Forecasting Wavefront Temporal Characteristics

 

Will the adaptive optics system be fast enough to follow the wavefront temporal evolution?

The atmospheric seeing, expressed as the FWHM of a long exposure image at an aberration free telescope (FWHM $\approx \lambda / r0$) is the cumulative effect of numerous sheets of refractive index perturbations all the way from about 20 km altitude down to the telescope enclosure (dome, mirror and instrument seeing are excluded from this memo as they will be from the VLT observatory). Each turbulence sheet at altitude h has its own r0(h) and moves with the wind at a velocity v(h) in the direction $\theta(h)$. If each sheet bears a fraction $\alpha(h)$ of the total turbulence (as r0 varies as the 3/5 power of the turbulence, we have $\alpha(h)= [\frac{r0} {r0(h)}]^\frac{5}{3}$), the resultant wavefront corrugations horizontal velocity at ground level is

$$V0=[\sum \alpha(h) \vec{v}(h) ^{\frac{5}{3}}]^{\frac{3}{5}}$$ (2)

and the coherence time will be proportional to the time needed for the wavefront to move by one coherence cell:

$$\tau 0 \approx 0.3 \frac{r0}{V0}$$ (3)

It is thus clear from Fig. 7 that for a given seeing vertical distribution V0 will be much larger -and $\tau_{o}$ much smaller- during austral winter. Moreover, 24-hour ECMWF predictions of wind velocity would as such, even with the 46% error displayed in Table 8, allow to classify the next night as potentially slow or rapid. Moreover, considering the rather high correlation coefficients given in Table 7, it is believed that a statistical post-processing of the same type as described in Section 3.1 could also recover part of the systematic forecast errors.

 

2||c|| 2c||m/s

$$\mid \mid$$ site & hour ECMWF corr err

Antofagasta Analysis 0.918 -0.36 2.11

12GMT 24h For. 0.813 -3.36 4.31

48h For. 0.781 -0.24 5.09

Quintero Analysis 0.854 1.04 4.26

12GMT 24h For. 0.785 0.95 6.13

48h For. 0.748 1.05 7.24

 

2|c||Antofagasta 2c||Quintero

1993 89-93 1993 89-93

Analysis 20% 21% 52% 31%

24h For. 48% 46% 98% 62%

48h For. 63% 58% 118% 80%