Statistical Structure of the Atmospheric Optical Turbulence at Teide Observatory from Recalibrated Generalized SCIDAR Data

Mon. Not. R. Astron. Soc. 410, 934–945 (2011) doi:10.1111/j.1365-2966.2010.17492.x

Statistical structure of the atmospheric optical turbulence at Teide Observatory from recalibrated generalized SCIDAR data

, B. Garc´ıa-Lorenzo1,2 and J. J. Fuensalida1 2 1Instituto de Astrof´ısica de Canarias, C/Via Lactea S/N, 38305 La Laguna, Tenerife, Spain 2Dept. Astrof´ısica, Universidad de La Laguna, C/Astrof´ısico Francisco Sanchez,´ E-38205 Tenerife, Spain

Accepted 2010 August 5. Received 2010 August 5; in original form 2010 July 8 Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021

ABSTRACT The characterization of the optical turbulence structure at an astronomical site requires a proper 2 data base of the refractive-index structure constant, CN (h). Our team has been obtaining gen- 2 eralized SCIntillation Detection and Ranging (SCIDAR) observations to monitor CN (h)from 2002 November–2009 January at Teide Observatory (Tenerife, Canary Islands, Spain). The 2 Teide CN (h) data base includes useful data from 153 nights of generalized SCIDAR measurements obtained at the 1.5-m Calos Sanchez´ Telescope. The overestimation of the turbulence strength as a consequence of generalized SCIDAR data processing has been analysed for all double stars and analysis-plane combinations used in our observations. If this overestimation of the turbulence is not taken into account, the median total seeing and isoplanatic angle derived from the turbulence proﬁles in the data base are 0.70 and 2.47 arcsec, respectively. 2 We have recalibrated all the derived CN (h), correcting for this overestimation. The statistical optical turbulence structure above Teide Observatory is derived by combining the 93 662 2 individual CN (h) that constitute the data base at this site. More than 85 per cent of the total optical turbulence is concentrated in low-altitude layers (<5 km above sea level). The optical turbulence structure presents an evolution of the layers in both strength and altitude. Only the turbulence concentration at the observatory level shows a similar turbulence strength over a standard year. The median values of total seeing and isoplanatic angle of 0 = 0.64 arcsec and θ0 = 2.83 arcsec demonstrate the excellent quality of the Teide Observatory astronomical site for the implementation of adaptive optics systems. Key words: atmospheric effects – instrumentation: adaptive optics – site testing.

of efficient systems working with one or several deformable mir- 1 INTRODUCTION rors. These parameters represent convenient measurements of the Atmospheric optical turbulence drastically degrades the potential strength (r0), vertical distribution (θ0) and temporal variation (τ0) spatial resolution of ground-based telescopes larger than around of the atmospheric optical turbulence. They can be obtained from 20 cm. Adaptive optics systems were devised to compensate for measurements of the refractive-index structure constant as a func- 2 the distortions introduced by the turbulence in the wavefront tion of altitude (CN (h)) and the vertical wind profile (V(h)) through of the light reaching the pupil entrance of these telescopes. How- the following equations (Roddier, Gilli & Vernin 1982a; Roddier, ever, the larger the telescope diameter the more difficult it becomes Gilli & Lund 1982b): to compensate properly for the effects of atmospheric turbulence. −3/5 2 2 The current 10-m class and future 40-m class telescopes need to r0 = 0.423k CN (h)dh , (1) compensate for the prevailing turbulence conditions at the observing site by a factor from ∼50 (for 10-m class telescopes) to ∼200 −3/5 / 2 2 5 3 (for a 40-m class telescope) in order to exploit their potential spatial θ0 = 2.914k CN (h)h dh (2) resolution capabilities. A proper characterization of the statistical behaviour of the parameters describing the atmospheric turbulence and 3/5 at any particular site – namely Fried’s parameter (r0), the isoplanatic C2 (h)dh θ τ τ = 0.314r N , (3) angle ( 0) and the coherence time ( 0) – is crucial for the design 0 0 2 5/3 CN (h)V (h) dh where k is the optical wavenumber. Therefore the distribution E-mail: [email protected] of the refractive-index structure constant with altitude and its

