a. Case study

On 9 March 1998 an intense squall line moving over the Melbourne WSR-88D site coincided with a TRMM overpass. The dBZ values measured by the WSR-88D and PR are shown in Fig. 1 for a height above the surface of 3 km. The three panels show maps of dBZ_m (top), dBZ (center), and dBZ_GV (bottom) where the resolution cell for all products is 4 km × 4 km × 1.5 km. (In this paper, quantities derived from the WSR-88D data are denoted by the subscript GV—ground validation.) A similar set of plots is shown in Fig. 2 but at a height of 1.5 km. Note that the common area, the area observed by both radars, is smaller in this case because of earth-curvature and surface-clutter effects in the WSR-88D and surface-clutter effects at off-nadir incidence angles in the PR. Surface contamination in the PR return manifests itself as an enhancement of the radar return along parallel lines near the edges of the swath, an effect that can be seen clearly in the top panel of Fig. 2. For the results presented in the paper, volume elements where the surface clutter dominates are discarded.

Differences between the results shown in the top and center panels of Figs. 1 and 2 can be interpreted primarily as the change in the radar reflectivity factors after attenuation correction is introduced. A more quantitative way of displaying the differences is shown in Figs. 3 and 4, where scatterplots of dBZ_m versus dBZ (top) and dBZ_GV versus dBZ (bottom) are shown at heights of 3 and 1.5 km, respectively.

The scatterplot of dBZ_m versus dBZ at a height of 6 km (not shown) indicates that the two quantities are nearly identical and that the attenuation from the storm top to a 6-km height is usually negligible even in an intense rain case such as this. In descending from 6 to 3 km (Fig. 3) we find a strong increase in the apparent attenuation suffered by the PR signal. Examination of the data in Fig. 3 (top) shows that for dBZ values greater than about 40 dB, the attenuation correction often exceeds 10 dB and can be as large as 26 dB. Scatterplots of the corrected dBZ and the dBZ_GV data shown in Fig. 3 (bottom) indicate that the two quantities are well correlated, with a correlation coefficient, ρ, of 0.93. On the other hand, attenuation correction gives dBZ values that, on average, are 2.1 dB greater than those obtained from the WSR-88D. Using angular brackets to denote the mean value, the results are the following: 〈dBZ_m(h = 3 km)〉 = 33.05 dB, 〈dBZ(h = 3 km)〉 = 35.02 dB, and 〈dBZ_GV(h = 3 km)〉 = 32.90 dB. These trends persist as the height is changed from 3 to 1.5 km (Fig. 4). At this near-surface altitude, the maximum difference between dBZ_m and dBZ is nearly 40 dB (Fig. 4, top). Despite the presence of strong attenuation, the corrected dBZ values are well correlated with the dBZ_GV values, ρ = 0.95, whereas the correlation coefficient between dBZ_m and dBZ_GV is 0.78. As in the 3-km case, however, the mean value of the PR-derived reflectivity factor with attenuation correction is over 2 dB larger than that derived from the GV radar: 〈dBZ_m(h = 1.5 km)〉 = 30.64 dB, 〈dBZ(h = 1.5 km)〉 = 34.25 dB, and 〈dBZ_GV(h = 1.5 km)〉 = 32.04 dB. As discussed in the next section, some of the discrepancies between dBZ_GV and dBZ can be attributed to non-Rayleigh scattering effects at the higher frequency, different viewing geometries, and attenuation effects in the WSR-88D.

b. Non-Rayleigh scattering and related effects

The primary reasons for comparing data from the PR and ground-based radars are to determine the relative calibration accuracy of the radars and to assess the performance of the attenuation correction and rain-rate estimation procedures used in the PR algorithms. There are a number of factors that interfere with achieving these objectives, however. One source of error arises from inaccuracies in geolocation. The location of a particular PR radar volume along the beam is computed from the latitude and longitude of the estimated surface range gate, normally taken as that gate where the return power is maximum. [The actual determination of the surface is somewhat more involved; details can be found in Kozu et al. (2001)]. Errors in these data and variations in topography contribute to uncertainties in the location of the PR radar volume relative to that of the GV volume.

