Aviation Safety Paper on Operations Under Meteorological Hazard with Early Detection

Atmospheric Research 258 (2021) 105620

Available online 13 April 2021 0169-8095/© 2021 Elsevier B.V. All rights reserved.

On the characterization of mountain waves and the development of a warning method for aviation safety using WRF forecast

J. Díaz-Fernández a, *, P. Bolgiani a, D. Santos-Muñoz b, c, M. Sastre a, d, F. Valero a, e, L. I. Sebastián-Martín d, S. Fernández-González c, L. López f, M.L. Martín d, e

a Department of Earth Physics and Astrophysics, Faculty of Physics, Complutense University of Madrid, Madrid, Spain b High Resolution Limited Area Model Consortium (HIRLAM), Spain c State Meteorological Agency (AEMET), Madrid, Spain d Department of Applied Mathematics, Faculty of Computer Engineering, University of Valladolid, Valladolid, Spain e Institute of Interdisciplinary Mathematics (IMI), Complutense University of Madrid, Madrid, Spain f Atmospheric Physics Group, IMA, University of León, León, Spain

A R T I C L E I N F O

Keywords: Mountain waves Icing Wave clouds WRF model Warning method Decision tree

A B S T R A C T

Mountain wave and icing episodes are adverse meteorological conditions that can affect aviation safety and air traffic management in the vicinity of airports. This study presents a mountain wave characterization performed for the winter months from 2001 to 2010 in the center of the Iberian Peninsula, close to an important orographic barrier and next to the busiest Spanish airport. Sixty-eight episodes were simulated using the Weather Research and Forecasting model (WRF). Five simulated atmospheric variables (wind direction, wind speed, atmospheric stability, liquid water content and temperature) were evaluated in several grid points at 2800 meters above sea level in leeward, windward and over the summit of the mountains. Based on the percentiles and thresholds obtained from the characterization, a decision tree was developed with the aim to forecast and warn the occurrence of mountain waves, wave clouds and icing events. The decision tree and the three warning methods were validated against satellite images. The results show satisfactory scores, with a percentage correct of detection above 70% for the three warnings.

1. Introduction

Meteorology has always been connected with aviation. In fact, a large number of meteorological phenomena affect flight plans and aviation safety. Aircraft icing and turbulence owing to mountain waves are likely to be dangerous in departure and arrival operations in the vicinity of airports (European Union Aviation Safety Agency, 2019; Bolgiani et al., 2018; Gultepe et al., 2019). According to the National Transportation Safety Board (2014), meteorological conditions were considered the principal cause of aviation accidents in 37% of the cases, with icing and turbulence associated with mountain waves being the main causes in the 2000–2011 period in the USA. In addition, weather hazards represented approximately 15% of the accidents and serious incidents in the European Risk Classification Scheme for 2019 (Euro- pean Union Aviation Safety Agency, 2019). This classification ranked ice in flight as the third most hazardous type of event and all types of clear air turbulence (CAT) and mountain waves as the 23rd.

Even though there are several systems incorporated to prevent (anti- icing systems) or eliminate (de-icing systems) the presence of ice on the exposed frontal surfaces of the aircraft, the conjunction between icing and turbulence can affect the aircraft safety in flight (Buck, 2000). The last recorded incident relative to icing in flight in Spain occurred in September 2017, at 180 km southeast of Madrid-Barajas Adolfo Suárez airport (LEMD hereafter, as per the airport’s International Civil Aviation Organization code; ICAO). The aircraft, with 26 persons on board, suf- fered an uncommanded loss of altitude of 507 m due to icing conditions (Civil Aviation Authority of Spain. Accident and Incident Investigation Commission, 2017).

Mountain waves are formed in the leeward side of the mountain when the wind flows perpendicular to the orographic barrier. Hereafter, these lee waves are referred and mentioned as cloud bands and moun- tain waves along the manuscript. Wind is forced to climb up the wind- ward slopes, passing the summit of the mountain. If this air ascends into a stable layer, a gravity restitution process can create a wave-like pattern

* Corresponding author at: Department of Earth Physics and Astrophysics, Faculty of Physics, Complutense University of Madrid, 28040 Madrid, Spain. E-mail address: [email protected] (J. Díaz-Fernández).

Contents lists available at ScienceDirect

Atmospheric Research

journal homepage: www.elsevier.com/locate/atmosres

https://doi.org/10.1016/j.atmosres.2021.105620 Received 15 December 2020; Received in revised form 2 March 2021; Accepted 5 April 2021

i An update to this article is included at the end

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which can propagate several kilometres downwind (Broutman et al., 2001). Alternate cloud bands due to higher and lower temperatures are produced in the leeward side by the updrafts and downdrafts caused by mountain waves (Bolgiani et al., 2018). In the downdrafts the temper- atures are higher due to adiabatic process of compression. However, the adiabatic process of expansion produced in the updrafts generates a temperature decrease and a liquid water content (LWC) increase (Smith et al., 2002; Geresdi and Rasmussen, 2005). On the other hand, the collision and coalescence processes produce supercooled large drops growth and constitute the principal source of aircraft icing (Fernández- González et al., 2014).

