Optical turbulence forecast over short timescales using machine learning techniques Turchi A.a Masciadri E.a and Fini L.a

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Optical turbulence forecast over short timescales using

machine learning techniques

Turchi, A.a, Masciadri, E.a, and Fini, L.a

aINAF-Osservatorio Astroﬁsico di Arcetri, L.go Enrico Fermi 5, Firenze, Italy

ABSTRACT

Forecast of optical turbulence and atmospheric parameters relevant for ground-based astronomy is becoming an

important goal for telescope planning and AO instruments optimization in several major telescope. Such detailed

and accurate forecast is typically performed with numerical atmospheric models. Recently short-term forecasts

(a few hours in advance) are also being provided (ALTA project) using a technique based on an autoregression

approach, as part of a strategy that aims to increase the forecast accuracy. It has been proved that such a

technique is able to achieve unprecedented performances so far. Such short-term predictions make use of the

numerical model forecast and real-time observations. In recent years machine learning (ML) techniques also

started to be used to provide an atmospheric and turbulence forecast. Preliminary results indicate however an

accuracy not really competitive with respect to the autoregressive method or even prediction by persistence.

This technique might be applicable joint to atmospheric model. It is therefore interesting to investigate the main

features of their performances and characteristics (also because there is a great number of algorithms potentially

accessible) to understand if results achieved so far can be further improved using ML. In this study we focus on

a purely machine learning application to short term forecast (1-2 hours) of astroclimatic and other atmospheric

parameters above VLT.

Keywords: simulations,machine learning,forecast,optical turbulence,atmosphere,adaptive optics

1. INTRODUCTION

Accurate forecast of speciﬁc atmospheric parameters, including Optical Turbulence (OT), is becoming a fun-

damental tool for ground-based astronomy, with the complexity of the instruments growing larger and larger

toward the Extremely Large Telescope (ELT) era. OT is one of the main limiting factors for the achievement of

high angular resolution from ground-based observations, though in general the atmospheric conditions impact on

all the observations performed on top-class telescopes (e.g. Precipitable Water Vapor (PWV) limiting infrared

observations [1]). To overcome OT limitations, Adaptive Optics (A0) instruments were developed in the last

decades, however also their performance depends on the atmospheric and OT conditions, and peak correction

can be achieved only in speciﬁc and relatively rare cases of perfect weather, which depends not only on the seeing

() OT parameter, but also on the isoplanatic angle (θ0) and the wavefront coherence time (τ0) [2,3,4]. The

large adoption of Wide Field AO (WFAO) adaptive optics systems, and their growing complexity, means that in

the future the atmospheric conditions will have an even more deep impact on the scientiﬁc output of a top-class

telescope, and their ability to fully utilize their AO capabilities to approach diﬀraction-limited performance. An

atmospheric and OT forecast is thus critical in optimizing the schedule of a telescope by matching observations

with the required atmospheric condition that will allow an optimal scientiﬁc output [9]. The ALTA Center

project∗, i.e. the OT and atmospheric forecast tool supporting the Large Binocular Telescope (LBT), has seen

heavy development in recent years [5,6]. A similar forecast tool is under development for ESO’s Very Large

Telescope (VLT). Preliminary results on forecast performances are summarized in [7].

These tools are using the Astro-Meso-NH mesoscale atmospheric model [8] that simulates the whole atmo-

sphere in a limited but high resolution region centered on the telescope, and provide excellent results in terms of

accuracy (see [5] for a short summary), and typically provide long-term forecasts which are made available few

hours before sunset and covering the whole night.

Send correspondence to Alessio Turchi - e-mail: alessio.turchi@inaf.it

∗http://alta.arcetri.inaf.it

arXiv:2210.11236v1 [astro-ph.IM] 20 Oct 2022

In recent years however new forecast techniques are becoming available, which use autoregression (AR) meth-

ods to combine the long-term forecast of mesoscale models and the telemetry data coming from the telescope

sensors, and are able to provide short-term forecasts over a window of 1-4 hours, regularly updated during the

night of observations [5].