Apart from the problem of matching the radar volumes in space and time is the issue of non-Rayleigh scattering effects at the PR frequency. Increases in the radar reflectivity factor are usually associated with an increase in the number concentration of large particles, the backscattering cross sections of which can be significantly different for the 10-cm wavelength of the WSR-88D and the 2.17-cm wavelength of the PR. This non-Rayleigh scattering effect can be estimated using measured DSDs. For this purpose we employ DSDs measured in Switzerland (courtesy of Dr. Matthias Steiner). The results can be summarized by the mean difference, Δ_X, between the radar reflectivity factors at 13.8 GHz (PR) and 3 GHz (WSR-88D), given that the radar reflectivity factor at 3 GHz exceeds a threshold of X dBZ:

View Expanded

For spherical particles, the results are shown in the first section of Table 1. For example, for the 3309 DSDs for which dBZ(3 GHz) > 30 dBZ, the mean difference between the 13.8- and 3-GHz radar reflectivity factors is 0.767 dB, where the mean dBZ(3 GHz) is 34.47 dBZ. A secondary effect arises from the fact that raindrops are nonspherical. Letting 2b and 2a represent the lengths of the major and minor axes of the oblate then, using the relationship of Pruppacher and Beard (1970), the ratio of a and b is given by

abD_eq(3)

where D_eq is the diameter (mm) of the equivolume sphere. To perform the calculations we assume that the GV radar beam is directed along the horizon with either horizontal or vertical polarization, while the PR incidence is nadir-directed. Particle canting is neglected so that the symmetry axis of the particles is assumed to be along the vertical. The results of the table show that if the ground-based radar is horizontally polarized then Δ_X is approximately the same for oblates as for spheres. Since the WSR-88D is horizontally polarized, these results are relevant to the comparisons presented here. For vertical polarization, Δ_X increases substantially relative to the other cases where we find that for dBZ(3 GHz) > 35 dBZ, the average dBZ at 13.8 GHz exceeds that at 3 GHz by nearly 3 dB.

A third cause of discrepancies between the PR and GV arises from signal attenuation in the GV radar. Although this effect usually can be neglected at S band, in the 9 March 1998 case discussed in the previous section, and for several other overpasses during the year, strong rain was present along a radial sector (see Figs. 1 and 2). From the drop size distributions described above, we find specific attenuation–rain rate (k–R) relationships at 3 GHz of k = 3.88 × 10⁻⁴ R^0.91 at T = 20°C and k = 6.68 × 10⁻⁴ R^0.91 at T = 0°C. Battan (1973) quotes one-way path attenuations per unit mm h⁻¹ [(dB km⁻¹)/(mm h⁻¹)] at 3 GHz that range from a low of 3 × 10⁻⁴ to a high of 9.2 × 10⁻⁴. For example, for a rain rate of 20 mm h⁻¹ over a 50-km path, the signal can be expected to produce a two-way path attenuation between 0.6 and 1.84 dB. This simple example shows that attenuation is not always negligible at S band (Ryzhkov and Zrnic 1995) and, like the non-Rayleigh scattering effect, serves to increase the discrepancy (assuming perfect measurements) between the radar reflectivities derived from the PR and WSR-88D.

We conclude from the above considerations that the most important correction factor is the effect of non-Rayleigh scattering at the PR frequency. The correction is nonlinear so that it must be applied at the level of the common-resolution data and not to the mean dBZ. Processing of other drop size distributions shows that the results depend, not surprisingly, on the particular set of DSDs used. Because of this, and the fact that the correction is relatively small for the majority of data, a modification of the PR data to account for non-Rayleigh scattering is not made in this paper. It should be noted, finally, that because the PR algorithm accounts for non-Rayleigh scattering effects in the selection of the R–Z relationship, correction at the dBZ level is not required in the estimation of rain rate (Iguchi et al. 2000).

a. dBZ comparisons

The set of all data collected at a height of 3 km from the 24 overpasses of the Melbourne site during 1998 is shown in the scatterplots of Fig. 5. Data points included in the plots are those for which dBZ_m > 15 dBZ and dBZ_GV > 10 dBZ. Consequently, if either the WSR-88D or PR does not detect rain at a particular element, the data are discarded. For the area-averaged rain rates considered later in the paper, this restriction is not enforced and the two datasets are processed independently. It should be noted that although the nominal threshold of the PR is 18 dBZ, the radar return power is obtained by subtracting the signal-plus-noise from a noise-only estimate. Because both quantities are random variables, values of dBZ_m below the threshold are sometimes encountered. The effect on the statistics from a change in the threshold values will be discussed at the end of this section.

