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BMeteorologische Zeitschrift, PrePub DOI 10.1127/metz/2018/0918 Energy Meteorology© 2018 The authors

Characterization of Spread in a Mesoscale EnsemblePrediction System: Multiphysics versus Initial Conditions

Sergio Fernández-González1, Mariano Sastre2∗, Francisco Valero2, Andrés Merino3,Eduardo García-Ortega3, José Luis Sánchez3, Jesús Lorenzana4 and María Luisa Martín5

1State Meteorological Agency (AEMET), Madrid, Spain2Department of Earth Physics and Astrophysics, Faculty of Physics, Complutense University of Madrid, Madrid,Spain3Atmospheric Physics Group, IMA, University of León, León, Spain4SCAYLE Supercomputación Castilla y León, Spain5Department of Applied Mathematics, Faculty of Computer Engineering, University of Valladolid, Segovia, Spain

(Manuscript received April 5, 2018; in revised form September 5, 2018; accepted October 12, 2018)

AbstractIn this research, uncertainty associated with initial and boundary conditions is evaluated for short-term windspeed prediction in complex terrain. The study area is the Alaiz mountain range, a windy region in thenorthern Iberian Peninsula. A multiphysics and multiple initial and boundary condition ensemble predictionsystem (EPS) was generated using the Weather Research and Forecasting model. Uncertainty of the EPS isanalyzed using an index based on the spread between ensemble members, considering its behavior underdifferent wind speed and direction events, and also during distinct atmospheric stability conditions. Theresults corroborate that physical parameterization uncertainty is greater for short-term forecasts (63.5 %).However, it is also necessary to consider the uncertainty associated with initial conditions, not only for itsquantitative importance (36.5 %) but also for its behavior during thermal inversion conditions in the narrowvalleys surrounded by mountains.

Keywords: wind, physical parameterizations, initial conditions, uncertainty

1 Introduction1

In the framework of climate change, the demand for re-2

newable energy is increasing as an alternative to tra-3

ditional energy sources, which are responsible for the4

emission of greenhouse gases (Torralba et al., 2017).5

During recent decades, wind energy has become one6

of the most economical options for new energy pro-7

duction facilities, and is second in terms of installed8

capacity (Santos et al., 2015). However, wind energy9

production needs accurate wind forecasts for integra-10

tion in the electric grid system (Najafi et al., 2016).11

In particular, it is vital to accurately estimate the ver-12

tical wind profile around the hub height of wind tur-13

bines (Draxl et al., 2014). In addition, wind shear and14

strong gusts may cause structural damage to wind tur-15

bines (Worsnop et al., 2017), so the forecast is crucial16

during extreme wind episodes in order to minimize dam-17

age, and for the optimal design of wind farms.18

Wind power production prediction is especially im-19

portant on short time scales, because wind energy pro-20

ducers need to know the power output they will be21

able to sell in the spot market (Costa et al., 2008). Be-22

cause global atmospheric models commonly underesti-23

∗Corresponding author: Mariano Sastre, Department of Earth Physics andAstrophysics, Faculty of Physics, Complutense University of Madrid. PlazaCiencias, 1, 28040 Madrid, Spain, e-mail: msastrem@ucm.es

mate wind speed (Jiang et al., 2017), the use of meso- 24

scale models is widespread within the scientific com- 25

munity for predicting wind speed at the hub height of 26

wind turbines, especially over complex terrain (Kunz 27

et al., 2010; Graff et al., 2014). In this regard, the 28

Weather Research and Forecasting (WRF) model has 29

been used during recent years for simulating wind flow 30

over complex terrain, with satisfactory results (Hari 31

Prasad et al., 2017). Nevertheless, there is uncertainty 32

in the wind speed forecast even using high-resolution 33

mesoscale models. One solution for estimating this un- 34

certainty is to develop an ensemble composed of sev- 35

eral individual simulations (Slingo and Palmer, 2011). 36

The main sources of uncertainty in atmospheric models 37

are related to initial conditions and model errors (Lee 38

et al., 2012). Initial condition uncertainty can be evalu- 39

ated using data from different global models (Buizza 40

et al., 2005) or by perturbing initial conditions, e.g., 41

with the method known as singular vectors (Molteni 42

and Palmer, 1993). Regarding model errors, uncer- 43

tainty can be estimated using different models or physics 44

parameterizations, or by modifying parameters in the 45

physics package (Berner et al., 2011). According to 46

Olsen et al. (2017), uncertainty associated with wind 47

speed forecasts by mesoscale models near the ground 48

is mainly associated with physical parameterizations, 49

lead time and spin-up of the model, and grid spacing. 50

© 2018 The authorsDOI 10.1127/metz/2018/0918 Gebrüder Borntraeger Science Publishers, Stuttgart, www.borntraeger-cramer.com

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2 S. Fernández-González et al.: Spread in a Mesoscale Ensemble Prediction System Meteorol. Z., PrePub Article, 2018

Table 1: Description of physics parameterizations, initial and boundary conditions used in 16 different simulations.

