1. Introduction
Knowledge of atmospheric winds is important for climate research and weather forecasting. An atmospheric motion vector (AMV) is a vectorial representation of the motion of atmospheric features derived from spaceborne measurements. AMVs are crucial for studying the dynamics of convective and extreme weather phenomena. This research can be conducted either directly (Bedka and Mecikalski 2005; Oyama 2017; Apke et al. 2018; Stettner et al. 2019) or via data assimilation (Velden et al. 2017; Zhao et al. 2021; Xie et al. 2023; Lu et al. 2022). AMV estimates are already routinely produced from the current global satellite constellation. AMVs are derived by tracking features (e.g., cloud-top properties, radiances, or water vapor) in sequences of geostationary (GEO) or high-latitude low Earth orbit (LEO) images spaced at regular intervals in time.
Future global 3D winds observing systems will likely involve a combination of active and passive measurement techniques (National Academies of Sciences, Engineering, and Medicine 2018). It is important to understand the robustness of passive AMVs to be able to properly account for their information and contribution to the global observing system. However, the accurate estimation of AMVs from time sequences of satellite images is a challenging problem. Previous work has demonstrated state-dependent uncertainties (Posselt et al. 2019), used emulation to model them (Teixeira et al. 2021), and demonstrated the limitations of feature tracking techniques that rely on minimizing the difference between subregions in sequences of images (described below in section 2 and hereafter referred to as pattern-matching techniques). Dense optical flow retrieval methods (section 3) have emerged as a promising methodology for obtaining vector winds from sequences of images (Stettner et al. 2019; Apke et al. 2018, 2022).
In this paper, we use a robust and efficient variational dense optical flow method that utilizes the conservation of pixel brightness across a pair of images with a regularization constraint. Our approach generates a dense vector field for every pixel in a pair of images. We analyze the performance of optical flow, as compared with pattern-matching techniques. Specifically, we analyze how the performance of optical flow and feature matching varies with respect to weather regime, temporal separation between images, and pressure level. This research represents a comprehensive study of 3D wind retrievals involving diverse water vapor datasets, hundreds of time snapshots, with data defined at various altitudes, with high spatial resolution, and extensive areal coverage.
To test the performance of the optical flow algorithm, we utilize as reference datasets several simulations that represent different weather phenomena (hereafter referred to as “simulations”) which provide water vapor variables and wind vector fields at various pressure levels. AMVs are subsequently derived using both feature matching and optical flow algorithms from a sequence of water vapor fields and compared to the simulation wind vectors. We estimate wind vector uncertainties for both feature matching and optical flow methods by comparing the wind estimates to the winds in the reference simulations.
We note at the outset that, while we intend this work to eventually inform current and future AMV retrieval applications, including design of future winds missions, we do not evaluate any particular satellite solution here. We conducted a comparison between notional infrared and microwave observations using a feature matching algorithm (Posselt et al. 2019), and we will extend this analysis to include the optical flow algorithm in future work.
It is also important to note that our study did not implement several advanced techniques known to significantly reduce errors in operational AMV retrieval methods. Specifically, our analysis focused on a base comparison between untuned feature matching and optical flow algorithms. This approach was chosen to establish a foundational understanding of the relative performance of these two methodologies in their most basic forms. We acknowledge that the application of operational tuning and optimization techniques, such as quality control, error correction, and filtering processes, can greatly enhance the accuracy and reliability of both algorithms. In particular, in operational use of AMVs, it is common to filter winds via the use of a quality indicator, which is used to remove winds that contain biases or noise. In addition, in data assimilation systems, winds are routinely thinned spatially to reduce correlation among observations (Cordoba et al. 2017; Lewis et al. 2020). We chose not to apply either of these techniques as our goal is to compare the feature matching and optical flow algorithms directly and because operational quality control and observation thinning depends on the application of interest; however, for feature matching, basic quality control is still performed by averaging wind estimates at grid points where both estimates are valid and the vector magnitude difference is less than a threshold—specifically, 30% of the maximum retrieved wind speed at each height level, calculated per image triplet. We note that, in practice, often only a small fraction (1%–2%) of the available winds is used in operational data assimilation systems. Consequently, we anticipate that the performance of both feature matching and optical flow would improve substantially once they have been fine tuned for operational use. This study provides a groundwork for future research to explore these enhancements and their impact on AMV retrieval accuracy.
