# Evaluating several methods to determine cirrus clouds properties using lidar measurements in Cuba and Argentina

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3 in calculations because they used estimated or real value of Kp. In the present paper we apply the method in order to analyze lidar signals acquired during different monitoring periods in the last 5 years. 2. Cirrus lidar equations The single-scattering Lidar equation has the form: ( R) β V ( R) = I α() R c exp 2 r dr 2 R R0 where the main variables are: (1) V(R) = Received power. β(r) = Backscatter coefficient. α(r) = Extinction Coefficient. R = Range. R0 = Reference Altitude. Ic = Instrumental constants. Backscattering and extinction coefficients at each point of atmosphere are related by the Bernoulli equation: ( R) = K ( R) β pα (2) The stable solutions of the Lidar equation for the extinction and backscattering coefficient could be derived considering 100% coupling between the emitter and the receptor telescope. The solution for the extinction and backscattering coefficients are showing in Eqs. (3) and (4) following the Klett [5,6] inversion method: [ S( R) S( R0 )] R0 exp[ S() r S( r )] exp α( R ) = (3) α 0 dr ( R ) R where: S 0 2 ( R ) 2 ( ) ( R) ln V ( R) ( R ) V ( R ) S =, (4) =, (5) 0 ln 0 R0 α(r0) is extinction coefficient at R0 (reference), and ( ) exp[ S( R) S( R0 )] ( R ) + 2 R0 exp[ S() r S( r )] β R = (6) β 0 0 dr K R p For cirrus clouds it is common to consider Kp constant at all levels. The signal-to-noise ratio (SNR) became one of the more important parameters during the lidar signal processing. The SNR parameter is very important for error estimation during the restitution process of cirrus optical and geometrical parameters [10]. The Kp or lidar ratio was calculated with the same methodology described for the Back-TOD [4]. 3. Signal-to-noise ratio problem Lidar measurements carried out in Argentina [11] contain many lidar signals acquired during the daytime, where the signal to noise ratio is less than three. During daytime measurements, the background noise present at those hours limits the dynamic range of lidar system. It is an instrumental limitation to improve in the near future. The spatial resolution of those signals is normally 6 m [7] and the total acquisition set the dynamic range up to 30 km (the useful Lidar signal from 300 m to 25 km at nighttime, decreasing to 20 km at daytime). Outside these heights only noise is present. One cirrus Lidar signal is obtained by averaging 20 seconds or more of signals acquired from laser shots backscattered by the atmosphere, in order to reduce the electrical Gaussian noise (200 or more laser shot by profile). In order to improve the SNR in the Argentine cirrus Lidar database, a pass-bass filter is applied in the obtained signal. If the filtering procedure were not carried out, many original signals would have to be discarded because they do not have the appropriated SNR. On the other hand, in the Cuban cirrus Lidar database, it is not necessary to apply the filtering procedure because the 75m vertical resolution results in an appropriated SNR. Three mathematical methods are commonly used to statistically improve the SNR. Once the Lidar signals are acquired and recorded we can average two or more originals signals, increasing the temporal resolution with the increase in SNR. A second method applied, reduces the spatial resolution from 6 m to 30 m or more (30 m is the spatial resolution used in the most lidar stations around the world) to improve SNR. The third one uses a numerical filter technique, i.e. a butterword or moving average filter. It is very important to note that in all cases, we loss either spatial or temporal resolution in the signal. However we accept a few losses in cirrus quality signal in favor of a SNR increase, i.e. 30 % or more. The three methods do not use the similar filter o statistical parameters to improve SNR, thus they are not able to carry out a comparison. Figures 1 to 3 illustrate the results of the application of three methods described above for improving the SNR. These figures show the results of the averaging of time series, digital filtering and reduction the spatial resolution of the lidar measurements of cirrus clouds during September 8, All of them reduce the present noise (red line), Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

4 but always we can observe the lost of signal level in comparison to original noisy signal (blue line). We can see averaged signal in Fig. 1. In Fig. 2 the Butterworth digital filter is applied over each signal. Finally the signal shown in Fig. 3 was averaged with the signals contained in the time series but decreasing the spatial resolution from 6 m to 30 m. In the set of figure, as we can see a priori, the digital filtered signal and the lowered resolution signal yield similar results, and are better than the averaged signal. To improve the SNR in the average method it is necessary to increase the number of averaged signals. Fig. 1. Averaged time series signal. Fig. 2. Digital filter applied over time series signals. 4. Calculating methods analysis For deriving the optical and geometrical parameters of measured cirrus the Double ended [3] and Back-TOD [4] techniques were analyzed. Both methods are based on the stable Klett s solution of inversion Lidar equation. The first one assumes a value of Kp derived with a Raman lidar. In our case we need to estimate this value from tables or statistics data from other latitudes because we have not this kind of measurement. The method calculates β(r) iterating backward and forward the signal until the same result is achieved in both directions. In this case a SNR higher than 2 is necessary [3]. Also the signals which do not fulfill the stable forward solution of lidar equation should be discarded. The second method calculates α(r) assuming as reference value, the value of cirrus extinction coefficient derived from the slope method [5,6] (graphical method). Then, this value is compared with another one calculated considering a maximum error (less than 0.01%) in the iterating procedure for deriving α(r). To be able to apply this procedure, the SNR value should be higher than 2. This method allows a valid estimation, to determine a Kp value, only when the molecular signal is present on top of the cirrus (continuity condition). Both methods combined assure the best use of the available signals. We carry out the derivation of α(r) iterating the values forward and backward assuming as reference values (αref) the integrated values in each one of the iterations. This procedure is conducted until the predefined error value is achieved, i.e., less than 0.1%. Because the original signal has been statistically improved with the filtering procedure, it is possible to calculate the Kp mean value for cirrus series. Using these combined methods we can analyze only one signal and obtain all the results. At the same time it is possible to derive all the results from a temporal series. Fig. 3. Spartial resolution reduction. 5. Lidar results We have currently applied the procedure to several Lidar signals from both sites. Here we discuss the preliminary results for four cases from Buenos Aires, Argentina, and one case from Camagüey, Cuba, in order to highlight the main results. A paper in preparation will present the results for both datasets Cuban data example Figure 4 shows the results of Camagüey Lidar Station measurement from June 7, 1994, Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

