• Aihara K., , Takabe T. , , and Toyoda M. , 1990: Chaotic neural networks. Phys. Lett. A, 144 (6–7), 333340.

  • Arsenio, A. M., 2000: Tuning of neural oscillators for the design of rhythmic motions. Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, CA, IEEE, 1888–1893. [Available online at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=844870.]

  • Arsenio, A. M., 2004: On stability and tuning of neural oscillators: Application to rhythmic control of a humanoid robot. Proc. IEEE Int. Joint Conf. Neural Networks (IJCNN), Budapest, Hungary, IEEE, 99–105. [Available online at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1379878.]

  • Barbounis, T., , Theocharis J. , , Alexiadis M. , , and Dokopoulos P. , 2006: Long-term wind speed and power forecasting using local recurrent neural network models. IEEE Trans. Energy Convers., 21, 273284.

    • Search Google Scholar
    • Export Citation
  • Bilgili, M., , Sahin B. , , and Yasar A. , 2007: Application of artificial neural networks for the wind speed prediction of target station using reference stations data. Renewable Energy, 32, 23502360.

    • Search Google Scholar
    • Export Citation
  • Chan, P. W., 2003: Application of LIDAR backscattered power to visibility monitoring at the Hong Kong International Airport: Some initial results. Proc. Sixth Int. Symp. on Tropospheric Profiling: Needs and Technologies, Leipzig, Germany.

  • Chan, P. W., , Shun C. M. , , and Wu K. C. , 2006: Operational lidar-based system for automatic wind shear alerting at the Hong Kong International Airport. Proc. 12th Conf. on Aviation, Range, and Aerospace Meteorology, Atlanta, GA, Amer. Meteor. Soc., 6.11. [Available online at https://ams.confex.com/ams/Annual2006/techprogram/paper_100601.htm.]

  • Choy, B. L., , Olivia Lee S. M. , , Shun C. M. , , and Cheng C. M. , 2004: Prototype automatic lidar-based wind shear detection algorithms. Proc. 11th Conf. on Aviation, Range, and Aerospace Meteorology, Hyannis, MA, Amer. Meteor. Soc., P4.11. [Available online at https://ams.confex.com/ams/11aram22sls/webprogram/Paper81363.html.]

  • Copper, J. D., and Coauthors, 2001: Failed retrograde transport of NGF in a mouse model of Down’s syndrome. Proc. Natl. Acad. Sci. USA, 98, 10 43910 444.

    • Search Google Scholar
    • Export Citation
  • Giraua, B., , and Torres-Huitzilb C. , 2007: Massively distributed digital implementation of an integrate-and-fire LEGION network for visual scene segmentation. Neurocomputing, 70, 11861197.

    • Search Google Scholar
    • Export Citation
  • Glushkov, A. V., , Khokhlov V. , , Serbov N. , , Svinarenko A. A. , , and Bunyakova Y. Ya. , 2009: Non-linear prediction method in short-range forecast of atmospheric pollutants: Low-dimensional chaos. Proc. Second Chaotic Modeling and Simulation Int. Conf. (CHAOS 2009), Chania, Crete, Greece, P54. [Available online at http://www.chaos2009.net/proceedings/PAPERS_PDF/Glushkov_et_al-Non-linear_prediction_method_in_short-range_forecast_of_atmospheric_pollutants_PAPER-CHAOS2009.pdf.]

  • Hannon, S. M., , Thomas J. A. , , Henderson S. W. , , and Huffaker R. , 1995: Wind shear, turbulence, and wake vortex characterization using pulsed solid-state coherent lidar. Air Traffic Control Technologies, R. G. Otto and J. Lenz, Eds., International Society for Optical Engineering (SPIE Proceedings, Vol. 2464), 94–102.

  • Hirasawa, K., , Murata J. , , Jinglu H. , , and Jin C. , 2000: Chaos control on universal learning networks. IEEE Trans. Syst., Man, Cybern. Part C: Appl. Rev., 30, 95104.

    • Search Google Scholar
    • Export Citation
  • HKO and IFALPA, 2005: Windshear and turbulence in Hong Kong—Information for pilots. Hong Kong Observatory, 40 pp. [Available online at http://www.weather.gov.hk/aviat/articles/WS-turb-booklet-web-ver.pdf.]

  • Howe, C. L., , and Mobley W. C. , 2005: Long distance retrograde neurotrophic signaling. Curr. Opin. Neurobiol., 15, 4048.

  • Jones, J. G., , and Haynes A. , 1984: A peakspotter program applied to the analysis of increments in turbulence velocity. Royal Aircraft Establishment Tech. Rep. 84071.

  • Karim, A., 2009: Chaos in semiconductor laser amplifiers. Proc. Second Chaotic Modeling and Simulation Int. Conf. (CHAOS 2009), Chania, Crete, Greece, MAICH, P82. [Available online at http://www.chaos2009.net/proceedings/ABSTRACTS_PDF/Karim-Chaos_in_Semiconductor_Laser_Amplifiers_ABSTRACT_CHAOS2009.pdf.]

  • Kwong, K. M., , Liu J. N. K. , , Chan P. W. , , Lee R. , 2008: Using LIDAR Doppler velocity data and chaotic oscillatory-based neural network for the forecast of Doppler velocities. IEEE Proc. Congress on Evolutionary Computation (CEC 2008)/2008 IEEE World Congress on Computational Intelligence (WCCI2008), Hong Kong, China, IEEE, 2012–2019.

  • Lawrance, A. J., , and Ohama G. , 2003: Exact calculation of bit error rates in communication systems with chaotic modulation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 50, 13911400.

    • Search Google Scholar
    • Export Citation
  • Lee, R. S. T., 2004: A transient-chaotic autoassociative network (TCAN) based on Lee oscillators. IEEE Trans. Neural Networks, 15, 12281243.

    • Search Google Scholar
    • Export Citation
  • Levitan, I. B., , and Kaczmarek L. K. , 2001: The Neuron: Cell and Molecular Biology. Oxford University Press, 632 pp.

  • More, A., , and Deo M. , 2003: Forecasting wind with neural networks. Mar. Struct., 16, 3549.

  • Öztopal, A., 2006: Artificial neural network approach to spatial estimation of wind velocity data. Energy Convers. Manage., 47, 395406.

    • Search Google Scholar
    • Export Citation
  • Perez-Munuzuri, V., , Souto M. J. , , Casares J. , , and Perez-Villar V. , 1996: Terrain-induced focusing of wind fields in the mesoscale. Chaos Solitons Fractals, 7, 14791494.