The paper is structured as follows. An overview of the feature matching algorithm used in this paper is given in section 2. A brief background of dense image alignment methods is provided in section 3, and a description of the optical flow algorithm used in our analyses is presented in section 4 and the appendix. Section 5 describes the simulation datasets employed in our studies. The comparisons between feature matching and optical flow, validated against the simulation wind fields, are presented in section 6. Discussions, conclusions, and plans for future work on AMV retrieval are outlined in section 7.
2. The feature matching method
Local area feature matching, a common technique for tracking atmospheric features in sequential imagery, is discussed in this section. In this paper, we specifically compare the AMVs generated by the optical flow method with those produced by the feature matching algorithm of Posselt et al. (2019). The feature matching algorithm works by identifying local gradients in the first image and matching them to corresponding gradients in the second image. These identified features are then tracked across subsequent images. The feature matching algorithm determines a search area containing a range of possible target coordinate matches for each source coordinate and then computes a cost function, which is a normalized sum of absolute differences over a specified window patch. Incorporating subgridding, the algorithm calculates the cost function for pattern differences on a per-pixel basis. This cost function is approximated using a second-order polynomial, and the algorithm identifies and returns the location of the minimum value within each subgrid, signifying the optimal match within this search area (Mueller et al. 2013).
The feature matching is applied to three sequential images, including the central image in terms of time. The algorithm examines every potential tracking window across the entire spatial image domain. For each valid estimate, the magnitude of the vector difference is calculated, and if it falls below a specified threshold, the average over the patch is deemed the retrieved velocity vector. The size of search grid boxes is adjusted according to the scale of the weather phenomena being analyzed. Larger grid boxes are used for extensive-scale phenomena, while smaller grid boxes are more suitable for phenomena of a smaller scale.
It is important to note that the algorithm in Posselt et al. (2019) does not guarantee a match for every grid point. The algorithm also does not return matches near image boundaries or effectively track features near regions with missing data. This includes regions where no water vapor retrieval is possible due to the presence of clouds (infrared observations) or precipitation (microwave observations), as well as areas in which data are not available due to topography. As a result, the vector field often exhibits oversmoothing in certain areas and erratic behavior in others, leading to a regionally constant speed map that lacks detail.
3. Background on dense optical flow and image alignment techniques
Image alignment refers to the process of finding a transformation that maps points from one image to corresponding points in another. Image alignment can be accomplished using methods from image registration and optical flow. Image registration techniques are widely used to identify transformations that align images captured at different times, and possibly, from different sensors or perspectives. These methods are commonly used in medical imaging and remote sensing. Some of the physical models for image registration are derived from the principles of continuum mechanics, and they include methods based on elasticity theories (Broit 1981; Bajcsy and Kovacic 1989; Dann et al. 1989) and viscous fluid flow (Christensen et al. 1996; D’Agostino et al. 2003). Notably, fluid image registration methods have proven successful for retrieving displacement fields in atmospheric and oceanic data (Yanovsky and Lambrigtsen 2016; Yanovsky et al. 2020).
On the other hand, optical flow methods focus on estimating the apparent motion of pixels, objects, or patterns between consecutive frames in a sequence of images. These methods are valuable for estimating motion and tracking objects. A variety of optical flow methods have been proposed, and many have proven effective for atmospheric tracking. For instance, the authors in Wu et al. (2016) utilized an optical flow algorithm based on polynomial expansion to derive AMVs. The study in Ouyed et al. (2021) computed AMVs from three consecutive images. The method in Apke et al. (2022) for deriving AMVs, particularly from water vapor imagery, leverages first-guess motions to aid in distinguishing wind-driven motions from other phenomena such as propagating waves. This approach, critical for enhancing the accuracy of the retrievals, underscores the importance of considering first-guess inputs in optical flow methodologies for more reliable AMV analysis.
