Statistical wind forecast for Reus airport

transcript

METEOROLOGICAL APPLICATIONSMeteorol. Appl. 17: 485–495 (2010)Published online 26 April 2010 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/met.192

Miquel Traveria,* Alejandro Escribano and Pablo PalomoCentre d’Estudis Superiors de l’Aviacio (CESDA), Universitat Rovira i Virgili Campus Aeronautic de Reus Carretera Aeroport s/n., 43200-Reus,

ABSTRACT: Crosswinds are usually a limiting factor for the normal operation of small size aircraft near an airport, andone of the first causes of weather related accidents. This paper presents a statistical downscaling model that provides a24 h wind forecast at Reus airport (Spain).

The model is trained with 6 years historic data (1 January 2000 to 31 December 2005). The predictors are variablesfrom two numeric weather prediction (NWP) model outputs: a mesoscale (MASS) and a global model reanalysis (GFS),at grid points near Reus airport. The predictands are the wind measured at the airport runway (METARs).

The downscaling model processes the historic data, making use of several data mining tools to optimize the forecastingaccuracy. Primarily, examples are separated into four clusters. Following this, a selection of the predictor variables is madewith every cluster. Finally, neural networks are developed to produce a wind forecast.

The downscaling model is relatively complicated, due to the different statistical techniques used, but has betterforecasting accuracy than the NWP models used and other simpler statistical downscaling models. Copyright 2010Royal Meteorological Society

KEY WORDS statistical downscaling; neural networks; self-organizing maps; genetic algorithms; wrapper feature subsetselection

Received 4 February 2008; Revised 16 November 2009; Accepted 18 February 2010

1. Introduction

Crosswinds are usually a limiting factor for the normaloperation of small aircraft near an airport and one of thefirst causes of weather related accidents. An operativewind forecast system can be very useful in improvingoperational safety.

Reus, a city with 100 000 inhabitants, has an interna-tional airport with the International Civil Aviation Orga-nization (ICAO) abbreviation of LERS. Reus is locatedin flat terrain, 10 km from the Mediterranean Sea andnear a mountain chain whose elevation is about 1000 m(Figure 1).

The wind in Reus has clear seasonal periods, usuallycoming from 270° to 360° caused by synoptic scalephenomena during the winter and usually from 135°

to 225° due to sea breeze during the summer (thisinformation can be obtained from Agencia Estatal deMeteorologıa (AEMET)).

The official weather forecasts for the airport are madewith deterministic numeric weather prediction (NWP)models (such as the High Resolution Limited Area Model(HIRLAM) (Unden, 2002) provided by the AEMET). Atlarge scales (synoptic and to a lesser extent mesoscale)and above the boundary layer these models are highlyaccurate, while their skill to predict the wind decreaseswithin the boundary layer as well as for local phenomena.

* Correspondence to: Miquel Traveria, Centre d’Estudis Superiors del’Aviacio (CESDA), Campus Aeronautic de Reus Carretera Aeroports/n., 43200-Reus, Spain. E-mail: mtraveria.pdi@cesda.com

To improve the deterministic forecast of the surfacewind (from 1 to 10 m from the surface) for a givengeographic point and time, filters used for NWP modeloutput are a good approach. This task is usually referredto as statistical downscaling. Some of the statisticalmethods most frequently used for local and short termweather forecasts are:

• Perfect-Prog (Perfect Prognosis) and Model OutputStatistics (MOS) are two of the first linear filters usedfor NWP models (Glahn and Lowry, 1972; Klein andGlahn, 1974; Carter et al., 1989; Brunet et al., 1998).A good review of other linear statistical techniques canbe found in Bretherton et al. (1992). A comparison ofseveral statistical downscaling linear methods for dailytemperature forecasting is in Huth (1999).

• Neural networks are used by many authors (Schizaset al., 1994; Hewitson and Crane, 1996; Hshied andTang, 1998; Trigo and Palutikof, 2001; Perez-Lleraet al., 2002; Marzban, 2003; Cavazos and Hewitson,2005). Self-organizing maps (SOM) are a type of neu-ral network that can be used for statistical downscalingpurposes too (Hewitson and Crane, 2002).

• Clustering and instance-based learning methods pro-vide good results as statistical downscaling methodsand show good forecasting skill for extreme events(Zorita et al., 1995; Zorita and von Storch, 1999;Gutierrez et al., 2004).

• Fuzzy logic is used in some cases for deterministicpredictions (Kaciauskas et al., 1998).

486 MIQUEL TRAVERIA et al.

Figure 1. The four GFS grid points used in the study, and the situationof Reus airport in between.

• Support vector machines (SVM) can be used as analternative to neural networks (Qiufen et al., 2007).

