• Heymsfield, G. M., Geerts B. , and Tian L. , 2000: TRMM precipitation radar reflectivity profiles as compared with high-resolution airborne and ground-based radar measurements. J. Appl. Meteor., 39 , 20802102.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iguchi, T., Kozu T. , Meneghini R. , Awaka J. , and Okamoto K. , 2000: Rain-profiling algorithm for the TRMM precipitation radar. J. Appl. Meteor., 39 , 20382052.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liao, L., and Meneghini R. , 2009: Changes in the TRMM version-5 and version-6 precipitation radar products due to orbit boost. J. Meteor. Soc. Japan, 87 , 93107.

    • Search Google Scholar
    • Export Citation
  • Panofsky, H. A., and Brier G. W. , 1968: Some Applications of Statistics to Meteorology. The Pennsylvania State University, 224 pp.

  • Shimizu, S., Oki R. , Tagawa T. , Iguchi T. , and Hirose M. , 2009: Evaluation of the effects of the orbit boost of the TRMM satellite on PR rain estimates. J. Meteor. Soc. Japan, 87 , 8392.

    • Search Google Scholar
    • Export Citation
  • Short, D. A., Hirose M. , and Nakamura K. , 2009: An interpretation of TRMM radar observations of shallow convection with a rain cell model. J. Meteor. Soc. Japan, 87 , 6781.

    • Search Google Scholar
    • Export Citation
  • Takahashi, N., and Iguchi T. , 2008: Characteristics of TRMM/PR system noise and their application to the rain detection algorithm. IEEE Trans. Geosci. Remote Sens., 46 , 16971704.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Takayabu, Y. N., Iguchi T. , Kachi M. , Shibata A. , and Kanzawa H. , 1999: Abrupt termination of the 1997–98 El Niño in response to a Madden–Julian oscillation. Nature, 402 , 279282.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery
    Fig. 1.

    Monthly time series of the probability of path-averaged reflectivity greater than 12 dBZ.

  • View in gallery
    Fig. 2.

    Composite distributions of measured path-averaged radar reflectivity for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

  • View in gallery
    Fig. 3.

    Monthly time series of the probability of path-averaged reflectivity greater than 24 dBZ but less than 32 dBZ.

  • View in gallery
    Fig. 4.

    Composite distributions of measured radar reflectivity at 2-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

  • View in gallery
    Fig. 5.

    Composite distributions of measured radar reflectivity at 4-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

  • View in gallery
    Fig. 6.

    Composite distributions of measured radar reflectivity at 10-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

  • View in gallery
    Fig. 7.

    Schematic of equal area annuli defined by distances where the BVG function decreases in 1-dB increments.

  • View in gallery
    Fig. 8.

    Distance (km) vs 10 log10[P(r)] for the modeled PR FOV before (dashed) and after (solid) boost.

  • View in gallery
    Fig. 9.

    Simulated radar reflectivity distributions for a circular echo area of radius 0.5 km and echo strength 34 dBZ, using PR FOV parameters representative of preboost (dashed) and postboost (solid) conditions.

  • View in gallery
    Fig. 10.

    Reflectivity distributions as in Fig. 9, but modified by probability of detection filters appropriate for preboost (dashed) and postboost (solid) conditions.

  • View in gallery
    Fig. 11.

    Simulated radar reflectivity distributions for a circular echo area of radius 3.0 km and echo strength 23 dBZ, using PR FOV parameters representative of preboost (dashed) and postboost (solid) conditions.

  • View in gallery
    Fig. 12.

    Reflectivity distributions as in Fig. 11, but modified by probability of detection filters appropriate for preboost (dashed) and postboost (solid) conditions.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 110 46 6
PDF Downloads 36 13 0

Effect of TRMM Orbit Boost on Radar Reflectivity Distributions

David A. ShortHydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan

Search for other papers by David A. Short in
Current site
Google Scholar
PubMed
Close
and
Kenji NakamuraHydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan

Search for other papers by Kenji Nakamura in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

Probability distributions of measured radar reflectivity from the precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite show a small, counterintuitive increase in the midrange, 20–34 dBZ, when comparing data from periods before and after the orbit altitude was boosted in August 2001. Data from two 2-yr time periods, 1999–2000 (preboost) and 2002–03 (postboost), show statistically significant differences of 2%–3% at altitudes of 2, 4, and 10 km and for path-averaged reflectivity.

