observations of precipitation associated with a cold front using a VHF wind profiler and a ground-based optical rain gauge Yen-Hsyang Chu and June-Shyen Song Center for Space and Remote Sensing Research, nstitute of Space Science, National Central University Chung-Li, Taiwan Abstract. n this paper the VHF radar returns from hydrometeors and reftactivity fluctuations associated with a cold front are analyzed. A composite analysis of the precipitation echo intensity and the vertical air velocity indicates that the vertical air velocity plays a vital role in the formation of the bright band. The observations show that the VHF radar reflectivity from precipitation at the height around the melting layer may be enhanced in the condition of weak vertical air velocity, while the bright band may be disrupted if the upward vertical air speed is as large as 1.2 m/s. The intense updraft may also diminish the echo intensity from reftactivity fluctuations through the mechanism of turbulent mixing, as first suggested by Chu and Lin [1994]. The corresponding observational evidence will be presented and discussed in this paper. Comparing the time series of the VHF precipitation echo intensity aloft with that of the surface rainfall rate indicates there is a systematic time delay in the two, which increases approximately linearly with height. The drop-off rate of the time difference is approximately equal to the average fall velocity of the raindrop. A regression analysis of the precipitation data between range-corrected VHF radar reflectivity Pr and ground-based rainfall rate R using the equation Pr = art3 is also made. t shows that has a tendency to decrease with height, while a is nearly height-independent. 1. ntroduction t has been recognized that a VHF/UHF radar is one of the most powerful instruments in the remote sensing of atmospheric precipitation. Compared with the conventional microwave meteorological radar, VHF/UHF radar has the advantage of simultaneously measuring the strengths and the dynamic properties of the hydrometeors and the atmospheric refractivity fluctuations in the precipitating environment. With this capability the interrelation between precipitation particles and the ambicnt air, the initiation of hydrometeors, the process of precipitation development, the mechanism of bright band formation and destruction, the drift of a precipitation system, and so on can be obscrvcd and investigated. During the last decade, studies of the precipitation made by using VHF/UHF radar primarily focused on the analysis of precipitation radar returns to obtain the precipitation-related parameters, such as height distribution of precipitation, terminal velocity of hydrometeors, drop-size distribution, bright band structure, and so on [Fukao et al., 1985; Wakasugi et al., 1986; Chu et al., 1991; Rajopadhyaya et al., 1993; Chilson et al., 1993]. Except for the parameters mentioned above, more information on the precipitation can be obtained if the rainfall rate recorded by the ground-based rain gauge is employed to compare with the radar measurement of precipitation aloft. For example, the empirical relation between precipitation radar reflectivity and ground-based rainfall rate can be established through such a comparison so that the surface rainfall rate might be estimated from the observed radar reflectivity from precipitation, provided the radar system has been calibrated carefully [Battan, 1973; Doviak and Zmic, 1984]. Re- Copyright 1998 by the American Geophysical Union. Paper number 98JD /98/98JD $ ,401 cently, Currier et al. [1992] also compared l-min-averaged radar reflectivity observed by using a 915-MHz wind profiler with rainfall rate recorded by a ground-based rain gauge and showed a good agreement between these two data sets. Although this kind of investigation has been carried out using conventional microwave meteorological radar and a 915-MHz wind profiler, to the authors' knowledge, comparison of precipitation measured aloft by using VHF radar with rainfall rate recorded by a ground-based optical rain gauge has not yet been made. The depletion of VHF turbulent echo power in an environment with precipitation and intense updrafts (at the velocity of several meters per second) has been reported recently [Chu and Lin, 1994]. Although a plausible mechanism of turbulent mixing between in-cloud and ambient air is proposed to account for this feature, more observational evidence is required to further support this scenario. n addition, observations of bright band have been made at a number of VHF radars [Fukao et al., 1985; Chu el al., 1991]. However, the interaction between the characteristics of the bright band and the vertical air velocity is not well documented. An analysis of observations of precipitation associated with a cold front made by using the Chung-Li VHF radar and a ground-based optical rain gauge is carried out, and the observational results are presented and discussed in this paper. The characteristics of the Chung-Li VHF radar and the optical rain gauge used in this study are introduced briefly in section 2. n section 3 the observational results are presented and discussed. The conclusion is given in section Characteristics of the Chung-Li VHF Radar and the Optical Rain Gauge The Chung-Li VHF radar is located on the campus of National Central University in Taiwan. The operational frequency

