This paper presents an example of the usage of ensemble weather forecasting for the control of satellite-based communication systems. Satellite communication systems become increasingly sensitive to weather conditions as their operating frequency increases to avoid electromagnetic spectrum congestion and enhance their capacity. In the microwave domain, electromagnetic waves that are conveying information are attenuated between the satellite and Earth terminals in the presence of hydrometeors (mostly rain drops and more marginally cloud droplets). To maintain a reasonable level of service availability, even with adverse weather conditions considering the scarcity of amplification power in spacecraft, fade mitigation techniques have been developed. The general idea behind those fade mitigation techniques is to reroute, change the characteristics or reschedule the transmission in the case of too-significant propagation impairments. For some systems, a scheduling on how to use those mechanisms some hours in advance is required, making assumptions on the future weather conditions affecting the link. To this aim the use of weather forecast data to control the attenuation compensation mechanisms seems of particular interest to maximize the performances of the communication links and hence of the associated economic value. A model to forecast the attenuation on the link based on forecasted rainfall amounts from deterministic or ensemble weather forecasting is presented and validated. In a second phase, the model's application to a simplified telecommunication system allows us to demonstrate the valuable contribution of weather forecasting in the system's availability optimization or in the system's throughput optimization. The benefit of using ensemble forecasts rather than deterministic ones is demonstrated as well.

Since a few decades ago, satellites have become absolutely essential in modern society. Their field of application is expanding constantly. Nowadays, they are widely used in various areas such as navigation, weather forecasting, disaster management or telecommunications. In fact, geostationary telecommunication satellites can offer global coverage, which makes them particularly attractive for bringing broadband Internet in isolated areas where the access to terrestrial networks remains very limited.

The data transmitted from satellites to Earth are conveyed by radio waves
whose frequency is comprised between 1 and 40 GHz. Frequencies within this
range are classified into frequency bands, dedicated to specific applications
for satellite communications but also shared with other systems as fixed
terrestrial wireless systems, microwave remote sensing instruments, radar or
positioning systems. These frequency band labels (L, S, C, X, Ku, Ka and Q/V)
are detailed in Table

Frequency bands used for satellite communications. More details in

To increase the overall capacity of communication satellites (and hence the
number of users of the system and/or the offered data rate), the use of the
Ka and Q/V bands, for which large modulation bandwidths are available, is
becoming widespread among operational systems. However, the possibility to
transmit data at a given data transmission rate is also dependent on the
power level of the electromagnetic wave received by the terminal. An
insufficient power level will result in data loss. Power losses between the
satellite and the Earth terminals are mostly caused by the dilution of the
wave in space during its propagation and by some atmospheric phenomena. In
particular, atmospheric gases and more importantly the presence of
hydrometeors attenuates electromagnetic waves. The scattering theories
(Rayleigh or Mie) tell us that the level of the attenuation depends on the
ratio between the hydrometeor diameter and the wavelength

Figure

Attenuation that exceeded 0.1 % of the time computed from

The margins required in some areas to maintain the communication 99.9 % of
the time can reach 30 dB at Q/V band in mid-latitude areas and even more in
tropical areas. In other terms, it means that to ensure the availability of
the link with a 99.9 % probability, a power 1000 times higher than the one
required to maintain the link without rain is needed. As the power onboard of satellites is a scarce resource, techniques to adaptively mitigate the
impairments have been developed

Other techniques require a forecast of the attenuation some hours in advance
in order to prepare and to optimize the link configuration through the
telecommand of the satellite. In this respect, the use of meteorological
forecasts constitutes a promising approach to control the decision process
associated with those fade compensation mechanisms. This has, for instance,
been studied in

To increase the attenuation prediction skill, probabilistic precipitation forecasts based on ensemble predictions could be used as long as cost–loss models are known and available.

The objective of this paper is to propose and describe a fully probabilistic
approach to forecast rain attenuation by forecasting the probability of
exceeding a given rain attenuation level rather than a deterministic value.
To this aim ensemble prediction systems

The organization of the paper is the following. The first section is devoted to the description of the model, where the different steps to obtain rain attenuation probability distributions conditioned to ensemble forecasts from Météo-France are described. In the second section, various scores are analyzed to assess the relevance of the proposed attenuation model. In the last section, the performances of the forecasts to maximize either the link capacity, the link availability or both are analyzed, considering concurrently measured attenuation data and the simulation of a simplified communication system.

