Short-range wind speed predictions for complex terrain using an interval-artificial neural network

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Energy Procedia 00 (2017) 000–000 Energy Procedia (2017) 000–000 Energy Procedia 125 (2017) 199–206 Energy Procedia 00 00 (2017) 000–000

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European Geosciences Union General Assembly 2017, EGU European Geosciences Union General Assembly 2017, Division Energy, Resources & Environment, ERE EGU Division Energy, Resources & Environment, ERE

Short-range wind speed predictions for complex terrain using an Short-range wind speed predictions for complex terrain using an The 15th International Symposium on District Heating and Cooling interval-artificial interval-artificial neural neural network network a,∗ a a Assessing the feasibility of using the heat Irene Schicker , Petrina Papazek , Alexander Kanndemand-outdoor , Yong Wanga Irene Schickera,∗, Petrina Papazeka , Alexander Kanna , Yong Wanga für Meteorologie und Geodynamik, ZAMG, Hohe Warteheat 38, 1190 Vienna temperature Zentralanstalt function for a long-term district forecast Zentralanstalt für Meteorologie und Geodynamik, ZAMG, Hohe Warte 38, 1190 demand Vienna a a

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc

Abstract Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Renewable energy such as wind andRecherche solar energy rely on favorable conditions. As Limay, load balancing the energy system is b Veolia & Innovation, 291 Avenueweather Dreyfous Daniel, 78520 France in Renewable energy such as wind and solar energy rely wind on favorable weather conditions. As load balancing in the energy system is c crucial accurate and tailored forecasts of the expected speed and power production are needed. A neural network based Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France(NN) crucial accurate and tailored forecasts of the expected wind speed and power production are needed. A neural network (NN) based approach for short-range wind speed forecasts was developed. Two different NN models were developed using observations and approach wind speed forecasts was developed. Two differentthe NN models wereand developed using observations and NWP datafor as short-range input. The interval-based NN (iANN) approach outperformed NWP models a MOS-based forecast and was NWP as input. interval-based (iANN) approach outperformed the NWP models and a MOS-based forecast and was able todata reproduce theThe observations at 25NN representative Austrian observation sites. able to reproduce the observations at 25 representative Austrian observation sites. Abstract © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2017 The Authors. Published by Elsevier addressed Ltd. Peer-review under responsibility of the Geosciences Union (EGU) General Assembly 2017 the – District heating are commonly in theof as one of the most effective for decreasing Peer-review undernetworks responsibility of the the scientific scientific committee committee ofliterature the European European Geosciences Union (EGU)solutions General Assembly Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017 – Division Energy, Resources and the Environment (ERE). 2017 – Division Resources the Environment (ERE). greenhouse gasEnergy, emissions from theand building sector. These systems require high investments which are returned through the heat Division Energy, Resources and the Environment (ERE). sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, Keywords: wind speed; nowcasting; neural network; Austria; complex terrain; NWP model prolongingwind the investment return neural period. Keywords: speed; nowcasting; network; Austria; complex terrain; NWP model The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were 1.compared Introduction with results from a dynamic heat demand model, previously developed and validated by the authors. 1. Introduction The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Within theannual past demand decade was the fraction of20% energy stemming from sustainable renewable sources increased (the error in lower than for all weather scenarios considered). However,energy after introducing renovation Within the past decadeenergy the fractionasofwind energy from renewable energy sources increased substantially. and stemming solar energy and,sustainable upand to renovation a certain extent, hydropower, on the scenarios, the Renewable error value increasedsuch up to 59.5% (depending on the weather scenarios combinationrely considered). substantially. Renewable energy asonwind andwithin solar to up a energy certain extent, hydropower, rely The value of slope coefficient increased average the range of up 3.8% to 8% sources per decade, thatpower corresponds the favourable weather conditions. Asuch careful balancing of theenergy load ofand, renewable on the gridon intothe the favourable weather conditions. A careful balancing of the load of renewable energy sources on the power grid in the decrease in the numberand of heating hoursrange of 22-139h the heating (depending on the combination of weather and hour-ahead, intra-day day-ahead is thusduring vital and requiresseason accurate on-the-fly available weather forecasts. hour-ahead, intra-day andtoday-ahead range thus function vital and requires accurate on-the-fly available weather forecasts. renovation scenarios considered). On accurate the otherispredictions hand, increased for 7.8-12.7% per decade (depending on the Several approaches exist provide andintercept uncertainty ranges of the expected wind speed and wind Several approaches exist to provide accurate predictions and uncertainty ranges of the expected wind speed and wind coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and power. Numerical weather prediction (NWP) models, especially the regional and local models, use nowadays spatial power. Numerical weather (NWP) models, especially the regional and local models, use nowadays spatial improve the accuracy of heatprediction demand estimations.