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Figure 1. (a) Typical image of the scintillation produced at the pupil plane of the 1.5-m Carlos Sanchez´ telescope when observing a double star (BS7948 in this case) with the generalized SCIDAR instrument (Rodriguez-Hernandez´ et al. 2007). The integration time was 1 ms and the analysis plane was 3 km. The black solid line marks the pupil footprint of the BS7948 brighter star, and the dashed line corresponds to the fainter one. (b) Normalized autocorrelation (diametral cut) of a disc of 1.524 m in diameter and central obscuration of diameter 0.565 m simulating the pupil of the 1.5-m Carlos Sanchez´ telescope where the generalized SCIDAR observations were obtained. statistical behaviour are crucial in the field of high-angular- The result of normalization in generalized SCIDAR data pro- resolution imaging through the atmosphere and the development cessing is an inexact estimation of the optical turbulence strength of efficient adaptive optics systems for large and extremely large as a result of the shift of the pupil images produced by each star 2 telescopes. For simplicity, we will refer to CN (h) as the optical on the detector (Johnston et al. 2002). The effects of this nor- 2 turbulence profile. malization on the determination of CN (h) were only analysed for The most contrasted and efficient remote sensing technique with turbulence at ground level (where commonly a large percentage of which to measure and characterize atmospheric optical turbulence the turbulence is concentrated), being almost negligible (Johnston is SCIntillation Detection and Ranging (SCIDAR) in both classical et al. 2002). However, this idea was generalized to any altitude and 2 and generalized versions (Vernin & Roddier 1973; Rocca, Roddier many measurements of CN (h) were obtained assuming that the er- & Vernin 1974; Avila, Vernin & Masciadri 1997; Fuchs, Tallon & rors due to the normalization were small enough to be negligible Vernin 1998; Kluckers et al. 1998; Avila, Vernin & Sanchez´ 2001; at any altitude (Avila et al. 1997, 2001, 2004; Fuchs et al. 1998; Johnston et al. 2002; Avila et al. 2004, 2006; Garc´ıa-Lorenzo & Kluckers et al. 1998; Prieur, Daigne & Avila 2001; Wilson et al. Fuensalida 2006; Garc´ıa-Lorenzo et al. 2007; Vernin et al. 2007; 2003; Tokovinin et al. 2005; Garc´ıa-Lorenzo & Fuensalida 2006; Fuensalida, Garc´ıa-Lorenzo & Hoegemann 2008; Garc´ıa-Lorenzo Egner, Masciadri & McKenna 2007; Vernin et al. 2007; Fuensalida et al. 2009a). In brief, the SCIDAR observing procedure consists et al. 2008; Garc´ıa-Lorenzo et al. 2009a). However, Avila & Cuevas of taking short-exposure-time (<5 ms) images of the scintillation (2009) demonstrated that the dependence of the error induced by patterns, I(r), produced when observing a double-star system at the normalization with altitude is strongly linked to the configura- the pupil plane of a telescope (classical SCIDAR) or at a virtual tion of the generalized SCIDAR observations (telescope diameter, plane placed a few kilometres below the pupil plane (generalized double-star parameters and position of the analysis plane); there are SCIDAR). In the case of generalized SCIDAR, the scintillation parameter combinations for which the relative errors are actually pattern produced by each star of the binary observed is shifted on negligible, but other combinations for which these errors are sig- the detector (see Fig. 1a). This shift depends on the position of the nificant. The analytical expression to calculate the relative errors detection plane. A sample of such scintillation images obtained at introduced during generalized SCIDAR data processing is (Avila & times separated by a constant delay allows the calculation of the Cuevas 2009) C2 h atmospheric turbulence profiles, N ( ), and also the velocity of the S(r − θ d) (r) = − 1, (5) turbulence layers detected. aS(r) + b[S(r + θ d) + S(r − θ d)] The processing of the generalized SCIDAR data consists of the where d is the position of the analysis plane with respect to the pupil calculation of the autocovariance image, (r), of a series of recorded plane (in metres) and θ is the angular distance of the double-star scintillation patterns. The autocovariance peaks allow the determi- system (in radians). a and b are parameters related to the difference nation of C2 (h) using numerical inversion. The procedure to esti- N in magnitude (m) of the two stars observed, given by mate the scintillation autocovariance is to compute the average autocorrelation of a series of scintillation images and to normalize by the 1 + α2 a = (6) autocorrelation of the average image of the same scintillation-image (1 + α)2 series (see equation 4). More details on the method and physics in- and volved can be found in Kluckers et al. (1998) and references therein. α b = , (7) (1 + α)2 I(r) ∗ I(r) where α = 10−0.4m. S(r) in equation (5) denotes the pupil auto- (r) = . (4) I(r)∗I(r) correlation, which can be calculated for any pupil function P (r)

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Table 1. Distribution of nights from 2002 November–2009 January on which useful generalized SCIDAR measurements were obtained at Teide Observatory. The number of individual turbulence proﬁles recorded each night is also included.