    • Search Google Scholar
    • Export Citation
  • Sánchez, I., 2006: Short-term prediction of wind energy production. Int. J. Forecasting, 22, 4356.

  • Sanyal, S., , Kim S. M. , , and Ramaswami M. , 2004: Retrograde regulation in the CNS: Neuron specific interpretations of TGF-β signaling. Neuron, 41, 845848.

    • Search Google Scholar
    • Export Citation
  • Shun C. M., , and Chan P. W. , 2008: Applications of an infrared Doppler lidar in detection of windshear. J. Atmos. Oceanic Technol., 25, 637655.

    • Search Google Scholar
    • Export Citation
  • Vincent, C., , Giebel G. , , Pinson P. , , and Madsen H. , 2010: Resolving nonstationary spectral information in wind speed time series using the Hilbert–Huang transform. J. Appl. Meteor. Climatol., 49, 253267.

    • Search Google Scholar
    • Export Citation
  • Wagener, T. J., , Demma N. , , Kmetec J. D. , , and Kubo T. S. , 1995: 2 μm LIDAR for laser-based remote sensing: Flight demonstration and application survey. IEEE Aerosp. Electron. Syst. Mag., 10 (2), 2328.

    • Search Google Scholar
    • Export Citation
  • Wang, L., , and Fu X. , 2005: Data Mining with Computational Intelligence. Springer, 276 pp.

  • Wilson, H. R., , and Cowan J. D. , 1972: Excitatory and inhibitory interactions in localized populations. Biophys. J., 12, 124.

  • Wolfson, M. M., , Delanoy R. L. , , Forman B. E. , , Hallowell R. G. , , Pawlak M. L. , , and Smith P. D. , 1994: Automated microburst windshear prediction. Lincoln Lab. J., 7, 399426.

    • Search Google Scholar
    • Export Citation
  • Wong, M. H. Y., , Lee R. S. T. , , and Liu J. N. K. , 2008: Wind shear forecasting by chaotic oscillatory-based neural networks (CONN) with Lee oscillator (retrograde signaling) model. Proc. IEEE Int. Joint Conf. on Neural Networks 2008 (IJCNN 2008), Hong Kong, China, IEEE, 2040–2047.

  • Wysoski, S. G., , Benuskova L. , , and Kasabov N. , 2008: Fast and adaptive network of spiking neurons for multi-view visual pattern recognition. Neurocomputing, 71, 25632575.

    • Search Google Scholar
    • Export Citation
  • Zeng, X., , Pielke R. A. , , and Eykholt R. , 1993: Chaos theory and its applications to the atmosphere. Bull. Amer. Meteor. Soc., 74, 631644.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., , Patuwo B. E. , , and Hu M. Y. , 1998: Forecasting with artificial neural networks: The state of the art. Int. J. Forecasting, 14, 3562.

    • Search Google Scholar
    • Export Citation
  • Zweifel, L. S., , Kuruvilla R. , , and Ginty D. D. , 2005: Functions and mechanisms of retrograde neurotrophin signaling. Nat. Rev. Neurosci., 6, 615625.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Map of HKIA and Lantau Island with the location of the lidar (square). Runway corridors are shown as arrows with the names marked alongside.

  • View in gallery

    The LORS model.

  • View in gallery

    The structure of the CONN.

  • View in gallery

    Bifurcation diagram of the LORS model.

  • View in gallery

    Bifurcation diagram of the LORS model for parameter set A.

  • View in gallery

    The appearance of the LORS model with parameter set A and different iterations number (N).

  • View in gallery

    The steady decline of the wind velocity along the glide path 07LA from position 1 at 2213 UTC to position 2 at 2313 UTC 9 Jun 2007.

  • View in gallery

    The forecasted radial wind velocity along the glide path 07LA by CONN between 2213 and 2313 UTC 9 Jun 2007.

  • View in gallery

    The forecasted radial wind velocity along the glide path 07LA by CONN between 2213 and 2313 UTC 9 Jun 2007 after applying median filter.

  • View in gallery

    The movement of the sea breeze that enters the glide path 07RA between 0405 and 0456 UTC 6 Jan 2009.

  • View in gallery

    The forecasted radial wind velocity along the glide path 07RA by CONN between 0405 and 0456 UTC 6 Jan 2009.

  • View in gallery

    The headwind profiles obtained by applying GLYGA algorithm with the (a) forecast and (b) actual measured lidar data.

  • View in gallery

    Percentage of overlap between forecast and actual warning area in the simulation on 6 Jan 2009.

  • View in gallery

    Correlation coefficient vs time for the simulation on 6 Jan 2009.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 132 132 15
PDF Downloads 70 70 14

An Artificial Neural Network with Chaotic Oscillator for Wind Shear Alerting

View More View Less
  • 1 Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
  • | 2 Hong Kong Observatory, Hong Kong, China
© Get Permissions
Full access

Abstract

Current research based on various approaches including the use of numerical weather prediction models, statistical models, and machine learning models have provided some encouraging results in the area of long-term weather forecasting. But at the level of mesoscale and even microscale severe weather phenomena (involving very short-term chaotic perturbations) such as turbulence and wind shear phenomena, these approaches have not been so successful. This research focuses on the use of chaotic oscillatory-based neural networks for the study of a mesoscale weather phenomenon, namely, wind shear, a challenging and complex meteorological problem that has a vital impact on aviation safety. Using lidar data collected at the Hong Kong International Airport via the Hong Kong Observatory, it is possible to forecast the Doppler velocities with satisfactory accuracy and validate the prediction model with the potential to generate the wind shear alert. Experimental results are found to be comparable to the actual measurement. Moreover, the selected testing cases and results show that the value of correlation coefficient between the predicted and lidar-measured wind velocities exceeds 0.9 with various window sizes ranging from 1 to 3 h. These provide areas for further research of the proposed model and lidar technology for turbulence and wind shear forecasts.