The bivariate Gaussian function, used to model idealized radar response functions, has mathematical properties that indicate an increase in field-of-view (FOV) size associated with an increase in satellite altitude can be expected to result in a narrowing of observed dBZ distributions, with a resulting increase in midrange values. Numerical simulations with echo areas much smaller and larger than the TRMM PR FOV before (4.3 km) and after (5.0 km) boost are used to demonstrate basic characteristics of the observed and expected distribution changes.

Corresponding author address: David Short, Applied Electromagnetic Research Center, National Institute of Information and Communications Technology, 4-2-1 Nukui-kitamachi, Koganei-shi, Tokyo 184-8795, Japan. Email: dshort@nict.go.jp

Abstract

Probability distributions of measured radar reflectivity from the precipitation radar (PR) on board the Tropical Rainfall Measuring Mission (TRMM) satellite show a small, counterintuitive increase in the midrange, 20–34 dBZ, when comparing data from periods before and after the orbit altitude was boosted in August 2001. Data from two 2-yr time periods, 1999–2000 (preboost) and 2002–03 (postboost), show statistically significant differences of 2%–3% at altitudes of 2, 4, and 10 km and for path-averaged reflectivity.

The bivariate Gaussian function, used to model idealized radar response functions, has mathematical properties that indicate an increase in field-of-view (FOV) size associated with an increase in satellite altitude can be expected to result in a narrowing of observed dBZ distributions, with a resulting increase in midrange values. Numerical simulations with echo areas much smaller and larger than the TRMM PR FOV before (4.3 km) and after (5.0 km) boost are used to demonstrate basic characteristics of the observed and expected distribution changes.

Corresponding author address: David Short, Applied Electromagnetic Research Center, National Institute of Information and Communications Technology, 4-2-1 Nukui-kitamachi, Koganei-shi, Tokyo 184-8795, Japan. Email: dshort@nict.go.jp

1. Introduction

The Tropical Rainfall Measuring Mission (TRMM) satellite is now in its twelfth year of operation, its lifetime having been extended by an orbit boost in August 2001 that reduced the rate at which the limited fuel supply, needed to maintain orbit altitude, was being consumed. The increase in altitude, from 350 to 402.5 km, affected attributes of the precipitation radar (PR), increasing its field of view (FOV) from 4.3 to almost 5 km and decreasing its sensitivity by 1.21 dBZ (Shimizu et al. 2009), as expected. Liao and Meneghini (2009) compared PR data to ground-based radar data before and after the boost, showing a stable PR calibration. Shimizu et al. (2009) showed boost-related changes in surface rain-rate estimates, attributing the changes to reduced sensitivity to light rain, undersampling of shallow rain, and a beam-mismatching effect. These changes are well understood and are considered here as primary effects of the orbit boost.

In the present study, we examine the boost effect on the observed probability distribution of measured radar reflectivity, noting a secondary effect: a minor increase in the interval from approximately 20 to 34 dBZ. This minor increase can be inferred from mathematical properties of a bivariate Gaussian (BVG) idealization of the PR FOV before and after boost, and it has been simulated by using an idealized representation of rain-echo areas sampled randomly by an idealized spaceborne radar. A more intuitive explanation makes use of the concept of the PR FOV as a spatial filter. The wider postboost filter reduces the occurrence of high and low dBZ values while increasing the probability of midrange values.