These alternating bands of temperatures, LWC and vertical wind speeds are characteristic features of mountain waves and they are associated with turbulence. These events are usual in the winter months, when winds are stronger, and the atmosphere is more stable (Wolff and Sharman, 2008). If the associated turbulence takes place in cloud-free regions it can be defined as clear air turbulence (CAT) (Evans, 2014). Additionally, vertical windshear originated from a lee wave may create another characteristic feature which is atmospheric rotors and the associated clouds (Udina et al., 2020), which may be very hazardous for aircraft in flight.

Condensation promotes wave clouds formation in the updrafts. These wave clouds occasionally develop in areas with temperatures below 0 ◦C. Due to the small residency time of the hydrometeors supercooled water may be created, generating aircraft icing conditions, which affect the aviation safety (Moran, 1989; Buck, 2000). Gent et al. (2000) define aircraft icing as the accretion of ice, through the solidi- fication of supercooled liquid drops, on the surface of an aircraft flying at temperatures at or below 0 ◦C. Aircraft icing is more likely to occur between − 2 ◦C and − 15 ◦C of atmospheric temperature, when the ef- ficiency of ice nucleation is low. Thus, liquid water drops prevail at temperatures above − 10 ◦C and solid hydrometeors are predominant at − 15 ◦C, creating a transition phase between both temperatures (Rogers, 1993; Ledesma and Baleriola, 2007). The Federal Aviation Administra- tion (2016) reported that in about half of the aircraft icing incidents, the temperature was between − 8 and − 12 ◦C and the altitude between 1500 and 4000 m above sea level (masl). Tafferner et al. (2003) use numerical simulations to establish several grades of aircraft icing. While LWC values lower than 0.1 g/kg for one hour did not affect aircraft safety, values between 0.1 and 0.5 g/kg could produce a light aircraft icing. However, LWC between 0.5 and 1 g/kg and greater than 1.0 g/kg could generate moderate and severe aircraft icing, respectively.

Forecasting mountain waves is not an easy process, because of the conjunction of several factors (orography, synoptic pattern, wind speed and direction, among others). For the pilots, it is crucial to know the area, altitude, timing and intensity of mountain waves. Nowadays, icing research is underdeveloped and needs to be improved for Numerical Weather Prediction (NWP) models (Thompson et al., 2017). The Weather Research Forecast (WRF) model is a non-hydrostatic NWP model, validated for both research and forecasting, and extensively used in meteorological studies. WRF has shown a very successful performance to study a number of meteorological phenomena, with widely different atmospheric conditions. A few examples correspond to simulations for sea-breeze fronts (Arrillaga et al., 2020), microburst events (Bolgiani et al., 2020), snowfall and heavy precipitation episodes (Fernández- González et al., 2015), planetary boundary layer evening transition (Sastre et al., 2012), a subtropical cyclone (Quitián-Hernández et al., 2020), aircraft icing (Fernández-González et al., 2014; Regmi et al., 2017; Bolgiani et al., 2018; Merino et al., 2019) or the mountain waves (Nygaard et al., 2011; Bolgiani et al., 2018; Conrick et al., 2018; Díaz- Fernández et al., 2020).

Regmi et al. (2017) and Bolgiani et al. (2018) used the WRF model to study weather patterns involved in aircraft icing reports associated to mountain waves, the earlier study simulating a fatal aircraft accident over the middle hills of the Nepal Himalaya and concluding that the presence of supercooled liquid water was the main factor leading to

aircraft icing. The first algorithms to forecast icing conditions using NWP models

were based on relative humidity and temperature (Schultz and Polito- vich, 1992; Thompson et al., 1997). In the last years, the cloud micro- physics schemes implemented in operational NWP models have allowed to develop new algorithms using the LWC (Olofsson et al., 2003; Gencer et al., 2010; Belo-Pereira, 2015). Other forecasting products relative to mountain waves are currently in use: The World Area Forecast Centres produce, among others, operational turbulence and icing forecasts for aviation (Gill, 2014). Also, the Significant Weather chart and the Ter- minal Aerodrome Forecast are used in the airports to forecast multiple aviation hazards including turbulence and icing (Storer et al., 2019).