resolutions of up to 1 km and a temporal forecast output resolutions of 1-hour. Depending on their forecast horizon, resolutions of up topredictions 1 km and aare temporal forecast resolutions of 1-hour. on their forecast horizon, new NWP model available either output every hour (forecast horizonDepending up to 12 hours, rapid update cycle © 2017 Themodel Authors. Published by Elsevier Ltd.either every hour (forecast horizon up to 12 hours, rapid update cycle new NWP predictions are available models) or every three to twelve hours (forecast horizon of 72 hours and more). Although the spatial (horizontal and Peer-review underthree responsibility of hours the Scientific Committee of 15th International on District and and models) or every to twelve (forecast horizon ofThe 72nowadays hours andalready more).Symposium Although the spatial Heating (horizontal vertical) and temporal resolutions of regional NWP models provide high-quality forecasts, they Cooling. and temporal resolutions of regional NWP models nowadays already provide high-quality forecasts, they vertical) are still too coarse for applications in the energy sector. Especially in regions with complex terrain (narrow valleys, are still too coarse for applications in the energy sector. Especially in regions with complex terrain (narrow valleys, Keywords: Heat demand; Forecast; Climate change ∗ ∗

Corresponding author. Tel.: +43-1-36026-2326 Corresponding Tel.: +43-1-36026-2326 E-mail address:author. [email protected] E-mail address: [email protected]

1876-6102 1876-6102©©2017 2017The TheAuthors. Authors.Published Publishedby byElsevier ElsevierLtd. Ltd. 1876-6102 ©under 2017responsibility The Authors.ofPublished by Elsevier Ltd.of the Peer-review scientific committee European Geosciences Symposium Union (EGU) 2017 – Division Energy, Peer-review under responsibility ofthethe Scientific Committee of The 15th International onGeneral DistrictAssembly Heating and Cooling. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-reviewand under of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017 – Division Energy, Resources the responsibility Environment (ERE). Peer-review under responsibility of the scientific committee of the European Geosciences Union (EGU) General Assembly 2017 – Division Resources and the Environment (ERE). Energy, Resources and the Environment (ERE). 10.1016/j.egypro.2017.08.182

