Since there is no possibility of reference in the free-field to quantise the mapping quality of planar measurements, numerical approaches have been used in recent years to create a transferability of simulated LiDAR data to real LiDAR data. Part of these studies are based on free-flow wind fields [77, 78], while the larger part investigates the interaction of the atmospheric boundary layer (ABL) with wind turbines [55, 79, 80, 81]. With ongoing research into the characteristics of LiDAR velocity data, these can be used to be better understood in the sense of more realistic wind turbine inflow conditions.
abstraction of the model permits. The underlying models are themselves numerical compromises, which were created from a large number of corresponding reference measurements or theoretical considerations in order to create a general recallability. Therefore, resulting modelled wake wind field can be seen as conditional parameterised wind field reconstruction, that are accepted based on a statistical assumption. In the following, an overview of wind field reconstruction is addressed.
Comparisons of the application of wake models with free-field measurements show that both the energy yield [86, 87] and, in particular, the predicted loads differ [88, 89]. Possible causes for deviations can be attributed to the inaccuracies in the evaluation, which have their origin, technically in the data set, or logically in the assumptions used. Technical obstacles can be found in the availability of high quality inflow and load data since four-dimensional wind fields and small-scale interactions of these with the rotor cannot yet be measured with sufficient spatial and temporal resolution.
In any case, the lack of suitable and holistic inflow data has the consequence that these have to be compensated by assumptions. The artificial filling represents a source of inaccuracies within the aim to minimise the difference between calculated and real loads and energy yields. To further refine the current calculation possibilities and to be able to map the interaction reality between inflow and turbine more precisely, it is necessary to analyse how far these differ. For this purpose, a new level of comparability of data must be created. Within the framework of comparability of synthetic and real data, the superordinate objective is first, to reproduce the effects of the wind field measured in free-field on a wind turbine and secondly, to compare the results of the simulation with the reconstructed synthetic wind field and the numerical model of the turbine with corresponding measured data. The specific in the wind field reconstruction is the assumption of the unknown information to be filled. Beyond this general definition, specific definitions are given anew in the framework of their application on varying scales of temporal, spatial and flow details.
While in the IEC Standard [6] the comparability was defined as sufficient by the statistical reproduction of flow characteristics in the form of the first two central moments and the spectral energy density within the included turbulence models for undisturbed inflow situations, studies show that the representation of specific wake situations by means of current wake models lead to deviations [88, 89].
With the further development of remote sensing instruments, it has become possible to measure wind fields in the free-field on different length and time scales. The technical achievement opens the possibility to use quasi-instantaneous planar and volumetric wind speed data for a reconstruction beyond the capabilities of stationary anemometry. As already specified in the preamble, short-range LiDAR can measure several hundred meters in upstream direction with high measurement frequencies, which is why they are particularly suitable for providing input for the operational control of wind turbines. While measurements with short-range LiDAR can be performed within the scope of research on turbines with currently sub-average rotor diameters outside the induction zone influenced by the rotor, the reconstruction of the inflow wind field at current average rotor diameters is confronted with the need to map the affected advection speed in the pre-pressure zone without the knowledge of the ambient speed [90].
Long-range LiDAR can record evolution of wind turbine wakes over several kilometres in downstream direction. In the here presented framework, long-range LiDAR are of particular interest when the measurements aim to investigate the wake behaviour of a specific turbine. The
reconstruction of wake wind fields using LiDAR systems seems to be the most promising method to date for the purpose of comparing real and synthetic inflow situations. The difficulty of statistically reproducing wake inflow situations can technically be explained by first, the novelty of the application of LiDAR systems as one-, two- and three-dimensional information-giving measurement techniques, as well as second, logically in the ambiguity of the quantisation and classification of associated flow characteristics of different wake situations. Standardised classification of wake inflow situations is necessary to summarise sufficient measurements or calculations to demonstrate a statistical correlation with a corresponding specific turbine behaviour. However, the representation of these wake classes in models first requires a definition of the classification and delimitation. Due to the variability of the wake, which is influenced by atmospheric, turbines and geographical conditions, an exact normalised categorisation is yet beyond the possibilities of the current state of knowledge and requires as preliminary work the mapping of real inflow situations in the form of reconstructions and simulations in order to recognise unambiguousness and similarities in the wake behaviour for different turbine and rotor geometries, atmospheric conditions, their environment and interactions among them.
As can be read later in Chapter 4, LiDAR measurements are already being used to reconstruct undisturbed and wake wind fields. Since the concept of reconstruction is constantly newly defined from study to study, a broad spectrum of wind field reconstructions is apparent in research. In general, every reconstruction is a certain parametrisation of a model and can therefore never represent the full reality, but only the perspective of the model. Depending on the scientific-pragmatic point of view, studies based on LiDAR measurements can be called per se reconstruction due to the measurements principle, capturing the LOS velocity as the derivative of the aerosol velocity [91]. Here, the inherent reconstruction model is based on the assumptions that aerosols at which the laser refracts are homogeneous in geometry and surface condition and can be seen as passive particles. Even elementary LiDAR measurements (VAD and DBS), as used in site surveys, reconstruct the longitudinal wind velocity and wind direction from the LOS velocities [66, 67, 70, 71, 72, 73] on the basis of the reconstruction assumption that the volume enclosed by the laser beam can be observed stationary. In the reconstruction of Kapp and Kühn [90], the reconstruction method includes the parameterisation of a synthetic wind field employing five parameters in order to achieve the smallest possible deviation from the real inflow field. The reconstruction of the undisturbed flow is particularly challenging concerning the correct mapping of turbulence, as Sathe and Mann [48] describe it, due to the volume averaging.
The reconstruction of wake wind fields is generally more difficult since assumptions about the wake behaviour have to be made for the free flow surrounding the wake. Iungo and Porté-Agel [52] reconstruct wake wind fields by combining volumetric PPI scans and using a 3D Delauny triangulation to bring them to a uniform grid from which they calculate the temporal mean. Iungo and Porté-Agel [52] do not model the wake wind field but use the interpolation as reconstruction assumption. Van Dooren et al. [55] use measurements from two distant LiDAR systems to reconstruct the wake of an offshore turbine to a 2D flow field in the temporal mean under the assumption of the Multiple-Doppler Synthesis and Continuity Adjustment Technique (MUSCAT). They also do not use explicit modelling of the wake but apply MUSCAT reconstruction to all data points in the same way. Fuertes and Porté-Age [80] reconstruct wake wind fields from a synthetic origin (LES) by linearly interpolating PPI, and RHI scans in temporal
average. They investigate the behaviour of the reconstruction error caused by the temporal and spatial quantisation of the scanning behaviour and the projection of the LOS velocities.
A different approach of reconstruction is based on the modal decomposition of the flow field using Proper Orthogonal Decomposition (POD). Both research teams of Bastine et al. [92, 93, 94]
and Iungo et al. [95] show that different approaches and implementations of POD can be used to dynamically reconstruct wake wind fields in high precision. In all studies, however, it is described that the reconstruction quality depends on the number and selection of modes.
However, some reconstructions do not aim to reproduce wake wind fields, but only to map properties of the wake. In studies including wake characterisations, the wake motion is mostly reconstructed in the form of the temporal resolved centreline motion to obtain information about the position and/or the atmospheric driven wake meandering [66, 69, 85]. In addition, the recovery of the wind speed deficit in downstream direction and geometric derivatives, such as the wake width, are considered [49, 53, 96, 97].