2. Data and analysis method

Measured radar reflectivity (Z) data from TRMM PR product 3A25 were used in this study. Product 3A25 is in a convenient form for survey studies of the type presented here. The data were generated by the TRMM Science Data Information System (TSDIS), using version-6 algorithms supplied by the TRMM Science Team. The Z data used here were not corrected for attenuation. For each 5° × 5° latitude–longitude box from 180°W to 180°E (72 boxes) and 40°S to 40°N (16 boxes), TSDIS calculates Z from each PR profile (Iguchi et al. 2000), preserving information at the resolution of the instrument. The Z data are then composited into monthly histograms having 30 bins, with bin widths of 2 dBZ [where dBZ = 10 log10(Z)] from 10 to 70 dBZ. The first bin is documented as 0.01–12 dBZ, but its probabilities appear somewhat noisy, so the analyses presented here use data from the second bin and upward, >12 dBZ. Even though the nominal sensitivity of the PR is usually given as 18 dBZ, lower dBZ values are often recorded because of radar noise, the noise estimation and subtraction procedure, and the signal-to-noise restrictions placed on determining significant echoes. The Z data includes dBZ histograms at 5 levels (2, 4, 6, 10, and 15 km) and a path-averaged Z for each PR profile containing precipitation echoes. The path-averaged Z was calculated by TSDIS by averaging Z values from storm top to the lowest clutter-free range bin. As a result, the path-averaged data contain information from all types of precipitation structures over land and ocean. The 3A25 data also includes the total number of PR FOVs located within each 5° × 5° box for each month. The Z and number of PR FOV data were combined to produce probability distributions of dBZ for this study.

There are numerous factors that were taken into consideration in the method for obtaining a probability distribution of radar reflectivity representative of instrument performance before and after the orbit boost. The geographic distribution of PR FOV data varies significantly in space and time because of the narrow swath width of the scanning instrument (less than 250 km). In addition, the probability of observing precipitation is small, and it also varies significantly in space and time. For example, a strong El Niño event was active in early 1998, displacing patterns of deep tropical convection from their normal locations, but ending around May of that year (Takayabu et al. 1999).

The PR takes more than 200 000 000 profiles per month but only about 4% indicate precipitation on average. The PR sampling area is confined to latitudes equatorward of about 36°N and 36°S, providing a full sampling of tropical latitudes and a partial sampling of midlatitude storm tracks. The number of PR FOVs per 5° × 5° area depends strongly on latitude, maximizing near the orbit turning points at 35°N and 35°S, and weakly on longitude for a given month because the PR swath is much narrower than the distance between consecutive orbits. The procedure for calculating a representative probability distribution of dBZ values from the monthly data was designed to remove effects of variability in geographic patterns of the number of PR FOV samples and the number of samples with significant precipitation echoes.

For each 5° × 5° latitude/longitude box a probability distribution was calculated for each month by taking the ratio of the number of FOVs with significant echoes, recorded for each 2-dBZ bin, to the total number of FOVs for the same 5° × 5° box. The 72 probability distributions at each latitude interval were then averaged to create one distribution for each of the 16 latitude intervals. The final probability distribution for each month was calculated as a weighted average of the 16 referred to above, with weights being proportional to the area of each 5° latitude interval. The PR coverage at the poleward edges of the orbit, the first and last latitude intervals, was assumed to extend to 36°N and 36°S.

3. Observed radar reflectivity statistics

Figure 1 shows a monthly time series of the area-weighted probability of path-averaged dBZ > 12. The 9% decrease in late 2001 from 0.0415 to 0.0380 is associated with the decrease in PR sensitivity of 1.21 dBZ (Shimizu et al. 2009). Figure 2 shows probability distributions of path-averaged dBZ constructed from an area-weighted monthly histogram data from the 2-yr periods marked with double-ended arrows (1999–2000 and 2002–03). The decrease in PR sensitivity is clearly evidenced in Fig. 2 by a decrease in the probability of dBZ < 20.

Figure 2 also shows a very small increase of about 3% in midrange dBZ values over the interval from 24 to 32 dBZ. The increase is the focus of the remainder of this study. The increase is more clearly represented in Fig. 3, which shows a monthly time series of the probability of midrange path-averaged dBZ values from 24 to 32 dBZ. There is a clear increase in late 2001 (August) just after the boost at the same time when the overall probability had decreased as shown in Fig. 1. Figures 1 and 3 both show an increase toward the end of the record. The increase may be due to natural climatic variability, but these aspects are beyond the scope of the present study.

The Student’s t statistic (e.g., Panofsky and Brier 1968) was used to test the statistical significance of postboost changes in the probability of path-averaged dBZ values. The 2-yr periods 1999–2000 and 2002–03 were chosen to avoid El Niño–related variability in early 1998 and an apparent upward trend from 2005 to the end of the record, both evident in Fig. 3.