2 11,402 CHU AND SONG: OBSERVATONS OF PRECPTATON < 3 2 Chung-Li VHF Radar Nov. 26, :.':'...'..c/...: (db)! LOCAL TME Figure la. Height-time distribution of the vertical echo intensity from clear-air refractivity fluctuations on November 26, 1993, LT. of this radar is 52 MHz (corresponding to 5.77-m wavelength), and the peak transmitted power is 180 kw. The maximum duty cycle is 2%, and the pulse width can be set from 1 to 999/as. The whole antenna array of the Chung-Li VHF radar consists of three independent subarrays. Each is constructed for a special observational purpose. The first one is the mesosphere- stratosphere-troposphere (MST) subarray, which is the oldest among the three existing subarrays and is used for the measurements of three-dimensional wind field, turbulence, layer structure, gravity wave, precipitation, and so on in the meso Chung-Li VHF radar has a large sidelobe (about -9dB with respect to the main beam) in the opposite direction at the zenith angle of 58 ø and because this radar is adjacent to the Taipei nternational Airport, the radar returns from the side- lobe and aircraft may seriously contaminate the echo signals on occasion. n order to abstract the desired echo signals from the contaminated radar returns, the Chung-Li VHF radar beam should be steered toward different directions so that the precipitation and the clear-air echoes with different Doppler fre- quency shift can be identified and separated unambiguously in the Doppler spectral domain. For that purpose, in this experiment one of the three independent antenna beams was steered consecutively toward east, north, west, and zenith in a sequence. The dwelling time for each direction was about 1 min. The Doppler spectra were calculated by using a 64-point fast Fourier transform (FFT) algorithm to the radar returns. Six raw spectra were averaged incoherently to produce an average spectrum for further analysis. n view of the complexity of the observed Doppler spectrum, the identification of the spectral components for precipitation and refractivity fluctuations could only be done manually. Once they were separated, the echo power, mean Doppler frequency shift, and spectral width for these two spectral components were estimated with the least squares method, in which the Gaussian curve was employed to best fit the corresponding Doppler spectral component nterrelation Between Ambient Air and Precipitation Particles Figures la and lb present the height-time distributions of the VHF echo powers from the refractivity fluctuations and precipitation, respectively, observed by using the vertically pointed radar beam. As shown in Figure la, a distinct layered structure with intermittent depletion in strength is observed in the height range from about 4 to 4.6 km. This feature not only occurs in the vertical profiles but also appears in the oblique ones (not shown here), indicating that the diminution of the refractivity echo power is systematic and meaningful. The physical mechanism involved in the decrease of refractivity sphere, stratosphere, and troposphere. The second one is the ionospheric subarray, which is employed for the investigations of the ionospheric electron density irregularities. The third one is the meteor subarray, which is used for the detection of the radar echoes from meteor trails. The antenna array employed in this experiment is the MST subarray. For more information on the characteristics of the Chung-Li VHF radar and the MST echo power will be discussed later. Figure la also shows that, in general, above the peak of the layer the refractivity echo subarray, see Rottger et al. [1990]. An optical rain gauge located at the Chung-Li radar station is employed to record the surface rainfall rate. The dynamic range of this rain gauge is mm/h. The analog output of the recorded precipitation intensity is sampled at the rate of Chung-Li VHF Radar Nov. 26, Hz (that is, with 10-s time resolution) and stored on a hard (db) disk for further processing. The range of operating tempera- 46 tures for this rain gauge is 1ø-50øC. 3. Observational Results and Discussion 3.1. Radar Parameters and Echo Signal Analysis The radar data employed for this study were taken by the Chung-Li VHF radar on November 26, 1993, from 0300 to 0414 LT. During this period a cold front with active convective cells and moderate precipitation was passing through the Taiwan area. The radar parameters used for this experiment were set as follows: The peak transmitted power for each module was 25 kw, the pulse width was 2/as, the interpulse period was 300/ s, the coherent integration time was 0.15 s, and the height coverage was set from 1.8 to 13.5 km, with 40 range gates recorded. Because the oblique antenna main beam of the Figure lb. particles LOCAL TME Same as Figure la, but from the precipitation