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steep slopes) the current NWP models with horizontal resolutions of 1 – 5 km are still not capable to simulate the atmospheric conditions sufficiently enough to provide tailored forecasts for wind farms especially for varying hub heights. Therefore, different approaches are used to post-process NWP forecasts. For the hour-ahead and minutes-ahead horizon statistical models such as stochastic differential equations (SDEs), sparse vector autoregression (sVAR) [1], ARIMA models (see e.g. [2]), semi-Markov chain models (see e.g. [3]) or mixed linear effect models can be applied [4]. For lead times beyond the first few hours, pure statistical models rapidly loose skill compared to NWP models. A common approach to provide tailored and accurate forecasts is to combine NWP model data with other methods such as computational fluid dynamics (CFD) models or machine learning approaches (neural networks, random forests, etc.). Such methods can be applied for forecasts of ultra-short (10 – 15 minutes up to one hour ahead), short term or in the days-ahead expected wind power production. For forecasts beyond the hour-ahead, methods such as artificial neural network (ANN), genetic algorithms (GA), random forest approaches, and hybrid methods combining ANN with GA are now widely used. [5] showed that using a data mining approach, a k-nearest neighbor model in combination with a principal component analysis and a filtering algorithm, produces reasonable results for wind farm monitoring and is a step towards forecasting of the expected wind power generation. Their filtering algorithm is based on a nonlinear parametric model which is trained by an evolutionary strategy algorithm. [6] showed that their multi-layer perceptron neural network (MLP-NN) outperformed different data mining approaches used in [5]. [7] used a feed forward neural network for daily wind speed predictions in a mountainous region in the state Himachal Pradesh in India. [8] applied a back-propagation neural network using the logistic sigmoid transfer function as activation function for different Turkish regions. [9] and [10] employed a feed-forward neural network with a multi-objective genetic algorithm and an autoregressive moving average model to estimate the wind speed uncertainties for 1-hour ahead predictions producing reliable forecasts. [11] used a multi-stage approach of a multi-layer perceptron neural network to predict the wind turbine power curve. A hybrid method using a backpropagation (BP) neural network and particle swarm optimization to predict 10-min ahead wind power was proposed by [12]. A similar approach was used by [13] employing an echo state network (ESN), a form of recurrent neural network, with tabu search and particle swarm optimization. [14] proposed a method based on ensemble empirical model decomposition (EEMD) to decompose the wind speed into different frequencies and feed it to a GA-BP neural network to forecast wind speeds. A detailed overview on artificial intelligence methods in wind energy systems can be found in [15]. This study aims at providing hourly forecasts for the nowcasting range (0 – 6 hours ahead) as well as for the medium range time horizon (6 –72 hours ahead) for observation sites in Austria in different complex and semi-complex terrain. Therefore, a neural network based approach was chosen as neural networks proved to be able to cover both nowcast and medium range time horizons. A temporal interval-based wind speed forecasting method was developed using a feed-forward neural network using using a combination of observation and NWP data as input. In a next step the proposed method will be applied to wind farm (SCADA) data. The paper is organised as follows: Section 2 describes the used data sets. Various aspects of the simulations carried out: study regions, model setup, and synoptic situation. In Section 3, the method and setup of the neural network approach is presented. Results are shown in Section 4, and conclusions are drawn in Section 5.

2. Data Observations as well as NWP forecast data are employed in this study to train, forecast and validate the proposed neural network. Observations with 10-min temporal resolution of the parameters temperature, wind speed and wind direction, relative humidity, and pressure of the Austrian station network, TAWES (Teil Automatische Wetter Station), are available. Model data available are ZAMGs’ INCA (Integrated Nowcasting through Comprehensive Analysis, Haiden et al. [16]) data, used as benchmark in the nowcasting range, and two numerical weather prediction (NWP) models developed within the international ALADIN project (http://www.cnrm-gamemeteo.fr/aladin), the ALARO and the AROME model [17]. Both models consist of a non-hydrostatic dynamical kernel but differ in the used physical parameterisations, the horizontal resolution and the forecast range [18]. AROME and ALARO data are used as input for the proposed neural network. Data of the two NWP models are bilinear interpolated to the locations of the used observation sites. In addition to the two NWP models and the INCA model a model output statistics (MOS) based forecast based on the operational concensus forecast of Woodcock and Engel [19], here called META, is used for



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05:00 10:00 15:00 20:00 01:00 06:00 11:00 16:00 20:00

hf (ALARO) = 6

ALARO-18 AROME-21

hf (AROM E) = 3

TAWES hf (IN CA) = 0

INCA hf (AN N ) = 45

hf (AN N ) = 0

ANN

Fig. 1. Availability of the NWP models AROME (red) and ALARO (blue) including their age as input to the proposed interval ANN (green) at 00 UTC and the corresponding INCA analysis and forecast (purple) for evaluation.

verification. The META model consists of 14 different NWP model input data, including two realisations of some models and ECMWF ensemble information. Depending on the availability of the NWP models the input data are composed in a way that the latest available NWP run is used as input for the ANN (Fig. 1). July 2016 was selected as test month for this study, containing frontal passages and thunderstorms. For this study, 25 observation sites (Fig. 2) were selected representing the different Austrian regions and terrain inhomogeneities. Observed temperature at 2 m height, wind speed and wind direction at 10 m height were used as input for the neural network. Observed wind speed was used for verification too. For wind energy, the relevant height of wind speed and wind power forecasts is the hub height. The proposed method is planned to be used for both observation sites with measurement heights of 10 m and for hub heights of wind farms. In a first step the method is applied to forecast the 10 m wind speed. The final method will be applied to wind farm data using NWP model output at a corresponding height.