Corresponding author address: K. M. Kwong, Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China. E-mail: kaming.kwong@gmail.com

Abstract

Current research based on various approaches including the use of numerical weather prediction models, statistical models, and machine learning models have provided some encouraging results in the area of long-term weather forecasting. But at the level of mesoscale and even microscale severe weather phenomena (involving very short-term chaotic perturbations) such as turbulence and wind shear phenomena, these approaches have not been so successful. This research focuses on the use of chaotic oscillatory-based neural networks for the study of a mesoscale weather phenomenon, namely, wind shear, a challenging and complex meteorological problem that has a vital impact on aviation safety. Using lidar data collected at the Hong Kong International Airport via the Hong Kong Observatory, it is possible to forecast the Doppler velocities with satisfactory accuracy and validate the prediction model with the potential to generate the wind shear alert. Experimental results are found to be comparable to the actual measurement. Moreover, the selected testing cases and results show that the value of correlation coefficient between the predicted and lidar-measured wind velocities exceeds 0.9 with various window sizes ranging from 1 to 3 h. These provide areas for further research of the proposed model and lidar technology for turbulence and wind shear forecasts.

Corresponding author address: K. M. Kwong, Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China. E-mail: kaming.kwong@gmail.com

1. Introduction

Wind shear and turbulence are weather phenomena that may adversely affect aircraft operations. Wind shear refers to a change in the wind direction and speed for typically 3 to 40 s resulting in a sustained change in the headwind to the aircraft. A decrease in headwind will result in decreased lift and this will lead to the aircraft flying below its planned flight path. Turbulence is caused by the rapid, irregular motion of air and can cause an aircraft to bump and jolt. In cases of severe turbulence, abrupt changes in the altitude of the aircraft may result in momentary loss of control and possibly even injuries to passengers and flight crew [Hong Kong Observatory and International Air Line Pilots’ Association (HKO and IFALPA) 2005].

The Hong Kong International Airport (HKIA) was built on an artificial island located north of mountainous Lantau Island, which has peaks rising to nearly 1000 m adjacent to valleys as low as 400 m. To the northeast of HKIA, there are also a number of smaller hills with peaks rising to 600 m (see Fig. 1). In this hilly, coastal environment, a wide variety of weather phenomena can cause the development of different local wind patterns, low-level wind shear, and turbulence (Shun and Chan 2008; Perez-Munuzuri et al. 1996). Since the opening of HKIA in July 1998, meteorological studies have been conducted to support the safety of aircraft landing and taking off, including the detection of wind shear and turbulence. To improve the detection of wind shear under rain-free conditions, a light detection and ranging (lidar) system was installed at HKIA in mid-2002. It is the first system of its kind in the world used in providing weather alerts to an operational airport.

Fig. 1.
Fig. 1.

Map of HKIA and Lantau Island with the location of the lidar (square). Runway corridors are shown as arrows with the names marked alongside.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Lidar is an optical analog of radar (radio detection and ranging). Lidar uses a ground-based pulsed laser to measure the velocity of small particles (aerosols) in the air. It can be used for detection of wind shear, clear-air turbulence, gust front, and wind profiling (Hannon et al. 1995; P. Cross 1997, personal communication; Wagener et al. 1995). The data collected by lidar have been put to good use in detecting occurrences of wind shear with high accuracy (Shun and Chan 2008), but there has been little research into the forecasting of wind shear.

In this paper we describe our research, which makes use of chaotic oscillatory-based neural networks and accurate Doppler velocities measured by lidar to forecast the occurrence of wind shear at HKIA. We focus on the prediction of the evolution of the wind field along the glide path of the airport. Section 2 introduces these ideas through a literature review. Section 3 presents the system architecture and methodology. Section 4 presents the experimental results and comparison. Section 5 provides our conclusion. Section 6 gives possible further research in future.

2. Literature review

In this section, we first describe the current methods of predicting wind shear and then introduce three important parts of our work, namely, chaotic oscillatory-based neural networks, the original version of the Lee oscillator (Lee 2004) and the enhanced version being considered in this study—the retrograde signaling modeling.

a. Wind shear prediction

The Lincoln Laboratory of Massachusetts Institute of Technology (MIT) has proposed an algorithm for predicting various types of wind shear due to microbursts. It uses machine intelligence techniques to determine Terminal Doppler Weather Radar (TDWR) images in different time sequences, with a detection probability of 72% and a false alarm rate of 27% for the unrestricted prediction mode, that is, when the microburst prediction algorithm is considered independent of the microburst detection algorithm (Wolfson et al. 1994).

However, the main causes of wind shear and turbulence in HKIA are not due to microbursts but 1) strong winds blowing across the hills over Lantau Island, or 2) a sea breeze that causes winds to turn westerly over the western part of the airport (HKO and IFALPA 2005). In fact, the reports received from aircraft pilots landing at or taking off from the airport indicate that many wind shear cases occur under nonrainy and clear-air conditions at HKIA, while TDWR has proved to be effective in rainy weather (Chan 2003; Choy et al. 2004).

b. Artificial neural network for winds prediction

Scalar time series analysis and prediction have been applied to many wind prediction problems (Vincent et al. 2010), but rarely to problems of wind forecast. On the other hand, artificial neural networks (ANNs) have been applied with great success to many prediction problems (Wang and Fu 2005) and show some success in other wind prediction problems. Typical examples are the mean monthly wind speed prediction by using hourly mean wind speeds (Bilgili et al. 2007), power output prediction of wind turbines (More and Deo 2003), wind potential prediction at various regions (Öztopal 2006), and long-term wind speed forecast and its potential for use in generating wind power (Barbounis et al. 2006). In all of these examples, however, the predictions were confined to mean hourly or monthly wind velocities covering relatively large regions. Therefore, their ability to provide a forecast in the present domain of interest within a much shorter time period (e.g., 10 min) and with localized considerations of chaotic behaviors of wind shear is not certain.

c. Chaotic oscillatory-based neural network (CONN)

The idea of chaotic neural network was proposed by Aihara et al. (1990). They stated that real neuron operations in neurophysiology are far more complex than simple thresholds. A more suitable activator of a neuron is believed to be a nonlinear output function. As a result, they developed a chaotic neural network to model the nonlinear behavior of neurons.

Chaotic behavior provides a rich library of behaviors to aid computer systems, such as weather forecasting (Kwong et al. 2008; Wong et al. 2008; Glushkov et al. 2009), communications (Lawrance and Ohama 2003), and robot control (Arsenio 2004) or laser control (Karim 2009). Neural networks mimic the flexible nature of biological systems and offer a wide range of potential applications. Scientists have started using neural network architectures and learning algorithms involving chaos for the storage in memory of analog patterns (Kotaro et al. 2000; Jones and Haynes 1984), for example, in face recognition systems. Chaotic neural networks may be applied to prediction and control or to better understand a biological neural network, such as the role of chaos in brain activities.

