Evaluation of electric field distortion at the Gaisberg Tower for continuing current measurements in lightning discharges

Upward lightning requires a distinct approach compared to downward (cloud-to-ground) lightning. Some lightning strikes are triggered by objects on the ground itself. The occurrence of such strikes depends on various factors, including the object’s geometric dimensions, structure, relative location within its environment, as well as the distribution and location of electrical charges within the thundercloud. This phenomenon takes place more and more often due to the spread of wind farms and higher buildings. In this article, simulation and calculation is carried out regarding the Gaisberg Tower in Austria which is actively used as a measurement and research site for lightning purposes. A finite element simulation is carried out to assess the electric field characteristics in the geometry. The close electric field measurement instruments are located 170 m away from the tower on an enclosure which must be considered during data analysis. The result of the created model is validated by former measurement data which confirms the arrangement of the model and creates the opportunity to directly transform the values of the electric field from the field mill to the tower during appropriate conditions.


Introduction
During upward lightning, the leader propagates from the ground object towards the charged region inside the thundercloud.The process is dependent on various factors which are e.g., height of the object, its relative location, shape and material characteristics, etc. and also on the other end the amplitude, height and volume of the charge composition in the thundercloud.The cloud charge structure is a very challenging factor to consider due to the several environmental factors involved during the formation of the charged regions, i.e., developing to mature level.A mature thundercloud with a complex multi pole structure is visible in Fig. 1.
2 Fig. 1.Conceptual model of the electrical structure in mature, mid-latitude convection [1] With the spread of high buildings and wind turbines, the occurrence of favourable factors regarding an upward lightning strike are more and more common.[2] For an upward leader to successfully create a return stroke, strong enough electric field is needed alongside the process to constantly evolve and ionize the volume on the way towards the thundercloud.Starting with a corona discharge and developing into a streamer then a leader requires corresponding cloud charge characteristics but in the observed geometry which is the key because of the fact that more and more highly inhomogeneous layout is created.This leads to less significant thundercloud properties causing greater electric fields locally and ultimately more upward strikes.In this paper, examination of the Gaisberg Tower and its environment is carried out using finite element modelling method.Using the layout parameters and local measurement arrangement, an electrostatic model is constructed which helps to better understand the electric field properties.

Connection between the examined geometry and upward lightning
Gaisberg Tower (GBT), visible in Fig. 2., is a 100 m high radio tower on the Gaisberg mountain and located 1287 m above sea level.It is near the City of Salzburg in Austria.The tower itself is used as a measurement site for lightning related research.The instrumentation creates the possibility to measure main lightning current parameters such as lightning peak current, charge transfer per stroke and per flash, current derivative (di/dt).[3] The research site is actively used to validate the data of the Austrian lightning location system (ALDIS), as well.Current parameters are measured on top of the tower which is an excellent place for upward leaders to form due to the elevated height because of the mountain and the extreme inhomogeneity caused by the tower dimensions.Fig. 2. The Gaisberg Tower and the measurement system on top [3] The upward lightning process starts with a corona discharge from the tower towards the cloud charge.If the properties of the electric field are appropriate, i.e., the ability to create adequate space charge on top of the object, a streamer and ultimately a leader can evolve.This requires also not only to have an initially great potential gradient but must be above the streamer gradient threshold to grow and form a dominant leader.Finally, a return stroke is occurring when the leader reaches the cloud charge or the possibly formed connecting leader from the cloud.The initiation process can be classified as self-initiated or other triggered.Former means that the electric field between the charge of the thundercloud and the object is increasing due to the movement of the cloud charge itself.When the charge layout creates the critical potential gradient values, the leader starts to evolve, and the upward lightning strike takes place.Other triggered upward lightning is created by the sudden change of electric field due to charge neutralization by a nearby intracloud or cloud to ground strike.More parameters and detailed information on this matter can be found in e.g., [3] [4] [5].The current measurement is the best way to illustrate the possible stages of an upward strike, visible in Fig. 3.Note that this is a schematic figure to illustrate the different parts of the phenomenon.Initial stage duration is typically up to a few hundreds of milliseconds and a return stroke takes place around a few tens of microseconds [3].It can be seen that there is an initial stage which is dominated by the initial continuous current (ICC).This part has relatively low current values compared to the return stroke period.It is worth noting that as it can be seen on the illustration the ICC carries much greater charge than the return stroke.In this phase, the electric field is only locally strong enough to ionize the environment and create space charge above the tip of the tower leading to a relatively stable discharge.The ICC pulses superimposed on the ICC can be measured during more significant leader inception cases which can reach the amplitude of lower return stroke region.Ultimately, if the electric field is severe enough to maintain a dominant leader propagating high enough, return stroke will occur.Potential gradient is also measured on site 170 m from the GBT on top of an enclosure.Since the superposition of the high frequency electric field and the static electric field parameters, created by the leader and cloud charge respectively, are in correlation of the previously detailed ICC [6], it is important to examine the phenomenon using this approach.The acquired electric field values must be of adequate accuracy and processed for proper usability.One of the measurement instruments is an electrostatic voltmeter to track the changes of static electric field.The data recorded by this device is used during the simulation presented in this paper.

