The AMSU Observation Bias Correction and Its Application Retrieval Scheme, and Typhoon Analysis

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1 The AMSU Observatio Bias Correctio ad Its Applicatio Retrieval Scheme, ad Typhoo Aalysis Chie-Be Chou, Kug-Hwa Wag Cetral Weather Bureau, Taipei, Taiwa, R.O.C. Abstract Sice most of AMSU chaels have a beam positio-depedet bias, it is crucial to remove such a bias for providig useful profiles of the atmosphere. Measuremet errors are estimated from the differeces betwee satellite observatios ad the simulated satellite observatios, which were obtaied from a radiative trasfer operator with 12-hours forecast of their iput. The measuremet errors estimated i this way will cotai the forecast error of a 12 hour forecast. The NMC method assumes that the statistics of differeces betwee forecasts at differet rages valid at the same time are the represetative of forecast error statistics. The differeces used i the NMC method have bee trasferred to brightess temperature i each AMSU chael with the radiatio trasfer operator. These data ca the be used to obtai the value of 12 hours forecast error i brightess temperature for each AMSU chael. Thus, the 12 hour forecast error i each AMSU chaels ca be removed whe the measuremet errors are estimated as metioed above. I this study, we carefully examie the AMSU beam ear Taiwa. A bias correctio method, which cocers the beam positio-depedet bias ad the effect of 12 hours forecast error used o the regressio equatios, has bee built. A data retrieval method based o oe-dimesioal variatioal scheme has also bee developed. Through the compariso of the retrieved profiles ad the backgroud fields, we foud that the method worked well ear the Taiwa area. Eve with quite accurate backgroud fields, the retrieved profiles have show positive impact to improve the fields. The results show that the improvemet made i the retrieval scheme over the backgroud error is about 0.45K i the temperature profiles, above 780 hpa. The study used corrected AMSU data to idetify thermal aomalies ad estimate taget wids that successfully aalyzed typhoo structure. Itroductio I the past few years much research has ivolved variatioal retrieval schemes. Variatioal retrieval methods are examied that uder a precise backgroud field provide better retrieval results (Eyre, 1989). A variatioal iteratio method was applied i this research. Oe importat issue i variatioal retrieval is to correct the satellite observatio bias ad to estimate radom errors. Observatio bias is estimated from the differece betwee observed brightess temperature ad simulated brightess temperature. Simulated brightess

2 temperature is calculated based o a forecast model through a RTE model. So the observatio bias is icluded i the umerical forecast model s error. I order to make the data correct for retrieval, a statistical correct scheme is eeded. Variatioal Methodology The solutio of the variatioal retrieval scheme is to get the miimum value of the cost fuctio. The it gets the best atmosphere parameter: x. The cost fuctio is writte as follows. J m { y y( x) } (1) b T 1 b m T 1 ( x) = ( x x ) C ( x x ) + y y( x) } E { b m x is backgroud (or iitial guess). C is covariace of backgroud error. y is observatio values. y(x) is simulatio values from RTE while atmosphere parameters are x. The cost fuctio is the sum of the deviatio betwee x ad the backgroud ad the deviatio betwee the observed value ad calculated value uder x situatio. So we should fid a proper x that lets the calculated value correspod to the observatio value relevatly. The methodology is usig Newtoia iteratio method(eyre 1989). x W + 1 = x b = CK + W T m b { y y( x ) K ( x x )} ( K CK T + E) 1 (2) Whe the value x +1 x is smaller tha a threshold, the above fuctio coverges. The covariace error of the backgroud field may be obtaied by statistical calculatio from the error of 12 hour forecast field (Parrish ad Derber 1992). Errors of other parameters are set as follows, surface air temperature is 2.34K, surface air humidity is 0.3 l(g/kg), surface temperature is 1.67K, surface pressure is 3.42hPa, the cotet of ozoe is 40 Dobso, cloud height is 200hPa, cloud fractio is 0.5 ad cloud liquid water cotet is 0.5mm. (Eyre 1990). Surface emissivity is described as i (Grody 1988) ε( ν ) ε + ε ( ν / ν ) k ν x 0 = (3) k 1+ ( ν / ν 0 ) Durig the retrieval procedure the corrected magitude of backgroud error depeds o the ratio of observatio error ad backgroud error, which is preseted by matrix E ad matrix C. The calculatio of the observatio covariace error is a little complicated. The estimated satellite observatio error icludes istrumet error, satellite data procedure error, radiatio trasfer model error ad error of radiatio model iput parameters. I summary, above items could be classified ito two items, that is systematic error ad radom error. Systematic error is possiblely corrected. Radom error is the diagoal elemets i matrix E. Because the limb