The aim of the present work is to characterize mountain waves events in the centre of the Iberian Peninsula using the optimum WRF model configuration developed by Díaz-Fernández et al. (2020). Once the mountain wave characterization is produced, a method to forecast the events is proposed, using some of the thresholds defined by Díaz- Fernández et al. (2020). This warning method is validated with a sample in which events and non-events of mountain waves and icing are included. These goals are within the framework of the SAFEFLIGHT research project which aims to improve of aviation safety in weather hazards related to aircraft icing and mountain waves using high reso- lution meteorological models.

The organization of this paper is as follows. A brief description of the study area and the used datasets is given in Section 2. Also, the nu- merical model set up and the satellite channels used to select the events are described. Section 3 details the methodology used to characterize the mountain waves and the development of the warning method based on a decision tree. The main mountain wave features are discussed in Section 4 as well as the verification of the proposed decision tree. Finally, summary and major conclusions are presented in Section 5.

2. Experimental design

2.1. Study area & datasets

The area chosen for this study is interesting due to the presence of four airports (Fig. 1a) south of a large orographic barrier. Air traffic is strictly regulated in the airport’s vicinity (particularly those with heavy traffic), since it is essential to anticipate and order flight trajectories long before landing. In fact, LEMD is the main and the busiest airport in Spain and the sixth in Europe, with more than 61 million passengers during 2019. Located in the centre of the Iberian Peninsula, the airport eleva- tion is 610 masl and it is placed 40 km south-east of the Guadarrama mountain range, which is part of the Central System. The Guadarrama range has a significant area with elevations higher than 2000 masl, being Peñalara the highest summit with 2428 masl. This mountain range runs for 80 km with a northeastern(NE)-southwestern(SW) alignment. Mountain waves are not uncommon on the leeward side of this range whenever the wind blows from the north-west. Thus, the selected spatial domain covers the windward and leeward sides of the Guadarrama mountains.

Within the aforementioned area of study, 120 marks are established (Fig. 1a) to perform the mountain waves characterization: 24 of them in the windward side, other eight over the Guadarrama mountains and 88 points in the leeward side. These locations are used to characterize the main atmospheric variables in the mountain wave development. First, the eight grid points over the Guadarrama summits are established. A 10-grid points buffer region is observed at both sides of the summits to avoid any distortion in the variables due to the complex orography. Then, considering the prevalent wind direction (NW) in mountain wave events previously observed by Díaz-Fernández et al. (2020), 11 consecutive grid points are evaluated leeward of each of the summit locations, which will cover at least one wavelength of the wave. Wind- ward, only three consecutive grid point are considered, as variables are much more stable in this region and differences are negligible between

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different locations. The mountain wave episodes are selected using satellite images

following the methodology established in Section 3. As the melting level is usually lower in winter and therefore aircraft icing conditions are more likely to occur, 68 mountain wave episodes are selected and simulated from November to March in the 2001 to 2010 period. In addition, six episodes between 2017 and 2020 are selected and simu- lated to validate the warning algorithm to detect turbulence and aircraft icing. From these six episodes, three of them are chosen for having wave clouds on the leeward side and other three episodes were randomly selected.

2.2. WRF

Version 4.0.3 of the WRF NWP model (Skamarock and Klemp, 2008) is here used for simulating the selected mountain wave events. Initial and boundary conditions are taken from the National Centers for Envi- ronmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR), with a temporal resolution of six hours and a horizontal spatial resolution of 0.5◦ (Saha et al., 2010). Each episode is initialized at 00:00 UTC and it is independently run in periods of 24 h. The first six hours are considered as spin-up time. Four nested domains are defined (Fig. 1b), following a two-way nesting strategy. Each domain has 121 × 121 grid points in north-south and east-west directions, and 40 sigma vertical levels. Fig. 1b depicts the outer domain (d01), which covers south- western Europe and North Africa with 27 km of spatial resolution. Domain d02 approximately encompasses the Iberian Peninsula with 9 km resolution. Finally, domains d03 and d04 are centred over the Guadarrama range and covering the area of study at 3 and 1 km, respectively.

A sensitivity analysis of the physical parametrizations to detect cloud bands associated with mountain waves was carried out by Díaz- Fernández et al. (2020) in the same study area. In Díaz-Fernández et al. (2020), several WRF model physics parameterizations were evaluated in

thirteen episodes with observed wave clouds using brightness temper- ature. Their results yield the optimum WRF model configuration for detecting mountain waves and the associated wave clouds in the Gua- darrama mountains. The same configuration is used in the current study: the Dudhia shortwave scheme (Dudhia, 1989) and RRTM longwave scheme (Mlawer et al., 1997) are used for radiation; the Unified Noah land-surface model described by Tewari et al. (2004), whereas the revised MM5 (Jiménez et al., 2012) is used as the surface layer scheme and the Yonsei University (YSU) (Hong et al., 2006) as the Planetary Boundary Layer (PBL) scheme; finally, the Thompson parametrization (Thompson et al., 2008) is chosen for the microphysics.

