1. Introduction
Multiparameter radar is a very useful tool for studying the microphysics of storms. Polarization diversity parameters such as differential reflectivity (ZDR) and specific differential propagation phase (KDP) have been used by researchers to identify and study water to ice transition regions in convective storms (Aydin et al. 1986; Balakrishnan and Zrnić 1990). Golestani et al. (1989) introduced difference reflectivity (ZDP). This parameter can be utilized to quantitatively estimate the fraction of ice and water in mixed-phase precipitation. Bringi et al. (1997) have analyzed ZDR columns, and linear depolarization ratio signatures, to infer rapid development in mixed-phase precipitation. In this paper we present a study of the evolution of water and ice contents in a convective storm case study, including a quantitative estimation of ice and water contents in mixed-phase regions.
Sikdar et al. (1974) estimated storm total latent heating rates from radar observations using the time history of reflectivity patterns and, subsequently, estimated the water content. With the advent of multiparameter radars this process can be done more accurately. In this paper we present a technique to estimate storm total latent heating rates for convective storms. Our paper is organized as follows. Section 2 describes the ZDP signal that is used to quantitatively describe the ice and water contents in mixed-phase precipitation. Section 3 describes the dataset used in this paper. Section 4 describes the estimations of the water budget and latent heating rates for a convective storm observed on 9 August 1991. The latent heat of condensation can be derived using multiple Doppler analysis. Latent heating estimates based on multiple Doppler analysis and multiparameter radar analysis are presented in section 5. Section 6 summarizes the important results of this paper.
2. ZDP analysis for rain–ice mixtures
In Fig. 1c, the deviation for the cluster of points when ZDP is between 35 and 40 dB is 10 dB when the absolute reflectivity is between 53 and 56 dB. The corresponding value of f is 0.9. It is important to remember that the ice fraction in this study does not refer to the fraction of ice mass or volume of ice in a mixed phase region, but it does refer to the fraction of the reflectivity signal in a volume arising from scattering by ice. The statistics of the ZDP parameter and its correlation with ZH are discussed in the appendix. In the following section, we utilize the ZDP-based analysis to study the microphysical evolution of a convective storm, observed during the Convection and Precipitation Electrification (CaPE) experiment.
3. Overview of dataset used for analysis
The dataset chosen for this study was recorded by the National Center for Atmospheric Research CP-2 radar on 9 August 1991 in Florida during CaPE. Details about CaPE can be found in Foote (1991). Characteristics of the CP-2 radar can be found in Bringi and Hendry (1990). The radar data were collected using plan position indicator volume sector scans with the angular limits and elevation steps adaptively determined by scan optimizer software.
Figures 2a–c show the constant-altitude plan position indicators (CAPPIs) of radar data of the storm cell under consideration. The storm under study was first detected at 1748 UTC. Henceforth, all heights are above mean sea level, and time is universal time coordinated (UTC). At 1751 UTC the peak reflectivity increased to 22.5 dBZ, and ZDR increased to 0.75 dB, evidence of drop formation through coalescence. About 10 min later (1800 UTC), a highly positive ZDR column had formed. A positive ZDR column persisted until 1809 UTC and then glaciated, releasing latent heat, accompanied by strong vertical growth. The height of the freezing level was 4.5 km (Bringi et al. 1997). The cloud cell of interest was detected (1755 UTC), about 4 km northwest of another cell that was in a more mature phase (see the CAPPI in Fig. 2a). Both cells were about 10 km northeast of an intense but weakening multicell thunderstorm.
Figures 2b and 2c show a CAPPI of the cloud cell at the 4.0-km height at 1809 and 1815 UTC, respectively. Contours of ZH start at 0 dBZ and increase by 10 dB, while ZDR is shown as a grayscale with darker shades representing larger ZDR. The cell is centered at X = 13, Y = −27 km in Fig. 2b, which also shows the positive ZDR column. In Fig. 2c the strength of the column has weakened considerably. Figures 3a and 3b show a vertical cross section along a line oriented southeast-northwest in Figs. 2b and 2c, respectively. The positive ZDR column in Fig. 3a is clearly visible at 1809 UTC, while at 1812 UTC the cloud has glaciated. At 1815 UTC, the reflectivity core was descending and the ZDR structure conforms to the more usual ice particles melting to drops situation.
