Objectives
The objectives of 2A25 is to correct for the rain attenuation in measured radar reflectivity and to estimate the instantaneous three-dimensional distribution of rain from the TRMM Precipitation Radar (PR) data. The estimates of attenuation-corrected radar reflectivity factor and rainfall rate are given at each resolution cell of the PR. The Estimated near-surface rainfall rate and average rainfall rate between the two predefined altitudes (2 and 4 km) are also calculated for each beam position.
Algorithm Overview
2A25 basically uses a hybrid of the Hitschfeld-Bordan method and the surface reference method to estimate the vertical true radar reflectivity (Z) profile. (The hybrid method is described in Iguchi and Meneghini (1994)). The vertical rain profile is then calculated from the estimated true Z profile by using an appropriate Z-R relationship.
The attenuation correction is, in principle, based on the surface reference method. This method assumes that the decrease in the apparent surface cross section (Dso) is caused by the propagation loss in rain. The coefficient a in the k-Z relationship k=a Zb is adjusted in such a way that the path-integrated attenuation (PIA) estimated from the measured Zm-profile will match the reduction of the apparent surface cross section. The attenuation correction of Z is carried out by the Hitschfeld-Bordan method with the modified a. Since a is adjusted, we call this type of surface reference method the a-adjustment method. The a-adjustment method assumes that the discrepancy between the PIA estimate from Dso and that from the measured Zm-profile can be attributed to the inappropriate choice of a values which may vary depending on the raindrop size distribution and other conditions. It assumes that the radar is properly calibrated and that the measured Zm has no error.
In order to avoid inaccuracies in the attenuation correction when rain is weak, a hybrid of the surface reference method and the Hitschfeld-Bordan method is used [Iguchi and Meneghini, 1994]. The PIA is first estimated from the precipitation echo alone. The weight given by the hybrid method to the PIA estimate from the surface reference increases as the attenuation estimate increases. When rain is very weak and the attenuation estimate is small, the PIA estimate from the surface reference is effectively neglected. With the introduction of the hybrid method, the divergence associated with the Hitschfeld-Bordan method is also prevented.
One major difference from the method described in the above reference is that in order to deal with the beam-filling problem, a non-uniformity parameter is introduced and is used to correct the bias in the surface reference arising from the horizontal non-uniformity of rain field within the beam. Since radar echoes from near the surface are contaminated by the mainlobe clutter, the rain estimate at the lowest point in the clutter-free region is given as the near-surface rainfall rate for each angle bin.
Caveats
1. 2A25 produces many output variables. Please read '2a25_variables.txt' carefully before using them. For example, negative numbers are stored in "rain" and "correctedZFactor" when the data are missing or in the possibly cluttered ranges.
(IMPORTANT)
If the input radar reflectivity factor Zm is below the noise level, the rain estimate there is set to 0. This procedure does not cause any serious problem except when the measured Zm becomes smaller than the noise level by rain attenuation. In such a case, even if some heavy rain exists near the surface, and the actual rain rate there is rather large, the number in "rain" is 0. To know whether such low radar reflectivity factors are caused by large attenuation or not, look at the forth bit of 'reliab' and the forth bit of 'rainFlag'.
2. The error estimates in 'rain' and 'correctZFactor' are given in 'errorRain' and 'errorZ'. However, these estimates indicate only very crude estimates. Because only the first order terms in the Taylor expansion is used in the calculation, the error estimates are not reliable at all when they are large.
3. 2A25 processes data in both 'rain certain' and 'rain possible' angle bins. It processes all data below the height at which the first 'possibly' rain echo is detected. In fact, almost all data in 'rain possible' angle bins and data between 'storm height possible' and 'storm height certain' in 'rain certain' angle bins are noise data. The users of the PR data should be aware of this fact, even though some of the weak echoes are produced by rain.
4. Over some area with a very high surface reflectivity, sidelobe clutters may appear in the radar signal and they are sometimes misidentified as rain echoes. 2A25 removes some of the sidelobe clutters internally, but not all sidelobe signals are completely removed.
5. 2A25 relies on the output of 1C21 to separate the surface cluttered ranges from the clutter free ranges. Because the clutter identification routine used in 1B21 is not perfect (it never can be), some surface clutter (mainlobe clutter) may be occasionally misidentified as rain echo in 2A25, particularly in mountain regions.
6. The range bin numbers in the output of 2A25 are all relative to the Earth's ellipsoid with the ellipsoid range bin corresponding to 79. For example, if the range bin number is 75, its height from the ellipsoid is (79-75)*0.25 = 1.0 km. This number is NOT the height above the actual surface.