Year Total Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Profiles 2002 — — — — — — — — — — 593 4201 4794 Nights ——— ———— — —— 1 4 5 Profiles 2003 0 635 0 308 1507 797 1342 5254 1448 0 0 0 11291 Nights 020 1322 8 2000 20 Profiles 2004 0 810 1223 2399 2425 0 1457 643 2910 1457 0 0 13324 Nights 012 3402 3 5300 23 Profiles 2005 467 0 680 1864 4389 2496 1622 4785 4793 1203 0 0 22299 Nights 103 3544 7 7200 36 Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021 Profiles 2006 103 1113 2151 2703 1669 2945 1379 3279 1765 0 0 766 17873 Nights 123 4343 5 2001 28 Profiles 2007 0 0 3483 3259 0 0 0 2014 2186 0 0 0 10942 Nights 006 6000 3 3000 18 Profiles 2008 0 381 0 3160 0 2341 0 2051 0 0 1353 533 9819 Nights 010 4040 4 0051 19 Profiles 2009 3320 — — — — — — — — — — — 3320 Nights 4—— ———— — ———— 4 Profiles Total 3890 2939 7537 13693 9990 8579 5800 18026 13102 2660 1946 5500 93662 Nights 6 6142115141130195 6 6 153 through (Avila & Cuevas 2009) July) and a completely automated generalized SCIDAR instrument (Rodriguez-Hernandez´ et al. 2007), both developed at the Insti- S = F −1 |F P |2 , (r) [ [ (r)] ] (8) tuto de Astrof´ısica de Canarias (Tenerife, Canary Islands, Spain). where F corresponds to the Fourier transform and F −1 to its Each detector pixel of both generalized SCIDAR instruments cov- inverse. It is important to note that the normalization during gen- ers a square 2.81 cm in side on the 1.5-m Carlos Sanchez´ Telescope eralized SCIDAR data processing leads to an overestimation of pupil. The data processing used a series of 1000 images of scin- the turbulence intensity for any of the possible parameter com- tillation patterns to derive the average normalized autocovariance binations. Turbulence profiles derived from generalized SCIDAR and five frames that are measurements of the two-dimensional (2D) observations affected by the normalization error can be corrected spatiotemporal cross-correlation functions separated by a constant 2 t C2 h for this induced error just by multiplying the retrieved CN (h)bythe temporal lapse of .The N ( ) systematic campaigns at Teide factor 1/[1+(h)] (Avila & Cuevas 2009), computing (r) through Observatory were carried out from 2002 November–2009 January equation (5) and using relation r = θ(d + h). with a frequency of about 4–6 nights per month. More than 150 Results derived from generalized SCIDAR observations taken at nights with useful generalized SCIDAR observations and around C2 Teide Observatory have already been published (Garc´ıa-Lorenzo & 95 000 individual N profiles constitute the data base of turbulence Fuensalida 2006; Garc´ıa-Lorenzo et al. 2007, 2009a,b), assuming profiles at Teide Observatory (see Table 1). The dome turbulence that errors at any altitude induced by normalization during the data contribution was removed from all the turbulence profiles recorded processing were negligible. In this paper, we obtain the actual error using a procedure based on the evenness properties with Fourier introduced by the normalization of the scintillation autocovariance analysis (Fuensalida et al. 2008). 2 in the calculation of the CN profiles recorded at Teide Observatory. The generalized SCIDAR observations recorded at Teide Obser- 2 All the CN profiles in the Teide data base have been corrected vatory were obtained by observing a set of 20 double stars (see for such an error. We present the statistical structure of the optical Table 2), selected based on the binary system parameters and their ◦ turbulence above Teide Observatory and its temporal evolution over visibility upwards of ∼70 above the horizon, allowing full moni- ayear. toring of the turbulence structure through the seasons.

2THEDATA 2.1 Error induced by generalized SCIDAR data processing Teide Observatory (latitude 28◦1800N, longitude 17◦3035W) 2 is located at an altitude of ∼2390 m above sea level on the is- The optical turbulence proﬁles, CN (h), derived from generalized land of Tenerife (Canary Islands, Spain). This astronomical site SCIDAR data are indeed an overestimation of the actual turbulence is ∼160 km distant from Roque de los Muchachos Observatory strength during observations (Avila & Cuevas 2009). As we have (latitude 28◦26N, longitude 17◦53W on La Palma island, Canary already mentioned, such an overestimation is the result of the shift Islands, Spain), one of the ﬁnal candidates for location of the between the pupil footprints of the two stars on the detector (see 2 European Extremely Large Telescope (42-m EELT). A monitor- Fig. 1a). The calculation of the error in CN (h) is carried out through ing programme of the atmospheric turbulence structure at Teide pupil autocorrelation (see equation 5) and knowledge of the pa- Observatory began in 2002 using the generalized SCIDAR tech- rameters of the double star observed (see Table 2). Fig. 1(b) shows nique. The 1.5-m Carlos Sanchez´ Telescope has been used in com- a diametral cut of the pupil autocorrelation of the 1.5-m Carlos bination with a manual generalized SCIDAR prototype (until 2005 Sanchez´ telescope derived through equation (8).

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Table 2. Main parameters of the double stars used in the generalized SCIDAR observations recorded at Teide Observatory. m1 designates the magnitude of the brightest star in the V band and m is the difference in magnitude between both stars. θ corresponds to the angular separation between the stars. The different positions of the analysis plane (d) with respect to the pupil plane used with each binary system 2 are also summarized, including the percentage of turbulence profiles (CN (h)) recorded for each configuration. The average percentage error induced during generalized SCIDAR data processing for each configuration is also included. Uncertainties indicate only the standard deviation of the averaged errors in altitude.

Double star αa δa m1 m θ d Percentage Average (J2000) (J2000) (arcsec) (km) of proﬁles error (per cent)

BS230 00h49m52s +27◦4238.9 7.00 0.10 4.6 5 0.96 14.0 ± 1.0 6 0.67 16.4 ± 1.0 BS282 01h00m03s +44◦4240.1 5.70 0.34 7.8 3 1.79 14.7 ± 3.4 4 9.12 19.2 ± 4.4