To develop the forecast model, it is needed to relate actual rain attenuation data to precipitation forecasts. The data used to this aim are detailed in a first part of this section. The elaboration and the development of the model is detailed in a second stage.

The attenuation due to rain on an Earth–space link can be characterized by measurement on Earth of power fluctuations of beacon signals (unmodulated signals) emitted by satellites. As the signal transmitted by the satellite has a constant power, the fluctuations of the received power are linked to the fluctuations of the tropospheric fade undergone by the signal during its propagation. Furthermore, the temporal scales of variation of water vapor, oxygen, clouds and rain attenuations differ significantly, which allows us to discriminate the various contributors to the tropospheric attenuation. In particular, the rain attenuation by large dominates the total attenuation and can easily be deduced from the fluctuation of the beacon. Another possibility is to isolate the attenuation due to rain from the other components using concurrent radiometric measurements, which can be used to quantify clouds and gaseous attenuation.

ONERA conducts its own measurement campaigns analyzing the 20 GHz (Ka band)
beacon signal of the Astra 3B geostationary satellite in various experimental
facilities. Throughout the years 2014 and 2015, Ka band attenuation
measurements were collected for two receiving sites located in Toulouse,
France (latitude 43.5

Ka band attenuation measurements operated by ONERA in
2014

Those rain attenuations have been used as predictands in the statistical model
discussed in Sect.

The probabilistic precipitation predictions are built upon the sampling using
the French global ensemble PEARP

The temporal variability of attenuation due to rain is high (5 min) compared
to the time resolution of the model forecasts (3 h). It would not make sense
to average rain attenuation data on a 3 h basis. Furthermore, this would
dramatically reduce the size of the training dataset used to compute the
complementary distribution function of attenuation conditioned to the PEARP
forecasts. The strategy adopted in order to provide a statistical link
between predicted rain amount and rain attenuation is the following. First,
we select all members of the PEARP forecasts archived in 2014 and 2015 around
the receiving station of interest. In some cases the weather forecast is
realistic, but even a slight phase error may lead to the double-penalty
problem

Probability of exceeding the attenuation threshold given in abscissas based on data recorded in 2014 and 2015 in Toulouse, France.

In the operative context, the goal will be to represent the future state of
the channel by a unique predictive attenuation distribution. Yet the PEARP
forecasts are constituted of 70 members. Each of these members leads to the
selection of a specific complementary distribution of rain attenuation. A
methodology must be defined in order to obtain a single probabilistic
estimation of the rain attenuation occurring in future. The formula of total
probability is written as follows:

This methodology is equivalent to averaging the 70 rain attenuation
distributions. An illustration is presented in Fig.

Probability of exceeding the attenuation threshold given in abscissas. Two distributions are selected according to the value of two ensemble members (black and green lines). The gray line stands for the average of those two distributions.

The use made of this predictive attenuation distribution will depend on the application of interest. One possible use is to get the attenuation threshold exceeded to only 0.1 % of the time, which is the tolerated unavailability threshold. This attenuation threshold is equivalent to the power margin required to prevent inappropriate communication interruptions.

The low spatial and temporal resolutions of the PEARP archives used for the learning process may cast some doubt on the utility of the attenuation forecasts. An appropriate use of the model requires an evaluation of its potential as well as weaknesses. A probabilistic forecast model is expected to present reliability and resolution. The reliability assesses the ability of a model to provide a probabilistic prediction of a given event close to the observed frequency of the same variable. The resolution is the ability to discriminate between events and nonevents.

Only scores based on binary events are considered here. In the first stage, the
reliability of the attenuation forecasts is addressed using the reliability
diagram and the rank diagram, also known as the Talagrand diagram. Resolution
is evaluated using receiver operating characteristic curves, referred to as
ROC curves hereafter, and sharpness diagrams. The scores proposed here are computed
using the available observations and model outputs over the 2-year period
defined above. Nevertheless, in order to evaluate the possible overfitting of
the statistical model, a bootstrapping approach is used:

The reliability of an ensemble model characterizes its ability to provide
forecast frequencies consistent with the observed ones. For example, let us
assume that the forecast system provides, for a particular event, a
probability of occurrence of

The reliability diagram consists in plotting the observed frequencies against the forecast probabilities, previously classified into a few bins. For perfect reliability, the curve must merge with the diagonal line. A reliability curve located to the right of the diagonal line is typical of a model overestimating the probability of the event. Similarly, a model systematically underestimating the probability event presents a curve located to the left of the diagonal line. It is also conventional to represent the climatological probability of the event in the forecast by a vertical line and the climatological probability of the event in the observation by a horizontal line. The last one brings complementary information on the model resolution. A forecast which provides the effective climatological probability has no ability to discriminate between cases of event and cases of nonevents, and this means that it has no resolution.