2.3. Satellites

Mountain wave events are selected using the products from the Meteosat satellite families. Up to December 2006, the visible channel (0.6 μm) of the Meteosat Visible Infra-Red Imager is available. From January 2007, the high-resolution visible channel of the Meteosat Sec- ond Generation Spinning Enhanced Visible and Infra-Red Imager is used. Both geostationary satellites are operated by the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT). The horizontal resolution is 2.5 km at nadir for the 0.6 μm visible channel and 1 km for the high-resolution visible channel and the temporal res- olution is 30 and 15 min respectively (Schmetz et al., 2002).

The Red-Green-Blue (RGB) satellite image composition (1.6 μm in the red beam, 0.8 μm in the green beam and 0.6 μm in the blue beam) is called “day natural colours” and allows to detect icing conditions (Lensky and Rosenfeld, 2008). This RGB composition presents ice clouds tops in cyan because solid phase hydrometeors absorbs the 1.6 μm band, and liquid water clouds are coloured white because of their large reflectance to all three bands. Thus, the satellite visible channel is used for the detection of cloud bands related to mountain waves and RGB composition is used to detect icing conditions during the diurnal period (08:00–17:00 UTC).

Fig. 1. (a) Elevation map of the study area (masl). Blue dots (windward), red triangles (Guadarrama) and black points (leeward) indicate the grid points where variables related to mountain waves formation are evaluated. Airports locations are marked with aircrafts symbols and named as per ICAO code. (b) WRF domain configuration. Outer boundary corresponds to outermost domain. LEMD location is marked with an aircraft symbol.

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3. Methodology

As stated above, mountain wave episodes are selected using satellite images for the winter months (November to March) from 2001 to 2010. A mountain wave event is only considered if several conditions are met:

- At least three alternate wave clouds in the leeward side with a par- allel orientation to the Guadarrama mountains.

- Brightness temperature of the clouds between 265 and 280 K (Díaz- Fernández et al., 2020).

- Wavelengths and transversal length greater than three pixels (15 km horizontal satellite resolution over the latitude of the study area). These length thresholds have been selected with the aim to detect the clearest events and considering the lower satellite resolution, which is 5 km at 40◦ latitude (Combal and Noel, 2009).

This method yields 68 mountain wave events which are then simu- lated using the WRF model. Results are taken hourly from 08:00 to 17:00 UTC, making a total of 680-time steps for evaluation.

Wind direction, wind speed, atmospheric stability, LWC and tem- perature data from the WRF simulations are obtained in each of the 120 grid points evaluated (Fig. 1a) at 2800 masl, as this is the altitude where the highest values of LWC were initially detected, in agreement with Díaz-Fernández et al. (2020) and Bolgiani et al. (2018). The variables show very similar results for every selected point in each of the defined areas, therefore the 120 grid points depicted are regrouped and aver- aged in three single results: windward, Guadarrama and leeward.

To characterize the phenomenon, the probability density functions are assessed and the percentiles (P) 10, 25, 50, 75 and 90 are computed for each of the five variables in the three areas. Once the characteristic values are determined for the mountain waves, the next objective of this manuscript is to provide a warning method to anticipate the hazardous events. To achieve this goal, a decision tree is developed. Threshold values for each variable are derived from the characterization for the physical process involved. Wind direction, wind speed and atmospheric stability allow to forecast mountain wave events. When the LWC is added, the decision tree can then detect the associated wave clouds. Additionally, if the temperature is also considered, the decision tree has the ability to detect the resulting icing conditions.

To evaluate the decision tree forecasting ability in a variety of meteorological situations, a sample of six days (10% of the total number of events) belonging to the period 2017–2020 (refer section 2.1) are used. Three days present wave clouds as per the aforementioned selec- tion methodology (one of them with an aircraft icing report in the study area by Bolgiani et al., 2018) and the other three days do not present clouds (randomly chosen). The simulations of theses six days are per- formed using the initial conditions chosen from the NCEP operational GFS 24 to 48-h forecast, at a 0.25◦ resolution (NCEP, 2015). The decision tree is then applied to the WRF data and the three warning levels are validated at hourly results against the satellite observations (wave clouds and icing conditions).

A contingency table (Table 1) is created form the dichotomous out- comes and several skill scores are subsequently computed to assess the warning ability of the decision. The following (Hamill, 1999; López et al., 2007; Kunz, 2007; Aznar et al., 2010) are calculated.

- False alarm ratio (FAR). It is estimated as the ratio between false

alarms (Y) and the total forecasted events (X and Y). The ideal score is 0.