3 CHU AND SONG: OBSERVATONS OF PRECPTATON 11,403 power drops off fairly sharply with height at the rate ranging from about -30 to -15 db/km, while below the peak of the layer the average gradient is relatively smooth and ranges from about 1.5 to 7 db/km. The contour plot of the precipitation echo intensity presented in Figure lb shows that most of the precipitation occurs below the height of 4 km, with the maximum centered at around 3 km. According to the radiosonde data taken by Pan-Chiaou rawinsonde station (about 25 km northeast of the Chung-Li VHF radar site) at 0800 LT, the level of 0øC isotherm (i.e., melting layer) is located at the tivity from precipitation is absent around the melting layer will be discussed later. Figures 2a and 2b present the height-time distributions of the vertical air velocity and the terminal velocity of precipitation particles, respectively. As shown in Figure 2a, four pronounced updrafts with velocities ranging from 0.5 to 1.2 m/s are observed in the height range km at around 0317, 0340, 0355, and 0410 LT, respectively. Another intense updraft appearing at 0401 LT in the height range km is also observed. nspecting Figures 2a and 2b in more detail shows that the occurrence of the intense precipitation coincides very well with that of the updraft, especially above km. Furthermore, a close examination of these two figures indicates that two types of precipitation are seen. One is the continuous precipitation which occurs in the warm region below km altitude of 4.2 km. Because the precipitation occurs primarily in the height range below the level of 0øC isotherm, this type of precipitation is thus categorized as warm precipitation. t is also noteworthy that after 0350 LT the precipitation echoes extend above the melting level and reach up to about 5.1 km, implying that the hydrometeors responsible for most of the and is associated with the relatively weak but constant upward VHF radar returns over this height range may take the form of vertical air motions in the height range from to 3.6 km. The solid particles. Although supercooled water droplets may co- other is the intermittent precipitation which appears above 3.6 exist with the solid precipitation particles above 0øC isotherm, km and accompanies the short-lived updraft extending to a heioht ahnve the level nf 0øC isotherm. n the. case nf the we believe that the VHF backscatter from supercoole droplets is minor compared with the contribution of solid particles. continuous precipitation we note that the steady updraft may The reasons are described below. t is well known that a su- supply sufficient water vapor from below, which contributes percooled droplet is in an unstable state. As a result, it will be significantly to the formation of the small droplets through the soon frozen as a supercooled water droplet collides with an ice condensation process. Once the small droplets are formed in particle. Moreover, in light of the fact that saturation vapor the warm region of the cloud, they will grow larger and larger, pressure over the supercooled water droplet is higher than that primarily through the process of coalescence [Fletcher, 1962; Rogers, 1979]. Eventually, these large hydrometeor start to fall over the ice particle, it is expected that the ice crystal will grow and become raindrops, as the updraft no longer sustains these and the supercooled droplet will be shrunk by transferring the large droplets. When the diameter and density of the raindrops water vapor from the latter to the former [Fletcher, 1962]. increase to the extent that the radar backscatter from these Under this environment it seems impossible for small superparticles is higher than the noise level, the identification of the cooled water droplets to grow and produce the significant precipitation echoes in the observed Doppler spectrum beradar backscatter. However, the existence of large supercooled comes possible. n fact, the feature of the increase in terminal drops above the 0øC isothermal, which are formed originally velocity with the decrease of height in the height range below the melting layer through the coalescence process and km presented in Figure 2b is concrete evidence implying the carried upward by intense updraft, cannot be ruled out. Examcoalescence of raindrops. Notice that because VHF radar reining the distribution of vertical velocity (as shown later in flectivity is proportional to the sixth power of the hydrometeor Figure 2a) reveals that for the present precipitation event the diameter, most of the observed radar reflectivities arise from vertical air speed is weak (smaller than 1.2 m/s) and cannot the scattering of the large precipitation particles. n view of the sustain the drops with diameter larger than 0.33 mm, indicating fact that the large raindrops abound at the lower height, as that the size of the supercooled water droplets in the height illustrated above, a height difference between the maximum of region above 0øC isothermal will be small. Therefore it may be precipitation echo intensity and the formation of small dropconcluded that the radar returns that occurred above the 0øC lets, as indicated in Figures lb and 2a, is expected accordingly. As for the case of intermittent precipitation, the interrelation between the development of precipitation and the dy- isothermal are generated mainly from the solid hydrometeors. t is well known that the water-coated solid hydrometeor will considerably enhance the radar reflectivity primarily due to the namic behavior of the ambient