Empirical modeling of the storm time geomagnetic indices: a comparison between the local K and global Kp indices
© Uwamahoro and Habarulema; licensee Springer. 2014
Received: 1 April 2014
Accepted: 6 August 2014
Published: 20 August 2014
This paper describes a neural network-based model developed to predict geomagnetic storms time K index as measured at a magnetic observatory located in Hermanus (34°25 S; 19°13 E), South Africa. The parameters used as inputs to the neural network were the solar wind particle density N, the solar wind velocity V, the interplanetary magnetic field (IMF) total average field B t as well as the IMF B z component. Averaged hourly OMNI-2 data comprising storm periods extracted from solar cycle 23 (SC23) were used to train the neural network. The prediction performance of this model was tested on some moderate to severe storms (with K≥5) that were not included in the training data set and the results are compared to the prediction of the global geomagnetic Kp index. The model results show a good predictability of the Hermanus storm time K index with a correlation coefficient of 0.8.
Geomagnetic storms are the common features of space weather causing a threat to ground- and space-based technology systems. Most of the intense geomagnetic storms are generally caused by fast coronal mass ejections (CMEs) which induce disturbances in the solar wind (SW). Geomagnetic storms occur as a result of the energy transfer from the SW to the Earth’s magnetosphere via magnetic reconnection. Hence, changes in the SW plasma and the interplanetary magnetic field (IMF) are important factors to consider when developing magnetic storm forecast models. At present, the physics of the magnetosphere and the interplanetary medium is not completely understood and there is still no comprehensive model of the solar-terrestrial environment. The current geomagnetic storm prediction tools are dominated by empirical models, relying mostly on the observable storm precursors in the SW (Fox and Murdin 2001). There have been various functional relationships proposed for magnetic storm prediction such models to predict the disturbance storm time (Dst) index from SW parameters proposed by Burton et al. (1975) and Temerin and Li (2002). Empirical prediction models include, among others, the neural network (NN) models that are known to have the property of learning from cases and with ability to handle complex nonlinear physical phenomena. This NN capability in space weather-related predictions has been demonstrated in various studies (e.g. Uwamahoro et al. 2012; Watthanasangmechai et al. 2012). In the domain of geomagnetic field, Segarra and Curto (2012) recently applied NN for the automatic detection of sudden commencements. Other various NN-based models for predicting geomagnetic storms using SW and IMF data as inputs have also been developed and used (Lundstedt and Wintoft 1994). In particular, Elman NN-based algorithms by Wu and Lundstedt (1996), Wu and Lundstedt (1997), and Lundstedt et al. (2002) demonstrated the ability to improve the Dst forecast.
Other than the prediction of the Dst index, models for predicting geomagnetic Kp index (from SW and IMF input parameters) have also been developed (Boberg et al. 2000; Costello 1997; Wing et al. 2005). The difficulties related to the prediction of Kp index during storm periods (with K p>5) were noticed by Wing et al. (2005). A few models have also been developed for the prediction of the locally measured K index including the work by Virjanen et al. (2008) and Kutiev et al. (2009). In their study, Virjanen et al. (2008) described the problems encountered when predicting the storm time K index on the basis of only previous K index values and suggested the necessity to consider SW parameters as model inputs. The study described in this paper explored the application of Elman NN techniques for predicting the locally measured geomagnetic K index at the Hermanus Magnetic Observatory. The results obtained are compared to the prediction performance of the global Kp index.
The motivation behind this study lies on the importance of the K and related planetary Kp indices in space weather modeling. The ability to predict the K index can find application, for example, in predicting geomagnetically induced currents (GICs) (Virjanen et al. 2008). On the other hand, the K-derived planetary Kp index plays a key role in the magnetospheric and ionospheric modeling (Wing et al. 2005). Regional ionospheric models, e.g. TEC prediction models and the South African Bottomside Ionospheric Model (SABIM), take into account the local magnetic conditions by using the a index, which are directly derived from the locally recorded K index (Habarulema 2010; McKinnell 2002). An accurate model to predict the local storm time K index might, therefore, make a significant contribution towards improving ionospheric and other regional space weather models that consider magnetic activity as input.
The data sets
Geomagnetic K and K p indices
Geomagnetic K index is a quasi-logarithmic local index of geomagnetic activity. The K index quantifies disturbances in the H component of the Earth’s magnetic field with an integer in the range of 0 to 9, with 1 indicating calm conditions and 5 or more indicating a storm. The K index is derived from the maximum fluctuations of the H component observed on a magnetometer during a 3-h interval. Ground stations (magnetometers) throughout the world monitor geomagnetic activity providing a local logarithmic K index. There is a close link between the local K and global Kp indices. The planetary-scale Kp index (Menvielle and Berthelier 1991) is derived from the average of fractional K indices at 13 subauroral observatories. The Kp index is based primarily on data from magnetic observatories at middle latitudes and its values are generated with a time resolution of 3 h. This index represents a quasi-logarithmic measure of the disturbance range, also having values between 0 (very quiet) and 9 (very disturbed). While the K is a measure of the local magnetic disturbance, the Kp index is a good measure of the global magnetic activity (Prölss 2004).
