1 Introduction

Atmospheric motion vectors (AMVs) from satellite data are important components for data assimilation in numerical weather forecasting systems. AMVs are particularly useful for weather forecasting where wind observations are very rare, such as in ocean regions or developing countries. Tetsuya Theodore (Ted) Fujita introduced the retrieval algorithm (Menzel 2001) that derives AMVs by tracking cloud and water vapor features through consecutive satellite imagery (Forsythe et al. 2005, Carr et al. 2018). Now, more than eight institutions around the world are producing AMVs using satellites (Santek et al. 2018, Deb et al. 2016, Chen et al. 2020, Oyama 2010, Sohn et al. 2012).

In general, AMVs in cloudy areas are retrieved using infrared channels, and cloud-free clear skies are retrieved using water vapor channels of geostationary satellites. Horizontal AMVs are typically calculated based on the cross-correlation coefficient (CC) method, which tracks the features of cloud or water vapor fields across specific time intervals (Santek et al. 2018). In the CC method, the target is located at time t and the tracking area is set at t + 1. It is assumed that the target has moved within the tracking area, and the movement of the target is analyzed. The target is traced to the location with the most similar shape, where the cross-correlation coefficient is the highest. The direction of movement of the water vapor can be tracked using three consecutive images (Schmetz et al. 1993). First, the backward vector is estimated using the first and second images, and the forward vector is calculated based on the second and third images. The two vectors are then averaged to yield a final vector (Oh et al. 2019).

However, the current method has some limitations in terms of tracking accuracy and forecasting. If there are multiple maximum correlation positions, then the CC method is unable to choose the position to be moved. In addition, it is difficult to track features that demonstrate little or no change in shape, as well as the feature is small, absent, or greatly changes shape over time (Lee and Song, (2017). Therefore, the AMVs in clear skies with smooth features calculated using the current algorithms are less accurate than the AMVs in cloudy areas. Second, the current algorithm for retrieving AMVs is unable to perform forecasting because it requires data from 10 min later than the present, which are not available.

Therefore, the movement of moisture should be accurately tracked to calculate the horizontal AMVs. In this regard, we attempted to apply the computer vision method called optical flow estimation, which is used to track features in clear skies. The optical flow is the distribution of apparent velocities of the movement of brightness patterns in an image (Horn and Schunck 1981). A traditional method of calculating optical flow is the Lucas-Kanade (LK) method, a registration technique that makes use of the spatial intensity gradient of the images to find a good match using a type of Newton–Raphson iteration (Lucas and Kanade 1981). However, the LK method is vulnerable when tracking large movements or when the light changes. Also, the LK method produces results with missing values because it only looks at a specific area. To improve such limitations, the pyramidal LK method calculates the displacement by applying the LK algorithm in a "pyramid" of images of the same scene at various resolutions (Lucas and Kanade 1981). There is also the Farnebäck method, also known as the dense optical flow calculation method. Unlike the LK or pyramidal LK method, which computes the flow for only a few features, the dense optional flow method computes the flow for all pixels. The Farnebäck method calculates the displacement field using the polynomial expansion transform (Farnebäck 2003).

Many studies have adapted optical flow estimation to improve tracking performance for retrieval of satellite-observed AMVs. Bresky and Daniels (2006) studied the feasibility of obtaining atmospheric motion using the LK method. They concluded that the mean vector difference of the optical flow method was lower than that of the CC method when applied to water vapor winds in clear skies using GOES-12. However, the LK method showed a limitation for tracking large motions and was not applicable when apposite features were not observed. Oh et al. (2020) calculated an initial estimate of AMVs using the pyramidal LK method. Since the pyramidal method helps to detect more features than the LK method in the same image, the accuracy increased from 5.296 to 5.804 m/s of root-mean-squared vector difference (RMSVD). Wu et al. (2016) calculated AMVs for all pixels using the dense Farnebäck method (including the image-pyramid scheme). Compared to the current CC method, the calculation time was shortened, maintaining the spatial consistency of the wind field. In a recent study, horizontal wind was calculated using the deep flow implementation of OpenCV (Ouyed et al. 2021; Weinzaepfel et al. 2013). This resulted in higher resolution of AMVs with a finer structure. Likewise, many previous studies have reported the adaptation of optical flow for AMV tracking based on the LK method or the Farnebäck method. Though these methods showed higher tracking performance than the CC method, each method still has some limitations in AMV retrieval. The LK method yielded sparse AMVs, resulting in low resolution because it observes only specific areas. With the dense Farnebäck method, prediction also is limited because t + 1 data are used to calculate the AMVs at time t.

