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Vol. 27（2022），113 ～ 125

Nearest Neighbor Techniques for the global and regional statistical analysis
of high temporal resolution CMIP6 surface wind speed with ECMWF
reanalysis and satellite winds.
Ponni. MAYA*1 and George. LAVIDAS *1*1 Department of Hydraulic Engineering, Delft University of Technology
Mekelweg 5, Delft, 2600AA, Netherlands

Abstract
Regional energy studies should include the effects of climate change in order to improve economic, social,and environmental development. Ocean surface winds have an important role in air-sea interaction, wave
modelling, and renewable energy assessment and development. Taking into consideration, there is researchcarried out for wind speed studies in various regions all around the globe.The IPCC 6th report suggests thehigh capturing capability of climate models in the newly developed Coupled Model Intercomparison Project
version 6 (CMIP6) with CMIP5. This study focuses on historical simulation analysis from CMIP6. The goal isto quantify the variation of 10m height surface winds over the globe and specific regions. The firstrealization(r1i1p1f1) of all the model simulations available for the CMIP6 at the time of investigation is taken
into consideration. The work includes 3 hourly Eastward surface winds (‘uas’; variable in CMIP6) andNorthward surface winds (‘vas’; variable in CMIP6) at 10m height from CMIP6. The climate model data arevalidated by comparing with the corresponding European Center for Medium-Range Weather Forecast(ECMWF) reanalysis wind components, satellite scatterometers, and radiometers datasets. Moreover, the work
focuses on the selection of the pre-eminent CMIP6 model historical simulation which is best for reproducing
the ‘real datasets’. The regional study is focusing on Japan. The change in seasonal and annual variation inwind speed is carried out with different statistical methods. An optimal machine learning approach is
introduced to find the best climate model wind for each ocean basin.
Key words : Energy, Wind, CMIP6, ECMWF, Scatterometers, Radiometers, CMEMS.

1. Introduction
Renewable energy resources are the basic components of social, economic, and environmental development(Danial Khojasteh et al, 2018). Global energy consumption over the last two decades has also increased drastically due
to various factors, such as climate change, economic recession, and the reduction of natural resources. This has caused
an increase in the demand for renewable energy production in global continents, which would help to mitigate futureclimate change. Moreover, the EU Commission considers energy efficiency policies to combat the European energy
crisis (Calanter P et al, 2022).
Intraseasonal, interannual, decadal, and multidecadal Climate Change studies have been on the rise due to theimpact of climate change in different sectors such as energy resources, health, infrastructure, natural hazards, andagriculture (Zittis G et al, 2022). Adaptation and mitigation plans against climate change are necessary for protecting
human beings and retaining development. The Intergovernmental Panel for Climate Change (IPCC) includes a longrecord of climate variables’ accretion for climate studies (Zelinka MD et al, 2020).
Within the framework of the IPCC, the Coupled Model Intercomparison Project (CMIP) provides a collaborative
platform to access and improve the knowledge of climate change irrespective of the past, present, and future. The 6th
Date of Manuscript Acceptance 2023.1.11
E-mail of corresponding author: p.maya@tudelft.nl

*

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phase of the WCRP Working Group Coupled Modelling (WGCM) on the Coupled Model Intercomparison Project(CMIP6) gives variable specific output data, which has proven to have a better performance than CMIP5 (Yasin
Zamani et al. 2019, WCRP). CMIP6 represents the most recent generation of climate models, which are now available.
The enormous application of these models leads to multiple statistical comparative studies on different temporal andspatial distributions (Martinez A,, 2022), which are time-consuming (suggest factors that relate ocean surface winds tostatistical comparative studies). However, ocean surface winds play a key role in air-sea interaction, wave modelling,
and renewable energy assessment and development (Schulz J et al, 2022). Thus a time-efficient analysis is necessary inorder to finalise the model outputs which needed much effort from various statistics.
This work introduces decision tree nearest-Neighbour algorithms for the optimised selection of Climate model
datasets which are approximately clones. These include K nearest neighbours (KNN) and Decision tree (Song T et al,2022). This space partitioning data structure algorithm is used to organise points in multi-dimensional space to avoid
brute force. For example, testing of the algorithm in different climate model winds at a 10 m height above the sea levelare used in this study due to their complex nature.

