GEOPHYSICAL RESEARCH LETfERS, VOL. 30, NO.4, 1180, doi:10.1029/2002GL016416, 2003

Effects of uncertainty in TRMM precipitation radar path integrated

attenuaqon on interannual variations of tropical oceanic rainfall

Franklin R. Robertson and Dan E. FitzjarraldNASA/Marshal\ Space Flight Center, USA

Christian Q. Kummerow

Colorado State University, USA

Received 9 October 2002; revised 20 November 2002; accepted 15 Deceml

[I] Consid~rable uncertainty surrounds the issue ofwhether precipitation over the tropical oceans (30° N/S)systematically changes with intetannual sea-surfacetemperature (SST) anomalies that accompany El Nino(wann) and La Nina (cold) events. Time series of rainfallestimates from the Tropical Rainfall Measuring Mission(TRMM) Precipitation Radar (PR) over the tropical oceansshow marked differences with estimates from two TRMMMicrowave Imager (TMI) passive microwave algbrithmS.We show that path-integrated attenuation derived from theeffects of precipitation on the radar return from the oceansurface exhibits interannual variability that agrees closelywith the rMI time series. Our analysis of discrepanciesbetween the PR rainfall and attenua:tion suggests thatuncertainty in the assumed drop size distribution andassociated attenuation/reflectivity/rainfa11 relationshipsinherent in single-frequency radar methods is a seriousissue for studies of interannual variability, INDEX TERMS:1655 Global Change: Water cycles (1836); 3314 Meteorology andAtmospheric Dynamics: Convective processes; 3354 Meteorologyand Atmospheric DynaJnics: Precipitation (1854); 3360Meteorology and Atmosph~ric Dynamics: R~mote sensing; 4522Oceanography: Physical: El Nifio. Citation: Robertson, F. R., D.E. Fitzjarrald, and C. D. Kummerow, Effects of uncertainty inTRMM precipitation radar path integrated attenuation oninterannual variations of tropical oceanic rainfall, Geqphys. Res.Lett.,30(4), 1180, doi:10.1029/2002GL016416, 2003.

I. Introduction

[2] It is well documented that El Nino-Southem Oscil-lation (ENSO) events, with marked SST changes over thetropical oceans, produce significant regional changes inprecipitation, water vapor, and radiative fluxes in the tropics[e.g. Ropelewski and Halpert, 1987; Sun and Trenberth,1998; Curtis and Adler, 2000]. However, we still cannotadequately quantify the associated net integrated changes towater and heat balance over the entire tropical oceanic or

.land sectors. Soden [2000] has noted that m contemporaryclimate models run with specified SST, precipitation varia-tions averaged over the tropical oceans seem much smallerin amplitude than those of satellite estimates. Robertson etal. [2001] showed that substantial disagreement existsamong contemporary satellite estimates of interannual var-iations in tropical rainfall that are associated with SSTchanges. Berg et al. [2002] have documented the distinct

copyright 2003 by the American Geophysical Union.0094-8276/03/2002GL016416$0~.OO

2.

~=A(r) =

Ze(r)

29 -

Jer 2002; published 25 February 2003.

differences between precipitation structure over the easternand western Pacific ITCZ and noted how various satelliteprecipitation algorithms may respond quite differently toENSO modulations of these precipitation regimes. Resolv-ing this uncertainty is important; ENSO, the most dominantcoupled mode in our climate system, represents a funda-mental perturbation of tropical monsoonal circulations.Furthermore, reproducing the regional and integrated rela-tionship between SST and precipitation is an importantthough obviously not sufficient test of how robustly climatemodels treat physical processes related to climate change-

[3] TRMM is the first satellite to carry both active andpassive sensors for measuring precipitation. Each of theseapproaches has its associated uncertainties. Passive esti-mates from the TMI are a less direct rainfall estimate sincethe radiometer responds to integrated liquid water, not justto raindrops. Variations in rain layer depth and influencefrom water vapor and surface wind variations can alsocomplicate ~xtracting clean interannual signals in rainfall.By comparison, the more direct measurement of hydro-meteors by the TRMM PR would seem to have lessuncertainty; however, the PR operates at a single frequency(13.8 GHz) so that microphysical assumptions regardingdrop size distributions come into play in the process ofcorrecting the measured reflectivity for attenuation andrelating reflectivity Structure to rainfall rate-

[ 4] The purpose of this paper is to document currentdiscrepancies between various TRMM algorithins in thecharacterization of interannual variability (IA V) and toprovide evidence that the source of this problem lies inmicrophysical uncertainties inherent in single-frequencyrainfall estimates derived from the PR. Our analysis is basedon the 3A25, 3B31, and 3Al1 TRMM data sets which aremonthly mean statistics of instantaneous retrievals (Level-2products) gridded to five degree spatial resolution. TheNational Oceanic and Atmospheric Administration Opera-tional SST products [Reynolds, 1988] are alsp used.

