1
Wind Speed and Direction Estimation from Wave Spectra using
Deep Learning
Haoyu Jiang
1,2,3
1
Hubei Key Laboratory of Marine Geological Resources, China University of Geosciences, Wuhan, 430000, China
5
2
Laboratory for Regional Oceanography and Numerical Modeling, Pilot Qingdao National Laboratory for Marine Science
and Technology, Qingdao, 266000, China
3
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou 511458, China
Correspondence to: Haoyu Jiang (Haoyujiang@cug.edu.cn)
Abstract. High-frequency parts of ocean wave spectra are strongly coupled to the local wind. Measurements of ocean wave
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spectra can be used to estimate sea surface winds. In this study, two deep neural networks (DNNs) were used to estimate the
wind speed and direction from the first five Fourier coefficients from buoys. The DNNs were trained by wind and wave
measurements from more than 100 meteorological buoys during 2014-2018. It is found that the wave measurements can best
represent the wind information ~1h ago, because the wave spectra contain wind information a short period before. The
overall root-mean-square error (RMSE) of estimated wind speed is ~1.1 m/s, and the RMSE of wind direction is ~14° when
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wind speed is 7~25 m/s. This model can not only be used for the wind estimation for compact wave buoys but also for the
quality control of wind and wave measurements from meteorological buoys.
1 Introduction
Sea surface wind and waves are important parameters for the marine environment and ocean dynamics. High-quality
simultaneous measurements of sea surface wind and wave information are helpful for the study of many oceanic and coastal
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phenomena. Such simultaneous measurements can be obtained from meteorological buoys and remote sensing satellites.
Many meteorological buoys can provide comprehensive wind and wave information including surface wind speeds, wind
directions, and wave spectra with high accuracy. However, the deployment and maintenance of these buoys and platforms
usually need relatively high costs. Therefore, meteorological buoys are very sparsely distributed and are almost only
available along the coastlines of developed countries.
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The earth observation satellite network, such as scatterometers, altimeters, and synthetic aperture radars can serve as
effective complements for the buoy network. Meanwhile, these remote sensors also have some limitations. Scatterometers
can retrieve both wind speed and direction with a wide swath and the best overall accuracy, but wave information is not
available from them. Besides, their temporal resolutions are (usually one or two revisits per day except for Polar Regions)
still much lower than in-situ measurements. Altimeters can simultaneously measure wind speed and significant wave height
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https://doi.org/10.5194/amt-2021-279
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(SWH), but wind directions and other wave parameters are not available from them. Besides, the cross-track spatial
resolution and temporal resolution of an altimeter are low because they can only measure the nadir. Synthetic aperture radars’
wave mode can provide wind speed, wind direction, SWH, and low-frequency wave spectra (high-frequency is not available
due to nonlinear imaging), but the accuracy of wind speed, wind direction, and SWH is usually not as good as those from
scatterometers and altimeters, and they are also limited by the sparse sampling. Moreover, most satellites have limited
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temporal resolutions and often perform worse in nearshore regions than in the open ocean due to the land contamination of
backscatter.
Another important data source for collocated winds and waves is compact wave buoys. These types of buoys are
usually low-cost and are suited for deploying in large numbers, and they perform better in measuring waves compared to
large meteorological buoys because their small sizes have a more sensitive response to short waves (Voermans et al. 2020).
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Although wave buoys are not designed for wind observation, Voermans et al. (2020) have shown that both wind speed and
direction can be estimated from the wave spectra using a 𝑓−4 spectral dependence in the equilibrium range. Their model can
estimate wind speed with a root-mean-square error (RMSE) of 2 m/s and wind directions with an RMSE of ~20° when wind
speed is higher than 10 m/s. Although this model has good theoretical support, the accuracy of this model is lower than
typical remote sensing retrievals. For example, altimeter-retrieved wind speed has a typical overall RMSE of 1.2-1.5 m/s
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(e.g., Jiang et al. 2020) and scatterometer-retrieved wind speed and wind directions has a typical overall RMSE of ~1 m/s
and 16° (e.g., Wang et al. 2021) when using buoys’ anemometer data as the reference.
Compact wave buoys are increasingly widely used in global wave observations. For example, more than 2,000 Spotter
buoys have been deployed in global oceans by Sofar Ocean Technologies (The location of these buoys can be viewed at
https://weather.sofarocean.com/) to improve the performance of their wave modelling (Smit et al, 2021). Although the data is
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not open to the public, more accurate wind estimation from wave spectra can definitely benefit users of such buoys.
Voermans et al. (2020) have shown the possibility to estimate wind speed and wind direction with wave measurements alone.
This study aims to improve the accuracy of such estimation as much as possible. A model based on a deep neural network
(DNN) is presented to achieve this goal. The rest of this paper is organized as follows: The simultaneous observations of
wind and waves to train the DNN model are introduced in Section 2, along with the structure and training method of the
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DNN. The main results are presented in Section 3. A brief discussion about the selection of the DNN input terms is made in
Section 4, followed by the concluding remarks in Section 5.