In the computer vision field, convolution neural network (CNN) models have contributed to higher tracking performance than simple methods like the LK or Farnebäck methods for the calculation of optical flow. Since the CNN method can extract deep features of the input images and learn with various image data, CNNs have achieved remarkable success in optical flow estimation (Tu et al. 2019). Therefore, we adopted a CNN model in this study to calculate AMVs at higher accuracy. Among the several CNN models, we chose the PWC-Net (CNNs for optical flow using pyramid, warping, and cost volume), which has both high accuracy and short calculation time among the existing end-to-end CNN models for flow (Sun et al. 2018). The PWC-Net-based method calculates AMVs based on the pixels rather than the targets, which enables the calculation of seamless AMVs. Then, linear regression can be applied to AMVs to each pixel by time, allowing AMV forecasting. The algorithm presented in this study uses a CNN model to provide seamless AMVs with higher accuracy. The AMVs forecast using only satellite data presented in this study will show a variety of uses in relation to weather nowcasting and forecasting and will increase the accuracy of wind-related disaster prediction, such as cyclones, hurricanes, and typhoons.

We describe the details of the algorithm and the data on which it can be implemented in the Data and Methods section below. The error analysis methods for algorithm validation are also explained in the next section. In the Results section, the performance and results of the proposed algorithm are explained in two parts. First, the application of CNN is explained to verify the performance compared to that of the current algorithm. We also specifically identified conditions under which the performance the accuracy was high. The second part of the Results section describes an attempt at AMV forecasting and its results. Finally, in the Conclusion and Discussion section, the results of this study are summarized and explained. In addition, the application points, which are the advantages of this study, and the limitations of this study are described, and topics for future study are discussed.

2 Data and Methods

The AMVs for cloud-free skies were derived by tracking water vapor observed by the geostationary satellite GEO-KOMPSAT-2A (GK2A) (Choi and Ho 2015). For retrieval of AMVs, infrared brightness temperature images of vapor of channels 08, 09, and 10 centered at 6.3, 7.0, and 7.3 \(\mu m\), respectively, over the Korean Peninsula were used. Wind at different altitudes could be estimated since each channel absorbs a different wavelength (Lee and Ahn 2023). For validation, we assumed that the AMVs calculated by the CNN (CNN AMVs) would have the same altitude as the closest GK2A AMVs. Therefore, the altitude of the CNN and GK2A AMVs both ranged from 250 to 750 hPa. Cloud masking was performed to distinguish the cloudy areas from the clear skies using Cloud Detection (Cloud Mask) from GK2A. The experiment was conducted using date from 2022, and AMVs were predicted at 7:10, 7:20, 7:30, and 8:00 UTC each day. We adapted the PWC-Net CNN for optical flow using pyramids, warping, and cost volumes for estimation of the optical flow and for forecasting AMVs. We chose to utilize the PWC-Net among the optical flow estimation networks because of its short calculation time and high accuracy (Sun et al. 2018).

Figure 1 depicts the flow chart of our suggested algorithm. The AMVs were calculated using only current time (t) data and data from 10 min prior (t-1), unlike current methods that use data for t-1, t, and t + 1 (10 min intervals). The AMVs were calculated by inputting the vapor channel images at times t-1and t into the CNN model, in which PWC-Net uses layers of convolutional filters to downsample the features for representation at the first layer. The warping layer warps features of the second image toward those of the first image using the double upsampled flow from the second layer. Next, PWC-Net uses the features to determine the matching cost for associating a pixel with its corresponding pixels in the subsequent frame. Linear regression is applicable to each pixel since the CNN AMVs are calculated using every pixel at all times. Therefore, it is possible to produce the subsequent AMVs using linear regression. In this study, AMVs after 10, 20, and 30 min and 1 h were predicted using three consecutive time points in 10 min intervals.