5 0.13 24.1 ± 5.5 Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021 BS546 01h53m31s +19◦1738.6 4.64 0.08 7.5 2 1.01 9.2 ± 1.7 3 1.39 13.7 ± 2.5 4 1.53 18.1 ± 3.4 BS1065 03h31m20s +27◦3418.5 5.60 1.01 11.3 3 0.70 32.4 ± 18.5 4 0.36 40.2 ± 19.3 5 0.63 46.3 ± 19.0 BS1424 04h31m24s +40◦0036.6 6.26 0.11 9.0 3 0.24 19.4 ± 7.1 4 0.14 25.5 ± 8.9 BS1821 05h29m16s +25◦0900.7 5.47 0.32 4.8 4 0.48 11.8 ± 0.9 5 0.65 14.9 ± 1.0 BS1847 05h32m14s +17◦0329.2 5.46 0.09 9.6 2 0.47 14.8 ± 6.6 3 2.31 22.2 ± 9.4 5 0.40 34.8 ± 12.6 BS1879 05h35m08s +09◦5602.9 3.30 2.07 4.4 5 0.04 34.8 ± 12.6 BS2217 06h15m39s +36◦0855.2 6.92 0.62 11.3 3 0.16 32.1 ± 17.9 BS2784 07h22m52s +55◦1653.0 5.78 1.08 15.0 3 0.10 44.4 ± 22.3 BS2890 07h34m35s +31◦5318.5 1.93 1.04 4.4 5 2.16 13.6 ± 1.0 BS3311 08h26m47s +26◦5607.7 6.17 0.12 5.1 3 0.74 9.5 ± 1.0 5 0.46 15.1 ± 1.4 6 1.10 17.9 ± 1.5 BS4057 10h19m58s +19◦5028.5 2.61 0.86 4.6 3 0.30 8.6 ± 0.8 4 0.43 11.4 ± 0.9 5 2.13 14.1 ± 1.0 6 7.74 16.6 ± 1.0 BS4259 10h55m36s +24◦4459.2 4.50 1.95 6.5 4 0.34 15.2 ± 2.1 5 0.54 18.7 ± 2.2 6 0.30 22.1 ± 2.3 BS5054 13h23m55s +54◦5531.3 2.27 1.68 14.5 2 1.93 35.0 ± 24.2 3 0.50 44.9 ± 24.1 6 0.08 63.8 ± 18.6 BS5475 14h40m43s +16◦2505.9 4.91 0.94 5.6 4 3.55 13.4 ± 1.7 5 3.00 16.3 ± 1.9 6 1.11 19.1 ± 2.0 BS5789 15h34m48s +10◦3220.7 3.80 0.00 4.3 5 1.50 13.5 ± 1.0 6 7.26 15.6 ± 1.0 7 0.38 18.0± 0.9 BS5834 15h39m22s +36◦3808.9 5.00 0.96 6.3 4 3.13 14.6 ± 2.0 5 0.08 18.0 ± 2.0 BS6730 18h01m30s +21◦3544.8 4.96 0.22 6.2 3 0.05 11.1 ± 1.6 4 12.99 14.0 ± 1.8 5 4.19 17.4 ± 1.9 6 0.61 20.7 ± 1.7 BS7948 20h46m39s +16◦0727.4 4.27 0.87 9.6 2 4.04 14.8 ± 6.6 3 4.24 22.3 ± 9.5 4 11.84 28.8 ± 11.6

Applying equation (5) for the different observational configura- induced during the generalized SCIDAR data processing. Fig. 2 tions of the generalized SCIDAR observations, we have calculated also includes the multiplying factor (as a function of altitude) to 2 2 the actual error induced in the retrieved CN profiles at this astronom- correct the CN profiles, giving an idea of the percentage error in the 2 ical site (see Fig. 2). The turbulence strength at any altitude should results derived from the CN -profile data base for Teide Observatory be multiplied by a factor 1/[1+(h)] to compensate for the error (Garc´ıa-Lorenzo et al. 2009a,b,c).

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Figure 2. Distribution as a function of the altitude of the error (left panel) induced during generalized SCIDAR data processing and the multiplying factor 2 (right panel) to be applied to the measured CN values derived from generalized SCIDAR at the 1.5-m Carlos Sanchez´ Telescope for all double stars and analysis-plane combinations used to record the data. Different shaded lines in each plot indicate different positions of the analysis plane used withthesame double star, as indicated in each plot.