2 Data and Methods
2.1 Collocated Wind and Wave Data
Many buoys from the National Data Buoy Center (NDBC) coastal-marine automated network can provide quality-
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controlled in-situ wave and wind measurements. More than 1.7 million records from 106 buoys in coastal and oceanic
regions during 2014-2018 were used in this study (Fig. 1). Most buoys’ anemometers are 4-5 meters from the sea surface,
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and the accuracy of them is within 1 m/s and 10° for wind speed and direction, respectively, in moderate sea state (in
extreme sea states, the swing and tilting of the buoy can introduce larger errors). The wind speed was converted to the
standard height of 10 m (U10) using the power law (Hsu et al. 1994), to be consistent with Voermans et al. (2020). This
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conversion was also tried using the log profile (Young 1995), which has almost no impact on the results. The buoy wave
data includes five Fourier coefficients of waves in the range of 0.02-0.485 Hz (47 frequency bins) from the translational or
pitch-roll information. The five Fourier coefficients are wave variance spectral density (E), mean and principal wave
direction at different frequencies (α
1
and α
2
), and first and second normalized polar coordinate of the Fourier coefficients (r
1
and r
2
), which are the minimum requirement to reconstruct the directional wave spectrum. These NDBC data, especially the
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offshore ones, are widely used in the validation of wind and wave remote sensing and numerical weather and wave models
(e.g., Jiang et al. 2016, Jiang 2020, Wang et al. 2021).
Figure 1. The bias (1st row) and RMSE (2nd row) of DNN-estimated wind speed and RMSE of DNN-estimated wind direction
(when wind speed is higher than 7 m/s, 3rd row) for the individual NDBC buoys in the North Pacific (left), the west coast of the
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United States (middle), and the Atlantic region (right). The overall RMSEs of wind speed and wind direction (when wind speed is
higher than 7 m/s) are ~1.1 m/s and ~14°, respectively, for the complete validation data set. Therefore, blue and red colors in
RMSE maps indicate below and above the overall RMSE, respectively.
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2.2 DNN Models for Estimating Wind Speed and Direction
As a nonparametric model, a DNN can theoretically be used to fit any form of function with any number of input
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parameters provided the network is wide and deep enough. DNNs are effective for the regression problem with more than
two input parameters and are widely used in the training of retrieving and correcting models in studies of ocean remote
sensing (e.g., Wang et al. 2020, Jiang et al. 2020). In this study, two DNNs were established with the same structure, one for
estimating wind speed and one for wind directions. In the beginning, the input layer of the DNN was set up in a “violent”
way which simply contains 235 (vectorization of five Fourier coefficients × 47 frequency bins) neurons. However, we will
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show in Section 4 that the input layer of the DNNs can be refined after obtaining the basic knowledge of how these models
work. Each of the 235 inputs was normalized to have zero mean and unit variance. The DNNs have two hidden layers with
64 neurons followed by an output layer with one term (wind speed or direction). The activation function is the rectified
linear unit (ReLU). It was tested that adding hidden layers and hidden neurons does not improve the performance of these
models. The 1.7 million buoy records were randomly divided into training (50%) and validation (50%) sets. The DNN for
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U10 was trained to minimize the RMSE between the target (buoy-measured) and output U10:
2
10
1
1
(1)
n
U i i
i
Loss RMSE y x
n
where y and x denote the output and target/reference parameters, respectively. The DNN for wind directions was trained to
minimize the distance between target and output unit vector corresponding to the wind direction:
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1
1
sin( ) sin( ) cos( ) cos( ) (2)
n
Dir i i i i
i
Loss y x y x
n
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For both DNNs, the training used the Adam optimizer with a batch size of 2048. The learning rate (initially set to 0.004)
was decreased by 50% if the loss of the training set did not decrease for three epochs, and the training process stopped when
the RMSE of the validation set did not decrease for eight epochs. The DNN was realized by PyTorch. Besides RMSE, the
bias, STandard Deviation (STD), and Correlation Coefficient (CC) were also selected as the error metrics to evaluate the
model performance:
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1
22
22
1 1 1
1
(3)
(4)
/ (5)
n
ii
i
n n n
i i i i
i i i
Bias y x
n
STD RMSE Bias
CC y y x x y y x x
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3 Results
The comparison between the collocated DNN-estimated and direct-measured U10 for the validation data set is shown as
a scatterplot in Fig. 2a, and the corresponding comparison for wind directions is shown in Fig. 2d. These results suggest that
estimating wind speed and direction from wave spectra using such a simple DNN works reasonably well. For wind speed,
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the DNN can give an estimation with an overall RMSE of ~1.3 m/s and a small overall bias. For wind direction, the RMSE is
~17° for U10 > 7 m/s (not shown). These results have some significant improvement compared to the error metrics of
Voermans et al. (2020).
Figure 2. (a-c) Comparison between wind speeds measured by buoys and those estimated by wave spectra. (a) Scatter plot of
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collocated DNN-estimated wind speed and direct-measured wind speed. (b) The same as (a), but the spectra were used to estimate
the wind speed one hour ago. (c) The bias, STD, and RMSE of the DNN-estimated wind speed one hour ago as a function of direct-
measured wind speed. The blue shadow indicates the empirical distribution function of direct-measured wind speed. (d-f) The
same as (a-c), but for wind directions.
When we checked the time series of DNN-estimated and direct-measured wind speed and direction (not shown), we
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found that the DNN-estimated wind seemed to have a 1-hour delay compared to the direct-measured wind. If the DNN-
estimated wind speed is compared to the direct-measured U10, the RMSE can be improved to 1.2 m/s. Different from the
capillary and capillary-gravity waves always in instant equilibrium with the local wind, gravity waves with relatively low
frequencies need a short period to grow. Therefore, the wave spectra might also better reflect the wind information a short
period before.
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Based on the above idea, the same DDN framework was trained against the wind one hour ago. Obtaining wind
information with only a 1-h delay is acceptable for most scientific and operational applications. The results of wind speed
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