In the following sections, a positive event will be defined as the overrun of
an attenuation threshold

Reliability diagrams showing observed relative frequency as a function of forecast probabilities for attenuation thresholds 1 dB (blue), 3 dB (green) and 6 dB (red). Inset boxes indicate the frequencies of use of the forecasts. The dotted lines represent the climatological probability. By convention, the horizontal dashed line represents the climatological probability of the event in the observations. The vertical dashed line represents the climatological probability in the forecast.

First of all, high probabilities are rarely met for those precipitation thresholds. That is why only low probabilities are shown. The shape of the reliability curves meets the expectations: the observed frequencies grow with the forecast probabilities and the curves deviate little from the diagonal line. This reflects the reliability of the attenuation forecast model and confirms its value for the forecast of the exceedance of attenuation thresholds. However, the reliability of our statistical model is not perfect; while low probabilities tend to be underestimated, high probabilities tend to be overestimated.

Rank histogram, also called Talagrand diagram, of probabilistic attenuation forecasts.

Block diagram of the discrimination process between positive and negative forecasts.

Another useful tool for determining the model reliability without
considering thresholds is the rank diagram, also known as the Talagrand
diagram

Resolution is another desired quality we expect from a probabilistic
prediction. The Brier score decomposition tells us that resolution is the
difference between the curves of Fig.

Another approach to address the resolution as well as the value of a
probabilistic prediction is to draw receiver operating characteristic
curves. ROC graphs are widely used, particularly in the area of medicine

ROC curve obtained averaging the 100-fold cross validation for
attenuation thresholds set to 1 dB (blue), 3 dB (green) and 6 dB (red).
The box plots indicate the standard deviation of each point. The diagonal
line corresponds to random forecasts. If the curve is far from the diagonal,
there is a high level of performance. The forecast probability

The true positive rate

The false positive rate, also called the false alarm rate

The ROC curve is a plot of

Confusion matrix for ROC curves construction.

As described in Sect.

Figure

Let

Based on the process described in Fig.

It should be stressed that the departure from the diagonal of the ROC curve
is equivalent for the three used values of

When the costs of false alarms and those of non-detection are in the same
order of magnitude,

In the previous part a methodology to develop a statistical forecast model of
rain attenuation based on numerical weather forecasting has been detailed and
evaluated. This final part is devoted to the description of methodologies for
the optimization of the offered capacity or of the economic value for a
predetermined user-oriented service offer. Both proposed methods use the
attenuation forecast model outlined in Sect.

As detailed in Sect.

Extract of possible modulation and coding schemes (MCSs) as defined in the
Digital Video Broadcasting – Satellite second-generation (DVB-S2X)
standard

In order to maintain the link even in adverse propagation conditions without
the need of radiating more power, an alternative is to adapt the link data
rate to the weather conditions. The idea is to modify the modulation and
coding used to carry the information as the tropospheric attenuation is
varying. Here, the purpose is not to detail the modulation and forward error
correction coding techniques. More information can be found in

The characteristics of some of the MCSs that are used in the following of the study
are listed in the Table

The capacity characterizes the data amount, in gigabit here, transmitted each
second on the RF channel. An attenuation threshold

To result in a valid transmission, the attenuation threshold noted

It is understood that an inaccuracy in the estimation of the tropospheric attenuation leads to an inadequate selection of the MCS, which can have significant consequences on the performances of the link. In case of overestimation of the tropospheric fading, a less efficient MCS than the one allowed by the real propagation conditions is selected. The difference between the capacity offered by the achievable MCS and the one used is lost. In case of underestimation, the selected MCS no longer guarantees the power margin required to face the propagation impairments. Such a scenario inevitably leads to the interruption of the communication, namely to the unavailability of the link and a null capacity. Therefore, it is clear that the underestimation of the attenuation is far more prejudicial than an overestimation.

To illustrate this it can be assumed that the attenuation of the link reaches
2 dB. According to the Table

It is now clear that the efficiency and the availability of the satellite transmission is highly dependent on the MCS selection, based on the analysis of the propagation attenuation. Nonetheless, the propagation losses affecting the link are not always known as it requires a feedback. As a function of the available information on the state of the channel, different modulation and coding strategies can be applied. These are detailed in the next subsection.