The correlation coefficient of dBZ and dBZ_GV for the entire set of 13 785 elements from the 24 overpasses is 0.90 (lower right-hand panel of Fig. 5). Scatterplots are also shown for divisions of the data into rain type (stratiform and convective—top panels) and surface background type (ocean, land, and coastal—middle and bottom-left panels). While the surface background classification can be applied to both datasets, this is not the case for the rain-type classification where different methods are used to analyze the PR and GV data (Awaka et al. 1998; Steiner et al. 1995). Because of this, the data plotted in the top panels of Fig. 5 comprise only those pixels for which the GV and PR classifications are in agreement; for example, the points plotted for stratiform rain correspond to elements for which both the GV and PR algorithms classify the rain as stratiform. These issues are discussed in more detail in the next section. A glance at the scatterplots for stratiform and convective rain shows that the data are more highly correlated for stratiform (ρ = 0.89) than for convective (ρ = 0.74) rain and that the mean dBZ in stratiform rain (〈dBZ〉 = 28.37 dBZ, 〈dBZ_GV〉 = 27.11 dB) is significantly lower than that for convective rain (〈dBZ〉 = 39.65 dBZ, 〈dBZ_GV〉 = 39.11 dBZ). In contrast, the division of data into ocean and land do not reveal any obvious differences, with correlations and means approximately the same. Histograms of the dBZ and dBZ_GV data for the six categories are pictured in Fig. 6, showing that the distributions of dBZ for the PR and GV data are in good agreement for all categories. Unlike the scatterplots where the data are compared element by element, the histograms are insensitive to registration errors.

The data in Figs. 5 and 6 are limited to a height of 3 km. The results, moreover, do not include the PR radar reflectivity factors before attenuation correction, dBZ_m. Tables 2–4, which summarize the comparisons at heights of 6, 3, and 1.5 km, give a more complete picture of the PR results relative to the GV both before and after attenuation correction. Listed in each table are the means and correlation coefficients for dBZ_m, dBZ, and dBZ_GV for the 24 overpasses as well as the weighted mean values, given on the last line of each table. The weighted mean is defined by

View Expanded

where N_i, is the number of common resolution elements in the ith overpass for which dBZ_GV > 10 dB and dBZ > 15 dB. The quantity 〈dBZ〉_i is the mean value taken over the N_i elements.

The statistics in Tables 2–4 were found by thresholding the PR data at 15 dBZ and the GV data at 10 dBZ. Although all PR rain data exceed 15 dBZ, GV rain data below the 10 dBZ threshold do exist and it is natural to ask how a change in the GV threshold would affect the statistics. As we note above, with a 10 dBZ threshold on the GV data, Δ(dBZ, dBZ_GV) = 1.12 dB, N = 7049 at 1.5 km and Δ(dBZ, dBZ_GV) = 0.83 dB, N = 13 785 at 3 km, where N is the number of data points. If we increase the GV threshold to 15 dBZ we obtain Δ(dBZ, dBZ_GV) = 0.92, N = 6824 at 1.5 km and Δ(dBZ, dBZ_GV) = 0.68 dB, N = 13 347 at 3 km. These results indicate that an increase in the GV threshold level to 15 dBZ, the same as the PR threshold, decreases the average difference at the 1.5 and 3-km levels. On the other hand, if we use all GV rain data, irrespective of the dBZ value, we find Δ(dBZ, dBZ_GV) = 1.35 dB, N = 7173 at 1.5 km, and Δ(dBZ, dBZ_GV) = 1.06 dB, N = 13 971 at 3 km. Clearly, if we do not threshold the GV data, the mean difference between the PR and GV increases because pairs of points will be included in the statistics for which dBZ > 15 dBZ and dBZ_GV < 10 dBZ so that the difference is at least 5 dB.