For each dBZ bin centered from 21 to 45 dBZ, the t statistic was used to test the null hypothesis that the average probabilities X1 and X2 were equal during the 2-yr periods before and after boost:
i1520-0426-27-7-1247-e1
A sample size of n = 24, representing monthly values over a 2-yr period, was used. The pooled standard deviation was given by
i1520-0426-27-7-1247-e2
where and are variances of the monthly bin probability values within the respective 2-yr periods.

Table 1 lists bin-by-bin statistics of changes in probabilities, comparing two 2-yr periods before and after the boost. Changes for values <20 dBZ are not listed but were all significant above the 99.99% level as expected. The increases of a few percent in midlevel values, 24–32 dBZ, were found to be significant at the 98% level. Table 1 indicates a transition region from 32 to 36 dBZ, where changes shifted from positive to negative, but the changes were not significant at the 98% level. Decreases of probability in the interval from 36 to 42 dBZ also tested as significant. These changes indicate a very minor narrowing of the dBZ distribution after boost, associated with a larger FOV.

Analyses of dBZ distributions at heights of 2, 4, and 10 km were also made to test the consistency of the results from the path-averaged dBZ data. These three heights provide Z measurements over a wide range of conditions. The lowest level includes deep and relatively shallow rain systems. The 4-km level is just below the radar bright band over much of the tropics, and the 10-km level includes data from deep systems.

Figure 4 shows probability distributions of dBZ values at 2-km altitude constructed from area-weighted monthly histogram data from the 2-yr periods 1999–2000 and 2002–03. A small postboost increase of about 2% from 28 to 34 dBZ tested as statistically significant using the Student’s t-test procedure described above. A postboost small decrease over the interval 38 to 48 dBZ (not shown) also tested as statistically significant.

Figure 5 shows probability distributions of dBZ values at 4-km altitude constructed from area-weighted monthly histogram data from the 2-yr periods 1999–2000 and 2002–03. A small postboost increase of about 2%–3% from 28 to 34 dBZ is statistically significant using the Student’s t-test procedure described above. A small postboost decrease over the interval 36–48 dBZ (not shown) also tested as statistically significant.

Figure 6 shows probability distributions of dBZ values at 10-km altitude constructed from area-weighted monthly histogram data from the 2-yr periods 1999–2000 and 2002–03. A postboost small increase of about 2%–3% from 20 to 24 dBZ is statistically significant, whereas smaller insignificant increases extending to 40 dBZ are not perceptible because of their low probability and the scale of the plot.

The comparison of measured reflectivity data from the TRMM PR, before and after orbit boost, shows a small systematic shift in the probability of midrange dBZ values (approximately 22–34 dBZ), with higher probabilities after boost. There is also some evidence of lower probabilities at higher dBZ values (approximately 36–48 dBZ) after boost, except at 10 km. The observed systematic shifts in measured dBZ distributions have motivated the idealized simulation experiments described below.

4. Idealized radar field of view

The idealized radar FOV described below has mathematical properties that reveal effects of a change in FOV size on the probability distribution of dBZ values, resulting from very small precipitation features. The basic concept is that the features occur randomly, one at a time, within the radar FOV. The dBZ distribution results from an ensemble of realizations, with the location of the feature being distributed uniformly within the FOV.

The two-way illumination function of the TRMM PR FOV can be accurately represented by a circularly symmetric bivariate Gaussian function (Heymsfield et al. 2000):
i1520-0426-27-7-1247-e3
where r = √(x2 + y2) represents the distance from the center of FOV, and x and y represent the east–west and north–south distances, respectively. The scale parameter σ determines the nominal FOV.
The nominal radar FOV is defined to be the distance at which (3) decreases by a factor of 6 dB (10−0.6) from its value at the center. Another useful property of the BVG function (3) is the sequence of distance values at which it decreases by integer values of a decibel (Short et al. 2009). The sequence of distance values corresponding to integer values of dB[P(r)] is given by
i1520-0426-27-7-1247-e4
For N = 1, 2, 3, … , (4) describes a sequence of radii. Circles constructed from the sequence delineate equal area annuli as shown in Fig. 7. The area of each annulus is a constant determined by σ, the BVG scale parameter:
i1520-0426-27-7-1247-e5

Because the sequential annuli have equal areas, the probability of the center of a randomly located rain area falling within any one annulus is equal to the probability that it would fall within any other annulus. This is important because the simulated dBZ value associated with an idealized rain area will depend directly on the distance of its center from the FOV center. These facts are helpful for interpreting simulations of dBZ distributions for idealized rain areas.