Fig. 2. Location of the selected 25 TAWES stations used for forecasting and validation.

3. The interval-artificial neural network (iANN) ANNs can be described as a computational approach to copy the problem solving way of a mammalian cerebral cortex by using a number of highly interconnected layers (input, output, and hidden) processing information based on their (dynamic state) response to external input. They gather knowledge by pattern recognition in a data set and train or learn through experience, they are not explicitly programmed. Mathematical models defining functions, distributions, learning algorithms or learning rules are used to describe the connection between the input layer and the output layer of a neural network. Each layer in an ANN consists of several nodes which imitate the neurons of a brain. The different layers and the nodes within each layer of an ANN are connected by links and interact with each other. Every link between the nodes is associated with a weight w. Thus, a node is provided with a weighted input, uses a transfer function and passes its result, the node value, to the other nodes. The weights of the inputs between the nodes are adjustable parameters, their sum represents the activation of a node. This weighted activation signal passes through the nodes transfer function and produces the node value. The interconnection, the weights, between the nodes and layers can be optimized using non-linear global optimization techniques during the training or learning process until the error in the predictions is minimized and the ANN reaches a certain level of accuracy. The trained ANN can then

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Input layer

age of observation

x0

observed temperature

x1

observed air pressure

x2

wind speed �� minutes ago

x3

wind speed �� minutes ago

x4

lead time

x5

prediction of wind speeds

x6

prediction of wind directions

x7

Hidden layer �

Hidden layer �

Output layer

z

wind speed

Fig. 3. A subset of input parameters to the proposed ANN and its structure.

be used to perform predictions for i.e., optimized transportation routes or wind speed and expected wind power of wind turbines. For this study, a classical feed-forward ANN was implemented consisting of one input layer, two hidden layers, and one output layer. The layers are chosen to be dense, i.e., fully connected to the next layer. The input layer consists of 17 input neurons, both hidden layers of 64 neurons each, and the output layer of one neuron, the wind speed forecast. For optimisation of the weights and the learning of non-linear relationships an objective function and an optimisation algorithm are defined. The weight optimisation can be considered as a continuous problem. This can be solved by the gradient descent method, a first-order iterative optimisation algorithm which uses a minimisation algorithm to find the local minimum of a function. Several different gradient descent methods are available, for this study the stochastic adaptive moment estimation (Adam) optimisation algorithm by [20] was used. The optimisation algorithm needs an objective function to be applied to, here the mean squared error (MSE) was used. This setup was chosen to build a baseline ANN with known parameters and drawbacks. The innovation of the proposed method lies on one hand in the combination of the input layers, which are observations and NWP data, as well as in the final applied interval and ensemble methodology. Different combinations of input data to the ANN were evaluated. Temperature and (reduced) pressure ten minutes before the forecast initialisation as well as wind speed of ten and 20 minutes before of the TAWES sites are used. Additionally, wind speed and wind direction of the initial forecast time and of the available NWP model are used. Depending on the model availability it can be either a single or a multi-model input to the neural network. Besides the meteorological information also the age of the NWP model and the age of the observations are used. The basic ANN setup, performing forecasts applying the neural network to all forecasting leadtimes at once, showed that the model outperformed the NWP forecasts and the INCA forecast but was not able to increase forecasting skills in the first hours (typically hours 0 – 6). The objective is the minimisation of the MSE for all forecasting hours simultaneously. Therefore, to increase the forecast skills also for the first hours, a restriction of the training data to values in the forecasting range of interest, speeding up also the training process, was applied. Separate ANNs for different time horizons are thus applied to create the forecast for the whole time horizon. The training and test data are decomposed into disjunct parts of the time horizon and the iANN is applied simultaneously to optimise for the different time ranges. A filter is applied and the individual forecasts are joined to retrieve one forecast for the whole time horizon (see Fig. 4). A local forecasting approach is applied providing forecasts by the iANN for each individual observation site. To be able to provide a robust forecast an ensemble is computed. The iANN is randomly initialised using ten different "model runs" yielding slightly different wind speed forecasts. These runs are averaged to provide a single, robust forecast. The training length is chosen as a sliding window approach considering the precious 120 days.