The system architecture of most chaotic neural network models is based on the computational neuroscience models developed from the theoretical work of Hodgkin and Huxley (Lee 2004). These computational neuroscience models focus on spiking neural dynamic behavior. The main stream of neuroscience has focused on the behavior of the neural populations. Celebrated models include the neural oscillatory model (Wilson and Cowan 1972). This theory has also formed the basis of many subsequent studies and models in the field of cognitive information processing (Sánchez 2006) and on the synchronization and desynchronization behaviors of the neural oscillators. The latest applications include pattern and memory associations, scene analysis, and pattern recognition (Wysoski et al. 2008; Giraua and Torres-Huitzilb 2007).

Apart from that, chaotic natures also have been found in the atmosphere. Although chaos theory limits the long-term prediction, it suggests a possibility for short-term prediction as random-looking data may contain simple deterministic relationships. Therefore, chaos theory can be used for prediction problems, especially when a good model is lacking (Zeng et al. 1993).

d. The Lee oscillator (Retrograde Signaling) model

Research studies on neuroscience and brain science in recent years have discovered that there are various phenomena in brain functions (Aihara et al. 1990) and behaviors of neurons are inactivated by triggering between excitatory and inhibitory neurons. Based on this, artificial intelligence (AI) scientists have developed a special type of artificial neural networks like chaotic oscillatory-based neural networks to simulate the neural behavior of human beings. A typical example is the Lee oscillator (Retrograde Signaling) (LORS) model. It has been developed based on the retrograde transport mechanism in axons, known as axonal transport or axoplasmic flow (Levitan and Kaczmarek 2001). Retrograde transport stands in opposition to anterograde transport. Anterograde transport (Levitan and Kaczmarek 2001) is the phenomenon where a cell body chaotic moves toward terminals or dendrites as part of the process of supporting axons, which cannot synthesize proteins. To compensate for this, receptors, which are signaling proteins and enzymes for the synthesis of neurotransmitter, must be moved to distant axon terminals or dendrites. In contrast, retrograde transport moves materials back to the soma. There are two hypotheses as to the function of this: recycling and signaling. Recycling suggests materials are returned from the terminal to the soma for degradation or reuse. Signaling assumes that postsynaptic cells can secrete substances to be picked up by nerve terminal, packed into vesicles and carried back to the cell body (Howe and Mobley 2005; Sanyal et al. 2004; Zweifel et al. 2005).

Neuroscientists have discovered some important findings in recent years. They found that the major functionality of retrograde transport is signaling, which is also named as retrograde signaling. Retrograde signals influence neuronal survival, differentiation, homeostasis, and plasticity (Howe and Mobley 2005; Sanyal et al. 2004; Zweifel et al. 2005). The latest research on neuroscience points out that those neurological diseases such as Alzheimer’s disease and Down syndrome are significantly related to malfunction of retrograde transport mechanism (Copper et al. 2001).

Figure 2 shows the improved model of the Lee oscillator, which consists of the neural dynamics of four constitutive neural elements: u, υ, w, and z. The neural dynamics of each of these constituent neurons are given by
e1
e2
e3
e4
where u(t), υ(t), w(t), and z(t) are the state variables of the excitatory, inhibitory, input, and output neurons, respectively; f() is the hyperbolic tangent function; a1, a2, a3, a4, b1, b2, b3, and b4 are the weight parameters for these constitutive neurons; ϑu and ϑυ (not shown in Fig. 2) are the thresholds for excitatory and inhibitory neurons; I(t) is the external input stimulus; and k is the decay constant. Making use of chaotic oscillators, we shall introduce nonlinear behavior into artificial neural network for prediction problems that are of chaotic nature behind. It can be easier to use the improved model to reshape the chaotic region, generate dual chaotic regions by tuning different parameters, and reduce computation time (about one-tenth of the number of iterations needed by the original model).
Fig. 2.
Fig. 2.

The LORS model.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

3. Methodology

This study applies chaos theory to the forecast of a mesoscale wind field using a model that combines a CONN with a LORS model. We intend to forecast the winds with data measured by the lidar system that covers the glide path area instead of merely a single point measurement, for example, point source data collected by a surface anemometer located near the runway. The following describe data preparation in general, the prediction of wind evolution, and wind motion.

a. Data preparation

Since local air density, local temperature variations, and local effects of cloud and rain are difficult to measure (Sánchez 2006) and lidar can only measure the Doppler velocities, we therefore collect the Doppler velocity data derived from glide path scans that are done by lidar. As a result from clutters like aircraft along the glide paths, isolated outliers of radial velocity may appear as “spikes” in the raw data. The first step is to process these spikes with the quality control algorithm (Chan et al. 2006). Those outliers are detected by comparing each piece of radial velocity with the data points around. If the difference between them is larger than a predefined threshold, it will be smoothed by a median filter with the window size equal to 5. The threshold is determined from the frequency distribution of velocity difference between adjacent range/azimuthal gates of the lidar over a long period of time. Data quality control is kept to a minimum in order not to smooth out the genuine wind fluctuations of the atmosphere (Chan et al. 2006).

In the next step, if there were no data for a particular location in the surveillance scan data and if valid velocity data were available at the neighboring positions, we could derive the velocity value through a linear interpolation of the velocities at the neighboring points.

To feed the data into the CONN model for learning, those selected data should be preprocessed by normalization, which is a transformation performed on the input data to distribute the data evenly and scale it into an acceptable range for the neural network. As the response of the model to external input stimulus falls between +1 and −1, the training and testing dataset were normalized by using minimum (−1) maximum (+1) normalization. Each set of training data is referred to the glide path 07RA (location in Fig. 1) at a specific time. The data included the Doppler velocities on a slant range, angle of elevation, and azimuth. These were used to train the result of the Doppler velocities along the glide path 07RA in the upcoming 3-min duration. The time interval between two training sets was around 4 min.

b. Structure of the chaotic oscillatory-based neural network

The CONN is the core part of this forecast system. CONN is made up of a multilayered perceptron (MLP) neural network and a LORS model. The MLP neural network is composed of one input layer, one output layer, and one or two hidden layers with several neurons, and the activation function of the hidden neurons and output neurons are replaced with the model instead of the sigmoid or hyper tangent function in traditional neural networks. The number of neurons in input and output layers are the number of data points along the selected glide path; while the number of hidden layers and hidden neurons are chosen experimentally since there is no simple clear-cut method for the determination of these parameters (Zhang et al. 1998). The following sections will introduce the training and testing processes of the CONN model.

c. Training and testing of the CONN

The CONN is trained with a 1-month period of Doppler velocity data collected by the lidar. A backpropagation learning algorithm is used for error correction and a momentum term is used to avoid local minima (Aihara et al. 1990). In the testing process, CONN learns from the root-mean-square error (RMSE) between the predicted result and the measured value from the lidar through backpropagation and uses the experience gained in the training process to generate the forecast for the next time interval(s). In the following simulation, the next time interval denotes 3–4 min following the given input at the time.