The selection method of the MCS depends on the nature of the available
information on the propagation channel. Four different scenarios have been
considered with various assumptions on the type of information available to
control the modulation and coding of the link:

The propagation channel is perfectly known.

The channel is unknown.

Probabilistic weather forecasts are available.

Deterministic weather forecasts are available.

Proposition of coding and modulation strategies as a function of the available information on the state of the channel.

The characteristics of those scenarios are summarized in the
Table

In the first scenario, the attenuation experienced by the link is supposed to be known. The optimal strategy can be adopted, namely to dynamically select the most suitable MCS considering the current propagation conditions.

This strategy is referred to as ACM for adaptive coding and modulation
(

The second scenario assumes the total absence of information about the
propagation conditions. When it is impossible to implement ACM, a constant
coding and modulation (CCM) scheme is applied to the transmission. The
objective is to use the MCS that will be compatible with the targeted
availability. From

The third scenario makes use of the weather forecasts. The model developed
and described in Sect.

In order to assess the interest of using probabilistic forecasts over deterministic ones, a last scenario consisting in using deterministic forecasts instead of PEARP forecasts is investigated. This strategy is referred to as PCM-D strategy (PCM-Deterministic). In the following sections, the first member of the PEARP ensemble, called the control member, is arbitrarily chosen as the deterministic forecast.

The adaptive coding and modulation based scenario that relied on currently experienced attenuation is obviously the most favorable. In theory, the ACM strategy allows a perfect optimization of the capacity and highly limits the unavailability. Thus, the programmed coding and modulation strategy based on the PEARP forecasts is not expected to be as efficient as the ACM one. Here, the aim is rather to enhance the performances offered by a constant coding and modulation strategy that relies only on local climatology, without requirement of real attenuation measurements and a return link. This point is discussed in the following subsection.

As explained, the PCM strategy would be particularly suitable for the
management of low Earth orbit satellite transmissions, for which return links
are only implemented at the level of the control station, not at the level of
the receiving stations. However, the lack of Ka band measurements for low
Earth orbit satellites prevents the model from being tested in this context.
As a first step, an evaluation of the performances of the PCM strategy is
thus proposed in the context of a geostationary satellite. A Ka band
transmission line between the geostationary satellite Astra 3B and the
receiving station located in Toulouse, France, has been simulated. The four
scenarios listed in the Table

The mission parameters used for the simulation are the following: a bandwidth
of 540 MHz, an elevation of the satellite of 35

The PEARP forecasts of 2014 and 2015 have been used as the input of the PCM and the PCM-D decision algorithm. The ACM strategy has been based on the Ka band measurements of the same years, assuming an idealized adaptation of the MCS to the channel state.

The target availability has been set to 99.9 % of the communication time.
Here a bootstrapping approach has been used again. The available samples were
partitioned in 10 subsets: 6 constituting the training dataset, 4
constituting the testing set. The procedure has been repeated 100 times and
the capacities obtained have been averaged. The mean capacities obtained for
ACM, CCM, PCM and PCM-D strategies are presented in Fig.

Mean capacities obtained for a target availability of 99.9 % considered from a geostationary satellite. Comparison of ACM, CCM, PCM and PCM-D deterministic strategies. The box plots indicate the standard deviation of the data.

As expected, the best performance has been obtained for the ACM strategy, which is an upper bound. Due to limited weather forecast predictability, the proposed PCM strategy is not able to offer the same level of capacity. Nevertheless, it is clear that, with an increase of the capacity close to 17 %, this technique significantly improves the throughput ensured by a constant coding and modulation technique without any prior knowledge on the instantaneous state of the propagation channel.

It also appears that the use of ensemble forecasts outperforms the use of deterministic forecasts. The results obtained are highly dependent on the systems parameters such as the satellite elevation, the ground station location or the transmission frequency. Furthermore, the use of higher frequencies (Q/V bands) or receiving stations located in tropical areas would inevitably result in even more noticeable differences in the achievable throughputs.

So far, the methodology proposed, consisting in programming the modulation and coding using weather forecasts in advance, requires us to set a level of target availability. In fact, the MCSs are chosen in order to ensure this availability. Without this constraint, the number of perspectives would certainly be increased. In the next part, a more general approach is adopted. A decision process based on the optimization of an economic value, taking into account both capacity and availability offered, is proposed.