Electrostatic modelling of the geometry
Modelling of the GBT and its vicinity must be carried out in a way to achieve the real ratios of the potential gradient difference between the measuring station and the tip of the tower which is the aim of this paper.It is important to have proper amplitude values for the initial stage of the discharge evolution.This must be done using the real geometry and an adequate method to represent it.A finite element model was constructed for this application, which is visible in Fig. 4.

Fig. 4. The modelled geometry
As it can be seen, the interesting areas, which are the tower top and the field mill are constructed with a very small element size mesh to ensure that the calculation of the electric field norm on the surface is accurate.Some important considerations in the model are e.g., perfectly conducting mountain top is modelled, the objects are grounded and the effect of the mountain level on the fair-weather current is neglected because it has a positive offset factor which is not applicable when comparing the field mill data and the electric field on the tower tip.The volume is air, using fair weather conditions.Fair-weather field is in a range of approx.100-200 V/m.[7] [8] This is maintained by the ionospheric potential which can be modelled by a far charged region above the geometry.In this simulated case the distance of this region is above 40 km to create the proper modelling of the homogeneous electric field only changed by the objects itself.Note that the value of the fair-weather field is greater generally on the Gaisberg mountain because of the elevated height that creates inhomogeneity on the surface of the planet which naturally leads to lower levels in the valleys around it.

Simulation results of fair-weather conditions
The electric field amplitude on ground level in the simulation was set to 180 V/m to meet the criteria detailed previously and measurement data.[9] This was adjusted using an empty geometry and calculation of the modelled ionosphere effect.After this, the simulation was carried out on a layout with and without the tower to assess its shielding effect, as well.The electric field norm can be seen in Fig. Electric field amplitudes were tracked from ground level towards the charged region in given coordinates based on the measurement locations in [9].Aim of [9] was to measure the field enhancement factor of the enclosure holding the field mill and the effect of the mountain.The result for the field mill station factor was 7.81 meaning the electric field is 7.81 times greater than close to the mountain surface 185 m far from the GBT (the field mill is 170 m away from it).Simulation results for the selected distances are visible in Fig. 6.The field shielding effect of the GBT is quite significant for 50 m distance from it at ground level x=0.For greater distances, further than the field mill this effect is negligible.Fig. 6.Calculated electric field at given distances from the GBT In Fig. 6., the effect of the field mill enclosure is also visible in case of the 185 m data on ground level.The maximum value of the field mill electric field is 1263 V/m.Table 1.summarizes the results.As it can be seen, the shielding effect of the tower at the field mill is 0.93% which can be neglected compared to the 50 m distance.It seems that the GBT has greater effect at 185 m but note that the effect of the enclosure is present here and the superposition of the two creates the greater shielding value.The previously mentioned enhancement factor of the enclosure can be calculated from the simulation by simply dividing the field mill electric field and the potential gradient at 185 m with the GBT in the geometry.This leads to a simulated field mill enhancement factor of 7.205 which is quite close to the measured value mentioned previously which validates the simulation and vice versa.The difference can be caused by several factors, e.g., although the finite element method uses extremely small mesh size, its residual error cannot be zero, the material characteristics and completely accurate modelling of the geometry is not possible either, on the other hand the measurement instrument has its own uncertainty, as well.
Using the simulation, the factor between the tip of GBT and the field mill can be calculated simply by dividing the calculated electric field amplitudes on their surface which equals to 5.55.For lower calculation error, this value is not rounded.In the given geometry, this can be used to convert the measured data to the tower during fair-weather circumstances.[10] If there was thunderstorm activity, the usability of the factor should be evaluated, e.g., if the charge composition is far enough then the factor will be appropriate but if the symmetry is broken due to short distances, it is no longer applicable.This must be considered also during upward lightning.Naturally, if there is large enough space charge on top of the tower, it would also influence the electric field and the applicability conditions are not met, further investigation is needed.

Conclusion
In this paper, the electrostatic examination of the GBT and its vicinity is carried out using finite element method.A realistic model of the geometry was created to analyse the potential gradient at different points of interest.Fair-weather conditions are used for calculation and former measurement data for validation of the model.The model can be used to assess the shielding effect of the GBT and also to transform measured electric field data to the tip of the tower when conditions are appropriate.During fair-weather, the enhancement factor of GBT has been determined.Since the simulation results are validated by the former measurement data, the modelled geometry itself can be used for research during different conditions, e.g., thunderstorm activity which leads to upward leader initiation.

Fig. 3 .
Fig.3.Schematic current diagram of upward lightning strike[3] a) Electric field in the geometry and b) zoomed on the field mill layout during fair weather in  •  −1 , colour scaled from 0 to 1  •  −1

Table 1 .
Summary of simulated electric field amplitudes at ground level