Figure 3 shows the structure of the CONN being used in the simulation. The crosses on the left of input nodes represent patterns of current winds along the selected glide path that were measured by the lidar system, while the crosses on the right of output nodes represent the forecast of the winds along the selected glide path in the next time interval(s). In the figure, there is one hidden layer with several hidden neurons. Characters A and B in the neurons indicate different parameter settings used with the model as discussed in sections 2b, 2c, and 2d. These parameters were chosen experimentally. Table 1 presents the values of the parameters used in the study. The reason of using two different parameter settings is to balance the oscillating power of individual oscillators in the CONN. The oscillator with strong oscillating power will cause the forecast result to become noisy and vice versa.

Fig. 3.
Fig. 3.

The structure of the CONN.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Table 1.

Values of the parameters used in the CONN.

Table 1.

The bifurcation diagram of LORS model in Figs. 4a,b shows the output response of the model to an external input stimulus with parameter set A and parameter set B, respectively. In those figures, the x axis represents the external stimulus (I) from the connected neurons in the previous layer to the Lee oscillator, and the y axis represents the output of the Lee oscillator corresponding to the external stimulus.

Fig. 4.
Fig. 4.

Bifurcation diagram of the LORS model.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

The bifurcation diagram of LORS model with parameter sets A and B is composed of three main regions, P, Q, and R, respectively. From the neural dynamics point of view, region P [(−1.0 to −0.4) in Fig. 4a and (−1.0 to −0.3) in Fig. 4b] and region R [(+0.4 to +1.0) in Fig. 4a and (+0.3 to +1.0) in Fig. 4b] form the sigmoid-shape region, which corresponds to the nonchaotic neural activities in the oscillators; and region Q [(−0.4 to +0.4) in Fig. 4a and (−0.3 to +0.3) in Fig. 4b] is the hysteresis region, which corresponds to the area of chaotic behavior that results when a weak external input stimulus is received.

As LORS model provides a chaotic progressive growth in the neural dynamics, it can be used as an effective chaotic bifurcation transfer unit for contemporary neural networks. Figures 5a,b show different shapes of the chaotic region in the bifurcation diagram of the model for parameter set A with different values of parameter a1 (a1 = 0.1 in Fig. 5a, a1 = 0.4 in Fig. 5b). Figures 5c,d show the shape of the chaotic region for parameter set A with different values of parameters b3 and b4 (b3 = 2.0 in Fig. 5c, b4 = 1.0 in Fig. 5d). It is found that the shape of the chaotic region will have a great change for different values of parameter used. These parameters act as control in modeling the chaotic changes of winds in our domain interest.

Fig. 5.
Fig. 5.

Bifurcation diagram of the LORS model for parameter set A.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

We note that neural oscillators depend on parameters that have to be tuned to achieve the desired performance. However, neural oscillators have highly nonlinear dynamics and the parameters of neural oscillators are difficult to tune (Arsenio 2000, 2004). Although there is much literature on chaos control and tuning the parameters of neural oscillator, most of it is mainly concentrated on oscillation control or the frequency, amplitude, and phase of the neural oscillator (Arsenio 2000, 2004; Hirasawa et al. 2000), but few studies discuss the shape of the bifurcation diagram that being used as the transfer function in CONN.

In order for the CONN system to explore more output variations in the chaotic region of the LORS model, we propose to adjust the iteration number of the same parameter set during the training process. This is in addition to tuning the weights between input layer, hidden layer, and output layer of the network. Figure 6 gives the bifurcation diagram, which shows various output responses of the LORS model with different iteration number N corresponding to an external input stimulus with parameter set A. The x axis represents the external stimulus (I) from the connected neurons in the previous layer to the Lee oscillator, and the y axis represents the output of the Lee oscillator.

Fig. 6.
Fig. 6.

The appearance of the LORS model with parameter set A and different iterations number (N).

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

The proposed learning mechanism of CONN model will introduce a random generated iteration number N, which is assigned to every neuron in hidden layers and output layer during the initialization of CONN. In the training process, neurons in output layer produce several output responses according to the input stimulation, and five output responses are chosen in the following simulations, with the assigned iteration numbers.

For example, if a value of 10 is assigned as the iteration number to the first neuron in the hidden layer during initialization, this neuron produces 5 output responses using N ± 2 (in this example N = 8, N = 9, N = 10, N = 11, and N = 12 are used) with the same parameter set in the current training epoch. After comparing the outputs with the actual measured data from lidar system, the one with the smallest error value is selected as the output of that neuron.

d. Wind shear detection and alert generation in the forecast result

Hong Kong Observatory has developed an algorithm, which is named glide-path scan wind shear alerts generation algorithm (GLYGA) to detect wind shear events automatically from the headwind profiles derived from lidar data (Chan et al. 2006). GLYGA is now used for capturing wind shear events and providing wind shear alert service at HKIA in real time with high accuracy, but not in the forecast aspect.

By applying GLYGA to the results predicted by CONN model, it is possible to verify the forecasting ability of the CONN model and provide testing of whether wind shear alerts can be generated with the proposed model.

To do so, the forecasted radial velocities along a glide path are put together to construct a headwind profile that suggests the winds to be experienced by aircraft along the glide path while landing or departing. In addition, the velocity difference between adjacent data points along the headwind profile is calculated to construct a velocity increment profile that is used to magnify the change of velocities and make it easy to capture the ramp. There will be the wind shear ramp detection process where wind shear ramps refer to the peaks and troughs in the velocity increment profile. During the ramp detection process, the ramps are detected by comparing each data point of the profile with the neighboring points on both sides. The normalized wind shear value ΔV/H1/3 (Jones and Haynes 1984) is used in prioritizing the wind shear ramps detected from a headwind profile where ΔV is the total change of the headwind and H is the ramp length. An alert message would be generated if any one of the wind shear ramps picked up by the ramp prioritization operations or the wind changes exceed the alert threshold, which is set as 14 kt for the actual measured lidar and 12 kt for the forecast made by the CONN model.