Much effort in local wind forecasting has been dedi-cated to predict wind energy at wind farms, and statisti-cal downscaling methods are widely used in operationalmodels. The project ANEMOS (an EU Research andDevelopment Project for forecasting wind power at windfarms) provides a good literature overview of wind pre-diction methods in use and under development (ProjectANEMOS, 2003).

Wind forecasting using statistical downscaling methodsat a location uses data from NWP models which areloaded with two relevant types of error:

1. The kinetic subgrid-scale processes are not properlyresolved by an NWP model.

2. Numerous spectral analyses have shown that dynamicmodels are limited by an effective length-scale (e.g.Denis et al., 2002a, 2002b; Skamarock, 2004; Hamil-ton et al., 2008). This effective length-scale dependson the horizontal resolution of the model. For exam-ple, Skamarock (2004) has shown that especiallyfor the kinetic energy (which is closely related towind) the effective length-scale is at least seventimes the horizontal grid spacing. Hence, any sim-ulation of wind-related processes on scales smallerthan this effective length-scale suffers from a loss ofinformation.

A statistical downscaling model is intended to addressthe first error source. To reduce the second error sourcedata from so many grid points as the effective length-scale indicates should be used. Nevertheless, the use oftoo big an input pattern adds a limitation for the statis-tical downscaling methods, and the forecasting accuracydecreases at its turn. The usage of four grid points is thecompromise PLANIMIA adopts.

PLANIMIA is a statistical downscaling forecast modelthat uses output from NWP systems and provides a windforecast for the following day at 1200 UTC for Reusairport (local standard time is UTC + 1 or + 2 dependingon the time of year).

A comparison of the predicting skill of PLANIMIAwith the other statistical downscaling methods referencedabove is difficult, because it depends much on theparameters predicted, the time and spatial scale, as wellas the geographical area under study. Furthermore, the

type of prediction found in the above mentioned articlesis deterministic in some cases and probabilistic in others,and different indices to express the predicting abilityare used. In order to evaluate the PLANIMIA forecastability, it is compared with two NWP models, and witheight simpler statistical downscaling models predictingthe wind at LERS. The parameter used is the forecastaccuracy, which compares the forecast wind with themeasured wind.

This paper is structured as follows. Section 2 describesthe data used in the study. Section 3 describes themethodology to develop the statistical downscalingmodel. Section 4 describes PLANIMIA predicting accu-racy and compares it to other forecast models. Section5 describes the results and the errors. Section 6 presentsthe conclusions.

2. Data

The predictands used for the present work, i.e. theinput data used to do the prediction, are obtainedfrom two NWP model outputs: one global and onemesoscale.

• The global model is the Global Forecast System (GFS)(Sela, 1980). The historic data are from the reanalysis4× daily, 2.5° resolution, made at the U.S. NationalCenters for Environmental Prediction (NCEP). Thetime range is from 1 January 2000 to 31 December2005. Four nodes around Reus are used (Figure 1).The variables for every node are shown in Table I. Thedaily data are downloaded from the GFS operationalmodel from NCEP.The usage of only four nodes instead of a greaternumber penalizes by losing some information, but hasthe advantage of reducing the number of data in theinput pattern, which is a benefit for the statisticalmethods used here.

• The mesoscale model is the Mesoscale AtmosphericSimulation System (MASS) (Kaplan et al., 1982) runat Servei Meteorologic de Catalunya (SMC) with a

Table I. Variables used from the GFS model output.

GFS data

UGRD 1000h12 (Vx at 1000 hPa at 1200 UTC)UGRD 700h12 (Vx at 700 hPa at 1200 UTC)VGRD 1000h12 (Vy at 1000 hPa at 1200 UTC)VGRD 700h12 (Vy at 700 hPa at 1200 UTC)RH 1000h12 (relative humidity at 1000 hPa at 1200 UTC)RH 925h12 (relative humidity at 925 hPa at 1200 UTC)T 1000h12 (temperature at 1000 hPa at 1200 UTC)T 925h12 (temperature at 925 hPa at 1200 UTC)T 850h12 (temperature at 850 hPa at 1200 UTC)T 700h12 (temperature at 700 hPa at 1200 UTC)ABSV 1000h12 (absolute vorticity at 1000 hPa at 1200 UTC)P sfch12 (surface pressure at 1200 UTC)PRATE sfch12 (precipitation rate at surface at 1200 UTC)

STATISTICAL WIND FORECAST FOR REUS AIRPORT 487

grid size of 8 km. The boundary conditions are theIntegrated Forecast System (IFS) model from the Euro-pean Centre for Medium-Range Weather Forecasts(ECMWF). The MASS model run at SMC has beenwithout modifications for the period from 1 January2000 to 31 December 2005. Only the nearest node tothe airport (4 km away) has been provided for thisstudy (Figure 1). The variables are at 1200 UTC andat 1800 UTC.The reason for using the 1800 UTC prediction is thatsome features at 1200 UTC are not included in theinput pattern (such as the vertical lapse rate), but themodel can generate relevant phenomena at 1800 UTC(such as strong sea breezes). Therefore, using variablesthat the MASS calculates for 1800 UTC provides someinformation that is not included in the set of variablesat 1200 UTC. If the variables at 1800 UTC are notrelevant for the prediction these are discarded throughthe data selection process, or they will remain asneutral with no effect on the prediction, as explainedin a subsection below. Table II shows the variablesincluded in the input pattern.