FAR = Y

X + Y (1)

- Probability of detection (POD). It is the ratio between hits (X) and the total observed events (X and Z). A value of 1 is the perfect forecast.

POD = X

X + Z (2)

- Frequency BIAS. It is the ratio between all events forecasted and all events observed. The best score is 1, but for aircraft safety reasons, a slight overestimation (BIAS >1) is preferable than an underestimation, provided the rest of the skill scores yield better results. Despite over- estimating may generate an economic burden, a surprise event implies a risk for the flight.

BIAS = X + Y X + Z

(3)

- Percent Correct (PC). It is defined as the sum of hits and correct non-events (W) divided by the total number of events analysed. The range of PC is between 0 and 1, with 1 for a forecast perfectly matching the observations.

PC = X + W

n (4)

- Critical Success Index (CSI). It is estimated as the ratio between hits and the sum of hits, false alarms and surprise events (Z). A value of 1 is the perfect score.

CSI = X

X + Y + Z (5)

4. Results & discussion

This section is structured as follows: first, the behaviour of the considered atmospheric variables is assessed by means of probability density functions and related percentiles to elucidate the thresholds involved in the mountain waves formation process. Second, the decision tree for warning is developed and validated.

4.1. Mountain waves characterization

Bolgiani et al. (2018) and Díaz-Fernández et al. (2020) demonstrated the WRF model ability to reproduce mountain waves. In this subsection, the threshold values of several atmospheric variables that can induce the mountain wave formation are defined. For that purpose, the hourly re- sults for the selected 68 mountain wave events are evaluated. The av- erages for the wind direction, wind speed and atmospheric stability variables at 2800 masl are chosen. However, with the aim to capture the wave cloud in the leeward side, only the maximum LWC and the mini- mum temperature grid point is considered. It is recalled that atmo- spheric stability is calculated as temperature lapse rates over pressure differences.

Both wind speed and direction are evaluated on the windward side, as this is where these variables govern the genesis of the phenomenon before being forced to climb up the orographic barrier. Fig. 2a shows that the dominant wind direction for the total of wave clouds events is NW, with a prevailing wind direction between 295◦ and 003◦ in the 80% of the sample hours with presence of wave clouds. The 50% of the time it is between 308◦ and 346◦. These data are in agreement with the orog- raphy of the domain, as the Guadarrama range has an approximate SW- NE alignment. The wind speed probability density function (Fig. 2b) shows wind speeds slightly higher when wave clouds are present. A cut- off point between both distributions can be observed at 16.4 m/s (percentile 35 for wave cloud events). The percentiles for wave clouds show that the 80% of the hours the wind speed is between 12.7 and 24.2 m/s.

Table 1 Contingency table for a dichotomous verification of forecasts.

Observed

YES NO Forecast YES X Y

(Correct events forecast) (False alarms) NO Z W

(surprise events) (non-events)

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The previous wind direction results match with a characterization of the surface wind climatology in this zone presented by Lorente-Plazas et al. (2015). In addition, Bolgiani et al. (2018) observed for a mountain

wave event in the same study area a wind speed of 21.1 m/s and west- northwest directions at approximately 3300 masl. Both observations, although made on the leeward side of the mountain, are within the 80%

Fig. 2. (a) Wind direction average rose for the mountain wave cloud events and (b) probability density functions of wind speed (m/s) average for the total of mountain wave cloud events (blue line) and non-events (red line). Both evaluated at 2800 masl on the windward side. The tables beside both figures depict the wave cloud case percentiles values for (a) wind direction and (b) wind speed.

Fig. 3. Probability density functions of atmospheric stability (K/Pa) average for the mountain wave clouds events (blue line) and without them (red line), both evaluated at 2800 masl over the Guadarrama mountains. The table beside the figures depicts the wave cloud case percentiles values for atmospheric stability.

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range of the characterization here presented. Analyzing 13 wave cloud events, Díaz-Fernández et al. (2020) obtained very similar results for P10 and P90 wind direction with a somewhat lower wind speed for both percentiles.

One of the indispensable conditions for the mountain lee waves formation is a stable atmosphere over the mountain (atmospheric sta- bility values above 0 K/Pa), above the region where the wave will be propagated. Also, a neutral stability (atmospheric stability equal 0 K/Pa) attenuates the horizontal propagation of the cloud bands in the leeward side (Koch and O’Handley, 1997). Accordingly, atmospheric stability values are evaluated on the eight selected points over the Guadarrama mountains (Fig. 3). A similar distribution can be noted in the probability density functions for wave clouds events and non-wave cloud cases. The mode value is centered, approximately, on a neutral stability (− 0.01 K/ Pa for wave clouds and 0.00 K/Pa for non-wave cloud events). For wave clouds events, the median (P50) shows neutral stability and 80% of the values from − 0.06 to 0.05 K/Pa. Díaz-Fernández et al. (2020) observed a similar leptokurtic distribution with more concentrated results around neutral stability in mountain waves events. These results are in agree- ment with other related mountain wave related studies (Fernández- González et al., 2014; Fernández González et al., 2019).