4. Simulation results

In this section, we present two simulation results from a number of simulations on capturing the change of wind by CONN, and comparison of wind shear alerts captured from the forecasted result and actual measured data.

a. Capturing the change of winds by CONN

First of all, the simulation demonstrates the ability of CONN on forecasting the wind in common weather conditions. A case occurred on 9 June 2007 is chosen for the study. Figure 7 presents the actual lidar measurement of the radial wind velocity along the glide path 07LA between 2213 and 2313 UTC 9 June 2007. In the figure, the x axis is the distance away from the end of the runway in nautical miles (nmi). The y axis is the wind velocity in meters per second. Colored lines indicate lidar observations along the glide path, and color lines from a deep color to a light color indicate the corresponding wind velocity at different time. The figure also indicates the steady change of headwind to tailwind with respect to the aircraft movement direction (viz., positive to negative) along the glide path 07LA from position 1 at 2213 UTC to position 2 at 2313 UTC (as highlighted on Fig. 7).

Fig. 7.
Fig. 7.

The steady decline of the wind velocity along the glide path 07LA from position 1 at 2213 UTC to position 2 at 2313 UTC 9 Jun 2007.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Experiments show that training the CONN with around one month of data can produce the best forecast result. Therefore, a training set is constructed from the data recorded between 0002:44 UTC 1 May 2007 and 1842:51 UTC 9 June 2007, and a testing set is constructed from the data recorded between 2211:44 and 2311:53 UTC 9 June 2007 for this simulation. Figure 8 shows the forecast of the wind profile along the glide path 07LA done by CONN. This model can capture the occurrence of the steady change of headwind to tailwind with respect to the direction of aircraft movement. There is a rapid increase in the forecast radial wind velocity of about 6 kt from some of the time intervals that are not found in the actual measurements. Note that those of the rapid increase in the forecast can be understood as the computational noise of the CONN. With the use of a median filter, we may obtain a more acceptable forecast result as shown in Fig. 9. Although the magnitude of the rapid increase after the media filter is much smaller than the preset wind shear alert threshold, we continue to enhance the predictive capability of the CONN model by improving the learning algorithm so as to minimize the effect of such problems.

Fig. 8.
Fig. 8.

The forecasted radial wind velocity along the glide path 07LA by CONN between 2213 and 2313 UTC 9 Jun 2007.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Fig. 9.
Fig. 9.

The forecasted radial wind velocity along the glide path 07LA by CONN between 2213 and 2313 UTC 9 Jun 2007 after applying median filter.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

b. Capturing the wind shear from the forecast

We note that one of the major causes of wind shear at HKIA is due to the influence of sea breeze (HKO and IFALPA 2005), which often gets developed in fine weather and light wind conditions. As lidar works best in fine weather, it can be relatively easy to identify the movements of sea breezes. Accordingly, a significant case of wind shear that took place on 6 January 2009 with large magnitude wind shear ramps is selected by HKO for our study. We focus on testing the wind shear alert generation over the glide path area at HKIA by the proposed CONN with the GLYGA algorithm.

In this simulation, a training set is constructed from the data recorded between 0242:46 UTC 1 December 2008 and 0603:57 UTC 1 January 2009, and a testing set is constructed from the data recorded between 0403:09 and 0454:58 UTC 6 January 2009. Figure 10 shows the overall changes of the wind along the glide path 07RA between 0405 and 0456 UTC 6 January 2009. Figure 11 shows the forecast of the wind profile along the glide path 07RA made using the CONN model. Again, color lines from a deep color to a light color in the figures indicate the corresponding wind velocity at different times.

Fig. 10.
Fig. 10.

The movement of the sea breeze that enters the glide path 07RA between 0405 and 0456 UTC 6 Jan 2009.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Fig. 11.
Fig. 11.

The forecasted radial wind velocity along the glide path 07RA by CONN between 0405 and 0456 UTC 6 Jan 2009.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Figure 12 shows the headwind profiles obtained by applying GLYGA algorithm with the actual measured lidar data and simulation results about the sea breeze being picked up on 6 January 2009 over the arriving runway corridors 07RA at different time slots. Figures on the left-hand side present the forecast made by CONN; figures on the right-hand side present the actual measured data from lidar. In these figures, the x axis denotes the distance away from the runway end in nautical miles and the y axis on the left-hand side denotes the head wind measured in knots, while the y axis on the right-hand side denotes the altitude of the glide path measured in feet. The area highlighted in pink shows the detected wind shear ramp(s).

Fig. 12.
Fig. 12.

The headwind profiles obtained by applying GLYGA algorithm with the (a) forecast and (b) actual measured lidar data.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

In this simulation, the system forecast can capture most of the detected wind shear events. There are totally 14 time slots between 0405 and 0456 UTC. In the actual measured headwind profiles, wind shear events are detected at 8 time slots between 0405:08 and 0433:03 UTC and the system has successfully captured 7 of them. For example, a wind shear ramp with magnitude 14 kt is alerted to be appearing between 0.3 and 1.4 nmi away from the runway end at 0417:06 UTC, and there is a wind shear ramp with magnitude 15 kt being captured by GLYGA algorithm at the range 0.5–1.5 nmi away from the runway end at 0417:06 UTC in the actual measured headwind profile.

In those figures, the region that is marked as wind shear ramp, which is highlighted in the forecasting result, can basically cover the region where wind shear happened in the actual measured headwind profiles and also with similar magnitude. Though the CONN model could not give the forecast with an exact match of that measured by lidar, the model has made a pretty good forecast on the incident of the wind shears that are about to occur, including the location and magnitude of the wind shear occurrences.

Tables 2 and 3 show the performance statistics of CONN model in wind forecast. The correlation coefficient and RMSE within the forecasting period are listed in the tables. In simulation 1 (9 June 2007), the correlation coefficient between the actual measured data and forecast drops from 0.96 to 0.67 and the RMSE grows from 1.98 to 2.97 m s−1 and starts dropping; while in the simulation on 6 January 2009, the correlation coefficient drops from 0.81 to 0.7 and the RMSE keeps fluctuating around the average value (1.47 m s−1).

Table 2.

Performance statistics of CONN model on wind forecast in simulation 1 (9 Jun 2007).

Table 2.
Table 3.

Performance statistics of CONN model on wind forecast in simulation on 6 Jan 2009.

Table 3.

Figure 13 illustrates how the percentage of overlapping wind shear warning area can be derived between the CONN forecast and actual measured data in the simulation on 6 January 2009. Typically, the alert region detected at 0405:08 UTC contains an overlapped area:
eq1
Similarly, other alert regions are computed and shown in Fig. 13 with corresponding percent of overlap.
Fig. 13.
Fig. 13.