Table II. Variables used from the MASS model output.

MASS data at 1200 UTC and 1800 UTC

Ph12 (pressure at surface) Ph18 (pressure at surface)T sfch12 (temperature atsurface)

T sfch18 (temperature atsurface)

T 850h12 (temperature at850 hPa)

RH 1000sfch12 (relativehumidity)

RH 1000sfch18 (relativehumidity)

Vx sfch12 (Vx at surface) Vx sfch18 (Vx at surface)Vy sfch12 (Vy at surface) Vy sfch18 (Vy at surface)Vx 850h12 (Vx at 850 hPa) Vx 850h18 (Vx at 850 hPa)Vy 850h12 (Vy at 850 hPa) Vy 850h18 (Vy at 850 hPa)Vx 500h12 (Vx at 500 hPa) Vx 500h18 (Vx at 500 hPa)Vy 500h12 (Vy at 500 hPa) Vy 500h18 (Vy at 500 hPa)

The Targets are the Vx and Vy wind componentsobtained from the Meteorological Aerodrome Report(METAR) at LERS. Since the wind may not be constant,an arithmetic mean between the wind at 1100 UTC,1200 UTC and 1300 UTC is used as a target.

After selecting only those records from the originaldatasets that include complete and reliable information,1746 historic cases (examples) remain to train andvalidate the forecast model. This number of cases isassumed to be large enough to cover many of thepossible meteorological situations, although it is usuallyaccepted that a dataset of 30 years is necessary for agood climatology (O’Hare and Sweeney, 1994). Thedependence of the forecasting accuracy on the number ofexamples is evaluated at the end of the following section.

3. Methodology

This section describes the methodology to develop thePLANIMIA forecast model. The objective is to map theNWP model outputs to the wind measured at the runwaythreshold and periodically published through METARreports. A well known approach to this downscaling prob-lem is to use a neural network and train it with the avail-able historic datasets. Nevertheless the wind at LERScan be caused by different meteorological situations. Forinstance, northerly winds could be produced by synopticscale systems, while southerly winds are usually relatedto the sea breeze. Therefore, data are divided into differ-ent clusters. A good description of the use of clusteringmethods for statistical downscaling is in Gutierrez et al.(2004). The conceptual architecture of PLANIMIA is pre-sented in Figure 2. The following subsections explain inmore detail the most relevant characteristics of the fore-cast model architecture.

3.1. Neural networks

A good overview of neural networks is presented byHaykin (1994). A neural network establishes a mathemat-ical relationship between predictors and predictands. Inthis study the predictors are variables from NWP modelsoutputs and the predictands are Vx and Vy at the airport.

Figure 2. PLANIMIA flux diagram.

The mathematical expression of a neural network withone hidden layer is:

Vk = g

H∑i=1

N∑j=1

wijxj − bi

− b′

where H is the number of neurons in the hidden layer,f and g are the so-called activation functions, wi , wij ,b′ and bi are the coefficients (weights and bias) to befitted during the training process. xj is the input patternvector. N is the dimension of the input pattern vector,or, in other words, the number of variables included inthe input pattern. Vk is the wind component predictedby the neural network. The mathematical expressions fora neural network with two or more hidden layers areextensions of the expression shown in Equation (1). Ifboth f and g (Equation (1)) are linear functions, theneural network acts as a linear regression. If f or g arenon-linear, the relationship is non-linear.

The eight neural networks of PLANIMIA (one for Vx

and one for Vy , times the four clusters (Figure 2)) areof the feed forward type with two hidden layers. Theactivation function for the hidden layers is the logisticfunction:

f (x) = 2

1 + e−2x− 1 (2)

The activation function for the output layer, g, is linear.The training is accomplished with the conjugate gra-

dient back-propagation with Polak-Ribiere updates algo-rithm (Demuth and Beale, 2005), because it is very fastand stable for the processed data and network archi-tecture. Each neural network is trained ten times withdifferent data subsets to make sure that the results arereliable (this procedure is known as cross-validation).

