Low-visibility conditions enforce special procedures that reduce the
operational flight capacity at airports. Accurate and probabilistic forecasts
of these capacity-reducing low-visibility procedure (lvp) states help the
air traffic management in optimizing flight planning and regulation. In this
paper, we investigate nowcasts, medium-range forecasts, and the
predictability limit of the lvp states at Vienna International Airport. The forecasts are
generated with boosting trees, which outperform persistence, climatology,
direct output of numerical weather prediction (NWP) models, and ordered
logistic regression. The boosting trees consist of an ensemble of decision
trees grown iteratively on information from previous trees. Their input is
observations at Vienna International Airport as well as output of a high resolution and an
ensemble NWP model. Observations have the highest impact for nowcasts up to a
lead time of

Low-visibility conditions require special procedures to ensure
flight safety at airports. These procedures slow down the air traffic and
result in a reduction of the operational airport capacity, leading to mean
economic loss for airports and airlines. In this study, we generate
predictions of low visibility at thresholds that directly connect to the
capacity-reducing procedures at Vienna International Airport. Accurate nowcasts of these
low-visibility thresholds can help in reorganizing flight plans and reducing the
economic losses. These forecasts, however, are not only important for flight
plan reorganizations. They also have an impact on long-term flight planning
to avoid expensive short-term reorganizations. This paper therefore focuses
on nowcasts with lead times from

Generally, low-visibility forecasts are generated with two different
approaches

Statistically based visibility forecasts were investigated first by

The operationally relevant visibility information for flight management is
the low-visibility procedure (lvp) state, a combination of
visibility and ceiling, which directly connects to capacity reductions at
airports. It was forecasted first by

The focus of this paper is therefore on determining the skill and most
important model predictors for lvp nowcasts up to a lead time of

Six years of data (November 2011–November 2017) are available to produce and evaluate forecasts, which result in 1177 observations when considering the cold season (October–March) at 06:00 UTC only. The forecasts are developed for one specific touchdown point at Vienna International Airport and consist of observations at Vienna International Airport and NWP model output. All observations used are measured close to the examined touchdown point.

The NWP model data used for forecast generation are from the atmospheric
high-resolution (HRES) model and the ensemble prediction system (ENS) of the
European Centre for Medium-Range Weather Forecasts (ECMWF). The HRES model
provides forecasts with hourly output until a lead time of

The ENS provides forecasts up to a

The response is the lvp state, which is
an ordered categorical variable that comes into effect when certain
horizontal and/or vertical visibility thresholds are crossed at airports. The
horizontal visibility thresholds are determined by observations of the runway
visual range (rvr), defined as the distance over which the pilot of
an aircraft on the centerline of the runway can see the runway surface
markings or the lights delineating the runway or identifying its centerline

The number of lvp states and their threshold values vary with the
location, size, and technical equipment of the airport. Vienna International Airport has
four different lvp states. Table

Definition of the lvp states with their thresholds in runway visual range (rvr) and ceiling (cei), their climatological occurrence probability, and their maximum operational capacity utilization for Vienna International Airport. The climatological occurrence probability is computed during the cold seasons (October–March) from November 2011 to November 2017 at 06:00 UTC.

The model predictors consist of observations and output of NWP simulations.
The observations used are the predictors that

The NWP model outputs used as predictors (Table

Some of the statistical models use a combination of observations and NWP
output as predictors. Observations are at points or along lines and as such
have larger variability than grid values of NWP output. Also the NWP errors
are larger due to model uncertainty and representation error

Observations, climatological information

To forecast the lvp state, we require models that are able to deal with ordered response variables. Ordered logistic regression (OLR), which projects the response by combining multiple linear features of the predictor variables, is a well-known statistical method for predicting ordered response variables. Another possibility is decision-tree-based ensemble modeling consisting of multiple merged decision trees. Decision-tree-based ensemble models allow interactions and – in contrast to the parametric OLR models – nonlinear effects.

Tree-based boosting is an ensemble method that often achieves rather accurate forecasts based on relatively simple base learners. More specifically, the approach develops the final model iteratively by repeatedly fitting a base learner to the model gradients from the previous iteration. Typically, the base learner is a simple statistical model with low computational cost, such as decision trees.