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input training data Observations NWPs (ALARO, AROME) metadata

adapt training process

filter data by forecasting range hf

restricted to hf = 0 − 1

restricted to hf = 2 − 3

restricted to hf = 4 − 6

train ANN

train ANN

train ANN

AN N (1) : hf = 0 − 1

AN N (2) : hf = 2 − 3

AN N (3) : hf = 4 − 6

forecast for hf = 2 − 3

forecast for hf = 0 − 1

test data

restricted to hf > 6

train ANN

AN N (4) : hf = 7 − 40

forecast for hf = 7 − 40 forecast for hf = 4 − 6

join ANN output to forecasts for all hf point forecast 1 get input data for n forecasts point forecast 2 point forecast 3

point forecast n

Fig. 4. Concept of the iANN using a split-forecasting approach applying the ANN to a specific range of the forecasting hour h f and joining the output of the single ANNs to one forecast.

4. Results Two versions of the proposed ensemble-neural network, one performing forecasts for all leadtimes (ANN AROME+ALARO) and the interval-based method which forecasts separately for selected leadtime time slices (iANN AROME+ALARO), were employed to forecast wind speed for a selected period for a representative subset of observation sites. For the interval-based iANN forecast an additional forecast was performed using only the AROME model as NWP input features (iANN AROME). Forecasts were carried out hourly for the next 40-hours for July 2016. Evaluation was carried out for the whole month and for selected case studies which included thunderstorms. Overall performance and three selected sites, Wien Hohe Warte, Kanzelhöhe, and Rax Bergstation (a mountainous site) are discussed in more detail. Results and scores (Tab. 1) of the non-interval ANN AROME+ALARO show that the overall performance of forecasts is better compared to the two NWP models and the INCA nowcasting. For the nowcasting range of 0–2 hours ahead, however, the ANN AROME+ALARO is outperformed by INCA nowcasting and the persistence (not shown here). Especially for the two mountainous sites Kanzelhöhe and Rax Bergstation the ANN is not able to reproduce the observations (MAE of 1.22 and 1.97, respectively). As the purpose of this study is providing wind speed nowcasts as well as medium-range forecasts, the ANN approach had to be modified to increase its skills in the nowcasting range. Therefore, an interval-based ANN approach

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Table 1. Mean absolute error and correlation of the NWP models, the INCA model, and the three different neural network forecasts, ANN AROME+ALARO, iANN AROME, and iANN AROME+ALARO, for all 25 selected sites and all leadtimes.