3 effect of AMSU is asymmetrical, limb adjustmet procedure is also ecessary. AMSU Bias Correct ad retrieval result The merit of variatioal retrieval ca be applied directly to satellite observatio data; it may avoid some errors which were caused durig preprocessig (Eyre 1989). AMSU limb effects alog the viewig agle are due to asymmetry, we must adjust for this. First, we plot the scatter diagrams of AMSU for each chael to each FOV. Before doig the adjustmet, the differece betwee observatio data ad calculated data are chose. This data should be estimated for its mea ad stadard deviatio. If ay chael differeces betwee observatio ad calculated are larger tha 3 times of the stadard deviatio, these data are treated as bad data. Chael 7, for four differet sca agles, are show i Fig. 1. Fig.1: Scatterig diagram of AMSU chael 7 for simulated Tb ad measured Tb from FOV of 1 to 4. The sca agle biases are a little differece. After proper data are selected, regressio coefficiets are calculated for each chael i * each viewig agle to correct the observatio. The adjusted brightess T = at + B b will be foud, where itercept. T B is the observed satellite brightess temperature, a is slope ad b is

4 About 900,000 data were used to get these coefficiets. Because estimated observatio systematic error ad radom error are icluded i the backgroud (forecast) error, the 12 hours forecast statistic error has bee trasferred to radiace. The the backgroud error ca be removed. AMSU chael 2 is used as a parameter to adjust surface emissivity, this adjustmet will be doe whe calculated Tb are equivalece to observed Tb. I reality it is ot a proper procedure, but it is more reasoable whe o observatios of surface emissivity exist. Real data o 22 Jue 2002 were tested, ad the improvemet of vertical temperature is sigificat, as show o Fig. 2. Figure 2. Real data o 22/Ju/ Z. Total 927 corrected satellite observatio were retrieved. (a)temperature (b)maxig ratio mea error covariace. Solid lie is backgroud error ad dash lie is error of retrieval. Limb Adjustmet o AMSU For the asymmetry of AMSU limb bias, statistical methods were cosidered. We tried to use the algorithm from Goldberg(2001). Because of misiterpretatio of the physical

5 coefficiet, some chaels of AMSU were ot corrected. The results are show o Fig 3. Surface chael 1,2 are correct, but others chaels are failed to be correct. Further ivestigatio is eeded. Typhoo Moitorig - methodology Uderstadig the thermal structure of typhoos is helpful to weather forecastig. It has bee examied that a relatioship exists betwee temperature aomalies ad the maximum wid ad cetral pressure of tropical cycloes.(kidder 2000) Whether to make a limb correctio to each FOV before

6 280 NOAA16_ _0416_14273 Compariso for Limb Correctio A4 200 A A2 240 A A5 230 A A A A A A9 230 A Figure 3. AMSU limb adjustmet results for NOAA 16 chael Dash lie meas raw data, red solid lie meas applied by NESDIS coefficiets, blue lie meas results i this study.