Simulation code Boundary conditions Radiation(shortwave/longwave)

Land surface model PBL scheme Surface layer

GFS 121 GFS 0.25° MM5 / RRTM NLSM YSU MOGFS 125 GFS 0.25° MM5 / RRTM NLSM MYNN MYNNGFS 131 GFS 0.25° MM5 / RRTM RUC YSU MOGFS 521 GFS 0.25° NG / NG NLSM YSU MOGFS 525 GFS 0.25° NG / NG NLSM MYNN MYNNGFS 531 GFS 0.25° NG / NG RUC YSU MOERA 121 ERA 0.75° MM5 / RRTM NLSM YSU MOERA 125 ERA 0.75° MM5 / RRTM NLSM MYNN MYNNERA 131 ERA 0.75° MM5 / RRTM RUC YSU MOERA 521 ERA 0.75° NG / NG NLSM YSU MOERA 525 ERA 0.75° NG / NG NLSM MYNN MYNNERA 531 ERA 0.75° NG / NG RUC YSU MO

However, an ensemble constructed by considering only51

model errors tends to be under-dispersive (Buizza et al.,52

2005).53

Therefore, in the present research, an ensemble pre-54

diction system (EPS) was developed that considers both55

initial and boundary conditions and model errors. The56

aim was to minimize the under-dispersive nature of57

EPSs (Hamill and Colucci, 1997). The WRF meso-58

scale model was selected because of its versatility, al-59

lowing the use of different initial conditions and mul-60

tiple physical parameterizations to build the ensemble.61

The main goal was to analyze the influence of both ini-62

tial and boundary conditions and physical schemes in the63

generation of spread over the study area, evaluating un-64

certainty depending on wind speed and direction, atmo-65

spheric stability in the planetary boundary layer (PBL),66

and reasons for the geographic distribution of the spread.67

The paper is structured as follows. In Section 2, the68

materials and methods are explained, including charac-69

teristics of the model, the index used for uncertainty es-70

timation, and the study area. Next, the experiments de-71

veloped and results are presented. Finally, an integrated72

discussion and conclusions are given.73

2 Materials and methods74

2.1 WRF model setup75

Version 3.6.1 of the WRF model was used for de-76

veloping the simulations used in this research. It is77

a non-hydrostatic mesoscale model (Skamarock and78

Klemp, 2008) that is commonly used within the sci-79

entific community. It has been proven a successful80

tool to simulate atmospheric conditions for studying81

different meteorological issues, including sea-breeze82

phenomena (Arrillaga et al., 2016), severe storms83

(Gascón et al., 2015a), aircraft icing (Fernández–84

González et al., 2014), radiation fog (Román-Cascón85

et al., 2016), snowfall events (Fernández-González86

et al., 2015; Gascón et al., 2015b), and PBL evening87

transition (Sastre et al., 2012). For the specific case of88

wind energy, the WRF model has also been used suc- 89

cessfully (Argueso and Businger, 2018). Regarding 90

initial and boundary conditions, the ERA-Interim re- 91

analysis (ERA) and National Centers for Environmental 92

Prediction Global Forecast System (NCEP-GFS) analy- 93

sis were selected, following the recommendations of 94

Carvalho et al. (2014). As a result, two sets of simu- 95

lations were defined by using distinct initial and bound- 96

ary conditions, i.e., NCEP-GFS analysis with 0.25° grid 97

size (Saha et al., 2010) and ERA reanalysis with hor- 98

izontal resolution 0.75° (Dee et al., 2011). In addition, 99

various land surface model, surface layer, radiation, and 100

PBL parameterizations were used for evaluating model 101

error, giving 16 different simulations. For the param- 102

eterization of radiation, the MM5 shortwave scheme 103

(Dudhia, 1989) and Rapid Radiative Transfer Model 104

(RRTM, Mlawer et al., 1997) were tested in one set 105

of simulations, and new Goddard (NG) shortwave and 106

longwave radiation schemes (Chou et al., 2001) were 107

tested in the other. Regarding the PBL scheme, the 108

Yonsei University (YSU) parameterization (Hong et al., 109

2006) and Mellor-Yamada-Nakanishi-Niino (MYNN) 110

scheme (Nakanishi and Niino, 2006) were used, be- 111

cause these two are often the best performing for local 112

wind and boundary-layer characteristics (Hari-Prasad 113

et al., 2017). The Noah Land Surface Model (NLSM, 114

Chen and Dudhia, 2001) and the Rapid Update Cy- 115

cle (RUC, Smirnova et al., 1997) were selected for sur- 116

face processes. In addition, the default land use and 117

land cover datasets included in the GFS 0.25 and ERA- 118

Interim databases are the ones considered. Table 1 shows 119