3.2. Clustering method

This subsection explains how clusters are defined fromdifferent wind situations over Reus. For the clusteringalgorithm an unsupervised clustering method is chosenfor two reasons: there is no knowledge beforehand aboutthe number of clusters, nor the nature of every cluster.The clustering algorithm selected is the Self-OrganizingMap (SOM) combined with k-means (Vesanto et al.,2000; Kohonen, 1995, 1997, 2001). An SOM is a typeof neural network that is trained without supervision (i.e.the user only provides input data, without target). Theresult is a two-dimensional map representing the inputspace and preserving the topological properties. Thishelps to visualize a multidimensional input space intoa two-dimensional map (Haykin, 1994; Kohonen, 1995,1997, 2001).

The process of selecting variables to define the clustersis as follows: a group of variables which can be relatedto the air movement over Reus is selected by a meteorol-ogist. Following this, a process of trial and error with theclustering algorithm (SOM with k-means) is conducted

Table III. NWP model output variables used to determine thedifferent clusters.

Model Variable at 1200 UTC

MASS Vx surface Vy surfaceMASS Vx 850 hPa Vy 850 hPaMASS Vx 500 hPa Vy 500 hPaGFS UGRD 700 hPa (node 1) VGRD 700 hPa (node 1)GFS UGRD 700 hPa (node 2) VGRD 700 hPa (node 2)GFS UGRD 700 hPa (node 3) VGRD 700 hPa (node 3)GFS UGRD 700 hPa (node 4) VGRD 700 hPa (node 4)

Table IV. Number of examples for every cluster.

Cluster 1 2 3 4

Number of vectors 525 390 487 344

to obtain a subset of variables that produces high differ-ences between clusters. This process must minimize threeparameters: the topographic error (percentage of vectorswhose first Best Matching Unit (BMU) and the secondBMU are not neighbours in the map), the quantizationerror (mean distance in the map from each vector to itsBMU), and the number of clusters (Vesanto et al., 2000;Kohonen, 1995, 1997, 2001). A good solution is foundwith four clusters, and the variables used to determinethe different clusters are shown in Table III. The numberof input vectors in each cluster is presented in Table IV.

3.3. Variable selection with genetic algorithms

This subsection explains the set of atmospheric variablesfor each cluster that shows the best forecast accuracywhen it is used as an input pattern to the neural network.The number of variables that compose the input pattern is74 (the pattern dimension), and the number of availablecases is 525, 390, 487 and 344, depending on the cluster.Given these values, a reduction of the input patterndimension is conducted for four reasons:

1. The curse of dimensionality is a strong reason toreduce the ratio (input pattern dimension/number ofcases) (Bellman, 1961);

2. If the input pattern contains features that are notnecessary, the neural network performance may bedegraded (Haykin, 1994);

3. Knowing the variables with higher predicting valuecan provide more information about the meteorologi-cal problem at hand, and,

4. The number of free parameters (weights and bias)in the neural network should be smaller than 150after investigating it with the Bayesian regularizationalgorithm (MacKay, 1992; Demuth and Beale, 2005).Otherwise overfitting can occur.

Principal component analysis (PCA) (Bishop, 1996;Gutierrez et al., 2004) is used to group the variables of

Table V. Presence/absence (1/0) of the different variables in the input pattern for the neural networks, as obtained with thewrapper selection method.

Cluster VxVy

N1 N2 Ph12sfch12

850h12

500h12

RH1000sfch12

Vxsfch12

Vysfch12

Vx850h

Vy850h

Vx500h

Vy500h12

Ph18 Tsfch18

T500h18

RH1000sfch18

Vxsfch18

Vysfch18

Vx850h

Vy850h

Vx500h

Vy500h

1 Vx 4 7 0.5 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 01 Vy 4 7 0.4 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 12 Vx 4 6 0.5 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 02 Vy 4 6 0.5 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 03 Vx 4 8 0.4 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 03 Vy 5 9 0.45 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 0 04 Vx 4 7 0.35 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 04 Vy 4 6 0.33 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1

00110000

00000010

00011010

10011000

λ T T T

Cluster UGRD1000h12pca

UGRD700h12pca

VGRD1000h12pca

VGRD700h12pca

RH1000h12pca

RH925h12pca

T1000h12pca

T925h12pca

T850h12pca

T700h12pca

ABSV1000h12pca

1 1 0 0 0 0 1 0 0 1 1 1 11 0 0 1 0 1 1 0 0 0 1 1 02 1 0 0 1 0 0 0 0 0 0 1 02 1 0 1 1 0 0 0 0 1 1 1 03 1 1 0 0 1 1 0 0 0 1 0 03 0 0 0 0 0 1 1 1 0 1 1 14 1 0 1 0 0 0 0 0 1 0 0 04 1 0 0 0 0 1 1 1 0 0 0 0

N1 and N2 are the number of neurons in the first and second hidden layers of the neural network, respectively. λ is the regularization parameterof the training process of the neural network.

the same type. PCA is a well known linear statisticaltool that is used to compress data with adjustable lossof information. It is observed that the variables ofthe GFS model are highly correlated at the four gridpoints around Reus. Therefore, the principal componentof every four variables is used. For instance, the fourvariables T 1000h12 (air temperature calculated by theGFS at 1000 hPa at 1200 UTC) are converted into onenew variable (T 1000h12pca). This reduces the patterndimension considerably from 74 to 34, and the lossof information is minimal. Once again, a compromisebetween the reduction of the input pattern dimension andthe information loss must be adopted.