A summary of the results at a 1.5-km height, using the standard dBZ thresholds, is depicted in Fig. 7. In the top panel a scatterplot of the mean of dBZ_m versus the mean of dBZ_GV is shown for the 24 overpasses. The size of each data point has been made proportional to the number of common-resolution elements (4 km × 4 km × 1.5 km) in the overpass for which dBZ_m > 15 dBZ and dBZ_GV > 10 dBZ. A similar plot is shown in the bottom panel but where dBZ has replaced dBZ_m as the dependent variable. The asterisk in each plot represents the weighted means of the relevant datasets. The correlation coefficient and standard error displayed on each plot are computed by assuming that each data point (overpass) is weighted equally. It should be noted that this quantity is not the same as the correlation coefficient given in the tables, where each common-resolution element is weighted equally. In the former case, from Fig. 7, ρ(dBZ, dBZ_GV) = 0.89 and ρ(dBZ_m, dBZ_GV) = 0.87, while in the later case, from Table 4, ρ(dBZ, dBZ_GV) = 0.90 and ρ(dBZ_m, dBZ_GV) = 0.84.

b. PR–GV rain rate comparisons

If the same Z–R relationship was used to estimate rain rates from the ground-based and spaceborne data, the results could be obtained in a straightforward manner from the Z results. This is not the case, however. The comparison is further complicated by the fact that the PR and WSR-88D rain-rate algorithms employ different stratiform–convective classifications and different Z–R relationships for each class. In this section we begin with comparisons of the rain rates irrespective of rain classification. This is followed by results on the classification agreement between the two radars and comparisons of fractional rainfall amounts from convective and stratiform rain.

Shown in Fig. 8 are the mean rain rates derived from the PR and GV common-resolution data for the 24 overpasses. For each overpass, the mean is computed from those elements at which both the PR and WSR-88D detect rain. As in Fig. 7, each point in the scatterplot represents the mean value from a particular overpass where the size of the data point is proportional to the number of raining elements in the common area. In performing the comparisons at each pixel, the near-surface rain rate from the PR data product is compared with the GV rain-rate product at a height of approximately 1.5 km. Because of surface-clutter effects, the near-surface rain rate derived from the PR is a function of incidence angle so that the spatial matching of the PR and GV datasets are probably less accurate than in the dBZ comparisons. Although the weighted means of the derived rain rates are in reasonably good agreement (〈R_PR〉_W = 8.5 mm h⁻¹, 〈R_GV〉_W = 7.6 mm h⁻¹), the scatter is relatively high. These variations arise from several sources: registration errors, differences in the radar reflectivities, and differences in the Z–R relationships that are applied to these dBZ fields.

A somewhat different way to present the comparisons is to compute the instantaneous area-average rain rate from PR and GV (Schumacher and Houze 2000). As in the previous case, only the area defined by the intersection of the PR and GV scans is considered. In contrast, however, the PR and GV calculations are done independently so that the requirement that rain be detected by both radars at a given 4 km × 4 km element is discarded. The instantaneous area-average rain rate for a particular overpass is computed from

View Expanded

where the summation is taken over all the (equal area) elements, M, that compose the common viewing area. In contrast to the previous results where the PR and GV data were resampled to a common grid, this is not required (and in fact not done) for the area-average computations. The results are shown in Fig. 9. It is noteworthy that the means of the area-averaged rain rates, represented by the asterisk, are quite close (1.25 mm h⁻¹ for the PR and 1.21 mm h⁻¹ for the GV) and that the correlation coefficient (0.95) is significantly higher than in the previous case. The improved agreement in the area averages comes about, in part, because the overpasses are weighted equally in computing the means for the entire dataset. Thus, the 9 March case in Fig. 8 (located at x = 11.2 mm h⁻¹, y = 17.7 mm h⁻¹), which has a large influence on the weighted mean, has a smaller weight in the mean of the area averages. One other reason for the improvement is that the registration errors that arise in matching the PR and GV data over the high-resolution grid are not a factor in the area-average rain-rate comparisons. Variability is also reduced because of spatial averaging.