According to the mountain waves formation process, LWC and temperature values are here evaluated on the leeward side, where the mountain wave is already present. The existence of LWC is a require- ment for the associated wave clouds to exist and the presence of tem- peratures below 0 ◦C is necessary for icing conditions to develop (Rauber and Tokay, 1991; Buck, 2000). However, wave clouds are commonly

found only in the upper part of the wave. Due to the alternating nature of the variables in this phenomenon, taking an average value would not guarantee capturing the required LWC or temperature, even if a cloud is simulated. Thus, only the maximum LWC and minimum temperatures are considered. Concerning LWC results, Fig. 4a shows a decreasing probability density as the values increase for wave clouds events and non-events. The first cut-off point between them can be observed at 0.15 g/kg (percentile 23). At least in the 79% of wave clouds events LWC is detected (values higher than 0 g/kg). The icing categories established by Tafferner et al. (2003) and an icing conditions study in the Guadarrama mountains (Fernández-González et al., 2014) declare 0.1 g/kg as the LWC lower threshold for icing risk. In the current study, this threshold matches with the first cut-off point and the 69% of the wave cloud events are above it.

The probability density functions for the minimum temperature (Fig. 4b) present a similar shape for both types of events. Even though the temperature is slightly lower for wave clouds events. The conjunc- tion of enough LWC and temperatures below 0 ◦C is essential for the presence of supercooled liquid water. In the selected wave cloud events, 99% of them register temperatures compatible with icing conditions. According with Huffman and Norman (1988), Rogers (1993), Wang (2010) and Fernández-González et al. (2014), the ice nuclei is not active with lower temperatures than − 12 ◦C/− 15 ◦C, so the nucleation process is inefficient, and the aircraft icing is therefore unlikely. The P10 value (− 14.7 ◦C) is within the optimum range in the characterization here presented for such icing.

Fig. 4. Probability density functions for the mountain wave clouds events (blue line) and without them (red line) at 2800 masl in the leeward side for (a) maximum LWC (g/kg) and (b) minimum temperature (◦C). The tables beside the figures depict the wave cloud case percentiles values for (a) maximum LWC and (b) minimum temperature.

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4.2. Decision tree & verification

Based on the previous results, the percentiles highlighted (bold font in the tables next to the Figs. 2 to 4) for each atmospheric variable are used as thresholds to build a decision tree capable to provide a warning method to anticipate the mountain waves and the icing risk events.

The hierarchy of the variables in the decision tree (Fig. 5) follows the sequence derived from the mountain wave formation process. In the first step, wind direction is evaluated. The thresholds (between P10 and P90) on the windward side are considered to detect 80% of the events. As per the characteristic values of this variable, if the wind direction does not belong to the interval [295◦ - 003◦], the decision tree dismisses the possibility of an event. When wind direction complies with the reques- ted range, wind speed is evaluated. In this second step, the lower threshold is established at the P10 value. Wind speed in the windward side less than 12.7 m/s results in a no-warning. For greater values, at- mospheric stability thresholds in Guadarrama are evaluated at the third step. A mountain wave is very unlikely if the atmospheric stability values are not found between − 0.06 K/Pa and 0.05 K/Pa (P10 and P90, respectively). Thus, if the atmospheric stability values are within this range, the decision tree yields a mountain wave warning. Although turbulence is not the subject of this study, a warning for this hazard may easily be computed by adding a fourth step to the decision tree. In fact, vertical winds associated with mountain waves are usually linked with turbulence (Wolff and Sharman, 2008) and CAT (Evans, 2014) when these events occur in cloud-free regions.

Since mountain wave conditions have been met, the next step in the decision tree is to evaluate the possibility of wave clouds. For this, the LWC threshold is assessed in the leeward side. A LWC of 0 g/kg indicates the presence of mountain waves without the associated clouds. On the contrary, LWC values greater than 0 g/kg (P10) provides a wave cloud warning (this implies that the mountain wave warning is also active, as can be seen in Fig. 5). When this is the case, a temperature range is established between 0 ◦C and − 14.7 ◦C (P10) in the leeward side for icing conditions detection. If this range is achieved, an icing warning is produced (as can be seen in Fig. 5, this implies that the mountain wave and wave clouds warnings are also active).