To reduce the input pattern dimension further andremove worthless variables from the input pattern, awrapper type feature selection method, using geneticalgorithms, is conducted (Kohavi and John, 1997; Guyonand Elisseeff, 2003; Cantu-Paz, 2004). In this studyfeature and variable are used as the same concept.

The philosophy of the wrapper methods for feature(variable) selection is to create different input patterns,test them with the learning machine (a neural networkin this case), evaluate their performance and select thosethat best perform. This process is usually iterative andends when a good solution is achieved.

The goal is to find a pattern composed of a set ofvariables out of 34 that minimizes the forecast error withthe neural network (Marzban et al., 1999). A thoroughscanning of all possible patterns is computationallyuntreatable. Therefore an intelligent search with geneticalgorithms seems a good approach for two reasons:

1. The function to optimize (for instance the meanerror between output and target) is not derivable.Hence gradient descend optimization algorithms arenot well suited, while genetic algorithms can resolvethe problem and find reasonable solutions, and,

2. Genetic algorithms usually explore the patterns spacereasonably well to avoid falling into local minima(Goldberg, 1989).

The variable selection process finds: (1) the inputpattern, (2) the number of neurons in the first and secondhidden layers, and, (3) the regularization parameter forevery neural network. In this process the size of theneural network is limited in order to reduce the number ofweights and bias to below 150. It is also essential that thefirst hidden layer number of neurons must be smaller thanthe pattern dimension, and the second hidden layer hasmore neurons than the first one. This is done in order toreduce the number of free parameters (weights and bias).

The results of the variable selection with the wrappermethod are shown in Table V, where 1 indicates presenceand 0 indicates absence of the variable in the inputpattern.

The input pattern dimension has been reduced from 34to 11 variables, in the average between the four clusters,and for both wind components. The selected variablesfor the input pattern differ from one neural network toanother, but as a general rule, the corresponding surfacewind component is always present. Other variables arepresent in many other input patterns, such as surfacerelative humidity, surface temperature, higher levelstemperature and surface absolute vorticity. There is thepossibility that variables included in the patterns have nopredicting value, they are neutral, but they survive theselection process (John et al., 1994). Once the variableselection is made, a feed forward neural network istrained for every case as explained in Section 3.1.

3.4. On the number of grid points used

This subsection addresses the number of grid points thatshould be used to obtain a good forecasting accuracy. To

Figure 3. GFS 16 grid points nearest to Reus.

that end, studies using neural networks to forecast thewind at LERS are done.

The forecasting accuracy is expressed by the root meansquared error (RMSE ) and the correlation coefficient (R).

The RMSE is defined as:

RMSE =√√√√ 1

N∑i=1

(vobservedi − vforecast

i )2 (3)

where vobservedi is the wind component observed and

vforecasti the wind component forecast. N is the number

of examples.The correlation coefficient, R, is defined as:

R =N · ∑

(vobservedi · vforecast

− (∑vobserved

) · (∑vforecast

)√√√√√

[N · ∑

(vobservedi )2 − (∑

vobservedi

·[N · ∑

(vforecasti )2 − (∑

vforecasti

Since the GFS reanalysis provides more than 25 yearsof records, datasets with GFS output from 5000 historiccases are used. The number of grid points used is 1, 4and 16, nearest to Reus (Figure 3). The observed windis obtained from the METAR dataset at LERS. All thevalues presented in this sub section are calculated bya cross-validation process with 10 iterations to obtainreliable results.

3.4.1. Effect of pattern reduction using PCA

In the following how much loss of information can beallowed through a PCA without losing much forecasting

accuracy is investigated. The use of a dimensionalreduction through a PCA mixes up the informationfrom the nodes. In this linear process some informationcontained in the whole group of nodes can be missed.Table VI shows the forecasting accuracy (R and RMSEbetween forecast and measurement) of a downscalingmodel based on neural networks. The dataset of 5000examples and 16 grid points is transformed by a PCA.The forecasting is done using a different number ofprincipal components to compare the different forecastingaccuracy.