Fig. 1
figure 1

A flow chart of the developed algorithm. Horizontal AMVs are obtained by inputting the brightness temperature images of two consecutive water vapor channels into a CNN model. Linear regression is applied to these horizontal AMVs to predict the AMVs of the next time

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GK2A AMV products and ECMWF (European Centre for Medium-Range Weather Forecasts) Reanalysis v5 (ERA5) hourly grid global data were used for the validation of CNN AMVs (Bell et al. 2021). To determine the difference in accuracy between CNN AMVs and GK2A AMVs, the vectors were compared with the wind data of ERA5. The wind field data of ERA5 with homogeneity and high accuracy were set as the ground truth values (Bell et al. 2021). In the ERA5 wind field data, the U and V components of winds of 250 to 750 hPa were used. GK2A calculates AMVs by dividing clear skies and clouds, and we used the atmospheric motion vector-vapor (6.3, 6.9, and 7.3 \(\mu m\))-clear sky target.

We calculated vector difference (VD) and RMSVD for validation (Le Marshall et al. 2004). The VD between satellite driven AMVs (ui and vi) and ERA5 wind (utruth and vtruth) is calculated as in Eq. (1):

$${(VD)}_{i}=\sqrt{{({u}_{i}-{u}_{truth})}^{2}+{({v}_{i}-{v}_{truth})}^{2}}$$
(1)

In Eq. (2), the RMSVD of AMVs is demonstrated according to the definition of Tokuno (1998) and compiled by Deb et al. (2014) as follows:

$$RMSVD= \sqrt{{(MVD)}^{2}+{(SD)}^{2}}$$
(2)

where \(MVD\) and \(SD\) are calculated as

$$MVD= \frac{1}{N}{\sum }_{i=1}^{N}{(VD)}_{i}$$
(3)

and

$$SD= \sqrt{\frac{1}{N}{\sum }_{i=1}^{N}{[{\left(VD\right)}_{i}-MVD]}^{2}}$$
(4)

For AMVs with different resolutions, such as the ERA5 wind field data and CNN AMVs data, we attempted to find the ‘nearest point’ for comparison. The differences in latitude and longitude of each data point were calculated, the point with the smallest sum of the two differences was designated as the 'nearest point,' and the AMVs at that point were compared.

3 CNN AMV Validation

As shown in Fig. 2, the CNN AMVs were seamless, while the GK2A AMVs had missing data. Seamless data means that the results come from every pixel with no missing data. This indicates more detail than results with missing data. These calculation is a result of GK2A tracking the target (target-based), while CNN tracks each pixel (pixel-based). The GK2A algorithm set a center of targets in the brightness temperature image and found a point where the targets have moved. Therefore, AMV was retrieved only in the area of the target, and the calculation could not be performed if it was difficult to identify the target (Oh et al. 2019). In comparison, CNN was able to obtain more complete results because it is a pixel-based algorithm that considers every pixel, allowing extraction of a larger amount of data than the target-based algorithm. Figure 2 shows calculations for 07:00 UTC on November 1, 2022, an arbitrarily selected date. The number of CNN AMVs calculated was 447,939, which was more than 600 times greater detailed than the 693 data points of GK2A AMVs. In general, CNN AMVs contained 200 to 1,000 times more data points than GK2A AMVs.