4. Radar estimates of the water budget and latent heating rates
a. Ice fractions
We have described the method of calculating ice fractions using the parameter ZDP in section 2. Once the fraction of the reflectivity signal due to ice is known, the mass of ice can then be estimated from an empirical relationship relating
First, we obtain an expression relating ZDP to Z in a region of only rain. In this manner a rain line may be obtained for this particular dataset. To do this, regression analysis was done in the pure rain regions of the storm for each radar volume scan. Pure rain regions are defined as those regions containing all liquid hydrometeors. In this analysis, the altitude of the pure rain regions are chosen to be about 2 km. This height is well below the melting layer (about 4.5 km) but high enough to avoid the ground clutter in the radar measurements and to contain ZDR values above 0 dB. Figure 4 shows the scatterplot of ZDP versus Z from radar data at a height of 2.5 km. Figure 4 also shows the regression line of the data. The data were thresholded at 20 dBZ to avoid gradient errors caused by partial filling of the radar resolution volume at low reflectivities. To find the fraction of Z contributed by ice at a given radar resolution volume, we compute the deviation of a measured Z–ZDP pair on the scatterplot from the rain line. As indicated in (8), a measured reflectivity value is expressed as the sum of the expected reflectivity based on the rain line plus the deviation from this line.
The ice fraction at each CAPPI grid point was computed as follows. Each observed value of ZDP was used to calculate the corresponding rain reflectivity value from the rain line. This value was then subtracted from the observed reflectivity to give the deviation from the rain line. The fraction of reflectivity due to ice was then calculated using (11). Small negative deviations caused by the statistical fluctuations of the radar return signals were set to zero since they would result in negative ice fractions. Also, it is assumed that deviations of greater than 10 dB from the rain line should be interpreted as pure ice. Therefore, at grid points where ΔZ > 10 dB, the ice fraction was automatically set to 1.0.
Vertical profiles of ice fraction (layer averaged) are shown in Figs. 5a and 5b. Starting at 1803 UTC the ice fraction calculations show that the storm is composed entirely of water up to 4 km. Above this level, there is an indication that glaciation has just started, as seen in the slight increase in f. Further glaciation is seen at 1805 UTC. The ice fraction profiles also show that glaciation continues until about 1820 UTC, decreasing to an altitude of about 4 km. Ice fractions increasing in magnitude and decreasing in altitude with time correspond to the descent of the precipitation core. Another feature evident in the ice fraction profiles is that the greatest glaciation occurs between 1809 and 1811 UTC. This time period shows not only the greatest increase in f per layer but also the greatest drop in altitude of the ice fraction line. Based on this progression, one would expect a large increase in the ice content of the cell during this period. Having calculated the ice fractions, it is now possible to calculate the liquid and ice water contents of the storm.
b. Liquid water content (LWC)
c. Ice water content (IWC)
d. Rainfall rate
Rainfall is a sink for the storm total LWC. To include as much of the effects of evaporation in the overall latent heating budgets as possible, the rainfall rate, R, should be computed at a level close to the ground, where rates of evaporation are typically highest. However, to avoid ground clutter contamination in calculations, R is computed at 2 km above the ground.
e. Latent heating estimates
The time profile of storm total liquid and ice water contents can be utilized in a water budget equation using a procedure similar to that proposed by Sikdar et al. (1974).
The only terms neglected in the above equations are deposition and sublimation rates. An observation of the melting layer profiles indicates that an increase in IWC occurs with a corresponding increase in f. This implies that IWC production is primarily a result of freezing. Potentially depositional growth can take place after glaciation. However, IWC decreases after glaciation. Therefore, we conclude that deposition and sublimation do not play a major role in the ice budget of this storm (Chandrasekar et al. 1991). Figure 8 shows the time series of storm total liquid and ice water contents for the cloud cell. Figure 9a shows three quantities derived from the radar observations: dM/dt, dI/dt, and R. As can be seen from (20) and (21), the latent heating from C − E can be obtained from dM/dt, dI/dt, and R by multiplying by the latent heat of vaporization, Lυ = 2.50 × 106 J kg−1. Similarly, the latent heating from F − Me is dI/dt times the latent heat of fusion, Lf = 3.34 × 105 J kg−1. Figure 9b shows these two component latent heating rates and the total latent heating rate for the storm. The small contribution of freezing and melting to the total heating budget arises from the smaller value of Lf.