4. The total variation based optical flow method
Before the computation of optical flow, it is often necessary to fill in missing or masked parts in the image sequence. These gaps can occur in areas covered by clouds or precipitation in water vapor data, or in regions with high elevation due to topography. These gaps need to be filled with suitable values to enable accurate optical flow calculation. To address this, we employ inpainting techniques. For important works on inpainting, we refer the readers to several foundational publications on inpainting (Bertalmio et al. 2000, 2001; Chan and Shen 2001; Shen and Chan 2002; Shen et al. 2003; Telea 2004).
Inpainting reconstructs missing or masked parts of images by extrapolating from neighboring areas. Specifically, we use biharmonic inpainting, which relies on the biharmonic equation (Damelin and Hoang 2018; Chui and Mhaskar 2010). It leverages the values of the known data in the nearby areas to produce smooth and coherent interpolations, effectively filling in these gaps. This process results in inpainted regions that are consistent with their surroundings. It should be noted that in this study, high-elevation regions lacking data are inpainted solely to facilitate optical flow computation, which necessitates dense water vapor fields. Postoptical flow computation, wind data from inpainted regions are not reported. Furthermore, this paper does not mask areas covered by clouds or precipitation.
After inpainting the missing regions, we compute the optical flow to determine the flow field u = (u1, u2), where u1 and u2 represent the horizontal components of the wind velocity. In appendix, the classical Horn–Schunck optical flow method is described. This method’s energy functional contains two terms: (i) a data fidelity term, defined as an L2 norm, and (ii) an L2-type regularization term, resulting in flow equations that involve linear terms in u1 and u2. The method penalizes structure in the optical flow, effectively smoothing the flow field.
In this work, our objective is to retrieve AMVs from a sequence of water vapor measurement images using an efficient and robust variational optical flow algorithm. The total variation (TV)-L1 optical flow algorithm, which we describe in appendix and consider in this paper, replaces the L2-type regularization with TV regularization constraint (Rudin et al. 1992) on the displacement fields, forming an L1-regularized problem (Zach et al. 2007; Wedel et al. 2009; Pérez et al. 2013; van der Walt et al. 2014). The total variation of a two-dimensional vector field u = (u1, u2) is defined as
In optimization problems, TV regularization plays a crucial role not only for preserving features, such as edges or regions with rapid changes, but also for addressing the aperture problem inherent in optical flow retrieval. This problem makes pixelwise retrieval of optical flow unfeasible, necessitating regularization for accurate estimations. Thus, TV regularization plays a dual role: it preserves discontinuities, edges, and structures, which is crucial in certain applications, and ensures overall smoothness in the flow field, thereby enhancing the accuracy of optical flow estimations in variational retrieval methods. There is a connection between TV minimization in optimization and image processing and shock capturing techniques in compressible computational fluid dynamics (Osher and Rudin 1990). In fact, the idea of TV minimization is conceptually related to total variation diminishing (TVD) schemes. These schemes are often employed for numerically solving the compressible Euler or Navier–Stokes equations, simulating fluid behaviors. Notably, TVD schemes are particularly beneficial in managing discontinuities or shocks, often present in such fluid flows (Harten 1983; Osher and Chakravarthy 1984; Gottlieb and Shu 1998).
Additionally, the data fidelity term used for minimization is the L1 norm of the nonlinear optical flow constraint, as described in appendix. The L1 norm (Alliney 1992; Meyer 2001) is more robust to noise and outliers in datasets than the L2 norm. Mathematically, for two two-dimensional scalar fields (or images) I and J, the L1 norm is defined as
The L1 norm offers a significant advantage over methods using the L2 norm, which is defined as
While the TV-L1 model, similar to the Horn–Schunck method, is based on the assumption of brightness constancy, it does not strictly enforce this assumption. Instead, the model accommodates deviations from the assumption through the inclusion of the L1 data fidelity and the TV regularization terms in its energy functional. These deviations can arise from dynamic changes such as noise, occlusions, varying illumination, or sources and sinks in data. The TV term promotes regional smoothness, which is particularly effective in natural scenes where coherent motion is often observed within specific regions. Furthermore, the robustness of the L1 norm against noise and outliers minimizes the impact of significant discrepancies that may arise from violations of brightness constancy or complexities such as noise fluctuations, temporal variations, or spatial discontinuities. The TV-L1 model’s balance in data fitting, noise and outlier resilience, and smoothness preservation make it especially suitable for analyzing atmospheric or meteorological imagery, which often contains varying structures.