a summary of all these combinations. More informa- 120

tion about the WRF model configuration for these sim- 121

ulations can be found in Fernández-González et al. 122

(2018). 123

We selected 15 days in May 2015, previously tested 124

and compared with observational wind measurements 125

by Fernández-González et al. (2018). These include 126

episodes with various wind intensities and directions 127

and atmospheric static stability conditions, whose rel- 128

ative frequency can also be consulted in Fernández– 129

González et al. (2018). The simulations were initial- 130

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Meteorol. Z., PrePub Article, 2018 S. Fernández-González et al.: Spread in a Mesoscale Ensemble Prediction System 3

Figure 1: WRF domain configuration (A) and orography of study area (B). Region shown in Fig. 1B coincides with domain 4 indicated inFig. 1A.

ized at 0000 UTC, with a temporary scope of 36 h and131

the first 12 h considered a spin-up period. Four nested132

domains with 100 × 100 grid points each were defined133

following a two-way nesting strategy, resulting in hori-134

zontal resolutions of 27, 9, 3, and 1 km (Fig. 1A). A total135

of 61 sigma levels were used, with greater resolution in136

lower levels to better simulate PBL processes.137

2.2 Spread index138

One of the most frequently used solutions to quantify139

uncertainty associated with an EPS is to evaluate the ex-140

isting spread between ensemble members (Grimit and141

Mass, 2007). During recent decades, several spread in-142

dexes have been defined using different methods (Hop-143

son, 2014). In particular, various spread indexes de-144

fined in Fernández-González et al. (2017) were con-145

sidered for use in our research, taking into account the146

peculiarities of the EPS examined.147

In the sensitivity analysis of Fernández-González148

et al. (2018) for the same EPS, four ensemble members149

were highlighted for results markedly worse than the150

others. Those members used both the RUC land surface151

model and MYNN PBL parameterization in the same152

simulation. In order not to include potential outliers de-153

rived from inadequate interactions between these param-154

eterizations, the aforesaid four ensemble members were155

disregarded in estimation of the spread index (SI), and156

the results obtained by these four simulations were not157

used at all in this work. With the aim of not increas-158

ing the slightly under-dispersive nature of the EPS, as159

detected by Fernández-González et al. (2018) when160

comparing the simulations with wind measurements in161

the study area, all remaining ensemble members were162

used for that estimation, resulting in an EPS composed163

of 12 ensemble members (EPS12). As a result, a mod- 164

ification of the SI defined by Fernández-González 165

et al. (2017) was used: 166

S I =

(EPS12maximum − EPS12minimum

EPS12mean

)× 100

(2.1)It should be noted that the variable used in this work to 167

calculate the SI index is the wind speed at 90 m above 168

ground level (a.g.l.) to be representative of the wind at 169

the hub height of wind turbines. 170

2.3 Study area 171

We selected a region in the northern Iberian Peninsula, 172

the Alaiz mountain range, where several wind farms are 173

located (Fig. 1B). The study area is at the confluence 174

of two of the windiest regions of the peninsula, the Up- 175

per Ebro Valley and the Eastern Cantabrian (Lorente– 176

Plazas et al., 2015). This region is characterized by 177

complex terrain, making necessary the use of mesoscale 178

models for proper simulation of wind flow. A complete 179

description of the study area is in Sanz Rodrigo et al. 180

(2013). 181

3 Results 182

3.1 Wind speed analysis 183

First, we describe wind speeds across the study area 184

during the 15 selected days, which is very helpful for 185

the analysis of spread spatial resolution analyzed the 186

following subsections. Fig. 2 shows the temporal aver- 187

age (A) and variance (B) of wind speed at 90 m a.g.l. in 188

domain 4, obtained by the ensemble mean of the WRF 189

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Figure 2: Temporal average (A) and variance (B) of wind speed at 90 m a.g.l. in domain 4, simulated by WRF ensemble mean during studyperiod.