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2 The error in the determination of CN strongly depends on the se- using an analysis plane at 4 km – the worst, in terms of errors lected double stars and the analysis planes for generalized SCIDAR induced by normalization, of the observational set-ups used with observations at the 1.5-m Carlos Sanchez´ Telescope (see Fig. 2). this double star. We will refer to these profiles as BS7948uncorrected. 2 The CN profiles recorded observing the double star BS5054 are the Fig. 3(a) shows the average turbulence profile during the night of most affected (see Table 2 and Fig. 2) by the error introduced in 2003 August 31 derived from BS7948uncorrected (black solid line). In the normalization during the generalized SCIDAR data processing, order to compensate for the error introduced during data process- with errors reaching 85 per cent above ∼16 km. Fortunately, only ing, we multiplied each individual BS7948uncorrected by the factor 2 / + 2.51 per cent of the total number of CN profiles in the data base 1 (1 ) (as a function of altitude) derived through equation (5) were obtained pointing to BS5054. In ∼36 per cent of the observa- (see dotted line in plot corresponding to BS7948 in Fig. 3a). We 2 tional configurations, errors in CN profiles up to 18 km (above the will refer hereafter to these corrected profiles as BS7948corrected. tropopause; Garc´ıa-Lorenzo, Fuensalida & Eff-Darwich 2004) do Fig. 3(a) also includes the average turbulence profile obtained from not exceed 15 per cent and hence might be considered negligible. BS7948corrected. It is important to note that, although turbulence 2 In contrast, 12 per cent of CN profiles are strongly affected by the strength is overestimated in BS7948uncorrected as a consequence of normalization effect, up to 50 per cent overestimation at 18 km. At the normalization during generalized SCIDAR data processing, the Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021 10 km, errors are almost negligible (<10 per cent) for 32 per cent of turbulence structure presents the same features as results derived the turbulence profiles, while 2 per cent of the configurations still from BS7948corrected. The average relative error [(BS7948uncorrected − overestimate the turbulence by a factor of 2. At the observatory level BS7948corrected)/(BS7948uncorrected + BS7948corrected) ∗ 100] is 17 per (∼2400 m), 48 per cent of the turbulence includes errors that can cent for this configuration, reaching a relative error of 41 per cent be considered negligible, while errors larger than 40 per cent were at 25 km above sea level. The lowest relative error in the turbulence found in 2 per cent of the observational configurations. The largest profile is 9 per cent at observatory level. number of turbulence profiles in the Teide data base were obtained Through equations (1), (2) and (3), we have calculated the total pointing to the double star BS7948, most of them using an analysis seeing (seeing = 0.98λ/r0), the boundary-layer (up to 1 km) con- plane of 4 km, and were affected by an average error of ∼29 per tribution to the seeing (BL), the free-atmosphere contribution to cent as a consequence of the data-processing procedure. Therefore, the seeing (FA), the isoplanatic angle (θ0) and the coherence time errors due to the normalization during generalized SCIDAR obser- (τ0). Fig. 3 shows the results obtained using BS7948uncorrected (black vations obtained at Teide Observatory are not negligible for many squares) and BS7948corrected (open circles). The statistical values of of the configurations. these parameters derived from uncorrected and corrected profiles Following Avila & Cuevas (2009), we have corrected the full are presented in Table 3. 2 data base of CN profiles for Teide Observatory for normalization As we already noted, the normalization of the autocovariance 2 effects by multiplying the retrieved CN strengths at any altitude by leads to an overestimation of the turbulence (Avila & Cuevas 2009). the calculated factor 1/[1+(h)] for each particular double star and Therefore the seeing values (total seeing, BL and FA) derived from 2 analysis-plane combination. the uncorrected CN (h) profiles are larger than the corresponding values obtained from the corrected profiles (see Figs 3, 4 and 5). In the case of the isoplanatic angle and the coherence time, the er- 2.2 Implications in the calculation of adaptive optics ror introduced by the generalized SCIDAR data processing results parameters in an underestimation of these parameters (see Figs 3, 4 and 5 and Table 3). The temporal behaviour of the observations of these atmo- We have selected three of the SCIDAR observational configurations spheric parameters does not differ when comparing values derived to assess the importance of the error induced during data processing from the uncorrected and corrected profiles. In the case of BS7948, (Avila & Cuevas 2009) in the calculation of the atmospheric pa- we obtained an overestimation of the total seeing by up to 22.7 per rameters relevant for adaptive optics (see equations 1, 2 and 3). The cent when using uncorrected values, with an average overestima- first one corresponds to the least propitious case (analysis plane at tion of 15.6 per cent. The BL and FA are also overestimated (by 4 km) of the set-ups used with the double star BS7948 (more than 15.7 per cent in the case of BL and up to 23.3 per cent for FA). 20 per cent of the turbulence profiles in the data base were obtained The isoplanatic angle is underestimated by 13.8 per cent on aver- pointing to this binary system). The second one corresponds to the age, while the coherence time presents an average underestimation configuration providing the lowest error of the configurations used: of 13 per cent. the double star BS4057 and analysis plane at 3 km (0.3 per cent of the profiles in the data base were obtained using this configuration). The third case corresponds to the profiles where the influence of the 2.2.2 The case of BS4057 and an analysis plane at 3 km normalization is worst, corresponding to the data acquired observing BS5054 and placing the analysis plane at 6 km (only 0.08 per The double star BS4057 (θ = 4.6 arcsec) and analysis plane at cent of the profiles were obtained through this configuration). As an 3 km were combined on only one night (2003 February 9) to obtain anecdote, the best and worst configurations were used on the same 234 individual turbulence profiles. Fig. 4(a) presents the average night (2003 February 9), during the starting steps of the monitoring turbulence profile derived from BS4057uncorrected and BS4057corrected at Teide Observatory, and never used again. (following the same procedure and nomenclature as for BS7948 in Section 2.2.1). The turbulence structure is practically the same. The average relative error between both average profiles is only 4.5 per cent, being below 5.5 per cent at any altitude. Fig. 4(b) shows the 2.2.1 The case of BS7948 and an analysis plane at 4 km temporal evolution of atmospheric parameters derived from the 2 We have selected the CN (h) profiles derived from generalized SCI- selected BS4057 generalized SCIDAR observations. The seeing is DAR observations on a particular night (2003 August 31) obtained slightly overestimated (4.9 per cent, 4.6 per cent and 5.1 per cent pointing to BS7948 (θ = 9.6 arcsec and m = 0.87 mag) and on average for seeing, BL and FA, respectively), while in contrast