The optical flow approach, as detailed in Zach et al. (2007), Wedel et al. (2009), van der Walt et al. (2014), derives AMVs from only two images and does not require initial guesses for any configuration or pressure level. These aspects significantly enhance the flexibility in their application across diverse datasets and in planning future satellite winds missions. Moreover, this study offers a comprehensive performance analysis of both feature matching and optical flow methods across various weather regimes, time intervals between images, and different pressure levels.
To assess the results generated by the optical flow algorithm, we use high-resolution simulations generated by a numerical weather prediction model (Skamarock et al. 2008). Specifically, simulations have been generated for four very different weather regimes (tropical cyclone early stage, tropical cyclone mature stage, extratropical cyclone, and nontropical-cyclone tropical convection), providing water vapor quantities and simulation wind velocity fields at different pressure levels. We then use the optical flow algorithm to derive the AMVs from a sequence of water vapor quantities. By comparing these AMVs to the simulation wind velocities, we can estimate AMV retrieval errors. Our findings indicate that the optical flow algorithm generates dense AMV fields for every pixel in a pair of images. This leads to effectively higher resolution wind fields compared to pattern-matching techniques, while yielding smaller errors in comparison to the feature matching method.
5. Simulation datasets
In our research, we aim to assess the results produced by the optical flow algorithm using four high-resolution, multiframe, simulated water vapor datasets. These datasets capture a range of weather conditions including tropical convection (TC), the Harvey early development stage (Harvey EDS) and Harvey late development stage (Harvey LDS) of a tropical cyclone, and an Extratropical cyclone (ETC) winter storm. To create the datasets, we utilized a high-resolution Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008) to generate simulations of the weather scenes. The ETC case was simulated using WRF V3.8.1, documented in Posselt et al. (2019), while the Harvey cases utilized WRF V3.6.1, documented in Posselt et al. (2022). For the TC case, the WRF V3.6.1 simulation was initiated at 0000 UTC 10 July 2008 with the NCEP final (FNL) analysis dataset, running at a single domain with a 3.5-km horizontal resolution. Key physical parameters encompassed the WRF single-moment 6-class microphysics scheme (WSM6) (Hong and Lim 2006), the Yonsei University (YSU) planetary boundary layer scheme (Hong et al. 2006; Hong 2010), and the Rapid Radiative Transfer Model for general circulation models (RRTMG) shortwave and longwave radiation schemes (Iacono et al. 2008). The initial 6 h served as a spinup period, with data analysis starting at 0600 UTC 10 July 2008.
The WRF simulations provide data on water vapor quantities as well as wind velocity fields. Table 1 provides detailed descriptions of the four datasets that capture the weather regimes analyzed in our study. Corresponding geographic domains for these datasets are illustrated in Fig. 1. The datasets were generated for three pressure levels: 850, 500, and 300 hPa.
Description of analyzed datasets.
Geographic domains for the datasets described in Table 1. Water vapor fields are shown.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
We utilized the feature matching algorithm of Posselt et al. (2019) and the total variation based optical flow algorithm discussed in this paper to extract AMVs from multiframe sequences of water vapor fields. For the feature matching algorithm, we employed three sequential images to retrieve AMVs. The feature matching search area was set to 45 × 45 grid points for the TC and ETC datasets and 11 × 11 grid points for the Harvey EDS and Harvey LDS datasets. In contrast, the optical flow algorithm required only two images, with no need for initial guesses for the AMV retrieval.