Although the results shown in Figs. 8 and 9 are encouraging, rain rate is not the only parameter of interest. Stratiform–convective classification has attracted much interest in analysis of TRMM data because of different average latent heating profiles associated with each rain type (Houze 1989; Yuter and Houze 1997; Atlas et al. 2000). Moreover, segmenting the Z–R relationship into rain categories has been promoted as a means to improve rain-rate retrievals (Tokay and Short 1996; Amitai 2000). Comparisons of rain classification from the PR and GV radars are instructive because the classification algorithms are based on different structural characteristics of the reflectivity field. Because the PR has good vertical resolution, particularly at nadir, yet somewhat crude horizontal resolution (4 km × 4 km), the PR classification algorithm relies heavily on brightband detection to indicate the presence of stratiform rain (Awaka et al. 1998). In the absence of a well-defined bright band, the PR algorithm then relies on a “standard” algorithm (Steiner et al. 1995) devised for applications to typical ground-based volume scans where the vertical resolution tends to be coarse and more reliable information is available on the horizontal storm structure.

Shown in Fig. 10 is the classification agreement (in percent) in rain type for the PR and GV radars for the 24 overpasses. As before, only those common-resolution cells are used where both radars detect rain. Apart from one case of very good correspondence (94%) and one of poor correspondence (55%), the classification accuracy for most overpasses is close to the average of 76%. It should be noted that the PR has three classifications: stratiform, convective, and other, whereas only the first two categories are defined in the GV algorithm. Clearly, when the rain type is classified as “other” by the PR it cannot agree with the GV designation. However, for the data obtained from the overpasses, the percentage rain in this category is a small fraction of the total.

Figure 11 shows the estimated percentage of total rainfall contributed by convective rain as determined independently by the PR and GV. Although the correlation is good, 0.95, the PR classifies a somewhat smaller percentage of the rain as convective (73%) than does the GV (78%). The corresponding instantaneous area-average rain rates for stratiform (top) and convective (bottom) are shown in Fig. 12. When compared to the results in Fig. 9, where the area-averaged rain rates are computed irrespective of rain type, the conditional results show a slight decrease in the correlation. The stratiform category in particular shows a smaller correlation coefficient (ρ = 0.90) and larger discrepancy in means (〈R〉 = 0.29 mm h⁻¹, 〈R_GV〉 = 0.24 mm h⁻¹) than does the convective category where ρ = 0.94 with 〈R〉 = 0.95 mm h⁻¹ and 〈R_GV〉 = 0.97 mm h⁻¹.

c. Fractional rain volume

While the statistics discussed above are instructive, they cannot be used to answer the following question: What fraction of the total rainfall does the PR miss because of its low sensitivity at light rain rates? To answer it, let f_GV(R_GV | R_GV > 0) denote the probability density function (pdf) of rain rate from the GV, conditioned on rain. The same quantity derived from the PR data is written as f_PR(R_PR | R_PR > 0). These conditional pdfs are obtained from the corresponding histograms of the data from the 24 overpasses. It also should be noted that, as in the analysis leading to Fig. 9, the PR and GV datasets are processed independently.

The fractional rain volume contributed by rain rates smaller than R, F_υ(R) can be written

View Expanded

Plots of F_υ(R) (multiplied by 100) for the GV and PR data are shown in Fig. 13. We can estimate the fraction of the rain volume missed by the PR by comparing F_υ at the light rain rates with the corresponding values from the GV. For example, at R = 0.5 mm h⁻¹, we have F_υ−GV(R = 0.5) − F_υ−PR(R = 0.5) = 1.4% and F_υ−GV(R = 1) − F_υ−PR(R = 1) = 2.3%. These estimates are similar to those obtained by Schmacher and Houze (2000) using the Kwajalein radar–PR datasets (2.3%) and by Bolen and Chandrasekhar (2000) using the S-pol–PR comparisons (3%).