the behavior of the tapeer-‐brain algorithm over tropical oceans
TRANSCRIPT
The behavior of the TAPEER-‐BRAIN algorithm over Tropical Oceans Philippe Chambon1, Jérémie Aublanc2 and Rémy Roca2
1. Current affilia.on: NASA GSFC, Greenbelt MD USA ([email protected]) 2. OMP/LEGOS, Toulouse, France
1. IntroducAon
3.1 General funcAoning of the algorithm
3.2 Error variance modeling strategy
3.3 A simple sampling error model for satellite esAmates
2. The TAPEER-‐BRAIN algorithm for Megha-‐Tropiques
3.3 Error propagaAon from instantaneous to accumulated rainfall
3.4 The TAPEER-‐BRAIN product
3. Intercomparison of TAPEER-‐BRAIN and TMPA V7
4. Toward the use of TAPEER-‐BRAIN error bar for verificaAon of ensemble forecasts
5. Conclusion and perspecAves 6. References
The TAPEER-‐BRAIN approach aims to associate an error to 1°/1-‐day rain accumulaDons, by deriving an esDmate of each of the three error terms considered
Rainfall accumulaAon esAmaAon of TAPEER-‐BRAIN • AdaptaDon of the UAGPI technique (Xu et al., 1999) • BRAIN algorithm (Viltard et al., 2006) provides rain rates from PMW
Instantaneous rain product errors + MulDple data merging method errors
Orbit and instrument characterisDcs
S2 ≈ S2CalibraAon + S2Algorithm + S2Sampling
CalibraDon / inter-‐calibraDon of instruments
σX: standard deviaDon of the samples (X) used to build the rain accumulaDon
Number of independent samples
σX2
Nind S2 Sampling =
Uncertainty on the mean of a sampled random variable (Roca et al.,2010), over a surface A and period T : In space : independent samples
N ind = . A T
d2 τ In Dme : independent samples T/τ A/d2
Ex : [12°N – 17°N ; 3°W – 3°E]
d ≈ 61 km τ ≈ 1.2 h
ComputaAon of Nind : variogram analysis
Variograms are computed over the high resoluDon intermediate rain fields (Eq. 1) and aggregated over 5°x5° areas and 10-‐day periods (Eq. 2) before fibng exponenDal models to derive d and τ from staDsDcally robust variograms.
(Eq. 1)
(Eq. 2)
Local characteriza-on of d et τ, updated every 10 days to catch the intra-‐seasonal variability of Nind (Chambon et al., 2012)
The magnitude of the two terms S2Algorithm and S2CalibraDon is related to errors at the instantaneous scale which propagate at the accumulated scale.
Figure 5: Distribu.on of differences between TAPEER accumula.ons aSer systema.c errors propagated on BRAIN rain rates of medium intensity ( 2 mm.h-‐1 à 10 mm.h-‐1 ) and a control run
+100 % +80 % +60 % +40 % +20 %
Rel. difference (%) Rel. difference (%) Rel. difference (%) Rel. difference (%) Rel. difference (%) PropagaDon of idealized errors : o random errors on the instantaneous rain rates o systemaDc errors on the instantaneous rain rates o random errors on GEO IR data
A new algorithm for rainfall esDmaDon from satellite data has been developed in the framework of the Megha-‐Tropiques mission. It aims to provide daily quanDtaDve precipitaDon esDmaDons at one-‐degree resoluDon over the whole Tropical belt. The TAPEERBBRAIN (Tropical Amount of PrecipitaDon with an EsDmate of ERrors) algorithm is based on a merging approach of passive microwave instantaneous rain retrievals and observaDons from geostaDonary cloud top sensiDve Infrared channels. A dedicated error model involving rainfall auto-‐correlaDon calculaDons is then used to characterize the associated sampling uncertainDes. The algorithm error term of the error budget is derived from the microwave retrieval uncertainty analysis. A descripDon of the TAPEER-‐BRAIN algorithm is provided in SecDon 2. The TAPEER-‐BRAIN algorithm is applied for the summer 2009 and the winter 2011 using available conical scanning microwave imagers (TMI, SSMI, AMSRE for 2009). The distribuDon of rainfall esDmates (including the associated errors) is first presented. This dataset is then compared in SecDon 3 with the recently released TRMM-‐3B42 V7 over the Tropical Oceans. Regions with consistencies/discrepancies are highlighted for future research. In SecDon 4, we discuss an ongoing effort to set up a verificaDon method of ensemble rain forecasts using TAPEER-‐BRAIN error bars.