Mean Absolute Error (MAE) time horizon

AROME

ALARO

ANN AROME+ALARO

iANN AROME

iANN AROME+ALARO

INCA

1.36 1.36 1.36 1.39 1.39 1.41

1.26 1.26 1.28 1.29 1.29 1.29

0.86 0.88 0.93 0.96 0.98 0.98

0.79 0.87 0.96 0.99 0.99 1.00

0.76 0.86 0.94 0.98 0.99 0.98

0.89 1.03 1.33 1.36 1.35 1.38

1h 2h 6h 12 h 24 h 36 h

Correlation R time horizon

AROME

ALARO

ANN AROME+ALARO

iANN AROME

iANN AROME+ALARO

INCA

0.52 0.52 0.52 0.51 0.51 0.50

0.58 0.57 0.57 0.56 0.56 0.56

0.79 0.78 0.76 0.75 0.74 0.74

0.80 0.78 0.75 0.74 0.74 0.73

0.82 0.79 0.76 0.73 0.73 0.74

0.80 0.75 0.61 0.60 0.60 0.60

1h 2h 6h 12 h 24 h 36 h

was implemented (see Sec. 3) using different neural networks for different leadtime time slices. In addition, as in general the AROME model yields better scores compared to the ALARO model not only due to its higher spatial resolution and physical parameterisations a forecast simulation based solely on AROME NWP forecast was carried out, the iANN AROME. Results show, however, that the combination of the iANN AROME+ALARO using wind speed and wind direction forecasts of AROME and ALARO yields better results compared to iANN AROME. This can be related on one hand to the selection of the 25 sites which included sites where the performance of AROME is worse compared to ALARO. On the other hand, there have been problems with AROME simulations during the selected episode related to the alpine pumping which was not represented reasonably enough by AROME. Similar to the ANN AROME+ALARO forecasts, results at the two mountainous sites of the two iANN forecasts are worse with an MAE of 1.20 and 1.77 for iANN AROME+ALARO and 1.29 and 1.83 for Kanzelhöhe and Rax Bergstation compared to other sites. This can be related to the fact that the MAE of both NWP models, AROME and ALARO, is worse compared to the non-mountainous sites. The site Rax Bergstation is located on the plateau next to a narrow and steep valley. With a spatial grid resolution of 2.4 km in the AROME model this leads to a smoothing of the topography of the respective grid point. Here, a solution could be using another grid point located at the plateau with suitable altitude or using an average of four surrounding grid points. Overall results indicate that in general, the iANN method is better especially in the nowcasting range. However, for leadtimes beyond 6 – 12 hours the ANN AROME+ALARO performs slightly better / comparable with the iANN AROME+ALARO although the scale is rather small. Here, one could adapt the interval selection and use smaller time slices for the medium range.

5. Conclusions A neural network wind speed forecasting frame based on a feed-forward neural network for Austria was developed for the intra-day to day(s)-ahead range. The non-interval based ANN results, using a single ANN for forecasts for all leadtimes, are able to outperform the NWP forecasts for leadtimes beyond the nowcasting range but are not able



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1.5 Wind speed (m/s)

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Wind speed (m/s)

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2057

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8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

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iANN - AROME+ALARO iANN - AROME ANN - AROME+ALARO

8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 01 July 2016 00 UTC - 31 July 2016 23 UTC

ALARO AROME INCA

Fig. 5. Mean absolute error for July 2016 over all forecast runs for all sites (top left), the site Wien Hohe Warte (top right), the site Kanzelhöhe, and Rax Bergstation. ALARO (green) and AROME (cyan) are the used NWP models, INCA nowcasting (blue) and the three neural network results (ANN AROME+ALARO in magenta, iANN AROME in dark purple, and iANN AROMe+ALARO in red.)

to reproduce the skills of INCA and the persistence method. Therefore, the setup was changed to an interval based method. The interval-ANN (iANN) based framework was developed providing forecasts for leadtime-slices which can be chosen as needed. It is able to train the neural network for the selected time slice separately and, thus, improving the forecasting skills. The iANN outperforms the NWP forecasts of AROME and ALARO as well as the MOS-based META wind speed forecasts for all considered lead times. Especially in the nowcasting range the iANN is able to reproduce the observations showing its skills for future wind speed and wind power forecast at selected sites. At sites where the NWP model grid points represent both mountain tops and valleys, thus, wind speed (and other meteorological parameters) of the respective grid point are valid for an average altitude between the two, the neural network is not able to reproduce the observations. At such grid points, or in other words, in regions with complex terrain where NWP model resolutions are too coarse to represent the local influences of the terrain post-processing methods such as neural networks or model output statistics need additional information to improve their skills. This could be solved using additional information such as altitude of the model grid point, slope and azimuth, etc.. Furthermore, neural networks need a certain amount of training data. Additional input data for training the model, for instance using past observation-NWP pairs of the past five years, could improve the results at those sites. References ˇ [1] Gallego, C., Pinson, P., Madsen, H., Costa, A., Cuerva, A. (2011). Influence of local wind speed and direction on wind power dynamicsâA˘ Tapplication to offshore very short-term forecasting. Applied Energy; 88: 4087-4096. [2] Kavasseri, R.G. and K. Seetharaman (2009). Day-ahead wind speed forecasting using f-ARIMA models, Renewable Energy, 34, 5, pp. 13881393, doi: 10.1016/j.renene.2008.09.006 [3] D’Amico, G., Petroni, F., and F. Prattico (2014). Wind speed and energy forecasting at different time scales: A nonparametric approach, Physica A: Statistical Mechanics and its Applications, 406, pp. 59-66, doi: 10.1016/j.physa.2014.03.034

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