24-hour ahead Temperature Forecasts

 

At which temperature should the air conditioning of the enclosure be preset during the day so that the telescope and primary mirror are in thermal equilibrium with the outside air at the beginning of the next observing night?

A chronologically first, non meteorological approach was to train some statistical engine on the large database available for ESO sites. An internal study was conducted ([Aussem 94]) and led to the results presented in Table 1 where the nearest neighbor technique clearly outperforms the neural nets, in particular with regards to the fine tuning of the forecast (prediction error smaller than 0.5 Celcius in 62% of cases). However as could be expected, none of these techniques can catch weather trends leading to abrupt temperature shifts of 2 to 6 degrees in 24 hour, representing about 15% of the time at Paranal during the season studied (Summer).

Could large $\Delta T$ be better predicted using meteorological models? obviously a global model such as ECMWF has a mesh much too large (ca. 60 km) for the steep terrain surrounding astronomical sites. Such a model has to be complemented either by a statistical post-processing such as Kalman filtering, or by a local area model (LAM) implementation. The study of 4 sample years conducted by [CRS4 97] concluded that the poorness of local measurements over the pacific was limiting the accuracy of ECMWF forecasts on the Chilean coast. A LAM initialized by erroneous forecasts without injection of additional observational data could obviously not improve the detection of unpredicted weather changes coming from outside its orographic limits.

Table 2 shows however that a simple Kalman postprocessing of ECMWF 24-hour forecasts successfully cancels the forecast systematic errors (the correlation coefficient of postprocessed forecasts is as good as for the analysis). As expected postprocessing alone is not able to remove synoptic errors so that large differences between actual and forecasted temperatures still subsist. Table 3 summarizes the forecast skill at 12 hour UT at Paranal as a function of 24-hour temperature changes, it shows that 55 % -(159+158)/572- versus 40 % -(112+117)/572- of the cases are brought inside the $\pm 1$ C range, and that 84 % versus 69 % are smaller than $\pm 2$ C. These performances are very similar to the results obtained with the statistical method of Table 1, however it is believed -but not proven- that the cases corrected by either methods have little in common, so that a mixture of both techniques (as proposed on Fig. 1) would consistently improve the forecast skill.

Let us examine the forecast skill in the cases when the telescope temperature would be 2 C or more warmer than the outside air, a situation which is detrimental for observations at all wavelengths (local seeing greater than 1 arcsec in the visible). Such cases are down by a factor of 2 from 15 % -(4+11+22+46)/572- to 7.5 % -(2+3+12+33)/572-. Converting the overall temperature unbalance of Table 3 into mirror seeing with a rate of 0.5 arcsec per positive degree and 0.1 arcsec per negative degree, we obtain a yearly average mirror seeing in the first hour of observation of 0.48 arcsec with persistence (T_n=T_n-1) down to 0.35 arcsec when Kalman filtered ECMWF forecasts are used.

$$\leq 2 \leq 1 \leq 0.5$$ Prediction error (Celcius)

Best Nearest Neighbor 84% 73% 62%

Best Neural Network 71% 43% 22%

Carbon Copy t_n=t_n-1 63% 36% 19%

caption

[24-hour Ahead Statistical Prediction of Ground Temperature] 24-hour Ahead Statistical Forecast of Ground Temperature at each hour of the day: hit rate of nearest neighbor and neural network methods over 18000 observations corresponding to Summer 89-90 at Paranal. Nearest neighbor predictions were carried out on a 5-tupple set of the type [ t_n-1,t_n-2,t_n-3,p_n-1,p_n-2 ]

 

$$\vert\epsilon^{Kal}\vert \vert\epsilon^{per}\vert$$ site N r^Kal r^per r^for r^ana

La Silla 1114 1.6 0.86 2.1 0.77 0.82 0.86

Paranal 572 1.1 0.88 1.5 0.80 0.79 0.87

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KFPP Scores

Global scores of persistence

caption

[Kalman Filter correction of large temperature forecast errors] Contingency table between errors of KFPP and T_2m daily variation at Paranal during the period 89-93 at 12GMT. Sum of the counts along rows (shown in the last column of the table) is the number of times T_2m has been forecasted within an error indicated in the first column of the table itself. Sum of the numbers along a column (shown in the last row), is the number of times T_2m has had a diurnal variation within the value shown in the first row. The generic count within a cell of the table gives number of times T_2m has been forecasted within an error indicated in the corresponding cell of the first columns when the daily variation of T_2m was that indicated in the corresponding cell of the last row.