29- 2 ROBERTSON ET Al EFFECTS OF UNCERTAINTY

Figure I. Time series of precipitation anomalies averagedover the tropical oceans from the TRMM PR 2A25 and TMIpassive microwave 2A12 and 3All algorithms. Time serieshave been normalized by their respective climatologicalvalues to yield fractional variability. SST anomalies (K)over the tropical oceans scaled by 1/5 are shaded.

tology for the period Jan 1998-July 2001. The anomalieshave been normalized by the 44-month mean so that theyrepresent fractional variations. The corresponding tropicalocean averaged SST anomalies are also presented. Both ofthe TMI-based passive algorithms [Wilheit et al., 1991;Kummerow et al., 200t] exhibit a tendency toward elevated(depressed) rainfall in association with warmer (colder) SSTanomalies. This is consistent with the behavior noted inother passive microwave data sets by Robertson et al.[2001]. In contrast, the TRMM PR anomalies are ofweakeramplitude and have essentially no correlation with SSTchanges. It should be emphasized that these anomaliesrepresent the integration of contributions by regional pat-terns of both positive and negative sign that possess muchlarger amplitudes; thus, accurate rainfall estimates areneeded to avoid the effects of cancellation error.

[ 8] Time series histograms of PIASR and PR rainfall offerinsight as to relationship between attenuation correctionsand rainfall. Figure 2a shows time series of interannualanomalies in PIASR averaged over the tropical oceans. Dataat four incidence angles (0,5, 10 and 15 degrees from nadir)available from the 3A25 data set have been averaged andscaled to account for the varying number of availablemonthly observations. The annual cycle for each of 30attenuation intensity bins was computed and removed.Although somewhat noisy, the resulting pattern showscoherent interannual variations in the frequency of attenu-ation intensities. For example, in JFMA 1998, aboveaverage counts are found at all attenuations >0.5 dE witha prominent maximum near 2.0 dE. Above 1.0 dE, most of1998 (except MJJ) shows anomalously higher frequenciesthan succeeding years. Below about 1.0 dB the patternbehaves in an opposite sense; generally below averageoccurrences dominate 1998 and above average counts arefound in the second half of 1999. Such a pattern isconsistent with shifts in the PIASR frequency distributionto larger (1998) and smaller (1999) values. Based onanalysis of crO data from non-raining cases, Meneghini etal. [2000] find the standard deviation (SD) of (cr~o-rain) overocean to vary from about 1.2 to 3.75 dE, depending onincidence angle. The SD statistics are used as a basis forreliability estimates used in the MLE procedure. PIAsR/SD> 3.0 is termed reliable, PIAs~SD < 1.0 is regarded as

The right-hand-side quantity represents an attenuationfactor, A(r), which measures the fraction of signal depletionover the distance r between the radar and a range gate withinthe precipitating footprint. Parameters a, r3 and E: are relatedto microphysical assumptions; their values are assumedinitially and modified as noted below. When the entirecolumn from the radar to the surface is considered, the two-way path-integrated attenuation to the surface (r = rsfc) isdenoted as PIAHB = -10 logloA(rsfc) and has units of dE. IfE: = 1.0 then (1) corresponds to the Hitschfeld-Eordan (H-E)

relationship [Hitchfeld and Bordan, 1954] which models therainfall attenuation correction by the power law relationshipinvolving Zm(r) in the integrand of (1). An unfortunateproperty of the H-E solution is that at large attenuation, A(r)approaches zero and unless the integral quantity on theright-hand-side of (I) is known to extraordinary accuracythe solution can become unstable. At high rain rates theinherent uncertainties in the quantity a(s)~(s) can oftenyield negative values for A(r) and preclude accuraterecovery of Ze(r).