The performance of a specific search area size for feature matching depends on the dimensions of the domain as well as the nature of the atmospheric phenomena being studied. In the case of the Harvey datasets, the area is not only smaller but also contains the hurricane’s development region within its bounds. As a result, a smaller search area was used. Using a larger search area on such a compact, dynamic domain could result in patchy AMV results, where finer details get lost and the wind structure appears overly smooth and generalized. Conversely, larger search areas are better suited for larger domains, where a small search area could result in capturing an excessive level of detail. This “excessive detail” implies focusing on small-scale variations, which may not be as relevant to analyzing large-scale wind patterns, and could potentially lead to higher errors. A larger search area, in contrast, facilitates the capture of main wind structures, avoiding the complexities of minute details. An analysis of the sensitivity of feature matching results to changes in search area sizes was provided in Posselt et al. (2019).
The project aims to highlight the relative computational costs associated with feature matching versus optical flow. Feature matching seeks to identify and subsequently match distinctive features between image pairs. In scenes that are rich in texture or have numerous unique features, there can be a large number of features to detect. This increases the computational cost during the matching process. Although the feature matching algorithm uses a pyramid structure to match features, the search remains exhaustive and time intensive. The size of the search area directly affects the number of features detected and, as a result, the time required for matching. In contrast, the optical flow algorithm processes every pixel at the same time and benefits from the efficient numerical methods and optimizations discussed in appendix.
From our empirical tests, we observed that the optical flow algorithm was about 800 times faster on the TC dataset, 1500 times faster on the ETC dataset, and 76 times faster on the Harvey datasets compared to the feature matching algorithm. The smaller difference in computational time between optical flow and feature matching for the Harvey dataset, compared to the TC and ETC datasets, is due to the smaller designated search area for the Harvey dataset, as mentioned earlier in this section. Additionally, the difference in computational costs for the TC dataset compared to the ETC dataset is attributed to the smaller image dimensions in the TC dataset. Given that feature matching avoids computing wind vectors near image boundaries, it consequently omits a proportionally larger image area for the TC dataset relative to the ETC dataset.
6. Results
a. TC dataset
We begin by considering a simulated water vapor dataset that captures tropical convection over the Maritime Continent from 0600 to 1027 UTC 10 July 2008. The dataset includes 224 images, each with dimensions of 999 × 1299 grid points, a spatial resolution of 3500 m, and a temporal resolution of 72 s, spanning a period of 4.5 h. It is defined at three pressure levels: 850, 500, and 300 hPa. Our study analyzes the full dataset at three different time intervals: 2.4, 9.6, and 12 min.
Pairs of sample water vapor images, along with their differences, from the TC multiframe dataset at all three pressure levels, are depicted in Fig. 2. The time interval between these pairs is 12 min. It can be observed that the data have more structure at lower altitudes (corresponding to higher pressure levels) compared to higher altitudes (corresponding to lower pressure levels). Additionally, water vapor quantities generally decrease in mass content with increasing altitude.
Pairs of representative sample water vapor images, taken 12 min apart, are shown for three pressure levels (850, 500, and 300 hPa), along with the differences between each pair. These images are part of a simulated water vapor dataset that captures TC over the Maritime Continent on 10 Jul 2008. The white pixels represent regions that have been masked due to topography. The color scale ranges differ between each layer.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figure 3 presents the corresponding wind speeds and wind vectors from the simulations, as well as AMVs obtained using both the feature matching and optical flow algorithms. Notably, wind speeds typically increase with altitude. The feature matching algorithm is unable to compute AMVs near domain boundaries and does not guarantee a match for every grid point. Also, feature matching cannot compute AMVs in areas that are close to those masked due to topography, as seen at the 850-hPa pressure level. Conversely, our approach employs biharmonic inpainting to fill in masked regions before performing the optical flow, thereby computing dense AMVs for every pixel in each pair of images. We can observe that the wind speeds and AMVs derived from the optical flow algorithm visually more closely resemble the wind field from the simulations, whereas the feature matching algorithm produces a speed map that is regionally constant and contains less detail.