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Figure 3. Results derived from the turbulence profiles obtained through generalized SCIDAR observations at the 1.5-m Carlos Sanchez´ telescope when observing (data from night 2003 August 30) the double star BS7948 (θ = 9.6arcsecandm = 0.87 mag) and the analysis plane at 4 km under the pupil plane. 2 (a) Average CN (h) obtained from the 348 individual uncorrected profiles (solid line) derived from the generalized SCIDAR observations using the indicated set-up. The dashed line corresponds to the average profile obtained through the 348 individual profiles corrected from the error induced by the normalization during data processing. The dome turbulence contribution was removed from individual profiles following the procedure in (Fuensalida et al. 2008) before 2 combining the profiles. The horizontal dotted line indicates the observatory level (∼2400 m). The horizontal axis is the CN strength on a logarithmic scale. The vertical axis is the altitude above sea level. (b) Evolution of the total seeing (in arcsec) along the observation derived using equation (1) and applying seeing = . 0.98λ/r0 (λ = 5000 Å). (c) Evolution of the boundary-layer contribution to the seeing (BL) in arcsec. (d) Evolution of the free-atmosphere contribution to the 2 seeing (FA) in arcsec. (e) Evolution of the isoplanatic angle in arcsec. (f) Evolution of the coherence time along the observation derived from CN profiles and velocities of the turbulence layers obtained through wavelet analysis (Garc´ıa-Lorenzo & Fuensalida 2006). In (b), (c), (d), (e) and (f) black squares correspond to the values derived from BS7948uncorrected and open circles to the values obtained from BS7948corrected (see text).

Table 3. Statistical values of the atmospheric parameters derived from the generalized SCIDAR observations obtained pointing to BS7948 for almost 1.5 h, BS4057 for slightly more than 1.5 h and BS5054 for upwards of 30 min (see text for conﬁguration and dates). Statistical values derived from data ignoring the errors introduced 2 by the normalization of the scintillation autocovariance in the calculation of CN (staruncorrected) are compared with those obtained from proﬁles after multiplying by the appropriate factor to compensate for such errors (starcorrected).

BS7948 BS4057 BS5054 uncorrected corrected uncorrected corrected uncorrected corrected

Seeing (arcsec) Average 0.81 0.70 0.65 0.62 0.73 0.49 Median 0.81 0.70 0.65 0.62 0.73 0.49 σ 0.10 0.09 0.07 0.07 0.08 0.05 BL (arcsec) Average 0.62 0.54 0.65 0.62 0.55 0.39 Median 0.63 0.55 0.66 0.63 0.55 0.39 σ 0.12 0.10 0.09 0.09 0.09 0.07 FA (arcsec) Average 0.42 0.36 0.44 0.42 0.40 0.24 Median 0.40 0.35 0.44 0.42 0.41 0.25 σ 0.12 0.11 0.07 0.07 0.08 0.05 θ0 (arcsec) Average 1.20 1.40 2.74 2.89 1.51 2.79 Median 1.23 1.43 2.61 2.76 1.48 2.72 σ 0.23 0.27 0.66 0.69 0.24 0.43 τ0 (ms) Average 3.54 4.07 2.43 2.55 2.75 3.90 Median 3.57 4.11 2.38 2.49 2.73 3.87 σ 0.74 0.86 0.34 0.36 0.40 0.57 r0 (cm) Average 12.66 14.65 15.82 16.60 13.96 20.76 Median 12.55 14.50 15.64 16.41 13.93 20.61 σ 1.78 2.14 1.77 1.86 1.55 2.34

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Figure 4. Results derived from the 234 individual turbulence proﬁles obtained through generalized SCIDAR observations at the 1.5-m Carlos Sanchez´ telescope when observing (data from night 2003 February 9) the double star BS4057 (θ = 4.6arcsecandm = 0.86 mag) with the analysis plane located at 3 km below the pupil plane. (a), (b), (c), (d), (e) and (f) are the same as in Fig. 3 but for BS4057 data.

Figure 5. Results derived from the 86 turbulence profiles obtained through generalized SCIDAR observations at the 1.5-m Carlos Sanchez´ telescope when observing (data from night 2003 February 9) the double star BS5054 (θ = 14.5arcsecandm = 1.68 mag) with the analysis plane located at 6 km below the pupil plane. (a), (b), (c), (d), (e) and (f) are the same as in Fig. 3 but for BS5054 data. the isoplanatic angle (5.1 per cent on average) and coherence time 2.2.3 The case of BS5054 and an analysis plane at 6 km (4.5 per cent) are slightly underestimated. Table 3 includes the statistical values for the atmospheric param- Although a small fraction (0.05 per cent) of the total number of tur- eters relevant for adaptive optics derived from the data acquired bulence profiles were obtained pointing to the double star BS5054 with the selected generalized SCIDAR configuration. (θ = 14.5 arcsec) and placing the analysis plane at 6 km, this is