Short-term AR aided forecasts are able to provide a huge gain, in terms of forecast error, on all the parameters

interested by this kind of prediction [5], though being limited to few hours in the future, and allow the telescope

operations to think about a diﬀerent kind of planning. A ﬁrst implementation of such strategy is currently

present in the ALTA project.

Other studies focused on implementing an OT forecast purely based on machine learning (ML), without the

input from an atmospheric model (which is based on physics), relying only on the measurements made available

from the telescope instruments and monitors [9]. These methods seem to provide a limited accuracy with respect

to the previously mentioned AR short-term forecasts, and share the same limitations on the future forecast win-

dows of very few hours. Despite this the implementation of such tools is very preliminary and it’s worth studying

their performances in order to explore their capabilities. The present paper is dedicated to this latter aspect.

Also any knowledge accumulated with these tools could prove instrumental in increasing the performances of the

already implemented short-term predictions, which huge beneﬁt for the telescope planning and scientiﬁc output.

In this contribution we will concentrate our attention on the Random Forest (RF) ML algorithm as it has

been already used for atmospheric forecasts [9]. We investigate the feasibility of a forecast of Optical Tur-

bulence (astroclimatic) parameters (seeing, wavefront coherence time (τ0), Isoplanatic Angle (θ0) and Ground

Layer Fraction (GLF), that is the C2

Nfraction at ground, and atmospheric parameters (Temperature, Relative

Humidity, Wind speed and direction), by using only instrument data from the telescope telemetry. This study

focuses on the VLT telescope and make use of data obtained from the Ambient Condition Database provided

by ESO†, which by far is one of the most complete collection of telemetry data with a wide range of measured

parameters with diﬀerent sensors, without any input from the long-term mesoscale model forecast. Speciﬁcally,

we are interested into characterizing the behaviour of the ML method with respect to diﬀerent parameters such

as the training sample length and a variation of the sampling temporal frequency of dataset. We also test two

diﬀerent applications for 1-hour and 2-hour future forecast, which are the most relevant for telescope real-time

applications. The aim is to evaluate the reliability of the ML method itself and pave the way to more complex

applications, which may also make use of input parameters coming from an atmospheric forecast model. We are

interested in identifying and characterizing the constraints imposed by the ML method. For the sake of simplic-

ity, in this preliminary study we use the RMSE error as the sole indicator for the forecast performance. Once

the methods and the optimal input sets are selected, we will focus also on the LBT telescope implementation

in future studies. We refer to ESO database for an in-detail explanation of all the parameters treated in this study.

2. ALGORITHM AND INPUT SET DEFINITION

ML saw a huge development in the last decades of XX century and rose to a widespread usage in the ﬁrst decades

of XXI century. The term can be used as a general hat to cover diﬀerent disciplines from Artiﬁcial Intelligence to

Neural Networks and Computational Statistics. In general we refer to ML techniques when based on algorithms

that make use of heterogeneous data to automatically “learn” and build a “model” that is used to produce a

desired output, using statistical methods. While a general discussion on the several categories of ML methods is

out of the scopes of this paper, in order to perform an atmospheric and OT prediction we are interested in the

broad class of Supervised methods, that is algorithms that are trained over pre-given set of inputs and outputs.

Among this general category, algorithms can be divided into Classiﬁers, that is methods that predicts general

categories as an output (e.g. bad/good seeing) and Regressors, that instead produce a real number (i.e. the

value of the seeing). This paper focuses on the Random Forest (RF) algorithm [10], already used in previous

similar studies [9]. The RF algorithm is one of the simplest yet robust methods that can be implemented, and

†http://archive.eso.org/cms/eso-data/ambient-conditions.html

thus is our choice for this initial investigation of the problem. The algorithm used in this study can be used as

both Classiﬁer or Regressor, however we will limit to the Regressor case for the sake of simplicity, leaving the

study of Classiﬁers to a future paper.