Figure1: General flow diagram of the TAPEER-‐BRAIN product
Assuming the various error sources to be independent, the error budget of rain accumulaDon can be wrijen as:
The methodology to esDmate the errors variance involves modeling the sampling error term and esDmaDng the remaining terms of the error budget with a forward error propagaAon method. Indeed, these remaining terms are related to errors on the PM instantaneous rain retrievals and calibraDon of Level 1 datasets.
Figure 2: Time empirical variogram (diamonds) and space empirical variograms (crosses) for a 5x5degrees area in Western Africa and a 10-‐day period in Summer 2009
Figure 3: Space variability of d for the first 10-‐day period of July 2009 (bojom panel). Ten day TAPEER rain accumulaDon for the ten-‐day period (top panel)
Figure 4: Time variability of d and τ for summer 2009 over a 5×5degrees window [7 – 12◦ E; 12 – 17◦ N]
The dominant errors propaga-ng at the accumulated scale in the TAPEER-‐BRAIN algorithm are systema-c errors on BRAIN medium rain rates (2 to 10mm/h)
A qualitaDve preview of the total error magnitude for the TAPEER-‐BRAIN esDmaDons was built from the error propagaDon results and the sampling error model. A best-‐case scenario of +20% bias and a worst-‐case scenario of +60% bias on medium rain rates were selected; for both of them, small and high rain rates are assumed to have low biases. Figure 7 on the right are previews of the corresponding best and worst total error maps of TAPEER-‐BRAIN.
Figure 7: Maps of TAPEER-‐BRAIN of accumulated rain and associated errors for July 30th, 2009
Under-‐esDmaDon of mean rain along coast lines
Over-‐esDmaDon of mean rain over Bay of Bengal, China and Philippines Seas
Mean Season Rain (mm) Over-‐esDmaDon
over mountains
June to September 2009
Number of Rainy Days
(0 mm rain/no-‐rain threshold) (1 mm rain/no-‐rain threshold)
Lower number of rainy days with low rain amount (0 to 1mm)
Lower number of rainy days along coast lines but bejer agreement over the tropical belt
October to December 2011
Mean Season Rain (mm)
Number of Rainy Days
(0 mm rain/no-‐rain threshold) (1 mm rain/no-‐rain threshold)
Under-‐esDmaDon over most of the oceanic area and over-‐esDmaDon over land
The sampling error model presented above was applied to TMPA V7 and compared with TAPEER-‐BRAIN taken their sampling errors into account (see Roca et al., 2010 for a full explanaDon of the comparison method)
This comparison between TMPA V7 and TAPEER-‐BRAIN over two seasons shows that (i) the main discrepancies between the two products in terms of mean seasonal rain are located along the coast lines, (ii) occurrences of small rain accumulaDons (0 to 1mm) are large over all oceans for TMPA V7, (iii) occurrences of rain accumulaDons larger than 1mm are in good agreement over all ocean. Over the four oceanic regions depicted above, Bias and RMS of the regression are variable from the summer season to the winter season, the Indian ocean box presenDng the smallest RMSreg for both periods. All comparisons lead to a FEBO (Frequency of Error Bar Ovelaping) greater than 75%.
R. Roca, P. Chambon, I. Jobard, P.E. Kirstejer, M. Gosset and J.C. Bergès, “Comparing satellite and surface rainfall products over West Africa at meteorologically relevant scales during the AMMA campaign using error esDmates”, J. Appl. Meteorol. and Climatol., vol. 49, no. 4, pp. 715–731, 2010.