C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 410, 934–945 942 B. Garc´ıa-Lorenzo and J. J. Fuensalida a clear example of the drastic consequences of the shift of the scintillation pattern produced by each star on the detector in generalized SCIDAR observations. Fig. 5(a) presents the average turbulence profile derived from BS5054uncorrected and BS5054corrected (following the same procedure and nomenclature as for BS7948 in Section 2.2.1). Again, turbulence structure is almost the same, but turbulence strength is clearly overestimated in average profiles derived from BS5054uncorrected data. The average relative error reaches 42 per cent in this case, with a maximum value of 75 per cent at 17 km. Fig. 5(b) shows the temporal evolution of atmospheric parameters derived from the selected BS5054 generalized SCIDAR observations. The seeing is largely overestimated (48.7 per cent, 40.5 per cent and 67.4 per cent on average for seeing, BL and FA, respectively), while the isoplanatic angle (45.7 per Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021 cent on average) and coherence time (29 per cent) are clearly underestimated. Table 3 includes the statistical values of the atmospheric parameters derived from the data analysed in this section. The figures in Table 3 demonstrate the drastic consequences when deriving statis- 2 tical values of atmospheric parameters using CN profiles retrieved from generalized SCIDAR observations in a non-appropriate configuration. The particular cases studied in this section show how the profiles C2 from generalized SCIDAR observations and any results derived Figure 6. Average (solid line) and median (dashed line) of the 93 662 N from them are affected by the normalization of the scintillation profiles obtained at Teide Observatory. Dome seeing was removed from the autocovariance during data processing. For any observational set-up individual profiles (Fuensalida et al. 2008) and profiles were corrected for the error induced during generalized SCIDAR processing (Avila & Cuevas it is important to evaluate the errors induced by such normalization 2009). The horizontal line indicates the observatory altitude (∼2400 m). and correct them.

3 STATISTICAL ATMOSPHERIC OPTICAL trated close to the ground level for any month at this astronomical TURBULENCE VERTICAL DISTRIBUTION site. The turbulence strength at the observatory level is quite stable We have combined all the individual turbulence profiles – corrected along the standard year (following the nomenclature used in Els for the errors induced during generalized SCIDAR data process- et al. 2009). Above 1 km, different features appear and disappear ing – obtained during 153 nights of useful generalized SCIDAR over the months. There is a clear turbulence feature at around 5 km observations at Teide Observatory in order to have a view of the above sea level that seems to evolve slightly in altitude but also turbulence structure at this astronomical site. Fig. 6 shows the aver- in intensity, being clearly present in the July and August statisti- age (solid line) and median (dashed line) turbulence profiles, both cal profiles. A second turbulence feature is present in the region being statistically representative of the optical turbulence structure between 11.5 and 15.5 km above sea level in almost all the statis- at Teide Observatory. The strength of the turbulence is largest at the tical turbulence profiles in Fig. 7. This feature evolves in altitude observatory level, steeply decreasing with altitude. Indeed, 60 per and strength, being in general more intense at lower altitudes. A cent of the total turbulence is concentrated at the boundary layer (up similar behaviour was found at Mt Graham International Observa- to 1 km above the observatory level) in the average profile, while this tory (Arizona, USA), where the peak of a turbulence layer moves percentage increases to almost 72 per cent in the median statistical 4 km in altitude and reduces its strength from winter to summer profile. At around 5 km above sea level there is a turbulence feature (Masciadri et al. 2010). The turbulence profiles recorded at San Pe- that is clearer in the average profile than in the median profile. At dro Martir´ (Mexico) also present a turbulence layer at this altitude around 15 km other turbulence concentrations of lower strength level (Masciadri & Egner 2006; Avila et al. 2004). This high-altitude appear. We found that most of the turbulence (upwards 85 per turbulence concentration could be related to the jet-stream wind, as cent) at Teide Observatory is concentrated in the first 5 km above has been suggested for San Pedro Martir´ (Mexico) and Mt Graham the site. (Masciadri et al. 2010; Masciadri & Egner 2006). However, it has Seasonal trends of the optical turbulence structure have already been shown that not all the wind vertical profiles have signatures been reported for different astronomical sites (Masciadri et al. 2010; of the jet stream above Teide Observatory (Garc´ıa-Lorenzo et al. Els et al. 2009; Garc´ıa-Lorenzo et al. 2009b, 2007; Fuensalida et al. 2009a). Furthermore, turbulence profiles presenting a high-altitude 2007; Masciadri & Egner 2006; Masciadri & Garfias 2001). Com- (11.5–15.5 km region) turbulence layer have been observed when bining the profiles obtained for the same months, we have derived wind vertical profiles do not present the jet-stream feature; quite the monthly average and median optical turbulence profiles (Fig. 7), to the contrary, no turbulence concentration has been detected in which constitute the seasonal evolution of the turbulence structure this region in the presence of strong high-altitude winds (see Ap- at Teide Observatory. The statistical significance is not the same for pendix A in Garc´ıa-Lorenzo et al. (2009a) for examples of such all profiles in Fig. 7, because the amount of data varies significantly behaviour). Therefore, we do not find clear evidence suggesting from month to month (see Table 1). As in the case of the global that jet stream is the driver of high-altitude turbulence at Teide Ob- statistical profile (Fig. 6), we find that the turbulence is concen- servatory. Not only the jet stream but also other factors might be

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2 Figure 7. Statistical monthly average (solid line) and median (dashed line) CN profiles for Teide Observatory (Tenerife, Canary Islands, Spain) obtained by combining optical turbulence profiles derived from generalized SCIDAR measurements from 2002 November–2009 January. Dome seeing was removed from 2 the individual profiles following the procedure proposed in Fuensalida et al. (2008). Errors induced by generalized SCIDAR data processing to retrieve CN (h) 2 have been also removed following the recipe of Avila & Cuevas (2009). The horizontal axis represents the CN strength (on a logarithmic scale) in units of m−2/3. The vertical axis corresponds to the altitude above sea level. The dotted horizontal line indicates the observatory altitude (∼2400 m). These profiles constitute the statistical seasonal evolution of the atmospheric optical turbulence structure above Teide Observatory. The labels at the right corner of each plot indicate the month and the number of individual turbulence profiles combined.