Table 2 lists pre- and postboost parameters of the BVG function used to represent the PR FOV in this study. The ratio of parameters is useful for interpreting simulated radar reflectivity distributions.

Figure 8 shows distance versus the BVG functions (3), before and after boost, in dB[P(r)]. The maximum “before” function is 1.31 dB higher than the “after,” which is consistent with Table 2. Beyond a distance of 2 km, the “before” BVG function is lower than the “after” as expected because it is narrower.

5. Simulated radar reflectivity distributions

The idealized form of the radar FOV can be used to simulate dBZ distributions resulting from modeled precipitation features. This allows a method for determining effects of changes in FOV size on the dBZ distribution.

The following procedure was used for simulating radar reflectivity distributions from a prescribed circular echo area. The simulation was carried out on a 10 km × 10 km Cartesian grid, with a spacing of 0.01 km and the FOV in the center of the grid. A sequence of simulations was done with the echo progressing toward the FOV center in steps of 0.05 km. The product of the echo strength and the BVG function was integrated for each member of the sequence, resulting in distance-dependent dBZ values for the echo, as in Short et al. (2009). Only the distance dependence of the simulated reflectivity was needed to compute a distribution because the FOV has radial symmetry.

Figure 9 shows simulated dBZ distributions for a 34-dBZ circular echo, 0.5-km radius, using the before- and after-boost BVGs. The echo size and intensity were chosen because the size is much smaller than the FOV, giving a good comparison to the theoretical limit of a point source, and the intensity produces dBZ values in the range of interest. The distributions can be thought of as resulting from the echo being placed randomly within a circle of radius 3.1 km, centered at the FOV centers, with only one echo affecting the FOVs at a time. The 3.1-km distance was chosen because it corresponded to the distance where the preboost simulated reflectivity was 12 dBZ less than the maximum and the postboost simulated reflectivity was 9 dBZ less than the maximum. Thus, 12 intervals, each 1 dBZ in width with areas of 2.51 km2, encompass the same area as 9 intervals, each 1 dBZ in width with areas of 3.36 km2 each, to within less than 1%. This limitation ensured a standard normalization factor for each distribution. Note that the ordinate in Fig. 9 could have been rescaled as a probability of occurrence by dividing by the area of the domain encompassed in the simulation [π (3.1 km)2 = 30.19 km2].

The distributions in Fig. 9 are nearly uniform in height, as expected from (5), and due to the small size of the echo area, relative to the FOV. The difference between maximum dBZ values for the two distributions is 1.27 dBZ, with the higher value associated with the preboost FOV, and very close to the theoretical value for a very small echo (1.31 dB, as indicated in Table 2). The minimum dBZ value is also associated with the preboost FOV, consistent with its response function being lower than the postboost FOV at a range of 3.1 km (see Fig. 8). The postboost distribution is narrower and higher than the preboost distribution, by a factor of 1.34, which is also consistent with Table 2. The narrower distribution is suggestive of the effects of a wider spatial filter in reducing maxima and minima, while increasing the probability of intermediate values.

Figure 10 shows the result of applying probability of detection (POD) filters to the distributions of Fig. 9. The POD filters were designed to mimic effects of radar noise on detection of weak echoes when a preset signal-to-noise ratio is used to discriminate between significant and nonsignificant echoes (Takahashi and Iguchi 2008). The POD filters are Gaussian cumulative distributions with means of 16 and 17.2 dBZ, representing before- and after-boost conditions and standard deviations of 2.5 dBZ. The 1.2-dBZ difference in means is consistent with the PR’s after-boost sensitivity change, whereas the standard deviation was tuned to match the shape of the low end tails seen in Fig. 2.

The POD filters effectively erase all information below 12 dBZ in Fig. 10. The surviving distributions show some characteristics similar to the observed distributions in Fig. 2. There is a midrange of values where the postboost area is higher than the preboost area, even though the model rain area was identical for both simulations. The peak value is higher for the preboost case. Only the FOV changed from small to large, consistent with the orbit boost.