The maximum positive net latent heating occurred between 1810 and 1813 UTC (see Fig. 9b) when the storm reached its maximum vertical development. Net latent heating decreased rapidly after this and then reached another smaller positive net latent heating peak at 1817 UTC. This second peak was accompanied by an enhanced E field detected by the National Oceanic and Atmospheric Administration P-3 (Bringi et al. 1997). The maximum negative net latent heating occurred between 1818 and 1820 UTC, after that the storm latent heating rate returned to a small stable value, indicating the ending phase of this storm cell. Also, from Fig. 9b, if the curve of total latent heating rate is integrated, the total heating would be much larger than the total cooling. This is easily understood in terms of the rainfall efficiency of the storm; that is, more water vapor is condensed into liquid water than is rained out of the storm, thus more latent heat is released to the environment than removed from it through evaporation.
5. Multiple Doppler analysis
Equation (23) gives the differential heating rate (J s−1), which upon integration through the cloud volume results in the total heating due to condensation/evaporation (assuming psuedoadiabatic ascent/descent).
6. Summary and conclusions
This paper presents the use of multiparameter data toward the study of mixed-phase precipitation. The ZDP parameter is shown to be useful for quantitative analysis in mixed-phase regions of storms. The application of ZDP is similar to that of the specific differential phase (KDP), where KDP is related primarily to the liquid phase of rain–hail mixtures. The primary intent of the paper was to introduce a technique for quantitatively analyzing the time evolution of convective water budgets using multiparameter radar data. Sikdar et al. (1974) used radar data to evaluate water and latent heat budgets in convective storms. With the introduction of multiparameter radars, two very significant advances have been made: 1) an estimate of the water and ice regions in a convective storm and 2) a method to quantitatively separate of rain and ice portions in a rain–ice mixture. In convective storms the mixed-phase region represents a significant portion of the storm. Therefore, accounting for rain–mixed-phase–ice transitions can significantly improve the quantitative estimates of water and ice contents.
This paper essentially presents a methodology demonstrating the application of the ZDP parameter to study the time evolution of convective storms. The parameter ZDP is fairly easy to measure and can be computed gate by gate for any radar measuring ZH and ZDR. The time evolution of estimated water budgets and rainfall rates were used to estimate the storm total latent heating rates. The latent heating estimates obtained from multiparameter radar compared fairly well with those obtained from multiple Doppler analysis. In addition, the latent heating time profile could be correlated with various microphysical and dynamic developments in the storm such as the vertical development and enhancement of electric fields. Thus, it appears that multiparameter radar data analysis using ZDP can be very useful in quantitative analysis of convective storms.
Acknowledgments
This research was supported by the National Science Foundation, ATM-9200761 (TH and VC) and ATM-9200667 (KK and JS). The authors acknowledge helpful discussions with Professor Bringi of Colorado State University.
REFERENCES
Aydin, K., T. A. Seliga, and V. Balaji, 1986: Remote sensing of hail with dual linear polarization radar. J. Appl. Meteor.,25, 1475–1484.
Balakrishnan, N., and D. S. Zrnić, 1990: Estimation of rain and hail rates in mixed phase precipitation. J. Atmos. Sci.,47, 565–583.
Bringi, V. N., and A. Hendry, 1990: Technology of polarization diversity radars for meteorology. Radar Meteorology, D. Atlas, Ed., Amer. Meteor. Soc., 153–190.
——, R. M. Rasmussen, J. Vivekanandan, and J. D. Tuttle, 1986a: Multiparameter radar measurements in Colorado convective storms. Part I: Graupel melting studies. J. Atmos. Sci.,43, 2545–2563.
——, ——, ——, and ——, 1986b: Multiparameter radar measurements in Colorado convective storms. Part II: Hail detection studies. J. Atmos. Sci.,43, 2564–2577.
——, V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić, 1990: An examination of the propagation effects in rainfall on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol.,7, 829–840.
——, K. R. Knupp, A. Detwiler, L. Liu, I. J. Caylor, and R. A. Black, 1997: Evolution of a Florida thunderstorm during the Convection and Precipitation Electrification Experiment: The case of 9 August 1991. Mon. Wea. Rev.,125, 2131–2160.