responsible for triggering turbulence at high-altitude levels such as turbulence profiles recorded is r0=16.90 ± 5.30 cm, while the tropopause level – which moves from ∼18.8 km in February to the median value is 15.79 cm. The average and median values ∼11.8 km in July above Teide Observatory (Garc´ıa-Lorenzo et al. obtained for the isoplanatic angle using the full data base are 2004) – and/or marked twists in wind direction (Garc´ıa-Lorenzo θ0=3.15 ± 1.65 arcsec and θ˜0 = 2.83 arcsec. If the overes- et al. 2009a). timation of the turbulence strength during the generalized SCI- The turbulence structure at Teide Observatory is quite similar DAR data processing is not considered, the statistical values of to the turbulence structure reported for the nearby Roque de los these parameters will be r0=15.29 ± 4.82 cm, r˜ = 14.44 cm, Muchachos Observatory (Fuensalida et al. 2007; Garc´ıa-Lorenzo θ0=2.76 ± 1.43 arcsec and θ˜0 = 1.43 arcsec. The uncertainties et al. 2007, 2009b). indicate only the standard deviation of the averaged measurements. These statistical values for the atmospheric parameters relevant for adaptive optics confirm the high quality of the Canary Islands astronomical sites for high-spatial-resolution astronomy. 3.1 Atmospheric parameters relevant for adaptive optics The large data base of atmospheric turbulence profiles above Teide Observatory can be used to calculate the statistical Fried’s pa- 4 SUMMARY AND CONCLUSIONS rameter and isoplanatic angle (through equations 1 and 2) that 2 characterize an efficient adaptive optics system for this site. The We have been monitoring CN (h) profiles since 2002 at Teide Obser- average value for Fried’s parameter obtained including all the vatory (Tenerife, Canary Islands, Spain). The total number of nights

C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 410, 934–945 944 B. Garc´ıa-Lorenzo and J. J. Fuensalida with useful generalized SCIDAR measurements is 153, 93 662 be- r0=16.90 ± 5.30 cm and θ0=3.15 ± 1.65, calculated at 2 ing the total number of CN (h) profiles recorded at this site. We have λ = 5000 Å. calculated the error induced during generalized SCIDAR data pro- The statistical optical turbulence profiles in this paper and the cessing as a consequence of the shift on the detector of each of the derived statistical values for the atmospheric parameters confirm double stars observed to record the data. These errors are significant the high quality of Teide Observatory in particular and the Canary for some of the observational configurations used at Teide Observa- Islands astronomical sites in general for adaptive optics systems tory. We have shown the effects of theses errors in the calculation of implementation. atmospheric parameters relevant for adaptive optics. Following the procedure proposed by Avila & Cuevas (2009), we have corrected 2 all the turbulence profiles in the Teide CN (h) data base. Combining ACKNOWLEDGMENTS all the corrected turbulence profiles, we have obtained the statistical turbulence profile representative of the turbulence structure at Teide This paper is based on observations obtained at the Carlos Sanchez´ 2 Telescope operated by the Instituto de Astrof´ısica de Canarias at Observatory. We have also derived the monthly statistical CN (h), which constitutes the seasonal evolution of the optical turbulence Teide Observatory. The authors thank all the staff at the observa- Downloaded from https://academic.oup.com/mnras/article/410/2/934/1029705 by guest on 05 October 2021 structure at this astronomical site and the characteristic atmospheric tory for their kind support. Thanks are also due to all the observers parameters. The main conclusions that we have derived from this who have recorded generalized SCIDAR data at Teide Observatory work can be summarized as follows. (J. Castro-Almazan,´ S. Chueca, A. de la Nuez Cruz, C. Hoegemann, E.G. Mendizabal, M.A.C. Rodr´ıguez-Hernandez´ & R. Gimeno). We also thank A. Eff-Darwich for help and useful discus- (i) The generalized SCIDAR data processing leads to an inexact sions. This work was partially funded by the Instituto de Astrof´ısica estimate of the optical turbulence strength that might exceed 15 per de Canarias and by the Spanish Ministerio de Educacion´ y Cien- cent at different altitudes for many of the observational configura- cia (AYA2006-13682 and AYA2009-12903). B. Garc´ıa-Lorenzo ac- tions used at Teide Observatory. knowledges support from the Ramon´ y Cajal programme by the (ii) The effect of the error introduced during generalized SCI- Spanish Ministerio de Ciencia e Innovacion.´ DAR data processing consists of an overestimation of the turbulence strength, but following the actual turbulence structure. (iii) The error introduced by the normalization during the pro- REFERENCES cessing of the generalized SCIDAR can drastically overestimate Avila R., Cuevas S., 2009, Optics Express, 17, 10 926 (Avila & Cuevas 2009) the seeing (total, boundary-layer and free- Avila R., Vernin J., Masciadri E., 1997, Applied Opt., 36, 7898 atmosphere contributions to the seeing), being as large as 50 per Avila R., Vernin J., Sanchez´ L. J., 2001, A&A, 369, 364 cent for high-altitude layers in some generalized SCIDAR configu- Avila R., Masciadri E., Vernin J., Sanchez´ L. J., 2004, PASP, 116, 682 rations used at Teide Observatory. 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C 2010 The Authors. Journal compilation C 2010 RAS, MNRAS 410, 934–945