Fig. 2
figure 2

Maps of AMVs velocity over the Korean peninsula as calculated by two algorithms. a CNN AMVs velocity is much more detailed than that of (b) GK2A AMVs since CNN AMVs are pixel-based, whereas GK2A AMVs are target-based. Calculated for 07:00 UTC on November 1, 2022

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Figure 3 depicts the comparison of the tracking performance of CNN AMVs and GK2A AMVs referring to the ERA5 wind field data as the ground truth. Each data point represents a monthly RMSVD value. In both CNN AMVs and GK2A AMVs, RMSVD decreased in the order of channels 08, 09, and 10, centered at 6.3, 7.0, and 7.3 \(\mu m\), respectively. Particularly with GK2A AMVs, the accuracy varied sensitively according to the altitude, represented by water vapor absorption channels. On the other hand, CNN AMVs provided a stable accuracy regardless of altitude. Furthermore, CNN AMVs generally showed similar or better tracking performance compared to that of GK2A AMVs. The mean RMSVD for channel 08 was 12.86 m/s for CNN AMVs and 19.96 m/s for GK2A AMVs; that for channel 09 was 12.65 m/s for CNN AMVs and 18.25 m/s for GK2A AMVs. For channel 10, the smallest RMSVD values were 12.32 m/s for CNN AMVs and 15.89 m/s for GK2A AMVs. The proportional reduction in error was reduced by 35.58%, 30.70%, and 22.44% for channels 08, 09, and 10, respectively. The CNN AMVs produced RMSVDs as low as 4.90 m/s, which implied a clear increase in accuracy.

Fig. 3
figure 3

Graphs showing the tracking performance of CNN AMVs and GK2A AMVs. Root-mean-square vector differences (RMSVDs) are shown using the wind field data of ERA5 as the ground truth. a, b, and c are the results calculated with the data of channels 08, 09, and 10, respectively

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Figure 3 shows the seasonal accuracy of CNN AMVs and GK2A AMVs. CNN AMVs showed relatively high accuracy in all seasons, and for channel 10, it showed similar accuracy to that of GK2A AMVs in January and December. The accuracy was higher in the seasons when the AMV velocities were small, which might be because the current GK2A AMV algorithm shows difficulty in tracking small movements, while our method tracks movements in every pixel. In August, when wind velocities are known to be small, the difference in RMSVDs was largest. In the case of channel 8, there is a difference of more than 10 m/s.

However, the CNN AMVs on channel 10 had as low of an accuracy as GK2A AMVs on some days. To determine the factors resulting in the lower accuracy, we divided data into high and low cases of RMSVD. As shown in Fig. 4, we tested the VDs of CNN AMVs and GK2A AMVs based on velocity for high and low accuracy cases. Both CNN AMVs and GK2A AMVs VDs increased as the AMV velocity increased, and the slopes of CNN AMVs were smaller than those of the GK2A AMVs. These findings implied that tracking performance was less prone to deterioration with increasing velocity for CNN AMVs. On the other hand, as shown in Fig. 4d, e, and f, the CNN tended to overestimate the AMV velocity. Therefore, the larger was the overestimation in AMVs, the lower was the accuracy. In conclusion, the overall tracking performance of the CNN-based algorithm was better than that of the GK2A algorithm, but the CNN-based algorithm tended to overestimate the magnitude of vectors.

Fig. 4
figure 4

Scatterplots of channel 10 show vector differences by AMV velocity. Scatterplots on the top line, a, b and c, represent high accuracy cases (1st day of July, August, and October) and scatterplots on the bottom line, d, e, and f, represent low accuracy cases (1st day of April, May, and December)

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4 Forecasting AMV

We attempted to forecast AMVs, which is not possible using the current GK2A AMV algorithm because it requires future data (10 min later) to calculate the present AMVs. Also, due to its target-based calculation, vectors of GK2A AMVs are located in various positions with time. CNN AMVs are able to be calculated for the present time without using future data, and the position of AMVs does not change significantly over time since the results are pixel based. These advantages made it possible to apply linear regression to each pixel of AMVs, enabling them to be forecasted.