Classical decision trees partition the predictor space into several regions,
depending on the correlations between the response and the predictor
variables, and fit a constant model to each terminal region. They are
particularly appealing as base learners in boosting because they can
naturally capture nonlinear patterns and interactions, handle predictors with
different scales (continuous, ordinal, and nominal), and are invariant under
monotone transformations of predictor variables

In this investigation, we employ the component-wise gradient boosting
algorithm suggested by

To estimate the prediction function

Set

Increase

Fit the gradient vector

Update the predictor function

Recompute the sum of the negative log likelihood

Iterate steps 2–5 until a stopping criterion for

An additional benefit of boosting decision trees is the automatic selection of the predictors with the highest impact on the response, which is based on the automatic selection of split variables in the decision trees. Moreover, the number of terminal nodes can be used to specify the interactivity of the predictors in the trees. The combination of the additive structure of the boosting algorithm and the nonparametric structure of the trees makes boosting trees into a powerful alternative for predicting ordered response variables.

The described algorithm is implemented in the R package mboost

The benefits of the boosting tree forecasts can be assessed by reference models. In this study, we apply several references, since their competitiveness changes with different lead time ranges.

A widely used benchmark reference for short lead times is the
persistence model

At the long end of the forecast horizon, climatology is a competitive reference model. Climatology always predicts the distribution of the response in the training sample.

For the comparison of the boosting tree performances to other statistical
models, we use
OLR, a well-known model for
ordinal responses.

Another reference is direct output of the ECMWF NWP model, which has included visibility since May 2015 and ceiling since November 2016. Thus, the predicted lvp state can be computed directly from the NWP model output for one cold season (2016–2017). For the HRES model, only deterministic lvp state forecasts can be computed because the model consists of one member only. The ENS model, however, consists of 50 members, and therefore probabilistic forecasts can be derived by merging the predictions of all 50 members.

The performance of probabilistic forecasts of ordered response variables,
such as lvp, can be assessed by the ranked probability score

To determine the performance of a particular model, all scores from the
individual forecast–observation pairs are averaged. For comparison of the
model score relative to a reference model, the ranked probability skill score
(RPSS) is used:

Bootstrapping is used to assess model uncertainty. We generate 1000 data samples, each with randomly drawn out-of-sample scores from the six cross-validation blocks with replacement. The size of each sample is identical to the overall number of forecast–observation pairs. After bootstrapping, the mean RPS is computed for each sample. The distribution of these mean scores describes the model uncertainty.

To provide useful information on the working process of the models and to
determine their most important inputs, a variable importance measure is
required. We use permutation accuracy importance, which

Moreover, to extract meaningful information on the most important predictors, permutation importance is conducted on each cross-validated sample. Afterwards, the results from the different samples are averaged to show the mean impact of each predictor on the forecast.

This section is about lvp state forecasts with lead times from

The performance of the boosting trees with different predictor setups and the
references persistence and climatology is given in
Fig.

Forecast performance of boosting tree models and the references
OLR, persistence, and climatology. The statistical models are based on
observations (OBS), NWP model output of the deterministic HRES ECMWF model
(HRES), and their combination (OBS+HRES). The forecast validation time is
always 06:00 UTC. Models with a lead time of

The boosting trees based on the HRES output also outperform climatology up to
a

The best performing boosting trees are the ones with the combined predictor
setup. With nowcasts of up to a

To analyze the performance of the boosting trees relative to other
statistical models, we compare them to OLR. Figure

When using only observations or HRES model output as predictors, the boosting trees perform again better than OLR, however with a lower improvement compared to the combined predictor setup. The reason for the higher improvement in boosting trees with the combined predictor setup is the integrated variable selection algorithm of the decision trees in the boosting model. Hence, only predictors that improve the predictive performance of the model are selected for forecast generation. In contrast, all available predictors are used for the forecast generation with standard OLR, as augmenting this model with automatic variable selection techniques would either be computationally intensive (e.g., stepwise or subset selection) or necessitate switching to another estimation technique (e.g., lasso instead of standard maximum likelihood).