Percentage of overlap between forecast and actual warning area in the simulation on 6 Jan 2009.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

Table 4 shows the comparison of the wind shear ramp magnitude found in the forecast and the actual measured values in the simulation on 6 January 2009. The reason of the overlap region and wind shear ramp magnitude values being zero at 0409:08 is that the forecasted ramp is smaller than the preset alert threshold. Fine tuning of the alert threshold may help to improve the forecasting ability of the system.

Table 4.

Comparison of the magnitude between the forecasted and actual measurement in simulation on 6 Jan 2009.

Table 4.

c. The validity of the forecast

As weather phenomena change from time to time, the performance of the forecast made by CONN tends to drop over a longer prediction period. To provide reliable forecasts, finding out the validity of the forecast and retraining the CONN for making the next forecast will be another critical task of the alerting system.

Figure 14 shows the change of correlation coefficient of the forecast and actual measured lidar data against time for a long trial in simulation on 6 January 2009. As wind shear events happened in the first 80 min, the phase difference between the forecasted wind shear ramp and actual wind shear ramp result in the dropping of correlation between the forecast and actually measured data. Along with the change of weather condition, there is a sudden drop at around 180 min and some fluctuation of the correlation coefficients. This sudden drop of correlation coefficient indicates that the trained CONN begins to lose its ability of making valid forecast. To overcome the problem, retraining of the CONN with the last updated data is needed. As the training of CONN is a time-consuming process, further research will aim to improve the current learning algorithm and hence reduce the training time for the forecasting process.

Fig. 14.
Fig. 14.

Correlation coefficient vs time for the simulation on 6 Jan 2009.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/2011JTECHA1501.1

5. Conclusions

With the lidar’s Doppler velocity data from Hong Kong Observatory, we have conducted research on the prediction of the mesoscale wind field. Experimental results show that CONN is able to capture the occurrence, evolution, and sudden changes of the winds along the glide paths in the vicinity of the Hong Kong International Airport.

The simulation results presented in the second half of section 4 have also shown that the forecasted Doppler velocities from CONN can further be used to generate wind shear alerts by transforming the forecasted results into the headwind profile and processed with the wind shear alerting algorithm GLYGA developed by HKO. The forecasting alerts can basically match with the actual observation from lidar at the time, alerting location, and magnitude of the occurrences.

6. Further work

The further work will be the switch from developing the forecasting model to minimizing the requirement for the computational resources, improving the quality of the forecast, and enhancing the accuracy of alert generation.

It is worthwhile to keep our focus on the winds along the glide paths as a potential means to capture the major features of the wind fluctuations. On the one hand, we will build on the current achievements and try to optimize the computational process and enhance the predictive capability of the CONN model by exploring better learning algorithms as well as finding out the most suitable parameter settings for different situations. On the other hand, we will also try to improve the quality of the forecast and the generation of alerts by comparing the forecasted result by CONN with the generated alert message from actual measured data by lidar, and the actual wind shear experienced by the aircraft that is recorded in the pilot report.

Acknowledgments

This work was supported in part by RGC Grant PolyU5224/07E, and lidar data kindly provided by Hong Kong Observatory.

REFERENCES

  • Aihara K., , Takabe T. , , and Toyoda M. , 1990: Chaotic neural networks. Phys. Lett. A, 144 (6–7), 333340.

  • Arsenio, A. M., 2000: Tuning of neural oscillators for the design of rhythmic motions. Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, CA, IEEE, 1888–1893. [Available online at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=844870.]

  • Arsenio, A. M., 2004: On stability and tuning of neural oscillators: Application to rhythmic control of a humanoid robot. Proc. IEEE Int. Joint Conf. Neural Networks (IJCNN), Budapest, Hungary, IEEE, 99–105. [Available online at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1379878.]

  • Barbounis, T., , Theocharis J. , , Alexiadis M. , , and Dokopoulos P. , 2006: Long-term wind speed and power forecasting using local recurrent neural network models. IEEE Trans. Energy Convers., 21, 273284.

    • Search Google Scholar
    • Export Citation
  • Bilgili, M., , Sahin B. , , and Yasar A. , 2007: Application of artificial neural networks for the wind speed prediction of target station using reference stations data. Renewable Energy, 32, 23502360.

    • Search Google Scholar
    • Export Citation
  • Chan, P. W., 2003: Application of LIDAR backscattered power to visibility monitoring at the Hong Kong International Airport: Some initial results. Proc. Sixth Int. Symp. on Tropospheric Profiling: Needs and Technologies, Leipzig, Germany.

  • Chan, P. W., , Shun C. M. , , and Wu K. C. , 2006: Operational lidar-based system for automatic wind shear alerting at the Hong Kong International Airport. Proc. 12th Conf. on Aviation, Range, and Aerospace Meteorology, Atlanta, GA, Amer. Meteor. Soc., 6.11. [Available online at https://ams.confex.com/ams/Annual2006/techprogram/paper_100601.htm.]

  • Choy, B. L., , Olivia Lee S. M. , , Shun C. M. , , and Cheng C. M. , 2004: Prototype automatic lidar-based wind shear detection algorithms. Proc. 11th Conf. on Aviation, Range, and Aerospace Meteorology, Hyannis, MA, Amer. Meteor. Soc., P4.11. [Available online at https://ams.confex.com/ams/11aram22sls/webprogram/Paper81363.html.]

  • Copper, J. D., and Coauthors, 2001: Failed retrograde transport of NGF in a mouse model of Down’s syndrome. Proc. Natl. Acad. Sci. USA, 98, 10 43910 444.

    • Search Google Scholar
    • Export Citation
  • Giraua, B., , and Torres-Huitzilb C. , 2007: Massively distributed digital implementation of an integrate-and-fire LEGION network for visual scene segmentation. Neurocomputing, 70, 11861197.

    • Search Google Scholar
    • Export Citation
  • Glushkov, A. V., , Khokhlov V. , , Serbov N. , , Svinarenko A. A. , , and Bunyakova Y. Ya. , 2009: Non-linear prediction method in short-range forecast of atmospheric pollutants: Low-dimensional chaos. Proc. Second Chaotic Modeling and Simulation Int. Conf. (CHAOS 2009), Chania, Crete, Greece, P54. [Available online at http://www.chaos2009.net/proceedings/PAPERS_PDF/Glushkov_et_al-Non-linear_prediction_method_in_short-range_forecast_of_atmospheric_pollutants_PAPER-CHAOS2009.pdf.]