atmosphere is more compliincrease of their index of refraction. Calculation shows that cated. n the warm precipitation process, hydrometeors are when 10% of a typical ice crystal has melted, its backscattered only in liquid form. n the cold precipitation process, changes intensity is approximately 90% of the value which would be in the phases of hydrometeors must be considered. The invesbackscattered by an all-water drop of the same radius [Fletcher, tigation shows [Rogers, 1979] that the ice embryos are gener- 1962; Battan, 1973]. This situation may occur as the solid hy- ated in the snow region of the convective cloud through both drometeors are falling and melting in the melting layer. More- the processes of depositing water vapor on the ice nucleates over, the effects of aggregation and coalescence of the melting and the freeze of supercoole droplets which are carried by the and nonspherical ice crystals may further increase the radar updraft from below. Following the formation of the ice emreflectivity. n general, the backscattering cross sections of the bryos, the growth of ice particles will take place through the water-coated, oriented, and anisotropic hydrometeors can ex- aggregation and accretion processes. The ice particles become ceed those of all water particles of the same mass by a factor of half melted and coated with a film of water when they are 10 or more [Atlas et al., 1953]. Examining Figure lb in more falling in the melting layer. Under this situation the radar detail shows that there is indeed a distinct peak of precipitation reflectivity from these melting ice particles will be enhanced echo power at the height of 4.2 km (i.e., center of the melting considerably due to the increase of the dielectric factor, causlayer) around 0405 LT. By contrast, at around 0355 LT, no ing the formation of the bright band at the level around the distinct maximum of radar reflectivity is observed at the same melting layer. Many other factors, including falling velocity of height. The reasons why the enhancement of the radar reflec- the melting hydrometeors, the size and the shape of partially

4 11,404 CHU AND SONG: OBSERVATONS OF PRECPTATON Vertical Air Velocity t 0.4 m/s t ß ß t ß ß. t. t. t t,.,?t* ' t t???, t ß t t ß.,. t,, t t, t t t,, t t? t t? ß * t ß t t t., ß t ß t., t t ß, t.,ttt,t t t t t t.. f t t t t, t * t t t. t. t LOCAL TME Figure 2a. Height-time distribution of the vertical air velocity on November 26, 1993, LT. melted ice particles, temperature profile, density of ice crystals of some of the above factors have been given by several inves- (or snowflakes), growth and disintegration of precipitation par- tigators [Wexler, 1955; Battan, 1973; Fabry and Zawadzki, ticles, and vertical air velocity, may also influence the forma- 1995], the connection between the bright band formation and tion of the bright band. Although the quantitative assessments the vertical air velocity is still not well documented. n the Terminal Velocity of Precipitation Particles 5.7 5m/s LOCAL Figure 2b. Same as Figure 2a, but for the terminal velocity of the precipitation particles. TME

5 CHU AND SONG: OBSERVATONS OF PRECPTATON 11,405 following, the observational evidence showing the effect of in this case the size spectrum of the hydrometeor will be broad updraft on the formation of the bright band will be presented at the height around the melting layer. Although it is possible and discussed. A careful examination of Figures 2a and 2b shows that around 0405 LT the upward vertical air velocities in the height range around the melting region are relatively weak and far to estimate the hydrometeor size distribution from the observed VHF Doppler spectral width of precipitation echoes, a problem arises as to how to remove the contribution of the clear-air spectral width caused by beam broadening and tursmaller than the terminal velocity of the precipitation particles, bulent broadening effects. t is believed that the observed and a pronounced bright band is observed around the height of Doppler spectral width of precipitation echoes is the convolu- 0øC isotherm (Figure lb). By contrast, at around 0357 LT, tion of the spectral width of refractivity fluctuations with the although the relatively strong vertical air velocity (about 1.2 hydrometeor size distribution, provided the precipitation parm/s) is still smaller than the terminal velocity of precipitation ticles are frozen in the background wind [Wakasugi et al., 1986; particles (about 2.1 m/s), no radar reflectivity enhancement is Gossard et al., 1990]. Under this assumption the mathematical seen around the height of 0øC isotherm (Figure lb). The dif- relation of the Doppler spectra between precipitation particles ference of the radar reflectivities in the two is about 8 db, and and refractivity fluctuations for a vertically pointed radar beam the averaged vertical air velocity in the height range km can be formulated as at 0357 LT is greater than that at 0405 LT by a factor of 3. Furthermore, Figure 2b also shows that the terminal velocity of S r ( o) : St(o) ( ) S p ( o) - o)o) (1) the hydrometeors at these two instants are fairly similar, imwhere Sr(o)) is the observed precipitation Doppler spectrum, plying that the sizes of