The high variability in the RPSS analysis indicates the high complexity of
predicting lvp states. Generally, fog can arise and dissipate with small
atmospheric changes, leading to big challenges in forecasting this parameter
numerically

Predictions of the models with the combined predictor setup are best overall; however, they also have the highest variability. Their forecasts are affected by many predictors and lead to stronger varying forecasts for the particular models due to the varying weights of the predictors. To provide information on the most important predictors with different lead times, variable importance analysis is applied.

The predictors with the highest impact on the forecast are analyzed with
permutation importance applied to the boosting trees with the combined
predictor setup (Sect.

Predictors of Table

Forecasts with a lead time of

The impact of observations decreases strongly for nowcasts with lead times
from

As the forecasting horizon increases from

The performance of models with the combined predictor setup converges to
HRES-based models at lead times longer than

Medium-range forecast performance of boosting trees based on HRES
and ENS information, and the reference models with
their uncertainty (boxes show the 25th to 75th percentile range, and whiskers show the 5th to
95th percentiles).

Figure

The performance of the boosting trees and climatology is shown in
Fig.

In order to obtain more information of the benefit of the statistical models, we compare them to the raw output of the NWP models. The raw lvp state is computed from the visibility and ceiling of the NWP model output. Since ceiling has been only available from November 2016 on, an out-of-sample comparison between the forecasts of the statistical models and the raw NWP model output is computed between December 2016 and November 2017 (cold season only). We therefore train the boosting trees with cold season data from December 2011 to November 2016 and compare their performance with the raw NWP model output for the remaining period.

Figure

HRES-based raw output performs better than climatology only up to

Predictors of Table

The most important predictors for statistically based medium-range lvp
forecasts are again analyzed with permutation importance.
Figure

Dew point depression (dpd) has highest impact for both models with a

When the skill of the model forecasts over climatology decreases, the number
of predictors with an impact on the forecast also decreases. In HRES-based
models, only one predictor has an influence on predictions with

Predictions of lvp (low-visibility procedure) states have been developed for
flight planning with different horizons using boosting trees. The lvp state,
which is the relevant variable for flight regularization due to low
visibility at airports, is categorical and consists of multiple thresholds of
horizontal and vertical visibility. Former studies predict the horizontal and
vertical visibility separately, which then can be combined by the air traffic
management

Short-term regulations are defined with predictions up to the next 2 h, which are most important for the flight controllers. These forecasts are the most accurate ones and are mainly driven by latest observations of the lvp state, dew point depression, and visibility.

For reorganizations of flight plans, the air traffic management can use the
predictions with lead times from

Long-term flight planning requires medium-range forecasts with lead times
longer than

The ECMWF NWP models also provide information on visibility and
ceiling. Both
variables can be used to predict lvp directly. However, these variables are
not included in the statistical models because their data archive is too
short. Comparisons between direct lvp state forecasts from the NWP models and
the boosting trees were made for one cold season and just showed a small
difference in the performance between a

In summary, we saw that probabilistic lvp forecasts based on boosting trees
have a benefit over all reference models until a lead time of
approximately

The complete statistical modeling is based on the software
environment R

For lvp state forecasts at Vienna International Airport, the log likelihood

RPSS comparison between boosting trees
and ordered logistic regression for lead times from

The concept of this study was developed by all authors together. SJD conducted the majority of this paper, including statistical modeling, model evaluation, and paper writing. PK supported the statistical modeling and evaluation. GJM contributed meteorological expertise, while AZ contributed expert knowledge to statistical modeling. All the authors collaborated in discussing the results and commenting on the manuscript.

The authors declare that they have no conflict of interest.

This study has been supported by the Austrian Research Promotion agency FFG 843457 and the PhD scholarship of the University of Innsbruck. We want to thank Markus Kerschbaum, Andreas Lanzinger, Martin Steinheimer, and the meteorologists at Vienna International Airport for helpful discussions as well as Caren Marzban and Julie Bessac for their very constructive suggestions. Moreover, we thank the Austro Control GmbH for providing access to the observation data and the Zentralanstalt für Meteorologie und Geodynamik for providing the ECMWF data.

This paper was edited by Francis Zwiers and reviewed by Julie Bessac and Caren Marzban.