It can be observed that the accuracy increases asthe number of principal components (hence the cumu-lative variance) increases. There is, however, a differentbehaviour between both wind components. While theaccuracy (R and RMSE ) of Vx forecast saturates witha cumulative variance of 0.95, the accuracy of Vy fore-cast does not saturate, and can be improved by acceptingmore principal components into the input pattern, up toa cumulative variance of 1.0. This is an insight that thereis more spatial correlation for Vx than for Vy .

In PLANIMIA the PCA is applied by taking a cumu-lative variance of 0.95 for both wind components, inorder to obtain a good compromise between input pat-tern reduction and information conservation. The presentanalysis using 5000 examples suggests that the cumu-lative variance of 0.95 is good for Vx component, butapparently not optimal for Vy component. Nevertheless,it must be remembered that PLANIMIA uses less than5000 examples, and the reduction of the input patterndimension is essential to get an optimal forecasting accu-racy. The use of a cumulative variance of 0.95 in thePCA is assumed as a safe value for PLANIMIA.

Table VI. Forecasting accuracy comparison using different cumulative variance from the PCA.

0.8 of cumulativevariance

NO PCA

Vx Vy Vx Vy Vx Vy′ Vy Vx Vy

R 0.62 0.43 0.63 0.48 0.64 0.57 0.65 0.61 0.65 0.65RMSE (m s−1) 2.71 2.33 2.66 2.27 2.65 2.14 2.62 2.06 2.62 1.99

A neural network is developed for each case. The input pattern dimension is reduced conserving those principal components whose cumulativevariance is 0.8, 0.9, 0.95, 0.99 and no PCA. The results are expressed in m s−1.

Table VII. Forecasting accuracy comparison using differentnumber of GFS grid points around REUS. A neural network isdeveloped for each case. The results are expressed in m s−1.

1 Grid point R = 0.60 R = 0.50RMSE = 2.77 RMSE = 2.27

4 Grid points R = 0.66 R = 0.53RMSE = 2.59 RMSE = 2.21

16 Grid points R = 0.67 R = 0.60RMSE = 2.56 RMSE = 2.10

3.4.2. Number of grid points

As stated in the Introduction, the effect of the numberof grid nodes used can be of certain relevance and mustbe investigated. To obtain the best out of the model, theglobal net of the GFS model should be used as inputpattern. A safe value is using as many nodes as theeffective length-scale of the model indicates. Any numberof grid nodes below the former values will introducesome errors and a slight degradation of the forecastingaccuracy.

Table VII presents the forecasting accuracy of neuralnetworks using different number of grid points (1, 4 and16) and 5000 examples without using PCA dimensionreduction. This table shows that the forecast accuracyslightly improves (RMSE improvement below 5%) as thenumber of grid points increases from 1 to 4 and to 16 forboth Vx and Vy .

For the studies presented in this section it is empha-sized that the use of a greater number of grid points andprincipal components helps to improve the forecastingaccuracy slightly (RMSE improvement below 10%), butwhen the number of examples is low, the input patterndimension must be reduced and a compromise must befound. PLANIMIA is an example of such compromise.

4. PLANIMIA predicting accuracy

To evaluate the PLANIMIA predicting accuracy, themodel is compared to eight simpler statistical down-scaling models (four linear and four non-linear neuralnetworks with one hidden layer: The four non-linear mod-els are set up with g linear and f logistic, as defined inEquation (2)) and to the MASS and GFS models (the

GFS wind forecast is a pondered mean between the fournodes). Every statistical downscaling model uses MASSand/or GFS outputs as input variables. A PCA is appliedto that input pattern to reduce its dimension and keeping95% of the cumulative variance in all cases before it isfed to the neural network. The neural networks used foreach model are of the feed forward type, trained with theback propagation algorithm. The size of the hidden lay-ers is adjusted to obtain fast and reliable results in eachcase. The predicting accuracy of the statistical down-scaling models has been calculated by a cross-validationprocess. These statistical downscaling models are listedbelow, and are the same for Vx and Vy (in parenthesisthere is the name of the model as presented in Figures 4,5, 6 and 7).

1. Linear models:• Input pattern from MASS and GFS output data

(MASS + GFS (linear));• Input pattern from MASS output data (MASS

(linear));• Input pattern from GFS output data (GFS (lin-

ear)), and• Input pattern from MASS and GFS output data, and

a PCA is applied to reduce dimension (PCA(GFS+ MASS)).

2. Non-linear models:• Input pattern from MASS and GFS output data

(MASS + GFS (nonlinear));• Input pattern from MASS output data (MASS

(nonlinear));• Input pattern from GFS output data (GFS (nonlin-

ear)), and,• Input pattern from MASS and GFS output data, and

a PCA is applied to reduce dimension (PCA(GFS+ MASS)(nonlinear)).