model during the study period. In Fig. 2A, the strongest190

winds are at the highest elevations, coinciding with the191

mountain ranges. On the contrary, weaker wind speeds192

are evident in the small valleys, but not the Ebro Val-193

ley (Figs. 2 and 1B). In that valley, the wind is usually194

channeled, so it attains large values.195

Subsequently, over the 15 days of the study pe-196

riod, variance of the wind speed ensemble mean was197

estimated at each grid point of domain 4 (Fig. 2B).198

In that way, temporal variance of the simulated wind199

speed during the study period was obtained. It is re-200

markable that greater variance is seen on the leeward201

side of orographic barriers, considering that northerly202

winds prevail in the study area, as demonstrated by203

observational measurements analyzed in Fernández–204

González et al. (2018). In the rest of domain 4, the205

variance is less, indicating a more stable wind speed.206

3.2 Uncertainty quantification: vertical and207

temporal evolution of spread208

In this subsection, the uncertainty is evaluated by means209

of the SI. In this endeavor, the uncertainty quantifi-210

cation was analyzed under different scenarios. First,211

the episodes were distinguished as a function of wind212

speed. When the ensemble mean speed at 90 m a.g.l. was213

> 7 m s−1 (considered a reference value because it was214

approximately the average wind speed in domain 4 dur-215

ing the study period), the event was categorized as one216

of “strong wind”. A wind speed < 7 m s−1 was defined217

as a “weak wind” event. Second, regarding the wind di-218

rection at 90 m a.g.l from the ensemble mean, we differ-219

entiated between north wind (wind direction 0° ± 60°)220

and south wind (180° ± 60°) events. Finally, the events 221

were separated depending on atmospheric static stabil- 222

ity, which was estimated by potential temperature (θ) at 223

38 and 97 m a.g.l. (for being consistent with the method- 224

ology followed by Fernández-González et al., 2018), 225

estimated by the ensemble mean. As a result, the events 226

were categorized as “unstable” (dθ/dz < 0), “neutral” 227

(dθ/dz = 0), “stable” (dθ/dz > 0), and “thermal inver- 228

sion”. 229

Fig. 3A shows SI average values at different heights 230

in domain 4 throughout the study period, under dis- 231

tinct meteorological situations. It is remarkable that the 232

spread, and consequently the uncertainty, during weak 233

wind episodes (95 %–97 %) was almost double that of 234

strong wind episodes (45 %–52 %). Because the SI val- 235

ues are percentages, this difference cannot be attributed 236

to the magnitude difference between weak and strong 237

wind events. In the same way, uncertainty was consider- 238

ably greater during southern wind events (79 %–82 %) 239

than northern ones (60 %–63 %). Indeed, after analyzing 240

the database, we found that strong wind events were re- 241

lated to northerly winds, and weak wind events mainly 242

connected to southerly winds. Therefore, episodes of 243

strong winds with a northerly component are very pre- 244

dictable in the study area. On the contrary, forecast un- 245

certainty increases markedly during episodes of weak 246

winds with a southerly component. The reason may 247

be that the orography is much more complex south of 248

the study area, which creates strong turbulence with 249

southerly winds (Sanz Rodrigo et al., 2013). The flow 250

is much less turbulent under winds with a northerly com- 251

ponent, because the wind comes from the Cantabrian 252

Sea and is channeled by the orography to the study area 253

(Lorente-Plazas et al., 2015). 254

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Figure 3: Average SI during study period in domain 4 at different heights under distinct meteorological conditions (A). Daily evolution ofSI at 90 m a.g.l. during days with (blue) and without (red) thermal inversion (B).