hydrometeors responsible for the radar rofloc tixzitw ro nnrc xqmatelv the same. C)n the basis n½ these St(o)) represents the Doppler spectrum of refractivity fluctuobservational results a plausible mechanism for the depletion ations, Sp(o) - o)o) is the size distribution of precipitation of precipitation echo power associated with intense updraft at particles in the Doppler spectral domain centered at Doppler the height around the melting layer is as follows. t is well frequency o)o, and represents the convolution operator. known that the terminal velocities of the ice particles above the Note that the shape of St(o)) is usually assumed to be Gaussian melting layer are between 0 and 2 m/s [Battan, 1973]. f the because of beam broadening and turbulent broadening effects updraft is so strong that most of the ice particles with smaller [Woodman and Chu, 1989]. Superficially, the shape of Sp(o) - %) terminal velocity (or diameter) are forced to move upward due is not Gaussian due to the exponential form or Gamma pattern to the air drag effect, the density of hydrometeors existing in the melting region will be considerably reduced. n this case, the radar reflectivity arising from these relatively large but low-concentration melting hydrometeors will be smaller than of the drop-size distribution [Marshall and Palmer, 1948; Ulbrich, 1983]. However, because the radar echo power from precipitation is proportional to the sixth power of the diameter of the precipitation particle, the pattern of Sp (o)- o)o) will be that for the case of weak updraft. Except for the low density quasi-gaussian in the Doppler spectral domain [Atlas et al., effect, another important mechanism which may blur the organized structure of the bright band is the turbulent mixing associated with a strong updraft. The turbulent mixing will diffuse and disrupthe stratification which is necessary for the melting layer to be well defined, causing the absence of bright band through the process of convective overturning. 1973]. Consequently, for the sake of mathematical simplicity, the shape of Sp (o)- o)o) can be treated with Gaussian form, resulting in the reasonable approximation of Gaussian pattern to Sr(o)). n this case, the information of the size distribution of the precipitation particle can be separated from Sr(o)), which is contaminated by St(o)), through the following relation: Recently, severe depletion of turbulent echo power in a convective cloud with intense updraft and moderate precipita- O.p2 2 o-, 2 (2) tion has been observed using the Chung-Li VHF radar [Chu where,, and are the variances of Sr(o)), Sp(o) - o)o), and and Lin, 1994]. A plausible mechanism for this phenomenon St(o)), respectively. Because rrp can be treated as an indication has been proposed by using the turbulent mixing between of the breadth of hydrometeor size distribution, the larger rrp warm and humid in-cloud air and cool and dry ambient air is, the broader the size distribution will be. Following the entrained into the cloud following a strong updraft. n the procedure mentioned above, Figure 3 presents the height-time present precipitation event, although the vertical air velocities are not strong (smaller than 1.2 m/s), the depletion of the distribution of rrp (in units of hertz). As indicated, the height range around the melting layer an enormously large Doppler refractivity echo power is still observed in the height range of the melting layer at around 0315, 0340, and 0357 LT, as shown spectral width indeed occurs at 0357 LT. This feature, combined with the destruction of the bright band and the depletion in Figures la and 2a. This feature illustrates again the close connection between the depletion of refractivity echo power of the clear-air echo power, gives conclusivevidence of the and the updraft. Therefore the above observations of the deexistence of the turbulent mixing. struction of the bright band and the weakness of the refractiv- t is generally recognized that the number of large raindrops ity echo intensity, which all are associated with the turbulent tends to increase with rainfall rate and that the large raindrops mixing, strongly suggesthat at around 0357 LT, significant contribute the most to the radar reflectivity. n view of the fact turbulent mixing occurs over the 3.9 to 4.5-km height range. that the broad raindrop-size distribution leads to the large As mentioned above, the mixing process of in-cloud and Doppler spectral width of the precipitation echoes, it is anticoutside-cloud airs plays a crucial role in the destruction of the ipated that the stronger the radar reflectivity, the broader the bright band and depletion of the clear-air echo power. More- Doppler spectral width is. Comparing Figure 3 with Figure lb over, Hauser and Amayenc [1981] show that if the turbulent shows that except for the region where the significant mixing motion of the ambient air is so active that the precipitation process of in-cloud air with outside-cloud air takes place, in particles with different diameters distributed above and below the melting layer are mixed thoroughly, it can be expected that general, the large rrp coincides very well with the intense radar reflectivity, consistent with the theoretical expectation.

