2.1

Generalized DIMM: GDIMM

The Differential Image Motion Monitor¹⁷ (DIMM) is a well known and widely used instrument because of its simplicity. It is based on a small telescope with an entrance pupil made of 2 small sub-apertures (6cm diameter) observing a bright single star with a short exposure time. The Generalized DIMM¹⁰ (GDIMM) is a DIMM updated by adding a third sub-aperture at the entrance pupil (see Fig. 2). This third sub-aperture (10cm diameter and 4cm central obstruction) allows the instrument to deduce the isoplanatic angle and the wavefront coherence outer scale.

Figure 2.

GDIMM instrument installed on the Calern Observatory.

The most important parameter measured by the GDIMM is the seeing, which is deduced from the Angle of Arrival (AA) fluctuations of the perturbed wavefront. These AA fluctuations are measured through the two 6cm sub-apertures with the well known DIMM method.

Another important parameter for astronomy and free space optical links is the isoplanatic angle θ₀ leading to the angular distance from which the incoming wavefront is uncorrelated. It is deduced from the scintillation of a single star measured through a 10cm pupil with a 4 cm central obstruction. The principle of this θ₀ estimation method is based on the similarity of the theoretical expressions of θ₀ and the scintillation index s.^{18, 19} However, Ref. 20 shown that the scintillation can be affected by the presence of the Moon in the nearby of the observed bright star. Therefore, in such conditions, the isoplanatic angle deduced form scintillation could be also affected by the Moon light.

The most difficult parameter to measure is the wavefront coherence outer scale L₀. The GDIMM instrument uses the variances of AA fluctuations through different size sub-apertures by means of the von Karman model (see Ref. 3 for more details).

In the other hand, the coherence time τ₀ relevant for adaptive optics and interferometry, is given by , where the effective wind speed, is a weighted average of the wind speed on the whole atmosphere. r₀ is the well known Frieds parameter. Ref. 21 has shown that it is possible to deduce the effective wind speed from the temporal structure functions of the AA fluctuations.

The GDIMM instrument is fully automatic and all parameters are measured and computed in real time and are uploaded on the CATS website* (see Fig. 3). This website is daily used by observers in Calern Observatory during the observations.

Figure 3.

GDIMM results uploaded in real time on the CATS website.

2.2

The Profiler of Moon Limb: PML

The PML instrument is a profiler of the with the high vertical resolution. The is the structure constant of the refractive indexe fluctuations of the atmosphere. It gives information of the turbulence energy of each layer. The PML instrument is based on a differential method by observation of the lunar or solar limb through two sub-apertures (see Fig. 4). The Moon or Solar limb acts as a continuum of double stars with all possible angular separations required between two points to scan the atmosphere with a very fine resolution. Doing measurements on both Sun and Moon, the PML instrument gives also access to daytime measurements which are really important for free space optical links.

Figure 4.

Left: PML instrument installed on the Calern Observatory. Right: Vertical resolution reached by the PML (red) and by the forecasting tool (black) (see section 2.3)

The vertical profile of the is deduced from the measurement of the angular correlation of the fluctuation differences in the wavefront AA deduced from the motion of the Moon (or Sun) limb image. The AA fluctuations are measured perpendicularly to the lunar (or solar) limb leading to transverse correlations for different angular separations along the Moon (or Sun). For more details about the computation method, see Refs. 3, 14. Fig. 4, right, shows that the highest vertical resolution, Δh = 100m, is reached for the ground layer and it decreases progressively to Δh = 2000m for the highest layers (h > 15km).

From this vertical profile, it is easy to compute integrated parameters such as the seeing or the isoplanatic angle. This later is also deduced from AA correlations along the Moon or Sum limb²⁰ and it is not biased like the one deduced by the GDIMM with the presence of the Moon (see section 2.1).

Since 2015, the PML instrument has acquired a large database which has been used within several astronomical and optical telecommunication projects. Figure 5 shows the PML data distribution computed monthly and hourly between 2015 and 2019. It appears that there are more measurements during the summer and during the day. This is mainly due to the fact that the Moon is not always visible.

Figure 5.

PML data distribution between 2015 and 2019. Left: monthly count. Right: Hourly count.

2.3

Calern forecasting

The last tool we have developed for CATS station is the forecasting of atmospherical and turbulence conditions. We use the non-hydrostatic mesoscale model called Weather Research and Forecasting (WRF) developed in the National Center for Atmospheric Research (NCAR), USA.²² This model allow us to predict weather conditions within a tridimensional domain. From this weather forecasts we use an empirical model deduced from the analysis of balloon radio-sounding launched around the world.^{4–7, 23} This model called BDTM (Balloon Derived Turbulence Model) follows equations hereafter:

where the is the structure constant of temperature fluctuations, χ is the vertical gradient of the potential temperature θ, h is the altitude, U and V are the wind speed respectively in the direction West-East and South-North, and s is the horizontal wind shear. ϕ(h) is the vertical profile deduced empirically from the analysis of the balloons radio-sounding,

Where ‹›_m is the median value.

Finally, from we can deduce the following the well-known Gladstone’s formula and others integrated parameters (seeing, isoplanatic angle, coherence time).

where P(h) and T(h) are respectively the vertical profiles of the atmospheric pressure and absolute temperature.

Since the end of July 2019, we have implemented a fully automatic prediction tool above the Calern Observatory using the aforementioned models. This prediction cover the next 48h and upload the results on the CATS website (see Fig. 6).

Figure 6.

Calern Forecasting results available every day on the CATS website.

In Ref. 7, we have used these predictions and the CATS database to constrain the empirical model by local measurements. This upgrade, called SL (Site Learning) method, brings a real improvement as shown in Fig. 7. Indeed, regarding these plots it appears that the predicted seeing is closer to the measured one and the dispersion is lower. This SL method is continuously improved thanks to the continuous expansion of the database.

Figure 7.

Scatter plot shown as box plot of the seeing forecasted using both BDTM (left) and SL (right) method and measured with GDIMM. The box corresponds to interval between first and third quartile. Within the box, the median values is plotted. The whiskers corresponds to extrema.

The last ongoing implementation about the predictions concerns the possibility to use our large database in Machine Learning (ML) algorithms. This possibility offers the advantage to have short-terms predictions (<2h) with a better accuracy that the one obtained from forecasting models. For more detailed about this tool currently in development, see Ref. 24.

In parallel, an ongoing study tries to retrieve the vertical profiles of the outer scale L₀ from measurements and predictions of weather conditions. This work could allow us to use also a theoretical model in complement of the empirical method presented here above. The preliminary results of this study are presented by A. Rafalimanana in another paper of this ICSO conference.