Figure 11 shows simulated dBZ distributions for a 23-dBZ circular echo, radius 3 km, using the before- and after-boost BVGs. The echo size and intensity were chosen because the size is larger than the nominal FOVs, giving some indication of how the shapes of the simulated distributions change as the echo area increases and the intensity produces dBZ values in the range of interest. The total areas represented by the two distributions are within less than 1% of each other, as was the case for Fig. 9.

The distributions in Fig. 11 are not uniform in height, showing some distortion because of the large size of the echo area relative to the FOV. The difference between maximum dBZ values for the two distributions is 0.33 dBZ, with the higher value associated with the preboost FOV and much smaller than the theoretical value for a very small echo (1.31 dB, as indicated in Table 2). The minimum dBZ value is also associated with the preboost FOV, consistent with its response function being lower than the postboost FOV beyond a distance of 2 km (see Fig. 8). The postboost distribution is narrower and higher than the preboost distribution, by a factor of about 1.15, smaller than that associated with the very small echo simulation used to create Fig. 9 and closer to the observed differences shown in Figs. 2, 4, 5, and 6.

Note that the distortion of the distributions shown in Fig. 11, relative to uniform, is larger for the preboost FOV because the contrast between FOV and echo size is larger for the preboost case. The distribution shapes in Fig. 11 give an indication of a transition toward the limiting case of an echo much larger than the FOVs: the maximum dBZ values would be identical and the widths of the distributions would trend toward zero, becoming delta functions at the maximum value.

Figure 12 shows the result of applying POD filters to the distributions of Fig. 11. The POD filters are identical to those described for Fig. 10. Differences between the pre- and postboost simulated distributions show some similarity to the differences in observed distributions (Figs. 2, 4, 5, and 6), with larger area (probability) in the midrange and lower areas (probabilities) at the high and low ends.

6. Discussion

One effect of the TRMM orbit boost on probability distributions of radar reflectivity measured by the PR was an increase of about 2%–3% in midrange dBZ values, determined by comparing distributions for two 2-yr periods: 1999–2000 before the boost and 2002–03 after the boost. The increase was observed for radar reflectivity values between approximately 20–34 dBZ, depending on altitude. The increase can be simulated by combining idealized models of the PR field of view, before and after boost, with idealized radar echoes and can be inferred from mathematical properties of a bivariate Gaussian idealization of the PR FOV. A more intuitive explanation makes use of the concept of the PR FOV as a spatial filter. The wider postboost filter reduces the occurrence of high and low dBZ values, while increasing the probability of midrange values.

A simulation with a 0.5-km radius echo area was used to quantitatively illustrate effects of a small echo on the increased occurrence of midrange dBZ values when the FOV size was increased from 4.3 to 5.0 km, as was the case of the TRMM PR. A second simulation with a 3-km radius echo area was used to quantitatively illustrate effects of large echo areas on the postboost increased occurrence of midrange dBZ values.

Model simulations with larger echo areas indicate a reduction in the contrast in the probability of midrange dBZ values when comparing large and small FOV effects. The difference in the maxima dBZ value also decreases because in the limit of an echo area much larger than the FOV both pre- and postboost FOVs would show the same dBZ level. This suggests that dBZ distributions observed by the PR in stratiform rain areas would show smaller differences than those observed in convective rain areas because of the smaller spatial scales generally associated with convective precipitation. The model results also suggest some caution in interpreting changes and trends in the pre- and postboost PR data. Some portion of the change may well be associated with simple geometric effects.

The simulation procedure used here could be described as representing an ensemble viewpoint, where members of the ensemble are uniformly distributed at random locations with respect to the FOV center. A more complex ensemble viewpoint, exploited by Short et al. (2009), allows variability in the size of the echo area or its dBZ value while requiring at the same time that each variation be uniformly and randomly placed with respect to the FOV center. The variability in echo size and/or intensity, not exploited here, can be tuned to generate simulated distributions with long right-end tails, as seen in Fig. 2. The objective of the more complex approach is to roughly imitate effects of the variability of natural echo areas with random locations with respect to radar FOVs on observed distributions of radar reflectivity.