7. The value of a in the k-Z relationship (k = aZb) and the value of a in the R-Z relationship (R = a Zb) used in the final calculations of "correctZFactor" and "rain" are not the same as the numbers given in "attenParmAlpha", "ZRParmA". ("attenParmBeta" and "ZRParmB" are the same as the final values.) To get the final value of alpha at a given height, first calculate the alpha by linearly interpolating the values given in "attenParmAlpha", and then multiply the result by 'epsilon' for that angle bin. To get the final value of 'a' at a given height is not possible only from the data given in the output of 2A25. Similar to the case of 'alpha', first calculate the 'a' at a given height by interpolating the numbers in "ZRParamA", and then multiply it by nubfCorrectFactor[][1] and then further multiply it by the ratio of the terminal velocity at the given height to that at the sea level. This ratio is not given in the output of 2A25. It is calculated in 2A25 by using equation (9) in "Terminal Velocity of Raindrops Aloft" by G.B. Foote and P.S. du Toit in J. Applied Meteorology, pp.249-253, vol.8, 1969, and standard atmospheric pressures at 21 altitudes. The numbers at 21 heights are as follows:
1.00000
vratio[0] /* Terminal velocity ratio
at 0 km */
1.04900
vratio[1] /* Terminal velocity ratio
at 1 km */
1.10200
vratio[2] /* Terminal velocity ratio
at 2 km */
1.15900
vratio[3] /* Terminal velocity ratio
at 3 km */
1.22000
vratio[4] /* Terminal velocity ratio
at 4 km */
1.28600
vratio[5] /* Terminal velocity ratio
at 5 km */
1.35800
vratio[6] /* Terminal velocity ratio
at 6 km */
1.43500
vratio[7] /* Terminal velocity ratio
at 7 km */
1.52000
vratio[8] /* Terminal velocity ratio
at 8 km */
1.61100
vratio[9] /* Terminal velocity ratio
at 9 km */
1.71200
vratio[10] /* Terminal velocity ratio at
10 km */
1.82100
vratio[11] /* Terminal velocity ratio at
11 km */
1.94000
vratio[12] /* Terminal velocity ratio at
12 km */
2.06600
vratio[13] /* Terminal velocity ratio at
13 km */
2.20100
vratio[14] /* Terminal velocity ratio at
14 km */
2.34400
vratio[15] /* Terminal velocity ratio at
15 km */
2.49600
vratio[16] /* Terminal velocity ratio at
16 km */
2.65900
vratio[17] /* Terminal velocity ratio at
17 km */
2.83300
vratio[18] /* Terminal velocity ratio at
18 km */
3.01700
vratio[19] /* Terminal velocity ratio at
19 km */
3.21400
vratio[20] /* Terminal velocity ratio at
20 km */
(I plan to modify
the code and give the final values in "attenParmAlpha" and "ZRParmA" in
the next version. Please watch out for the note of changes.)
8. The rain rate estimate from a given reflectivity factor depends on the storm type and the phase of precipitating particles. 2A25 essentially uses only two types of storm; stratiform or convective. Since the classification of storm types may not be perfect, since there are intermediate states between stratiform and convective rain, and since the estimate of the zero-degree C height and the phase classification are rather crude, the estimates of rain rate may include large errors.
File Format
The file content description
for 2A25 can be found in the Interface Control Specification (ICS) between
the Tropical Rainfall Measuring Mission Science Data and Information System
(TSDIS) and the TSDIS Science User (TSU) Volume 4: File Specifications
for TSDIS Products - Level 2 and 3 File Specifications. It is available
at:
http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4.pdf.
Known Deficiencies
Note that since the algorithm has been tested only for a few rain cases, more deficiencies may be found in the future.
1. The non-uniform beam filling correction tends to over-correct the attenuation in some heavy rain range bins. This happens probably because the range dependence of apparent attenuation coefficient in non-uniform rain cases is neglected. To avoid the unrealistically large Z-factors and rain rates, a limit for the non-uniform beam filling correction for attenuation is introduced.
2. Sidelobe contamination occurs when the nadir surface cross section is very large. A simple routine to remove such sidelobe clutter is included in the algorithm, but it does not completely remove the sidelobe signals. Care must be taken when small signals are used.
Planned Improvements
Work is underway to do careful validation of the 2A25 algorithm by comparing its results to other validation data. Any shortcomings of the algorithm identified by this work will be addressed to the best of our ability.
Since the initial choice of the Z-R relationship for each rain type affects the rain estimates substantially, effort will be made to find the Z-R relationships suitable for the algorithm.
References
Iguchi, T., and R. Meneghini, "Intercomparison of Single Frequency Methods for Retrieving a Vertical Rain Profile from Airborne or Spaceborne Data," Journal of Atmospheric and Oceanic Technology, Vol. 11, No. 6, pp. 1507-1516, 1994.
Kozu, T., and T. Iguchi, "A preliminary study of non-uniform beam filling correction for spaceborne radar rainfall measurement," IEICE Trans. Commun., E79-B, pp. 763-769, June 1996.
Iguchi, T., T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto, "Preliminary results of rain profiling with TRMM Precipitation Radar," Proc. of URSI-F International Triennial Open Symposium on Wave Propagation and Remote Sensing, Aveiro, Portugal, pp. 147-150, 1998.