6 11,406 CHU AND SONG: OBSERVATONS OF PRECPTATON 2.1 km ß ß 3.0km ß ß 3.9km 2.4km, ß km " '-' 4.2km km x x 3.6km * ß 4.5km ß * 4.8km ß 5.1km Hz , LOCAL TME Figure 3. Height-time variation of the deconvolved Doppler spectral width %, of the precipitation echoes. For the definition of %, see the text.. Relation Between Radar Reflectivity and Surface Rainfall Rate Figure 4 presents the height-time distributions of the precipitation echo intensities observed by the radar beams pointed toward the vertical (solid curve), north (dotted curve), east (dashed curve), and west (dash-dotted curve) directions and the time series of the surface rainfall rate (curves in the bottom panel) recorded by optical rain gauge. As indicated, two precipitation events can be identified clearly. For the first event appearing in the period from 0300 to 0335 LT, the patterns of the time series for the vertical beam are very similar to those for oblique beams below 3.6 km, indicating the existence of a uniform and organized rain cell with horizontal size greater than 2.5 km over the Chung-Li radar site. For the second event occurring after 0340 LT, the patterns are quite complicated, and a significant dissimilarity in the time series between vertical and oblique beams is seen. This behavior implies that the precipitation system responsible for this event is not as uniform as the first one and seems to be a complex system containing several small and spatially separated rain cells. A comparison of the time series of the surface rainfall rate with those of the precipitation echo intensity at different heights shown in Figure 4 indicates an obvious time difference between them. This phenomenon occurs because it takes some time for the raindrops formed at the upper level of the cloud to fall to the ground. By using the cross-correlation technique, the average time delay of the surface rainfall rate relative to the precipitation radar returns at different heights for the period from 0300 to 0335 LT can be estimated, as presented in Figure 5. Figure 5 shows that the time lag decreases linearly with the decrease of height at the average slope of -5.2 m/s. This value is quite close to the averaged fall velocity (not terminal velocity) of the raindrops presented in Figures 2a and 2b. A careful examination of the precipitation event after 0340 LT also shows similar behavior. The good agreement between the drop-off rate of the time lag and the average raindrop fall velocity suggests that the time difference between the precipitation time series at each height and the surface rainfall rate can be estimated approximately in terms of the averaged vertical Doppler velocity of the raindrop, provided that the precipitation aloft measured by the radar and the corresponding surface rainfall rate recorded by the ground-based rain gauge can be linked unambiguously. On the basis of the above observations, it is possible to establish the empirical relationship between the VHF radar reflectivity and the surface rainfall rate through regression analysis. t is well known that under the approximation of Rayleigh scattering, the average radar echo power from the precipitation particles can be given by [Rogers, 1979] CK 2Z Ps = r 2 (3) where C is a constant depending on the radar parameters; K = (m 2-1)/(m 2 + 1), where rn is the complex index of refraction of the hydrometeor; r is the range; Z is the reflectivity factor and defined as Z = E Di f N(D) D6 dd, (4) where D i is the diameter of the ith particle; N(D)dD is the number of precipitation particles with diameters between D and D + dd per unit volume; and E v denotes the summation over the unit volume. t is well recognized that N(D) is strongly related to the rainfall rate R. Therefore, as would be expected from equation (4), Z is a function of R. Empirically, the relation between Z and R can be expressed [Battan, 1973]

7 CHU AND SONG: OBSERVATONS OF PRECPTATON 11,407 By substituting (5) into (3), this reduces to z :4a. (5) Ps = r2 (6) where a = CK2A. f we take the logarithm to both sides of (5) and let Pr = Ps r2, it becomes log (er) '-- log (a) +/3 log (R) (7) Therefore the coefficient A and exponent /3 of (5) can be estimated by fitting (7) to the observed data. Once the regression equation is established, the surface rainfall rate might be inferred by using the observed value of range-corrected echo intensity Pr, provided the radar system has been calibrated appropriately. Figure 6 presents an example showing the linear ß 4.5km 5dB km 3.9 km [ i i 3.6km. X ß TME LAG (minute) Figure 5. Height distribution of the average time delay of the surface rainfall rate relative to the precipitation echo signals at different heights for the period from 0300 to 0335 LT. The straight line with a slope of -5.2 m/s displayed in the plot is the best fit to the data. km <... ß km,,, "'l"' -,/...., -,.' ' --.-' 4.,"- "'-- ' i ' i i 12 Log(Pr) = 1.22*Log(R) km... J , 035O LOCAL TME Log(R) Figure 4. Comparison of the multiheight time series of the precipitation echo intensities observed by the radar beams pointed toward vertical (solid line), east (dashed line), north (dotted line), and west (dash-dotted line) with the record of surface rainfall rate (curves in the bottom panel) recorded by the optical rain gauge. Figure 6. Scatter diagram (in logarithm scale) of the precipitation echo power (Pr) at the height of 3 km versus the surface rainfall rate (R), where the range correction to the precipitation echo power and the compensation of time delay to the surface rainfall rate are both made. The straight line with a slope of 1.22 and intercept of is the best fit to the data.