Among the results according to static atmospheric255

stability, a remarkable decline of uncertainty was ob-256

served for more unstable static stability. Therefore, the257

greatest uncertainty was during thermal inversion situa-258

tions (SI = 90 %–93 %). The spread was still large when259

the static atmospheric stability was categorized as sta-260

ble (68 %–74 %), but the forecast was more predictable261

during neutral (53 %–54 %) and unstable (47 %–48 %)262

conditions. These results are consistent with those of263

Fernández-González et al. (2018), who claimed that264

wind speed is less predictable during thermal inversions.265

Concerning the uncertainty at different heights, it266

increased (larger SI values) at lower levels of the PBL267

(except during weak wind events). This effect was more268

noticeable during strong wind events, and when the PBL269

was stable. The greater uncertainty at the lower levels of270

the PBL might be caused by errors associated with the271

physical parameterizations (Frediani et al., 2016).272

Subsequently, we investigated the temporal evolution273

of the spread. The behavior was very different during274

days characterized by thermal inversions during night-275

time, so we decided to differentiate it in Fig. 3B. Dur-276

ing episodes without a thermal inversion (red lines in277

Fig. 3B), a daily cycle is not evident in the SI values,278

because the uncertainty does not show great differences279

between day and night. However, events characterized280

by a thermal inversion show a daily cycle in which the281

uncertainty is much greater during the nighttime (co-282

inciding with the development of a thermal inversion283

layer in the PBL), with a more predictable wind flow284

during the diurnal period. Fernández-González et al.285

(2018) observed a diurnal cycle of wind speed when the286

PBL was statically stable in the study area, with stronger287

wind speeds during daytime, mainly because of radiative288

processes. The reason may be that stability decreases289

during the daytime, while wind speed increases. This290

reduces the uncertainty because, as mentioned above, 291

strong wind and unstable events are more predictable. 292

3.3 Spatial distribution of uncertainty 293

Finally, the spatial distribution of uncertainty within 294

the study area was evaluated. In addition, we examined 295

the uncertainty linked to physical parameterizations (by 296

measuring only the spread within the ensemble members 297

as generated by a specific initial condition database) 298

or initial and boundary conditions for various scenarios 299

of wind speed and direction and of atmospheric static 300

stability. 301

Fig. 4A–H shows the SI caused only by the physi- 302

cal parameterizations. The spread associated with those 303

parameterizations represents 63.5 % of the total spread, 304

and was thus the main source of uncertainty in the 305

EPS developed herein. During southern wind events 306

(Fig. 4B), there were several strong uncertainty regions, 307

mainly in low-altitude areas. The pattern is similar for 308

weak wind situations (Fig. 4A), although moderate-to- 309

high uncertainty is widespread over the study area (ex- 310

cept at higher altitudes). For northern wind episodes 311

(Fig. 4F), the uncertainty is considerably less than in 312

the case of a south wind component (Fig. 4B). How- 313

ever, the appearance of several areas of moderate uncer- 314

tainty is remarkable, which are on the leeward side of the 315

orographic barriers (Fig. 1B). This pattern is similar in 316

the strong wind panel (Fig. 4E), reaffirming that strong 317

wind episodes are mainly related to the north wind com- 318

ponent. In conditional and unstable conditions (Fig. 4G 319

and H), there is an area of moderate uncertainty in the 320

northwest part of the study are, coinciding with a narrow 321

gorge of West–East orientation (Fig. 1B). This orienta- 322

tion can produce a shadow effect during northerly and 323

southerly wind episodes, causing weak winds (as seen in 324

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Figure 4: Average SI in domain 4 under distinct meteorological conditions generated only by physical parameterization uncertainties (A–H),and only by initial condition uncertainties (I–P).

Fig. 2A) that are, as mentioned above, less predictable.325

When the PBL was categorized as stable (Fig. 4D), the326

configuration shows a strong similarity to the northerly327

wind events, but with greater uncertainty. Nevertheless,328

the most impressive results appeared when a thermal in-329

version layer was present in the PBL (Fig. 4C), with SI330

values exceeding 100 %. In these cases, the uncertainty331

was extraordinarily great in the valleys of the study area332

(Fig. 1B), with the exception of the Ebro Valley, which333

apparently does not experience this process. The reason 334

may be the wind channelling effect, which makes wind 335

speed more predictable in that valley. 336

Initial and boundary conditions only contributed 337

36.5 % of the total spread, although the uncertainty that 338

initial conditions produced cannot be ignored because it 339

is very important during certain weather conditions. As 340

shown in Fig. 4I–P, there are extremely large SI values in 341

the small valleys during thermal inversion and southerly 342

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wind component periods (Fig. 4J and K). It is in these343