  • Hannon, S. M., , Thomas J. A. , , Henderson S. W. , , and Huffaker R. , 1995: Wind shear, turbulence, and wake vortex characterization using pulsed solid-state coherent lidar. Air Traffic Control Technologies, R. G. Otto and J. Lenz, Eds., International Society for Optical Engineering (SPIE Proceedings, Vol. 2464), 94–102.

  • Hirasawa, K., , Murata J. , , Jinglu H. , , and Jin C. , 2000: Chaos control on universal learning networks. IEEE Trans. Syst., Man, Cybern. Part C: Appl. Rev., 30, 95104.

    • Search Google Scholar
    • Export Citation
  • HKO and IFALPA, 2005: Windshear and turbulence in Hong Kong—Information for pilots. Hong Kong Observatory, 40 pp. [Available online at http://www.weather.gov.hk/aviat/articles/WS-turb-booklet-web-ver.pdf.]

  • Howe, C. L., , and Mobley W. C. , 2005: Long distance retrograde neurotrophic signaling. Curr. Opin. Neurobiol., 15, 4048.

  • Jones, J. G., , and Haynes A. , 1984: A peakspotter program applied to the analysis of increments in turbulence velocity. Royal Aircraft Establishment Tech. Rep. 84071.

  • Karim, A., 2009: Chaos in semiconductor laser amplifiers. Proc. Second Chaotic Modeling and Simulation Int. Conf. (CHAOS 2009), Chania, Crete, Greece, MAICH, P82. [Available online at http://www.chaos2009.net/proceedings/ABSTRACTS_PDF/Karim-Chaos_in_Semiconductor_Laser_Amplifiers_ABSTRACT_CHAOS2009.pdf.]

  • Kwong, K. M., , Liu J. N. K. , , Chan P. W. , , Lee R. , 2008: Using LIDAR Doppler velocity data and chaotic oscillatory-based neural network for the forecast of Doppler velocities. IEEE Proc. Congress on Evolutionary Computation (CEC 2008)/2008 IEEE World Congress on Computational Intelligence (WCCI2008), Hong Kong, China, IEEE, 2012–2019.

  • Lawrance, A. J., , and Ohama G. , 2003: Exact calculation of bit error rates in communication systems with chaotic modulation. IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 50, 13911400.

    • Search Google Scholar
    • Export Citation
  • Lee, R. S. T., 2004: A transient-chaotic autoassociative network (TCAN) based on Lee oscillators. IEEE Trans. Neural Networks, 15, 12281243.

    • Search Google Scholar
    • Export Citation
  • Levitan, I. B., , and Kaczmarek L. K. , 2001: The Neuron: Cell and Molecular Biology. Oxford University Press, 632 pp.

  • More, A., , and Deo M. , 2003: Forecasting wind with neural networks. Mar. Struct., 16, 3549.

  • Öztopal, A., 2006: Artificial neural network approach to spatial estimation of wind velocity data. Energy Convers. Manage., 47, 395406.

    • Search Google Scholar
    • Export Citation
  • Perez-Munuzuri, V., , Souto M. J. , , Casares J. , , and Perez-Villar V. , 1996: Terrain-induced focusing of wind fields in the mesoscale. Chaos Solitons Fractals, 7, 14791494.

    • Search Google Scholar
    • Export Citation
  • Sánchez, I., 2006: Short-term prediction of wind energy production. Int. J. Forecasting, 22, 4356.

  • Sanyal, S., , Kim S. M. , , and Ramaswami M. , 2004: Retrograde regulation in the CNS: Neuron specific interpretations of TGF-β signaling. Neuron, 41, 845848.

    • Search Google Scholar
    • Export Citation
  • Shun C. M., , and Chan P. W. , 2008: Applications of an infrared Doppler lidar in detection of windshear. J. Atmos. Oceanic Technol., 25, 637655.

    • Search Google Scholar
    • Export Citation
  • Vincent, C., , Giebel G. , , Pinson P. , , and Madsen H. , 2010: Resolving nonstationary spectral information in wind speed time series using the Hilbert–Huang transform. J. Appl. Meteor. Climatol., 49, 253267.

    • Search Google Scholar
    • Export Citation
  • Wagener, T. J., , Demma N. , , Kmetec J. D. , , and Kubo T. S. , 1995: 2 μm LIDAR for laser-based remote sensing: Flight demonstration and application survey. IEEE Aerosp. Electron. Syst. Mag., 10 (2), 2328.

    • Search Google Scholar
    • Export Citation
  • Wang, L., , and Fu X. , 2005: Data Mining with Computational Intelligence. Springer, 276 pp.

  • Wilson, H. R., , and Cowan J. D. , 1972: Excitatory and inhibitory interactions in localized populations. Biophys. J., 12, 124.

  • Wolfson, M. M., , Delanoy R. L. , , Forman B. E. , , Hallowell R. G. , , Pawlak M. L. , , and Smith P. D. , 1994: Automated microburst windshear prediction. Lincoln Lab. J., 7, 399426.

    • Search Google Scholar
    • Export Citation
  • Wong, M. H. Y., , Lee R. S. T. , , and Liu J. N. K. , 2008: Wind shear forecasting by chaotic oscillatory-based neural networks (CONN) with Lee oscillator (retrograde signaling) model. Proc. IEEE Int. Joint Conf. on Neural Networks 2008 (IJCNN 2008), Hong Kong, China, IEEE, 2040–2047.

  • Wysoski, S. G., , Benuskova L. , , and Kasabov N. , 2008: Fast and adaptive network of spiking neurons for multi-view visual pattern recognition. Neurocomputing, 71, 25632575.

    • Search Google Scholar
    • Export Citation
  • Zeng, X., , Pielke R. A. , , and Eykholt R. , 1993: Chaos theory and its applications to the atmosphere. Bull. Amer. Meteor. Soc., 74, 631644.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., , Patuwo B. E. , , and Hu M. Y. , 1998: Forecasting with artificial neural networks: The state of the art. Int. J. Forecasting, 14, 3562.

    • Search Google Scholar
    • Export Citation
  • Zweifel, L. S., , Kuruvilla R. , , and Ginty D. D. , 2005: Functions and mechanisms of retrograde neurotrophin signaling. Nat. Rev. Neurosci., 6, 615625.

    • Search Google Scholar
    • Export Citation
Save