The rmse is calculated at five ranges of measuredwind for Vx and for Vy , separately: fast < 0, medium< 0, slow, medium > 0 and fast > 0, which corre-spond to wind speed, v in m s−1, −7.71 < v, −7.71 ≤v < −2.57, −2.57 ≤ v ≤ 2.57, 2.57 < v ≤ 7.71, 7.71 <

v, respectively (in knots, −15 < v, −15 ≤ v < −5,−5 ≤ v ≤ 5, 5 < v ≤ 15, 15 < v, respectively). Thechoice of this distribution of wind speeds and the useof knots, is based on the final use of PLANIMIA,

Figure 4. Vx forecast errors (rmse) at the five wind ranges: fast <

0, medium < 0, slow, medium > 0 and fast > 0. The four dashedlines link forecast errors from the following linear statistical models:X MASS + GFS (linear), MASS (linear), GFS (linear) and PCA(GFS + MASS) (linear). The two thick lines link forecast errors fromthe two numerical models: MASS (NWP) and GFS (NWP). The

thickest line links PLANIMIA forecast errors.

Figure 5. Vx forecast errors (rmse) at the five wind ranges: fast < 0,medium < 0, slow, medium > 0 and fast > 0. The four dashed lineslink forecast errors from the following non-linear statistical models: XMASS + GFS (nonlinear), MASS (nonlinear), GFS (nonlinear) and

PCA (GFS + MASS) (nonlinear). The two thick lines link forecasterrors from the two numerical models: MASS (NWP) and GFS

(NWP). The thickest line links PLANIMIA forecast errors.

which is highly relevant to small size aircraft oper-ations (1 knot = 0.514 m s−1). The relative numberof observed cases for each wind range is shown inTable VIII.

5. Results and error evaluation

This section presents the predicting accuracy of PLA-NIMIA and compares it to the MASS and GFS out-puts, and to other eight simpler statistical downscalingmodels.

Figure 6. Vy forecast errors (rmse) at the five wind ranges: fast <

0, medium < 0, slow, medium > 0 and fast > 0. The four dashedlines link forecast errors from the following linear statistical models:X MASS + GFS (linear), MASS (linear), GFS (linear) and PCA(GFS + MASS) (linear). The two thick lines link forecast errors fromthe two numerical models: MASS (NWP) and GFS (NWP). The

thickest line links PLANIMIA forecast errors.

Figure 7. Vy forecast errors (rmse) at the five wind ranges: fast < 0,medium < 0, slow, medium > 0 and fast > 0. The four dashed lineslink forecast errors from the following non-linear statistical models: XMASS + GFS (nonlinear), MASS (nonlinear), GFS (nonlinear) and

PCA (GFS + MASS) (nonlinear). The two thick lines link forecasterrors from the two numerical models: MASS (NWP) and GFS

(NWP). The thickest line links PLANIMIA forecast errors.

5.1. Accuracy for all wind ranges

The rmse over all wind ranges of the forecasting modelsare shown in Table IX. The rmse of the statisticaldownscaling models is always smaller than those of thetwo NWP models. These two models present similarrmse between each other and for both wind components.The improvement in the accuracy of the statisticaldownscaling models, in relation to the NWP models,is high for the Vy component and small for the Vx

component. The reason for this behaviour is not clear,but indicates that there are some systems where statistical

Table VIII. Relative number of cases (to the nearest integer)observed in each wind range, for both wind components, Vx

and Vy .

Vx(%) Vy(%)

Fast < 0 0.5 1Medium < 0 10 8Slow 63 54Medium > 0 21 38Fast > 0 5 0

Table IX. Overall rmse of the forecasting models, expressed inm s−1.

Vx rmse Vy rmse

MASS (NWP) 3.3 3.2GFS (NWP) 2.8 3.3MASS + GFS (linear) 2.5 2.0MASS (linear) 2.6 2.0GFS (linear) 2.7 2.1PCA(GFS + MASS) (linear) 2.6 2.1MASS + GFS (non-linear) 2.4 2.0MASS (non-linear) 2.6 1.9GFS (non-linear) 2.5 1.9PCA(GFS + MASS) (non-linear) 2.5 2.0PLANIMIA 2.3 1.7

Table X. Prediction bias (in m s−1) of PLANIMIA and theMASS and GFS model.

Vx bias Vy bias

MASS −0.1 −0.05GFS −0.5 −1.7PLANIMIA −0.2 −0.2

The bias observed for PLANIMIA is slightly greater than MASS andsmaller than GFS.

downscaling can improve the NWP models better thanother systems. The non-linear models present a slightlybetter accuracy than linear models, and PLANIMIA isthe model with the best overall accuracy.

Another interesting parameter of a forecasting modelis the bias:

bias = 1

N∑i=1

(vobservedi − vforecast

i ) (5)

where vobservedi and vforecast

i are the observed and fore-cast wind component. N is the number of examplesused.