Figure 5 shows the accuracy of forecasted AMVs by lead time. The mean RMSVDs of forecasted AMVs were 2.74, 2.95, 3.41, and 4.79 m/s at lead times of 10, 20, and 30 min and 1 h, respectively. According to Fig. 5, the AMVs calculated by channel 08 showed the highest accuracy among the three channels. The RMSVD was 2.51 m/s when the lead time was 10 min and 4.44 m/s when the lead time was 60 min. The AMVs from channel 09 and 10 showed similar RMSVDs of 2.87 m/s and 2.84 m/s when the lead time was 10 min and of 5.32 m/s and 4.59 m/s with a lead time of 60 min, respectively. When linear regression was applied, the existing calculation error value increased, so the forecasting error in that area also increased. When the lead time was 1 h, the RMSVD was 4.79, which was 1.74 times larger than that with a lead time of 10 min. In Fig. 6a, the area with clouds was not included in the calculated AMVs. In Fig. 6b and c, it was confirmed that the error increased as the lead time increased. However, when comparing the forecasted values in Fig. 6c and d with the 6b reference CNN AMVs, the forecasted AMVs were overestimated, especially in the lower right of the graph. This is a limitation of linear regression forecasting due to its weakness at detecting changes in AMV because it assumes that motion will continue in the same direction and speed.

Fig. 5
figure 5

A graph showing the mean RMSVDs of forecasted AMVs by channel. Channels 08, 09, and 10 have higher RMSVDs in that order; when the lead time is 60 min, the RMSVD is about 3 times larger than when the lead time is 10 min. Overall, it shows a similar pattern regardless of the channel.

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Fig. 6
figure 6

Atmospheric motion vector has been forecasted with pixel-based results. a Image of the brightness temperature of water vapor from GK2A, b Reference AMVs calculated by CNN, c and d are the 10 min and 60 min forecasted AMVs with vector difference compared with (b). In (a), areas with clouds were masked when calculating and forecasting AMVs

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5 Conclusion and Discussion

AMVs are satellite outputs that directly affect a wide variety of meteorological fields. As a result, many previous studies have actively endeavored to develop better algorithms and to improve the performance of these algorithms. In this study, we calculated the horizontal AMVs for clear skies using the CNN model and attempted to forecast AMVs based on linear regression. The CNN AMVs calculated by the newly proposed algorithm showed more accurate water vapor tracking than the current GK2A algorithm. In particular, the overall accuracy was improved by resolving the increase in error with velocity of the AMVs. In addition to improving accuracy, the new algorithm presented in this study has the advantage of obtaining complete results. Our method can forecast AMVs up to 1 h later, which was not possible with the current GK2A AMV algorithm, because of these seamless results.

In conclusion, we proposed an algorithm that enables the calculation of more accurate AMVs using a CNN model and that produces seamless AMVs by forecasting. In this study, we showed that future AMVs can be predicted using only satellite data. These results will not only complement the limitations of current algorithms for calculating AMVs, but will also further expand the range in which satellite data can be utilized.

In this sense, it is expected that seamless AMV calculation and forecasting algorithms using geostationary satellites will have various applications. Since AMVs are used for weather analysis and forecasting accuracy (Velden and Young, 1994), the proposed algorithm will be utilized for the analysis and forecasting of most meteorological phenomena, such as hurricane weather forecasting (Goerss, 2000), tropical cyclone track forecasts (Velden et al. 1998, Lim et al. 2022), and monsoon analysis (Kumar and George, 2016). Seamless AMVs will be particularly useful for weather forecasting in regions where wind observations are very rare, such as in ocean regions or in developing countries.

However, some limitations of our method remain to be improved. Since the linear regression that we adapted to the forecasting assumes that future trends will be the same as current trends, it was difficult to account for rapid changes in AMVs. As a result, where the accuracy of the calculation was low, the accuracy of the forecast was also low. To overcome these limitations, the concepts related to multiple linear regression in statistics or random forest models in computer visions could be considered together. In addition, obtaining ground-truth data for optical flow in the real world is extremely difficult (Sun et al. 2018) and is much more limited in meteorology than in computer vision. Therefore, it is very challenging to develop a specialized CNN model for AMVs trained from meteorological satellite images. In other words, the accuracy of the method presented in this study is unable to be increased through learning, unlike artificial intelligence. For these reasons, it is necessary to test which of the various optical flow CNN models is the most efficient for AMVs. In addition, new state-of-the-art optical flow CNN models are continuously being developed, and we plan to continue to apply those models to AMVs.

However, beyond such limitations, we highlighted the advances in producing more accurate and predictable AMVs using CNN models in this study.