N. Viltard, C. Burlaud and C. Kummerow, “Rain Retrieval from TMI Brightness Temperature Measurements Using a TRMM PR–Based Database”, J. Appl. Meteor. Climatol., vol. 45, pp. 455–466, 2006.
L. Xu, X. Gao, S. Sorooshian, P. Arkin and B. Imam. “A microwave infrared threshold technique to improve the GOES precipitaDon index”, J. Appl. Meteorol., vol. 38, no. 5, pp. 569–579, 1999.
P. Chambon, I. Jobard, R. Roca and N. Viltard, “An invesDgaDon of the error budget of tropical rainfall accumulaDon derived from merged passive microwave and infrared satellite measurements”, Q. J. R. Meteorol. Soc., DOI: 10.1002/qj.1907., pp. 1-‐15, 2012a.
Good agreement with threshold at 1mm
One of the applicaDon of the TAPEER-‐BRAIN product concerns the evaluaDon of Ensemble PredicDon System (EPS). Indeed, the characterizaDon of the EPS simulaDons and of the spread of the ensemble can be related to the uncertainty esDmates provided along with the daily accumulaDon. A preliminary invesDgaDon is shown here where the ECMWF 50 members simulaDons are used for a day during the CINDY-‐DYNAMO experiment in November 2011 over the Indian Ocean.
Figures (a) and (b) show the TAPEER daily accumulaDon at 1°x1° resoluDon along with the error esDmates at 1 sigma. The meteorological situaDon corresponds to the early part of an acDve intra-‐seasonal perturbaDon as witness by the large precipitaDon structure in the Southern hemisphere. Smaller convergence lines yield to two other oceanic rain patches (East of Somalia and around 80°E in the southern ocean). Climatogical features over Indonesia are also observed. The uncertainty reaches up to 15mm at the core of the maximum of accumulated rain for that day and it otherwise smaller below 5mm. The two fields are rather smooth.
Figures (c) and (d) reveals the median and the standard deviaDon of daily accumulated rainfall for the ECPWF EPS. The lajer is used a metric of the spread of the ensemble. While the secondary maxima are well located in the simulaDons, the main rain features is smaller and less compact that in the observed field. The variance field is more scajered with larger values than TAPEER. This is obvious when a single member of the ensemble is plojed (Figure 3) that reveals intense rainfall in some grid points. The extent to which the variance of the ensemble and the error esDmaDon at 1 sigma in TAPEER can actually be compared quanDtaDvely requires further invesDgaDon.
Figures (a) and (b): TAPEER-‐BRAIN daily rain and error es.mates for Nov 18th 12:00UTC to Nov 19th 12:00UTC Figures (c) and (d): Mediane and Standard devia.on of ECMWF EPS forecast of daily rain for the same period as (a) and (b) Figure (e): One member of the ECMWF EPS forecast of daily rain for the same period as (a) and (b)
(a) (b)
(c) (d) (e)
Figure 6: Ra.o of algorithm errors and sampling errors depending on the kind of propagated idealized errors and their magnitude
TAPEER-‐BRAIN esDmates will be produced over the whole tropical belt at the 1degree/1-‐day resoluDon, using all available conical scanning PM imagers. Because of both the low inclinaDon of the Megha-‐Tropiques orbit and the large swath of the MADRAS instrument, one can expect the quality of the product to be enhanced in light of the encouraging performances of the TAPEER-‐BRAIN prototype presented in this poster over ocean and in Chambon et al. (2012) over land. In the TAPEER-‐BRAIN framework, the sampling error term is esDmated through a variogram computaDon technique, and the algorithm error term using an error propagaDon method with idealized error scenarios in BRAIN esDmates. Plans are being made to apply the error propagaDon methodology using BRAIN error characterizaDon derived from the data collected during the Megha-‐Tropiques CalibraDon/ValidaDon campaign over various rain regimes in Africa, India and Brazil.