[6] One advantage of viewing rainfall from a spaceborneradar is that an alternative estimate of path-integratedattenuation, can be obtained by comparing returned powerfrom the ocean surface in raining scenes with that from non-raining scenes [Meneghini et at., 2000]. Termed the SurfaceReference Technique (SRT), this approach is formulated as

PIASR = lj.0"° = (0"~o-rain) -O"~. (2)

where ((J~o-rain) denotes the nomlalized radar cross-section(NRCS) in rain-free conditions for a given incidence angleaway from nadir. The decrease in radar cross-section, ~(J°,due principally to precipitation, is expressed in dB. Withtwo alternative estimates ofPIA, one from the H-B solutionand one from changes in observed surface cross-section, the2A25 algorithm then uses a maximum likelihood estimator(MLE) technique to derive an optimum PIA estimate. Oncethis estimate is obtained the parameter E can be varied sothat A(r) in (1) is consistent with the optimum PIA estimate.Because the effect of E is to make a constant multiplicativeadjustment to a, this method of accommodating the SRTestimate of PIA is temled the "alpha-adjustment method"[Iguchi and Meneghini, 1994]. At heavier rainrates whereH-B estimates fail, the SRT provides accurate attenuationcorrections to enable retrieval of Ze. At very light rainrateswhere the H-B solution becomes most accurate, PIASRbecomes noisy because the attenuation signal falls to valuesnear inherent background variations in (J~o-rain .Alterationsin a imply a change in the drop size distribution (DSD) and,in turn, changes in the associated Ze-Rainfall relationship.Once E is detemlined, parameters in the power lawrelationships governing attenuation, reflectivity, and rainfallrate are adjusted so that they are consistent with the impliedchanges in the DSD.

3. Results

[7] The essence of the problem to be addressed here isillustrated in Figure I. Precipitation anomaly time series areshown for three different TRMM algorithms, each repre-senting the departures of rainfall rate averaged over thetropical oceans (30° N/S) from a monthly-resolved clima-

ROBERTSON ET AL.: EFFECTS OF UNCERTAINTY 29- 3

Figure 2. (a) Time series ofPIASR frequency distribution anomalies averaged over the tropical oceans; (b) Anomalies ofPIASR generated by integration of the frequency distribution above three intensities (.Ol~ 1.5 and 3.4 dB); (c) Time series ofPR rain rate frequency distribution anomalies averaged over the tropical oceans; (d) Anomalies ofPR rain rate generated byintegration of the frequency distribution above three intensities (5,27 and 48 mmh-1). Time series in (b) and (d) have beennormalized by climatological values.

gram anomalies are integrated above thresholds of 5, 27,and 48 mmh -I. It is clear that only for thresholds above 30to 40 mmh-1 does the IAVofrain rate resemble that of thePIASR. These striking differences suggest an inconsistencybetween PIA in 2A25 and PIASRT at moderate to lightrainfall rates-

( II] Supporting evidence for the sensitivity of PR rainfallto attenuation correction also comes from consideringprecipitation rates at higher altitudes in rain systems whereattenuation is much weaker. Ice formation and growthprocesses dominate rainfall production in deep convectionabove the freezing level (Stith et al., 2002]. Mixed phaseregions in deep tropical convection are typically confmed tolevels warmer than -10°C with the bulk of the precipitation

unreliable, and values falling between these limits aremarginally reliable. Only SRT measurements classified asreliable or marginally reliable are included in these histo-gram data. While the spatial and temporal averaging in theanalysis here undoubtedly reduce random noise, it is clearthat attenuation values below 1.0 dE should be regardedwith caution.

[9] By integrating the occurrence anomalies of the 30categories for each month we recover the total PIASRanomalies. Several thresholds of PIASR have been pickedas starting values: 0.01, 1.5, and 3.4 dE. Using a represen-tative attenuation-rainfall relationship of k = 0.024R 1.15

[Meneghini et al., 2000], and assuming a rain column depthof 5 kIn yields PIASR values corresponding roughly to rainrate thresholds of 0.05, 5.0 and 10.0 mmh-1. These calcu-lations (Figure 2b) reveal interannual variability of PIASRthat contrasts remarkably with the PR surface rainfallvariations presented in Figure I. Whereas the 2AI2 and2A25 time series in Figure I correlate at only 0.12, thecorrelation between the 2AI2 and PIASR time series usingthe 1.5 dE threshold is 0.75. Note that although the curveintegrating over all 30 PIASR categories results in thesmallest magnitude, it too is differs from the PR trace inFigure I.