When it comes to the use of a probabilistic forecast, the decision to change
the link MCS or not amounts to searching the forecasted probability above which the
forecast is considered positive. In this context the issue is to find the
forecast probability

So far, the required availability of the link has been set to 99.9 % in
order to respond to the operator's needs. In such a context, the probabilistic
attenuation forecast has to be considered positive when the chance of
exceeding the attenuation threshold of interest

This requirement of 99.9 % of availability is typical for communication
satellites, since the tolerance of the final users to communication outages
is highly limited. However, it is easy to imagine further applications for
which both availability and mean capacity have to be optimized without
prerequisites on any of these parameters. The challenge in this case is to
determine the optimal decision threshold, noted

As an example, still considering the particular case of an Earth observation
satellite. The images acquired by the satellite on its path must be
transmitted on Earth as soon as a receiving station is visible. The
visibility periods of the Earth's stations are limited to a few minutes.
Especially under rainy conditions, it could happen that the data sent by the
satellite do not reach the receiving station. In this case, data are
definitively lost. It might then be sometimes more careful to temporarily store
the data in the onboard memory while waiting for the next contact with the
ground. This strategy has been evaluated in

A methodology to determine

The ROC curves introduced in Sect.

To account for the high cost of lost data and for the successfully
transmitted ones, the economic value to be maximized, noted EV, is defined in
Eq. (

Decreasing the value of

In Fig.

Evolution of the mean economic value as a function of the decision
threshold used to discriminate between positive and negative forecasts. The
mean economic values have been obtained averaging the economic values computed
following Eq. (

It appears in Fig.

This study has presented a methodology for predicting the rain attenuation which affects the satellite transmissions. The sensitivity of satellite transmission to rain becomes particularly sensitive with the ongoing trend to use high-frequency bands, from 20 to 50 GHz. The proposed model exploits the probabilistic rain forecasts of the Météo-France short-range ensemble prediction system PEARP and delivers probabilistic attenuation forecasts at 20 GHz. In particular due to the inhomogeneity (in terms of temporal resolution) of the predictand used for the model's learning process, a bias into the model was expected. It turns out that reliability diagrams show forecast frequencies close to the observed ones. The figures obtained suggest that the statistical model shows only a small remaining bias. For a more complete assessment, rank diagrams and ROC curves demonstrate the model's ability to discriminate between event and nonevent cases and to give forecast frequencies different from the climatology ones. Consequently, it can be concluded that the model shows satisfactory reliability resolution and sharpness.

In satellite communication, the main concerns are the link availability and capacity. The primary hypothesis tested in the study was that the probabilistic weather forecasts could be very helpful to maintain the high availability required by the satellite operators while optimizing the capacity as far as possible. It has been shown that conditioning the type of waveform (modulation and coding scheme) used to transmit the information to probabilistic weather forecasts allows an increase of the mean capacity of the link while ensuring the availability of 99.9 % that is usually required. It has also been proven that the benefit is higher using probabilistic weather forecasts over deterministic ones.

The link availability and capacity are highly interdependent. Within a certain limit, increasing one of these parameters is detrimental to the other one. The request of high availability inevitably results in a limitation of the capacity, which may be particularly unfortunate in some contexts. It would then be sometime profitable to be able to find the least expensive combination of these two parameters.

In the last stage, a strategy to maximize the economic value accounting for the transmitted data volume as well as for the fraction of successfully transmitted data has been proposed. This economic value could be adapted to the targeted application. For this initial attempt to optimize high-frequency band satellite transmissions from ensemble weather forecast systems, encouraging results have been obtained. It should be stressed that the application to the forecast of rain attenuation around 50 GHz, or to more sensitive ground station locations such as in tropical regions, could show more value. Unfortunately, we do not have any attenuation observations for those contexts.

It also has to be mentioned that the horizontal resolution and the temporal
resolution of the PEARP forecast are non-negligible drawbacks as well. It
would make sense to replace the global ensemble PEARP by the regional
mesoscale ensemble prediction system AROME

As a conclusion, though perfectible, the model developed allows us to
demonstrate the benefit of using ensemble weather forecasts in the field of
satellite communications. The wide range of applications of the model
developed includes the following particularly relevant weather-dependent
applications, which could be addressed in further publications:

site diversity

deep space links

Data are available from the authors upon request.

ID performed the study. PA gave guidance on the use of the ensemble weather forecasts and on the statistical evaluation of the model. NJ and BB gave guidance on the modeling of the propagation and Satcom system.

The authors declare that they have no conflict of interest.

We sincerely thank the anonymous referees for the comments and suggestions on the earlier draft of this discussion paper. Edited by: Vassiliki Kotroni Reviewed by: two anonymous referees