cases when the uncertainty from initial and boundary344

conditions is critical. During weak wind events (Fig. 4I),345

the uncertainty pattern is similar to that of southerly346

wind component episodes, but the SI is smaller. For347

the remaining scenarios (strong winds, northerly wind348

components, and stable, conditional, and unstable sit-349

uations; Fig. 4L–P), uncertainty associated with initial350

conditions is almost negligible.351

Regions with greater variance (Fig. 2B) are not352

strictly associated with poor predictability (Fig. 4). For353

example, small valleys, which are characterized by small354

variance, stand out for having the greatest uncertainty.355

Therefore, wind speed variance for a specific location356

and period cannot always be associated with high or low357

predictability.358

4 Discussion and conclusions359

In general terms, the uncertainty associated with model360

errors is prevalent in short-term forecasts, because the361

spread grows faster in ensembles developed by com-362

bining different physical parameterizations rather than363

those developed by considering only different initial364

conditions (Stensrud et al., 2000). This is consistent365

with most of the results in the present work, although our366

findings indicate that considering both sources of uncer-367

tainty is very advantageous under certain weather con-368

ditions. In particular, the uncertainty generated by ini-369

tial and boundary conditions during thermal inversion370

conditions may be related to distinct inputs of relative371

humidity, especially at the surface level, a characteris-372

tic considered in the initial conditions of the NCEP-GFS373

analysis and ERA-Interim reanalysis. The importance of374

nearby moisture at the surface has also been observed375

during the transition from a diurnal convective to noc-376

turnal stable boundary layer (Sastre et al., 2015). This377

influences all the other PBL meteorological variables,378

including wind speed. It is also possible that the higher379

spatiotemporal resolution of the NCEP-GFS analysis380

gives more reliable initial conditions over complex ter-381

rain under certain weather conditions, such as the for-382

mation of a thermal inversion layer in the PBL during383

nighttime (Fernández-González et al., 2018) and the384

forecast of land surface skin temperature during day-385

time (Zheng et al., 2012). Regarding physical param-386

eterizations, the two PBL schemes considered in the387

EPS herein produced uncertainty, because MYNN PBL388

scheme estimates of wind speed are frequently smaller389

than those from the YSU PBL parameterization, some-390

times causing underestimation of wind speed (Fernán-391

dez-González et al., 2018). Results for the radiation392

schemes are not as unequivocal as the former, and for393

this reason they require further analysis.394

The main conclusions of this study can be summa-395

rized as follows:396

• Areas with stronger winds stand out for having397

greater predictability, which is very advantageous for398

wind energy purposes.399

• Greater variance is associated with the leeward side 400

of orographic barriers and in small valleys. 401

• In the vertical wind profile, uncertainty decreases 402

with height (except during weak wind events and 403

thermal inversion conditions). 404

• Strong northerly wind episodes show little forecast 405

uncertainty, but uncertainty increases markedly in 406

weak southerly wind events. 407

• Regarding static atmospheric stability, diminishing 408

uncertainty was observed from stable to unstable 409

static stabilities. The greatest uncertainty was for 410

thermal inversion conditions. This appears to be 411

linked to the observed diurnal cycle of ensemble 412

spread when a thermal inversion layer was developed 413

in the PBL, with greater uncertainty during night- 414

time. 415

• Although uncertainty generated by different phys- 416

ical parameterizations is quantitatively greater, the 417

uncertainty caused by initial conditions cannot be 418

discarded because it provides considerable infor- 419

mation under certain weather conditions, especially 420

southerly wind and thermal inversion episodes. 421

In future research, our method will be applied to 422

wider areas to see if the conclusions can be extended 423

to other regions. The results from this research can be 424

useful for the selection of the most viable locations for 425

installing wind farms. Such locations should not only be 426

chosen based on wind strength but also on uncertainty 427

in the wind speed forecast. 428

Acknowledgments 429

This work was partially supported by research projects 430

METEORISK (RTC-2014-1872-5), PCIN-2014-013- 431

C07-04 and PCIN2016-080 (UE ERA-NET Plus 432

NEWA Project), ESP2013-47816-C4-4-P, CGL2010- 433

15930, CGL2016-78702-C2-1-R and CGL2016-78702- 434

C2-2-R, CGL2016-81828-REDT, and the Instituto de 435

Matemática Interdisciplinar (IMI) of the Universidad 436

Complutense. Special thanks go to Steven Hunter and 437

Analisa Weston. To request the data, please contact 438

S. Fernández-González (sfernandezg@aemet.es). 439

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