Table X shows that the bias calculated for PLANIMIAis in between the two NWP models: smaller than GFSand slightly greater than MASS.

The correlation coefficients of the PLANIMIA windforecasts (measurement against forecast) are R = 0.787

for Vx , and R = 0.735 for Vy , calculated in representativedatasets.

5.2. Accuracy by wind speed range

Figures 4–7 show the predicting accuracy of PLANIMIAand the other models for different wind speed ranges.The following text summarizes the results shown in thesefigures.

1. Vx component:(a) PLANIMIA produces smaller or similar rmse

compared to MASS and GFS models. GFS pro-duces large error at fast wind ranges.

(b) Linear statistical downscaling models: all four lin-ear statistical downscaling models produce similarerrors to PLANIMIA with the relevant exceptionof the fast > 0 wind range.

(c) Non-linear statistical downscaling models: non-linear statistical downscaling models differ fromlinear ones at fast wind regions, but behave simi-larly at medium and slow wind ranges. Thereforethere is some advantage in using non-linear mod-els.

2. Vy component:(a) PLANIMIA produces smaller or similar rmse

compared to MASS and GFS models at fast winds,but presents a better performance at medium andslow wind ranges. GFS produces large error athigher wind ranges.

(b) Linear statistical downscaling models: all fourlinear statistical downscaling models present highrmse at the fast < 0 wind range, but get closerto PLANIMIA at the medium and the slow windranges. This is because a single neural network isnot the best approach to predict extreme events.

(c) Non-linear statistical downscaling models: non-linear statistical downscaling models present highrmse at the fast < 0 wind range, but smallerthan the linear models. Therefore, there is someadvantage in using non-linear models.

Most statistical downscaling models present a highrmse for highwinds, mainly due to the fact that themaximum number of observations occurs at low windsand the regression adapts to the size of the population.Furthermore, there are few cases at high winds andthe statistical forecast can fail for this fact. After therelatively complicated (in the sense of Zorita and vonStorch, 1999) PLANIMIA model, which produces goodresults, there is a remnant error at the slow wind range(rmse of about 1.7 ms−1 for Vx and 1.5 m s−1 for Vy)that seems hard to reduce with the methods used in thisstudy.

5.3. Bias by wind range

The PLANIMIA biases calculated for each wind range, inmeters per second, are shown in Table XI. PLANIMIA

Table XI. Bias of PLANIMIA forecast at the different windranges, expressed in m s−1.

Vx bias Vy bias

Fast < 0 3.9 8.8Medium < 0 2.7 3.8Slow 0.4 1.7Medium > 0 −2.2 1.7Fast > 0 −5.2 –

overestimates the Vx wind speed, and the negative valuesof the Vy component.

6. Conclusions

This paper describes PLANIMIA, a short range windforecast statistical downscaling model for Reus Airportwhich uses clustering techniques, variable selection withgenetic algorithms, PCA, and a final forecast with neuralnetworks.

PLANIMIA is compared to eight simpler statisticaldownscaling models. These are linear and non-linear neu-ral networks, combining several NWP models outputs asinput variables. PLANIMIA is the statistical downscalingmodel that presents the lowest rmse for all wind ranges.Error distribution through the wind range for these sta-tistical downscaling models is larger for stronger winds,probably because there are less data in the stronger windsregions. The forecasting accuracy of the non-linear sta-tistical downscaling models is slightly better than that oflinear models.

A complicated model such as PLANIMIA produces aslight improvement in forecast accuracy. The best advan-tage of PLANIMIA is that the rmse is always similar orlower when compared with previously presented fore-cast models. The PLANIMIA bias is between the twoNWP models, but tends to overestimate the wind speed,specially for fast winds.

The selected variables for the input pattern differ fromone neural network to another, but as a general rule, thecorresponding surface wind component is always present.Other variables are present in many other input patterns,such as surface relative humidity, surface temperature,higher level temperature and surface absolute vorticity.After the relatively complicated, but accurate, PLAN-IMIA model, there is a remnant error for lighter winds(rmse of about 1.7 m s−1 for Vx and 1.5 m s−1 for Vy).PLANIMIA presents smaller rmse than MASS and GFSoutputs for Vx and Vy .

Proposals for improving forecasting accuracy are toincrease the number of examples, to be able to enlargethe input pattern dimension safely. Hence, it would bepossible to include more grid points and capture the longrange effects form NWP models. In this new scenario itshould be investigated the effect of the PCA as dimensionreduction tool.

Acknowledgements

The authors would like to thank the Servei Meteorologicde Catalunya (SMC), who provided the MASS dataand the Agencia Estatal de Meteorologıa (AEMet) forproviding the METAR historic dataset at Reus airport.

This work has received the funding support of Fun-dacion Rego.

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Statistical wind forecast for Reus airport

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