The three types of warnings (mountain waves, wave clouds and icing conditions) obtained from the decision tree (Fig. 5) have been tested for six days as described in the methodology. Note that the initial conditions used to simulate such subsamples are those available for 24 h fore- casting, proving the ability of the decision tree to be used as an opera- tional tool. To perform the test, the aforementioned skill scores are calculated for the three types of warning during the diurnal period (08:00–17:00 UTC). Unfortunately, mountain waves with no clouds cannot be validated through the chosen satellite data. For this reason, cloud bands observations have been used to validate both mountain wave and wave cloud warnings. Icing is verified using the day natural colours RGB composition to detect liquid water clouds.

The validation results are presented in Table 2. While FAR is higher for icing (0.41) than for mountain waves (0.32), a perfect FAR can be noted in the wave clouds warning. Concerning POD, this skill score shows lower values for wave clouds and icing (0.63 and 0.59, respec- tively), revealing the best score for the mountain waves warning (0.78). Merino et al. (2019) simulated the mountain wave episodes observed in

Fig. 5. Decision tree for mountain waves, wave clouds and icing risk warning.

Table 2 Skill scores for the decision tree warnings.

Mountain waves

Mountain waves + Wave clouds

Mountain waves + Wave clouds + Icing

FAR 0.32 0.00 0.41 POD 0.78 0.63 0.59 PC 0.73 0.83 0.77

BIAS 1.15 0.63 1.00 CSI 0.57 0.64 0.42

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ten research flights over the Iberian Peninsula. The LWC was evaluated using the same microphysics and PBL parametrizations as this study and validated against in-cloud microphysics measurements. Their results for POD (0.56) and FAR (0.05) are quite similar to those obtained for the wave clouds warning. It is worth to note that, even if a POD of 0.6 may seem low, this is an acceptable value for aviation meteorology. For aerodrome forecasts the World Meteorological Organization (2005) states that any change presenting a probability lower than 30% should be disregarded. Probabilities higher than 30% and lower than 50% should be considered low, although must be included in the forecast. However, events with a probability greater than 50% must be consid- ered highly plausible and are shown in the forecasts as a certain event. Thus, the mountain waves, wave clouds and icing warning results are relevant from an operational point of view.

Regarding the PC skill score (Table 2), it can be noted that is high for the three warnings, being the best for wave clouds (0.83). This implies a success (observed and forecasted event and non-observed and non- forecasted event) of 73% for mountain waves and non-mountain waves, 83% for events with wave clouds and without them, and 77% for icing and non-icing conditions. The BIAS results may add valuable information to the previous skill scores values presented. First, it has to be noted that while the mountain wave warning is overestimating (1.15), the wave clouds warnings underestimates (0.63). There may be several reasons for this. Carvalho et al. (2014) demonstrated that the NCEP-GFS and NCEP-CFSR WRF conditions (both used in the current study) overestimate the wind speed, which partially explains the mountain wave warning results. In addition, as per Fernández-González et al. (2014), Bolgiani et al. (2018) and Díaz-Fernández et al. (2020) results, the WRF model is able to capture mountain waves even when there is no presence of clouds. As the validation can only be performed against cloud observations, the model may be correctly simulating an existing wave, which generates an overestimation. On the other hand, studies of Naud et al. (2014), Fernández-González et al. (2014), Huang et al. (2015) and Merino et al. (2019) prove that NWP models tend to underestimate LWC. This may partially explain the poor BIAS results for wave clouds warning. The icing warning shows a perfect BIAS score. Finally, the CSI values show similar results between the three warnings, being the wave cloud the best performer. The CSI considers only those situations where a forecasting exists (correct events, false alarms and surprise events; non-events are not considered), hence the results show that 57% of the mountain wave warnings are correct, wave clouds warnings present a 64% accuracy and 42% of the warnings for icing events are adequate.

One of the days chosen for the validation has an aircraft icing report studied by Bolgiani et al. (2018). The aircraft registered at 3300 masl an approximate west-northwest wind direction, wind speed of 21.1 m/s and a temperature of − 7 ◦C leeward of the Guadarrama mountains be- tween 16:00 and 17:00 UTC on 28 February 2017. The results of the decision tree for this particular day and time period yield an icing warning, which implies a mountain wave and the associated cloud warnings, in coherence with the reported observations.

Taking the validation data into account, it can be concluded that the three warnings present satisfactory results. The decision tree here developed could be implemented as an operational short-term fore- casting tool, allowing at least 24 h. This may improve the forecast of turbulence and icing associated to mountain waves south of the Gua- darrama mountains, which would have a significant impact in the safety of aircraft operations near LEMD and the other three airports in the domain. In addition, similar studies can be performed for other areas to adapt the warning tree to other airports.