2. Data and Methodology
2.1 Data
2.1.1 CMIP6 Models
To find the algorithm’s ability and performance, all the models under specific criteria are taken into account at thetime of investigation. The respective models are represented in Table 1. Historically, the available 11 model datasets
under the first realisation (r1i1p1f1) for particular variables are taken into account. The key variables used for thisstudy are zonal and meridional wind components(‘uas’ and ‘vas’: variable representation in CMIP6). The 3 hourly
10-metre surface winds are preprocessed before each analysis.
After merging the wind components in time, the Eastward surface winds (‘uas’; variable in CMIP6) and Northwardsurface winds (‘vas’; variable in CMIP6), measured at a height of 10 m from the CMIP6, and the ‘eastward wind’and ‘northward wind’ from CMEMS satellites, are regridded to a 1 degree x 1 degree (latitude and longitude) gridthrough bilinear interpolation. This is implemented in the Climate Data Operator (CDO). Every data is set into a
uniform calendar using CDO. The leap days are removed from the 11 CMIP6 model data and resampled to 6 hourly forcomparison against satellites. For Reanalysis datasets (Era 5) used in this study from ECMWF(section 2.1.3) ispreprocessed using the same reggriding procedure and setting the calendar with 3 hourly temporal resolution after
preprossessed .

2.1.2 Satellite Merged Dataset
The CMEMS (Copernicus Marine Environment Monitoring Service) surface winds, derived from scatterometers
and radiometers, are used for the comparison with the results from this study. These represent “real-time”
measurements. The optimised satellite blended data is produced from CMEMS IFREMER (ERS-1 and ERS-2),
NASA/JPL (QuikSCAT and RapidScat), EUMETSAT OSI (ASCAT-A and ASCAT-B), CNSA (HY-2A), ISRO
(OceanSat-2), from Remote Sensing System (SSM/I SSMIS, and WindSat) and NWP reanalysis. This has a 10 m 6hourly averaged eastward, and northward wind 10 m components for the period 1992-2014 is ideal for the validation of
CMIP6 winds, and is used in this study.

2.1.3 Atmospheric Reanalysis
In order to verify the results obtained by the satellite comparison, all the models are compared against thecorresponding European Center for Medium-Range Weather Forecast(ECMWF) reanalysis wind components for theperiod of 1992-2010. Reanalysis datasets are used to evaluate the climatological error anomalies and assess the
progress in modelling capabilities in various fields and observational system transitions. The fifth generation of
atmospheric reanalysis (Era5), produced by ECMWF, is used in this study. The Era5 has significantly improved quality
and quantity compared to previous global reanalysis (Hersbach H et al, 2020).

Nearest Neighbor Techniques for the global and regional statistical analysis of high temporal
resolution CMIP6 surface wind speed with ECMWF reanalysis and satellite winds

Table 1

CMIP6 Model and Institution

Model

Institution

IPSL-CM6A-LR

Institut Pierre-Simon Laplace, Paris 75252, France

GFDL-ESM4

NOAA, Geophysical Fluid Dynamics Laboratory, Princeton, NJ 08540, USA

MPI-ESM1-2-LR

Max Planck Institute for Meteorology, Hamburg 20146, Germany

AWI-ESM-1-1-L R

Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research,,
Germany

MIROC6
IPSL-CM5A2-IN
CA

MPI-ESM-1-2-H
AM

Japan Agency for Marine-Earth Science and Technology

Institut Pierre Simon Laplace, Paris 75252, France

ETH Zurich, Switzerland

GFDL-CM4.gn

NOAA, Geophysical Fluid Dynamics Laboratory, Princeton, NJ 08540, USA

GFDL-CM4.gr

NOAA, Geophysical Fluid Dynamics Laboratory, Princeton, NJ 08540, USA

CMCC-CM2-SR5

CMCC-ESM2

Fondazione Centro Euro- Mediterraneo sui Cambiamenti Climatici, Lecce
73100, Italy

Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici, Lecce
73100, Italy

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2.2 Methodology
2.2.1 Cosine Similarity
In huge data analysis, cosine similarity is a widely used method to find the measure of similarity between two
vectors in an inner product space. The calculation of cosine similarity is represented in equation(1),

(1)

Where
= component of the satellite vector= component of the model vector

2.2.2 Bias Error
Bias is calculated in each grid point over the selected domain by taking normal error represented in the equation (2)(2)

2.2.3 Euclidean Distance
The length of the line segment between each point for the model and corresponding with “real datasets” arerepresented by the Euclidean distance equation(3).

(3)

2.2.4 Chebyshev DistanceThe chessboard distance is (Yongjian et al. 2021) the distance between model and “real measurements” datasets,
defined as the greatest of their differences along any coordinate dimension in the vector space.