8 11,408 CHU AND SONG: OBSERVATONS OF PRECPTATON , relation between log (R) and log (Pr) at the height of 3 km, where the range correction to the observed precipitation echo intensity and the compensation of the time delay to the surface rainfall rate are both made. Figure 7 displays the height distributions of/3 and log (a) in the height range from 2.4 to 3.9 km, in which the mean values (solid curves) and the 95% confidence intervals (dashed curves) of/3 and log (a) are both shown. Note that the available data points at 2.1 km and above 3.9 km are so scarce that they are inadequate to calculate reliable log (a) and/3 with the least squares method. As indicated in Figure 7, it appears that there is a tendency for the mean value of/3 to decrease with height. nvestigation show that a number of factors may influence the value of/3, such as the geographic locality, rainfall type, drop-size distribution, atmospheric thermodynamic stability, synoptic weather conditions, and so on [Battan, 1973]. Although the behavior in which /3 decreases with height could be physically meaningful, it is not statistically significant because of a fairly large uncertainty interval in/3. This result implies that more observations and data analysis are required to investigate the physical and statistical behavior of decreasing with height in the exponent of (6). n addition, Figure 7 shows that log (a) with a considerably small 95% confidence interval seems to be height-independent. However, comparing Figure 7 with Figure lb indicates that an appreciable positive correlation between log (a) and radar echo intensity from precipitation is seen. Because the constants C and K have nothing to do with the dynamic behavior of the precipitation, the coefficient A in (5) dominates the property of log (a). n view of the close connection between A and Z, log (a) will be proportional to radar reflectivity from precipitation, as already shown in Figures 7 and lb. 4. Conclusion Case study results of the precipitation associated with a cold front observed with the Chung-Li VHF radar are presented an discussed in this paper. We show that not only the VHF backscatter from refractivity fluctuations but also the intensity of the bright band will be depleted in the presence of an intense updraft. Chu and Lin [1994] have shown that the de- pletion of clear-air echo power can be attributed to the turbu- lent mixing between warm and humid in-cloud air and cool and dry ambient air entrained into the cloud following a strong updraft. n this paper we postulate thathe plausible mecha- nism responsible for the depletion of the precipitation echo intensity accompanying an intense updraft in the height range of the melting layer is also the process of turbulent mixing by diffusing and disrupting the organized structure of the bright band. The observational evidence that the breadth of the size distribution of the hydrometeors in the height range of the melting layer is enormously large is shown to support this assertion. A combined analysis of the precipitation measured by the radar and a ground-based optical rain gauge shows a time difference in the two, which increases linearly with height. [ log(tz) The drop-off rate of the time difference is approximate to the Figure 7. Height distribution of/3 and log (a), where a and average fall velocity of the raindrops. After the range correc- /3 are the coefficient and the exponent, respectively, of the tion and time difference compensation to the data are both equation Pr = aro that is employed to best fit to the observed made, a power law expression as shown in (7), which links the data. The solid and dashed curves represent the mean values radar reflectivity from precipitation with the ground rainfall and 95% confidence intervals, respectively, of log (a) and/3. rate, is employed to best fit to the observed data. The results show that the exponent/3 tends to decrease with height, while the coefficient a, which is strongly correlated to the precipita- tion echo intensity, is height-independent. The explanation for these characteristics needs further investigation. Acknowledgment. This work is partially supported by the National Science Council (NSC) of Taiwan, Republic of China, under grant NS C M A10. 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