Chandrasekar, V., C. A. Atwater, and T. H. Vonder Haar, 1991: Convective latent heating estimates from radar data. Preprints, 25th Conf. on Radar Meteorology, Paris, France, Amer. Meteor. Soc., 155–158.
Foote, G. B., 1991: Scientific overview and operations plan for CaPE. NCAR Rep., Boulder, CO, 145 pp.
Golestani, Y., V. Chandrasekar, and V. N. Bringi, 1989: Intercomparison of multiparameter radar measurements. Preprints, 24th Conf. on Radar Meteorology, Tallahasse, FL, Amer. Meteor. Soc., 309–313.
Gorgucci, E., G. Scarchilli, and V. Chandrasekar, 1994: A robust estimator of rainfall rate using differential reflectivity. J. Atmos. Oceanic Technol.,11, 586–592.
Sachidananda, M., and D. S. Zrnić, 1985: ZDR measurement considerations for a fast scan capability radar. Radio Sci.,20, 907–922.
Seliga, T. A., and V. N. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor.,15, 69–76.
Sikdar, P. N., R. E. Schlesinger, and C. E. Anderson, 1974: Severe storm latent heat release. Mon. Wea. Rev.,102, 455–465.
Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distributions. J. Appl. Meteor.,22, 1764–1775.
Zrnić, D. S., V. N. Bringi, N. Balakrishnan, K. Aydin, V. Chandrasekar, and J. Hubbert, 1993: Polarimetric measurements in a severe hailstorm. Mon. Wea. Rev.,121, 2223–2238.
APPENDIX
Statistical Properties of the ZDP Signal
Standard error of ZDP signal
Correlation of ZDP signal with Z
We noted in section 2 that for rainfall, a scattergram between Z and ZDP falls on a straight line and any deviation from that would be used to identify regions that are not rain. Since we observe such scatterplots in nature, it is useful to understand the correlation between the parameters Z and ZDP.
We can see from the results of this section that Z is highly correlated with ZDP and hence the scatter between Z and ZDP diagrams are not perturbed by measurement errors. Thus, any deviation from the rain line is significant for the detection of regions that are not pure rain.
Scatterplots of ZDP(dB) vs ZH: (a) several gamma raindrop size distributions, (b) data from rainfall, and (c) regions of rain–ice mixture (from Golestani et al. 1989).
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) CAPPI at 4.0-km height of ZH contours with ZDR gray scales at 1803 UTC. (b) CAPPI at 4.0-km height of ZH contours with ZDR gray scales at 1809 UTC. (c) CAPPI at 4.0-km height of ZH contours with ZDR gray scales at 1815 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(Continued)
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) Vertical section along a SE–NW line in Fig. 2b at 1809 UTC. (b) Vertical section along a SE–NW line in Fig. 2c at 1815 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
Scatterplot and best-fit regression line of the S-band horizontal reflectivity (ZH) vs ZDP at 2.5-km height 1809 UTC 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) Vertical profiles of the average ice fraction (f) from 1803 to about 1813 UTC 9 Aug 1991. (b) Vertical profiles of the average ice fraction (f) from 1815 to about 1821 UTC 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) Vertical profiles of layer-total liquid water contents from 1803 to about 1813 UTC 9 Aug 1991. (b) Vertical profiles of layer-total liquid water contents from 1815 to about 1823 UTC 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) Vertical profiles of layer-total ice water contents from 1803 to about 1813 UTC 9 Aug 1991. (b) Vertical profiles of layer-total ice water contents from 1815 to about 1823 UTC 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
Time series of storm-total liquid and ice water contents on 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
(a) Time series of the time rate of change of liquid water content, dM/dt; ice water content, dI/dt; and rainfall rate, R, on 9 Aug 1991. (b) Time series of latent heating rates from condensation and evaporation (dash–dot line), freezing and melting (dashed line), and the net latent heat (solid line) on 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2
Time series of latent heating rates from the multiple Doppler analysis on 9 Aug 1991.
Citation: Journal of Atmospheric and Oceanic Technology 15, 5; 10.1175/1520-0426(1998)015<1097:MROOTE>2.0.CO;2