[10] To examine the behavior of rainfall at variousintensity thresholds an analogous treatment of the PR rain-fall rate frequency histograms using the 3A25 data ispresented in Figures 2c and 2d. The histogram data inFigure 2c show that in contrast to the PIASR result, muchof 1998 is dominated by decreased occurrences ofrainfall atall rates between about 0.5 and 40 mmh-1. In 1999 theanomalies largely switch sign. In Figure 2d rain rate histo-

Figure 3. Time series of precipitation anomalies averagedover the tropical oceans from the TRMM PR 2A25algorithm at the 2, 4 and 6 kIn levels. SST anomalies (K)over the tropical oceans scaled by 1/5 are shaded.

29- 4 ROBERTSON ET AL.: EFFECTS OF UNCERTAINTY

mass and Ze ~ 30 dBZ below the freezing level ( N5 km)[Petersen and Rutledge, 2001]. Thus, regions above thefreezing level exhibit much lower attenuation. Figure 3shows PR precipitation anomalies at 2, 4 and 6 km. The 4and 6 km levels bracket the freezing level typical fortropical oceanic regions. The interannual behavior at 6 kmis strikingly different from that at 2 and 4 km. Precipitationanomalies above 10% are present in early 1998 and arepersistently near -5% during 1999 and early 2000. It is notyet clear to what degree the 6 km PR time series representsvariations in ice mass above 6 km as opposed to interannualvariations in vertical penetration of the mixed phase regionwith its greater reflectivity. However, a preliminary analysisof the convective/stratiform partitioning of the 6 km pre-cipitation has shown roughly equal contributions to theinterannual signal. Since stratiform precipitation at 6 kmis unlikely to contain significant liquid water, the lA Vcannot be explained by mixed phase variations alone. The6 km time series bears a strong resemblance to the PIASRanomalies in Figure 2. with the correlation between the twotime series at 0.80. This level of agreement is similar to thatfound by Robertson et al. [2001] between two passivemicrowave algorithms-one based on scattering and theother on emission. Physically, one would expect the abun-dance of ice and precipitation rates at 6 km to be stronglyrelated to attenuating rain below the freezing level sincedeep convection dominates contributions by warm rainprocesses. Because of the abundance of ice and the lackof strong reflectivities above 6 km, very little attenuationadj~stment is ne~ded and Ze is largely independent ofPIASRcontributions. We can thus further infer from the strongcorrelation between PIASR and the PR at 6 km that anysystematic interannual biases in (J° must be rather minimalwhen averaged to large space and time scales and thatvariations in ocean sUrface returns are not determining theIAV in PIASR.

signal of deep convection. Lacking any adequate " ground "

validation of rainfall, this close agreement between twoindependent methodologies lends strong support to each asmeasures of interannual variations of precipitation. How-ever, we caution against using the present findings asquantitative validation of the passive algorithms since otheruncertainties remain. Ambiguities inherent in retrievingrainfall esti.mates from single-frequency radar measure-ments are serious for climate applications. Dual-frequencymeasurements from the planned Global Precipitation Mis-sion [Asrar et al., 2001] should remove many of theseuncertainties. In the meaptime, a more in-depth analysis ofthe PIASRT climatology from TRMM and its relationship topassive rainfall measurements should prove illuminating.

[13] Acknowledgments. This work was supported by the NASAGlobal Water and Energy Cycle Program, the Global Precipitation ProjectOffice, and the TRMM Science Program. The authors thank RobertMeneghini for insightful discussions concerning the 2A25 and SRTalgorithms.

4. Conclusions

(12] In summary, we have shown that at PIA valuescorresponding to rain rate thresholds of several mmh -I

and higher, the SRT method yields an IAV signal markedlydifferent from that of the PR 2A25 algorithm for regionsbelow the freezing level. Only for rain rates ~30 to 40mmh -I do PIASR variations match those of the rainfall

retrieval. A full explanation for this behavior is still beingsought. One factor could be the assigned relative errorproperties of the SRT and H-B attenuation estimates usedto retrieve the optimal PIA. However, for lighter rain rates,the PIASRT seems to be at odds with the PIA derived fromempirically-based a priori DSD estimates and the associatedparameters a, i3, a, and b that interrelate attenuation,reflectivity, and rain rate-regardless of how they may beadjusted in the MLE procedure. Unlike rainfall rate orreflectivity, PIASRT is free from any a priori microphysicalassumptions. The PIASR IA V was found to agree closelywith TRMM (and other) passive microwave estimates ofrainfall. Furthermore, the close agreement in IA V betweenPIASR and PR 2A25 precipitation at 6 km where attenuationis minimal suggests that both are robust in seeing the IA

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