Solar wind input parameters
The model was developed using hourly OMNI-2 SW and IMF parameters [B t ,B z ,V and N] data for both network training and testing sets. These data are from various spacecraft and are provided by the National Space Science Data Center available online on its OMNIWEB http://omniweb.gsfc.nasa.gov/html. The Kp index data used are provided by the National Geophysical Data center (NGDC) and are also available online on the website ftp://ftp.ngdc.noaa.gov/STP/GEOMANGETIC_DATA/.
An introduction to neural network prediction techniques
A neural network is an information processing system consisting of a large number of simple processing elements called neurons. NNs are characterised by (1) the pattern of connection between the neurons, (2) the method of determining the weights on the connections (training or learning algorithm) and (3) the activation function (Fausett 1994). For the NN models used for predictions, three types of neurons (or units) are defined: (i) input units, which are set to represent values within the time series, (ii) output units, which store the output values corresponding to a given set of input values and produce the results of the NN processing and (iii) hidden units, which keep the internal representation of the mapping.
Units in layers are connected by weights which keep the knowledge of the network and govern the influence of each input has on each output. Weights are adjusted by a learning process which involves the comparison of network calculations with input-output data for known cases. The process of adjusting weights is known as network training. During the training, weights are determined so that the network properly relates inputs to desired outputs. Hence, the network learns to predict outcomes from experience rather than from using causal laws (Macpherson et al. 1995).
A unique feature of NNs lies in their ability not only to learn the training data but also to generalise by predicting unseen patterns within the boundaries given by the training set. In general, solving a nonlinear problem with the NN technique requires (1) choosing a convenient network architecture, (2) selecting a large database of input-output pairs (patterns) that contains sufficient historical information about the time series, and (3) training the network to relate the inputs to the corresponding outputs. Several available NN training algorithms have been proposed (Bishop 1995; Fausett 1994; Haykin 1994) including the feed forward NN (FFNN) and the Elman neural network. To develop the local K and global index prediction model, the Elman neural network algorithm was used. The Elman NN (Elman 1990) is a type of network that belongs to the class of recurrent NNs commonly known as the Elman recurrent network (ERN). This consists of an input layer, a hidden layer and an output layer. It also has an additional context layer that always stores the output from the hidden layer and relays this information in the next iteration. Therefore, context neurons form a sort of short-term memory, very useful for improving prediction of sequences. This means that the state of the whole network at a given time depends on an aggregate of the previous states, as well as on the current inputs (Pallocchia et al. 2006). A simplified mathematical description of ERN can be found in various literature including a recent paper by (Cai et al. 2010).
Development of the NN model
Different NN configurations investigated with corresponding prediction performance
Results and discussion
Table 1 shows different NN configurations that were investigated with the corresponding prediction performance, evaluated by calculating RMSE and CC over the whole validation data set. From Table 1, it is clear that the developed model performs better when predicting the global Kp index than it does for the prediction of the local Hermanus K index. One among other possible reasons of this difference in prediction performance might be due to the fact that the global Kp index is derived from various K indices averaged and corrected to their respective magnetic latitudes observatories. The results from the developed model indicate a CC of 0.76 between the predicted and observed Hermanus K index and a CC of 0.88 for Kp index. Even though the data set used is not the same, this model prediction is comparable with the previous Kp index prediction by Wing et al. (2005) and Boberg et al. (2000). However, it is important to note that the latter models considered all the Kp s as input data, while the current model was developed using the Kp input data for only selected storm events.
The model’s K and K p indices prediction performance on the four selected individual storms
24 to 28 July 2004
07 to 12 November 2004
14 to 17 May 2005
23 to 25 August 2005
A NN-based model for predicting the storm time local K and global K p indices using SW and IMF input parameters has been developed. Many previous studies focused on developing models to predict magnetic storms as measured by the Dst index. However, some findings (e.g. Borovsky and Denton 2006) suggest that the Dst alone can, in some cases, be a poor indicator of the properties of a storm. The primary aim of this study was to explore the NN predictability of the locally measured storm time K index from SW and IMF parameters. The results obtained compare well with previous Kp (closely related to K index) predictions by Wing et al. (2005) and Boberg et al. (2000) noting however that contrary to these previous models, the current model involved Kp data for only selected storm events. The results obtained from the developed NN models are in line with what is already known about the SW control of geomagnetic activity. With a knowledge of the SW velocity, density, as well as the IMF strength and orientation, it is possible to predict well the energisation of the ring current and reproduce accurately the magnetic measurements recorded by ground-based magnetometers (Russell 1986). The developed model constitutes a step towards achieving real-time forecasts of the locally (Hermanus) measured K index. If achieved, the real-time prediction of the K index will contribute significantly to improving regional ionospheric modelling as well as other regional space weather models that consider the locally measured magnetic activity as input.
The authors would like to thank both the National Space Science Data Center and the National Geophysical Data Center (USA) for making available their data to us via the following websites: http://omniweb.gsfc.nasa/htmland ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/. This work was facilitated by a logistic support from both the University of Rwanda and the Space Science Directorate of the South African National Space Agency (SANSA), in Hermanus, South Africa.
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