7 retrieval or make a differet set of coefficiets for each FOV is a cotroversial problem. Zhu ad Kidder (2002) show that the RMS error is less tha 1.75K for the above two schemes. So here, the latter scheme was chose for further processig. AMSU has the capability to peetrate cloud, but the AMSU observatio still ca be iterfered by raidrops. It may cause the temperature too cool uder 700hPa i retrieval temperature profiles ear the typhoo ceter. So uder heavy raifall situatio chael 3-5 are ot recommeded be use i retrieval. Oly chaesl 6-11 were used to retrieve temperature profile. Whe temperature profiles are retrieved from AMSU, the 2 or 3 dimesio gradiet wid vectors ca be estimated usig the gradiet balace equatio. The algorithm to estimate the 2-dimesio gradiet wid is from the paper of Kidder (2000). I order to study the ceter of a typhoo, the 250hPa highest temperature aomaly is located. The method used to drive the 3-dimesio wid vector has bee described i Zhu etal. (2002). Typhoo Moitorig - result. The above techiques was applied o the typhoo of 16/Oct/ Z. As show i Fig 4, AMSU chaels 6-11 of NOAA-15 was used for the case study. The aomaly of temperature ear the ceter of the typhoo is obviously idetified. Aomaly warmig exteds from level 250hPa with aomaly of 7K to level 620hPa with a 4K aomaly. The warm core is a little iclied to the orth. The gradiet wid is chagig with the radius of typhoo ad pressure variace as show i Fig 5. Maximum wid speed is located at a radius about 100km. Mea maximum wid speed is about 25m/s. From the patter of the wid fields, positive vorticity exists i the lower layer of the typhoo. Weak egative vorticity is located o upper layers of the typhoo. The structure of the typhoo is reasoable, give geeral ackowledge. The core of maximum wid speed iclies to the outside, this is characteristic of a strog typhoo. Accordig to the empirical fuctio (Kidder 2000), the temperature aomaly is used to estimate the maximum wid speed ad radius of maximum wid speed. This typhoo has a maximum temperature aomaly of about 10.5K, so the maximum wid speed should be 46m/s, ad radius of maximum wid speed is 125Km. From Fig. 5 mea maximum wid speed is about 25m/s, which is the value of the mea azimuth agle. So the estimated wid speed is reasoable. Others cases were studied ad provided a reasoable aalysis. Coclusio AMSU data is a widely used i NWP ad weather aalysis. We applied proper adjustmet to correct the observatio error, allowig AMSU data to be used more precisely. Whe the observatio error is corrected, the 1D variatioal retrieval test shows that the correctig process is eeded.. Temperature aomalies ca be obtaied from retrieved temperature profiles. Based o these temperature profiles, the 2 ad 3dimesio wid vectors are

successfully drive. A local typhoo statistical aalysis database is ecessary for further utilizatio. Typhoos ofte make a severe disaster i the orthwest Pacific Ocea area.

8 successfully drive. A local typhoo statistical aalysis database is ecessary for further utilizatio. Typhoos ofte make a severe disaster i the orthwest Pacific Ocea area. AMSU may provide more precise iformatio o typhoo aalysis. Figure 4. Temperature aomaly aalysis profile obtaied from south to orth (right) o Typhoo HaiYe Figure 5. Gradiet wid profile (Mea azimuth) o typhoo HaiYe. The effect of ice particles o AMSU is eeded for further study. Precipitatio ad water vapor cotet were ot cosidered i this research. That will be the future task.

9 Refereces Eyre, J. R., 1989, Iversio of cloudy satellite soudig radiaces by oliear optimal estimatio: Applicatio to TOVS data. Quart. J. Roy. Meteor. Soc., 115, Eyre, J.R., 1990, The iformatio cotet of data from satellite soudig system: A simulatio study. Quart. J. Roy. Meteor. Soc., 166, Goldberg, M. D., D. S. Crosby, ad L. Zhou, 2001, The Limb Adjustmet of AMSU-A Observatios: Methodology ad Validatio, J. Appl. Appl. Meteor., 40, Grody, N.C., 1988, Surface idetificatio usig satellite microwave radiometers, IEEE Trasatios o Geosciece ad Remote Sesig, 26, Kidder, S.Q., ad Coauthors, Satellite Aalysis of Tropical Cycloe Usig the Advaced Microwave Soudig Uit (AMSU). Bull. Amer. Meteor. Soc., 81, Parrish, D. F. ad J.C. Derber, 1992, The atioal Meteorological Ceter s spectral statistical iterpolatio aalysis system. Mo. Wea. Rew., 120, Zhu, T., D. L. Zhag, ad F. Weg, Impact of Advaced Microwave Soudig Uit Measuremets o Hurricae Predictio. Mo. Wea. Rev., 130,

International ATOVS Processing Package: The algorithm development and its application in real data processing

International ATOVS Processing Package: The algorithm development and its application in real data processing Iteratioal AOVS Processig Package: he algorithm developmet ad its applicatio i real data processig Ju Li, W. Wolf, W. P. Mezel, W. Zhag, H.-L. Huag,. H. Achtor, H. M. Woolf 1. Itroductio Cooperative Istitute