5. Summary & conclusions

In the present paper, a characterization of 68 mountain wave epi- sodes (winter months from 2001 to 2010) in the leeward side of the Guadarrama mountain range in the Iberian Peninsula has been

performed using the WRF model. Several atmospheric variables have been evaluated in the leeward and windward side and over the moun- tain range with the aim to establish the thresholds involved in the mountain waves formation. Finally, using the thresholds above mentioned, a decision tree was designed and evaluated in order to create a warning method for mountain waves and icing events. The major conclusions of the paper can be summarized as follows.

- The main atmospheric variables involved in the mountain wave phenomenon are characterized during the diurnal period (08:00–17:00 UTC) for the area south of the Guadarrama mountain range, using the WRF model simulations. The variables evaluated are wind direction and speed averages on the windward side, atmo- spheric stability average over the Guadarrama mountain range, and maximum LWC and minimum temperature on the leeward side, all of them at 2800 masl. The results agree with satellite visible channels observations.

- Based on the mountain waves characterization results, 80% of the events present a wind direction ranging from 295◦ to 003◦ and wind speed in the 12.7 to 24.2 m/s interval, both on the windward side. The atmospheric stability spans from − 0.06 to 0.05 K/Pa over the Guadarrama summits. In the leeward side, the maximum LWC and the minimum temperature ranges must be considered from 0.00 to 1.06 g/m3 and from − 2.0 to − 14.7 ◦C, respectively, for icing conditions.

- A warning methodology based on a decision tree is developed using the thresholds obtained from the mountain wave characterization. The decision tree allows to forecast a warning for mountain waves, wave clouds and icing with a lead of at least 24 h before the event.

- The results of the warnings validation (against satellite images) present rather good PC values (above 70%), registering the wave clouds warning the best skill scores.

- When the decision tree is applied to a specific case study in the area, the warnings yielded are in accordance with the reported observations.

- The warning method developed may be implemented as an opera- tional short-term forecasting tool, improving aircraft safety in the vicinity of airports where the mountain waves and icing conditions can be critical.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was partially supported by research projects: PID2019- 105306RB-I00, PCIN-2014-013-C07-04 and PCIN2016-080 (UE ERA- NET Plus NEWA Project), CGL2016-78702-C2-1-R and CGL2016- 78702-C2-2-R (SAFEFLIGHT project), FEI-EU-17-16 and SPESMART AND SPESVALE (ECMWF Special Projects). J. Díaz-Fernández ac- knowledges the grant supported from the MINECO-FPI program (BES- 2017).

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Corrigendum

Corrigendum to“On the characterization of mountain waves and the development of a warning method for aviation safety using WRF forecast” [Atmospheric Research 258(2021) 105620]

J. Díaz-Fernández a, *, P. Bolgiani a, D. Santos-Muñoz b, c, M. Sastre a, d, F. Valero a, e, L. I. Sebastián-Martín d, S. Fernández-González c, L. López f, M.L. Martín d, e

a Department of Earth Physics and Astrophysics, Faculty of Physics, Complutense University of Madrid, Madrid, Spain b High Resolution Limited Area Model Consortium (HIRLAM), Spain c State Meteorological Agency (AEMET), Madrid, Spain d Department of Applied Mathematics, Faculty of Computer Engineering, University of Valladolid, Valladolid, Spain e Institute of Interdisciplinary Mathematics (IMI), Complutense University of Madrid, Madrid, Spain f Atmospheric Physics Group, IMA, University of León, León, Spain

The authors regret that the Fig. 2, Fig. 3 and Fig. 4 are incomplete, since the tables beside these figures were missed. The new Figures (together with the tables) that should have been published are as

follows: The authors would like to apologise for any inconvenience caused.

DOI of original article: https://doi.org/10.1016/j.atmosres.2021.105620. * Corresponding author at: Department of Earth Physics and Astrophysics, Faculty of Physics, Complutense University of Madrid, 28040 Madrid, Spain.

E-mail address: [email protected] (J. Díaz-Fernández).

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Fig. 2. (a) Wind direction average rose for the mountain wave cloud events and (b) probability density functions of wind speed (m/s) average for the total of mountain wave cloud events (blue line) and non-events (red line). Both evaluated at 2800 masl on the windward side. The tables beside both figures depict the wave cloud case percentiles values for (a) wind direction and (b) wind speed. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Probability density functions of atmospheric stability (K/Pa) average for the mountain wave clouds events (blue line) and without them (red line), both evaluated at 2800 masl over the Guadarrama mountains. The table beside the figures depicts the wave cloud case percentiles values for atmospheric stability. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 4. Probability density functions for the mountain wave clouds events (blue line) and without them (red line) at 2800 masl in the leeward side for (a) maximum LWC (g/kg) and (b) minimum temperature (◦C). The tables beside the figures depict the wave cloud case percentiles values for (a) maximum LWC and (b) minimum temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

J. Díaz-Fernández et al.