Random Forest Regression algorithm [10] is a decision-tree based method that tries to overcome the limita-

tions of its simpler cousins (namely overﬁtting of the training set) by averaging the result over several trees. In

the present study we selected 200 trees for the RF, seeing almost no beneﬁt in using more in terms of statistical

variation of the output. We used the scikit-learn implementation of RF [11] in this study.

RF operates by training the decision trees over a training set of input data by minimizing the mean squared

error between the produced output and the given pre-known output, while the performances are validated on a

testing set which is independent from the training one, and where previous knowledge of the output is not given

to the algorithm.

We focus in this contribution over 1-hour and 2-hour future forecast time scale. We remember that a diﬀerent

training has to be associated to a precise time scale forecast. Example: if one wants to perform forecasts at

a 2h time scales, he has to perform a training speciﬁc for that time scale. Our RF implementation executes a

forecast at each time available in the data (i.e. every 5 min if this is the sampling time), using 1 or 2 hour past

measurements as an input, respectively to forecast 1 hour or 2 hours in the future. These past data buﬀers must

have continuous consecutive data points (i.e. no holes) in order to successfully perform the forecast. We test the

performance of the method by comparing the RMSE averaged over all the forecasts computed on the test dataset.

Taking inspiration from Milli, J. et. al. [9], we decided to start by selecting the same set of input parameters.

Milli’s paper also make use of wind speed measurements at 200mb (jet stream level), however such measurements

are not available in ESO database and are technically complex to obtain, so the impact of 200mb wind is evaluated

separately. To do so we selected a limited data period from 2018-08-01 to 2019-08-01, with the training set from

2018-08-01 to 2019-02-01 (0.5 years) and Test set from 2019-02-01 to 2019-08-01 (0.5 years), where we managed

to obtain 200mb wind speed data from simulations done with a mesoscale model, since this solution has already

proven able to reconstruct the vertical proﬁle of the wind with extreme precision [12,13]. In Fig. 1we report

the results of this test, that show negligible diﬀerence in model performances (order 10−3), in terms of RMSE,

so we decided to remove the 200mb wind speed from the rest of the analysis.

Milli’s paper also adds a cyclical representation of the day of the year (sin/cos(sin/cos(Day of Year/365),

numbering each day from 1 to 365) and of the hour of the day (sin/cos(Hour of Day/24), numbering each

hour from 1 to 24), which helps the ML algorithm to build correlations with seasonal and daily variations of

meteorological parameters and have a little but not negligible eﬀect, as shown in Fig. 2.

The full set of input parameters used in this paper to forecast OT parameters (seeing , isoplanatic angle θ0,

wavefront coherence time τ0,C2

Nfraction at ground (GLF), is reported in table 1. The input set used to forecast

atmospheric parameters (temperature, relative humidity (RH), wind speed at 30m (WS) and Wind direction at

30m (WD), is reported in table 2.

3. FORECAST WITH RANDOM FOREST ALGORITHM

The ﬁrst test that we are interested to perform is to understand how the performance of the RF algorithm

changes with the length of the dataset used to train the method. For this purpose we selected data from diﬀerent

training sets deﬁned in tables 3for atmospheric parameters (left table) and OT parameters (right table). This

test is fundamental to understand how much past data is requested to saturate the ML performance.

We were forced to select diﬀerent periods for atmospheric and OT parameters training sets because OT monitor

instruments (DIMM and MASS) were updated after April 2016, thus forcing us to use a smaller sample for OT

forecasts in order to have homogeneous measurements taken with the same instrument. For this initial test we

decided to perform a resampling average over 5 minutes for all the input data.

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OpticalturbulenceforecastovershorttimescalesusingmachinelearningtechniquesTurchi,A.a,Masciadri,E.a,andFini,L.aaINAF-OsservatorioAstrosicodiArcetri,L.goEnricoFermi5,Firenze,ItalyABSTRACTForecastofopticalturbulenceandatmosphericparametersrelevantforground-basedastronomyisbecominganimportantgoalfortel...

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Optical turbulence forecast over short timescales using machine learning techniques Turchi A.a Masciadri E.a and Fini L.a

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