(4)

2.2.5 K Dimensional Tree (KD tree)
KDtree is an effective combination of both KNN and a Decision tree, to structure data in multi-dimensional space.
In order to avoid brute forcing, KD Tree works internally to construct the data points in a decision tree-like structure.
The structure involves the root node extended downward through branches until it reaches the parental node. This is the
widely used approach for the classification and grouping purpose of data sets (Bahzad Taha Jijo et al 2021). In thiscase, it works as a binary search tree where data in each node works as a k-dimensional data point in space.

Nearest Neighbor Techniques for the global and regional statistical analysis of high temporal
resolution CMIP6 surface wind speed with ECMWF reanalysis and satellite winds

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3. Result and discussion
3.1 Bias Error between the historical CMIP6 models and merged satellite product
The Bias error for all the 11 CMIP6 models is compared against CMEMS datasets for a temporal resolution for
6hrs over the global ocean basin for a period of 1992-2014 as shown in Fig(1a,1b,1c, and 1d) for the Japan region(latitude 26.1,63.3, longitude =122,157.9). Each figure represents different seasons (DJF- December January February)(MAM- March April May)(JJA- June July August) (SON- September October November). The 11 CMIP6 models
encounter a maximum range of bias from 8m/s to a minimum bias range of -8m/s for wind magnitude(Figure 1a,1b,1c,
and 1d)).

Fig. 1a The bias of DJF wind magnitude( in m/s, shaded) using CMEMS and CMIP6 wind datasets for the period
1992-2014. The corresponding model names are represented above each figure. Before computing all the data points
are regridded to a 1 degree x 1 degree (latitude and longitude) grid through bilinear interpolation. set into a uniform
calendar using CDO. The leap days removed 11 CMIP6 model data is resampled to 6 hourly for comparison against thesatellite merged CMEMS dataset.

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Ponni. MAYA and George. LAVIDASFor DJF(figure 1a), the maximum positive bias is shown for the models MPI-ESM1-2-LR, AWI-ESM-1-1-LR,
MIROC6, MPI-ESM-1-2-HAM, CMCC-CM2-SR5, IPSL-CM6A-LR. The models included in the same family fromthe Geophysical Fluid Dynamics Laboratory underestimates the satellite product in the selected domain for JJA.11
CMIP6 models overestimate the season MAM for the period 1992-2014(Figure 1b). MPI-ESM1-2-LR,
AWI-ESM-1-1-LR, and MPI-ESM-1-2-HAM have a high deviation in the bias for MAM. A higher underestimation ofwind magnitude for MIROC6 is shown for the season SON.
In the seasonal analysis over time for 22 years the models arise with contrast discrepancies among each other. The
selection of a model among the 11 CMIP6 is harder under these circumstances of results. According to the literature so
far multiple statistical analyses are put forward to figure out the best model out of the highly varying datasets for eachtemporal and spatial resolution.

Fig. 1bWind magnitude (in m/s, shaded) using CMEMS and CMIP6 wind datasets, for the season MAM for theperiod 1992-2014. The bias (m/s) is individually obtained and it is shaded in each figure.

Nearest Neighbor Techniques for the global and regional statistical analysis of high temporal
resolution CMIP6 surface wind speed with ECMWF reanalysis and satellite winds

Fig. 1csame as Figure 1a, for the season JJA for the period 1992-2014. The bias (m/s) is
individually obtained and it is shaded in each figure.

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Fig. 1dsame as Figure 1a, for the season SON for the period 1992-2014. The bias (m/s) is individually obtained
and it is shaded in each figure.

3.2 Cosine similarity(CS) between the historical CMIP6 models and merged satellite product for all
the seasons over a period of 1992-2014 for the Global scale.
The research, including the assessment of the CMIP6 datasets, is analysed using the measuring degree concept of
Cosine similarity (CS) (Figure 2). The value obtained for all the seasons for the cosine similarity is in a range of 0.976
to 0.987, representing the two vectors pointing in the same direction. Even though the CS values show a high similarity
between the CMIP6 models and Satellite data merged products in the inner product space, the difficulty arises for theconclusion in selecting the best model out of the selected CMIP6 models.

Nearest Neighbor Techniques for the global and regional statistical analysis of high temporal
resolution CMIP6 surface wind speed with ECMWF reanalysis and satellite winds

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Fig. 2 Cosine similarity of wind magnitude (in m/s) of 11 CMIP6 datasets and CMEMS satellite datasets at 10m
above sea level for all the seasons over the period 1992-2014. (a)- DJF, (b)- MAM, (c)- JJA, (d)- SON.