Acknowledgments

The authors thank Dr. Hirohiko Masunaga for his useful comments during the course of this study and Dr. T. Iguchi for his encouragement. The support of the Hydrospheric Atmospheric Research Center at Nagoya University is gratefully acknowledged by DAS.

REFERENCES

  • Heymsfield, G. M., Geerts B. , and Tian L. , 2000: TRMM precipitation radar reflectivity profiles as compared with high-resolution airborne and ground-based radar measurements. J. Appl. Meteor., 39 , 20802102.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iguchi, T., Kozu T. , Meneghini R. , Awaka J. , and Okamoto K. , 2000: Rain-profiling algorithm for the TRMM precipitation radar. J. Appl. Meteor., 39 , 20382052.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liao, L., and Meneghini R. , 2009: Changes in the TRMM version-5 and version-6 precipitation radar products due to orbit boost. J. Meteor. Soc. Japan, 87 , 93107.

    • Search Google Scholar
    • Export Citation
  • Panofsky, H. A., and Brier G. W. , 1968: Some Applications of Statistics to Meteorology. The Pennsylvania State University, 224 pp.

  • Shimizu, S., Oki R. , Tagawa T. , Iguchi T. , and Hirose M. , 2009: Evaluation of the effects of the orbit boost of the TRMM satellite on PR rain estimates. J. Meteor. Soc. Japan, 87 , 8392.

    • Search Google Scholar
    • Export Citation
  • Short, D. A., Hirose M. , and Nakamura K. , 2009: An interpretation of TRMM radar observations of shallow convection with a rain cell model. J. Meteor. Soc. Japan, 87 , 6781.

    • Search Google Scholar
    • Export Citation
  • Takahashi, N., and Iguchi T. , 2008: Characteristics of TRMM/PR system noise and their application to the rain detection algorithm. IEEE Trans. Geosci. Remote Sens., 46 , 16971704.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Takayabu, Y. N., Iguchi T. , Kachi M. , Shibata A. , and Kanzawa H. , 1999: Abrupt termination of the 1997–98 El Niño in response to a Madden–Julian oscillation. Nature, 402 , 279282.

    • Crossref
    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Monthly time series of the probability of path-averaged reflectivity greater than 12 dBZ.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 2.
Fig. 2.

Composite distributions of measured path-averaged radar reflectivity for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 3.
Fig. 3.

Monthly time series of the probability of path-averaged reflectivity greater than 24 dBZ but less than 32 dBZ.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 4.
Fig. 4.

Composite distributions of measured radar reflectivity at 2-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 5.
Fig. 5.

Composite distributions of measured radar reflectivity at 4-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 6.
Fig. 6.

Composite distributions of measured radar reflectivity at 10-km altitude for the 2-yr periods before (dashed; 1999–2000) and after (solid; 2002–03) orbit boost.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 7.
Fig. 7.

Schematic of equal area annuli defined by distances where the BVG function decreases in 1-dB increments.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 8.
Fig. 8.

Distance (km) vs 10 log10[P(r)] for the modeled PR FOV before (dashed) and after (solid) boost.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 9.
Fig. 9.

Simulated radar reflectivity distributions for a circular echo area of radius 0.5 km and echo strength 34 dBZ, using PR FOV parameters representative of preboost (dashed) and postboost (solid) conditions.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 10.
Fig. 10.

Reflectivity distributions as in Fig. 9, but modified by probability of detection filters appropriate for preboost (dashed) and postboost (solid) conditions.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 11.
Fig. 11.

Simulated radar reflectivity distributions for a circular echo area of radius 3.0 km and echo strength 23 dBZ, using PR FOV parameters representative of preboost (dashed) and postboost (solid) conditions.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Fig. 12.
Fig. 12.

Reflectivity distributions as in Fig. 11, but modified by probability of detection filters appropriate for preboost (dashed) and postboost (solid) conditions.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1426.1

Table 1.

Statistics of changes in path-averaged dBZ probabilities, comparing 2-yr periods before (1999 and 2000) and after (2002 and 2003) the boost. Degress of freedom denoted as DOF.

Table 1.
Table 2.

PR FOV parameters before and after boost. The ratio of the parameters, after:before, are useful for interpreting simulated radar reflectivity distributions.

Table 2.
Save