5 corresponding to mean values series. In alternated colors (red blue) we can see the range corrected filtered signals used in the calculations. The parameters calculated with the combined method proposed in this work are the extinction coefficient, optical depth and backscatter to extinction coefficient mean values of temporal series: α m = 0.72*10-4 m OD m = 0.2 Kp = sr -1 or Lidar ratio = 23.1 sr 6. Conclusions We report a combination of methods to derive the optical and geometrical properties of cirrus clouds. Also the preliminary results showed very encouraging performances. Results from Cuban measurement data process are consistent with former calculations. Optical depth distributions from four Argentine measurements cirrus processed data have the expected characteristics. The figures illustrate three Gaussian-exponential distribution cases and only one case with Gaussian distribution. We can see that the backscatter to extinction ratio can have very different values. We will derive a real statistical distribution after we finish processing more than 200 time series acquired since 2000 to the present. Fig. 4. Progressive lidar data from Camagüey Lidar Station. Acknowledgments This work has been supported by the Cuban National Climate Change Research Program grant and by the grant CU/PA04-UXIII/014 from Scientist Technology Cooperation Program between SECYT (Argentina) and CITMA (Cuba). This work was carried out with the aid of a grant from the Inter-American Institute for Global Change Research (IAI) CRN II 2017 supported by the US National Science Foundation (Grant GEO ) Argentine data base examples We present the results of four time series evolutions corresponding to: March 13, 2003; October 28, 2004; May 27, 2005 and September 10, The figures 5 to 9, 10 to 14, 15 to 19 and 20 to 24 show calculated parameters time series evolution for each sample respectively. We can see at first the time series evolution with the corrected data range [P(R) R 2 ] (Figs. 5, 10, 15 and 20) for each sample. Subsequently, the optical depth evolution (Figs. 6, 11, 16 and 21), and optical depth distribution (determine the cirrus clouds characteristics of each region) (Figs. 7, 12, 17 and 22) are shown. Furthermore, in Figs. 8, 13, 18 and 23 we can see the extinction coefficient evolution. Finally the backscatter to extinction coefficient (Figs. 9, 14, 19 and 24) is shown. The last of the parameter mentioned gives us an important microphysical characterization of cirrus clouds in our region. Backscatter to extinction coefficient (Kp) or the lidar ratio coefficient (1/Kp) is a very sensitive parameter for the mixing of ice crystals versus vapor water present inside cirrus. Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

6 March 13, Lidar data Fig. 5. Cirrus evolution (13/03/2003). Fig. 6.Optical Depth evolution (13/03/2003). Fig. 7. Optical Depth distribution (13/03/2003). Fig. 8. Extinction Coefficient (13/03/2003). Fig. 9. K p - (13/03/2003) Table I. Results (March 13, 2003). Kp (series averaged) sr -1 Lidar ratio equivalent sr. α m m -1 OD m 0.42 Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

7 October 28, Lidar data. Fig. 10. Cirrus evolution (28/10/2004). Fig Optical Depth evolution (28/10/2004). Fig. 12. Optical Depth distribution (28/10/2004). Fig. 13. Extinction Coefficient (28/10/2004). Fig. 14. Kp - (28/10/2004) Table II. Results (October 28, 2004). Kp (series averaged) sr -1 Lidar ratio equivalent sr α m m -1 OD m 0.39 Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

8 May 27, Lidar data Fig. 15. Cirrus evolution (27/05/2005). Fig. 16. Optical Depth evolution (27/05/2005). Fig. 17. Optical Depth distribution (27/05/2005). Fig. 18. Extinction Coefficient (27/05/2005). Fig. 19. Kp - (27/05/2005) Table III. Results (May 27, 2005). Kp (series averaged) sr -1 Lidar ratio equivalent sr. α m m -1 OD m 0.47 Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

9 5.2.4.September 10, Lidar data. Fig. 20. Cirrus evolution (27/05/2005). Fig. 21. Optical Depth evolution (10/09/2006). Fig. 22. Optical Depth distribution (10/09/2006). Fig. 23. Extinction Coefficient (10/09/2006). Fig. 24. K p - (10/09/2006) Table III. Results (May 27, 2005). Kp (series averaged) 0.08 sr -1 Lidar ratio equivalent 12.5 sr. α m m -1 OD m 0.45 Opt. Pura Apl. 41 (2) (2008) Sociedad Española de Óptica

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