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3.3a KDtree Euclidean distance calculation between the historical CMIP6 models and merged satellite
product
In this study, the K nearest neighbour is used as a classifier by using the Euclidean distance and Chebyshev
distance algorithms. For each new input, the KD tree figured out the nearest neighbour on the basis of Euclidean
distance (Figure 3.3a and Figure 3.3b) and Chebyshev distance (Figure 3.3c and Figure 3.3d). Here for the 11 models,the one which is closer to the query has a lesser Euclidean distance than the model it is testing, and so on. Of all themachine learning algorithms, the KNN is one of the widely used ones, because of its easily understandable design andadaptable nature(Shahadat Uddin et al 2022).
The accuracy of the KNN depends on the quality of the data. In this case, we have high-quality datasets due to thestructured preprocessing for both the training and query datasets. For large datasets, the prediction stage has a slowing
effect and requires high memory for the storage of training datasets, here we use decision tree techniques (KD tree) tomake the process faster. The KNN method implemented in the KDTree does not need a training period, because of its
simple and powerful nonparametric architecture.
In this case, the value of K is 11, which helps to find the 11 nearest neighbours for each query point. Thereby, we
can quantify the difference among them in the Euclidean distance. Similarly, the case is implemented in the calculationof the analysis of the Chebyshev distance (Figure 3.3c and Figure 3.3d).

Fig. 3a Kdtree Euclidean distance calculated (m/s) between CMIP6 datasets and CMEMS satellite merged
dataset for the period 1992-2014. The points represent each distance of the respective model.

Nearest Neighbor Techniques for the global and regional statistical analysis of high temporal
resolution CMIP6 surface wind speed with ECMWF reanalysis and satellite winds

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3.3b Kdtree Euclidean distance calculation between the historical CMIP6 models and Era5

Fig. 3b

Kdtree Euclidean distance calculated(m/s) between CMIP6 datasets and Era5 Reanalysis dataset for theperiod 1992-2010. The points represent each distance of the respective model.

3.3c Kdtree Euclidean distance calculation between the historical CMIP6 models and merged satellite
product

Fig. 3c Kdtree Chebyshev distance calculated(m/s) between CMIP6 datasets and CMEMS satellite merged
dataset for the period 1992-2014. The points represent each distance of the respective model.

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3.3d Kdtree Euclidean distance calculation between the historical CMIP6 models and Era5

Fig. 3d

Kdtree Chebyshev distance calculated(m/s) between CMIP6 datasets and Era5 Reanalysis dataset for theperiod 1992-2010. The points represent each distance of the respective model.

4. Discussion and Conclusion
This study uses the wind magnitude from historical CMIP6 high temporal resolution (3 hourly) and 1 degree x 1
degree (latitude and longitude) re-gridded spatial data for comparison in Japanese coast against "real datasets". The
domain experiences anomalous thermal advection, energetic mesoscale oceanic eddies, and vigorous air-sea
interaction, which can affect East Asia (Bunmei Taguchi (2009), Wenyu Zhou (2017). The "real datasets" mentioned
includes Era5 and CMEMS. To study the similarity and differences between each model dataset, statistical methods
such as Normal Bias and Cosine similarity are tested for all the seasons for a period of 1992-2014. The spatial bias of
CMIP6 with CMEMS represents a series of complicated underestimation and overestimation through out different
seasons. Even though the cosine similarity for the global regional analysis represents an exemplary result range
between 0.977 and 0.978 arriving to a conclusion about the best CMIP6 model is still a challenging task.
For each region, it is well-known that each temporal resolution selection of a model by doing multiple statistics istime consuming. In order to fulfil that gap, a K Dimensional tree is introduced in this research. This method actively
searches all the relevant data points in the multidimensional space against the "real measurements”, and denotes thebasis of distance calculation. Euclidean distance and Chebyshev distances are calculated for each model dataset, andnoted in the Figures 3a, 3b, 3c, and 3) respectively. The model IPSL-CM5A2-INCA has the least Euclidean distanceand Chebyshev distance for the years(1992-2014) for CMEMS and (1992-2010) for Era5. The model IPSL is chosen
for further studies in the selected regions. Irrespective of the area of interest and the temporal resolution, this nearest
neighbouring search(NNS) - which is a combination of KNN and Decision tree techniques - gives the most appropriate
model out of the clones, which is very difficult to group, and hence, quantify otherwise.

5. Acknowledgements
The research was a part of the PhD project funded by the Delft University of Technology and the Marine
Renewables Energies Lab. The CMIP6 datasets used in the study are archived on the website of IPCC. The Era5 dataset
from ECMWF and CMEMS from Ifermer. The authors express the acknowledgement to all the data providers
mentioned above.

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