Wind speed and wind vector fields from the simulation are displayed for reference, along with those derived by the FM and OF algorithms for a sample pair of images taken 12 min apart from the TC dataset. The white pixels represent areas masked due to topography or regions where FM does not produce matches.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figure 4 shows RMSVD errors obtained with feature matching and optical flow methods for the TC dataset at 2.4-, 9.6-, and 12-min time intervals and at 850-, 500-, and 300-hPa pressure levels. The RMSVD of AMVs obtained using the optical flow method are as low as approximately 2.5 m s−1 for the 850- and 500-hPa pressure levels. Compared to the feature matching algorithm, the optical flow algorithm improves AMV accuracy by an average of 45.9% across all pressure levels and time intervals.
RMSVD errors obtained using the FM and OF methods are presented for the TC dataset at various time intervals and pressure levels. The OF algorithm demonstrates an average improvement of 45.9% in AMV accuracy compared to the FM algorithm.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
The line plots in Fig. 5 (left) display the RMS magnitude of simulated wind vectors, the RMS deviation from mean wind vector, and the RMSVD of both the feature matching and optical flow results. All values are averaged over all time intervals and plotted against pressure levels for the TC dataset. Each box in the plot represents the interquartile range of the errors for AMVs derived using the feature matching (FM) and optical flow (OF) algorithms across all time intervals, displaying the lower quartile, median, and upper quartile values. The whiskers extend from each box, indicating the range of error values not categorized as outliers. Outliers, identified using the interquartile range, are depicted as individual circles. The RMS magnitude of simulated wind vectors line plot indicates an increase in wind speed with altitude. The errors in AMVs appear to be proportional to wind speed. It is important to note that the RMS magnitude of simulated wind vectors serves as a reference point. Essentially, this RMS magnitude can be thought of as the difference between the simulated vector field and an identically zero wind vector field. If the RMSVD from the retrieval exceeds the RMS magnitude of simulated wind vectors, it holds no value; if it is approximately equal, the retrieval still lacks substantial information. Comparatively assessing the RMS deviation from mean wind vector against the retrieved vector field is more informative. We observe that the RMSVD plot for the optical flow retrieval is significantly below that for the RMS deviation from mean wind vector. This lower RMSVD plot indicates that optical flow retrieval is more effective in depicting the wind patterns in our study, reflecting its utility in accurately representing atmospheric behavior.
(left) Line plots representing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of FM and OF results are plotted against pressure levels for the TC dataset. (right) Line plots showing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of FM and OF results are plotted against time intervals for the TC dataset.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
In Fig. 5 (right), the line plots depict the RMS magnitude of simulated wind vectors, the RMS deviation from mean wind vector, and the RMSVD of feature matching and optical flow results (averaged over all pressure levels) plotted against time intervals for the TC dataset. The boxes for feature matching and optical flow, displayed side-by-side, correspond to the same time intervals and are presented in such a manner for enhanced visualization and clarity. The whiskers signify the range of errors for the AMVs derived from feature matching and optical flow algorithms across all pressure levels. We observe a strong dependence of the feature matching results on the time interval. However, the optical flow results do not exhibit a significant dependence on time interval. The errors in optical flow are not only smaller but also robust to changes in time interval, offering greater flexibility in the planning of future missions.
b. Hurricane Harvey: Harvey EDS and Harvey LDS datasets
We now consider two simulated water vapor datasets that capture Hurricane Harvey in the Gulf of Mexico during its Harvey EDS from 1800 UTC 23 August 2017 to 0600 UTC 24 August 2017 and its Harvey LDS from 0600 to 1800 UTC 24 August 2017 (Posselt et al. 2022). Each dataset contains 361 images, each with dimensions of 297 × 297 grid points, a spatial resolution of 3000 m, and a temporal resolution of 120 s, spanning a period of 12 h. The datasets are defined at three pressure levels: 850, 500, and 300 hPa. Our study analyzes both full datasets at three different time intervals: 2, 6, and 10 min.
Pairs of sample water vapor images from the Harvey EDS and Harvey LDS multiframe datasets, along with their differences, are depicted in Figs. 6 and 7 at all three pressure levels. The pairs are 10 min apart. The data exhibit a similar degree of structural complexity in the images for 850- and 500-hPa pressure levels. However, for the 300-hPa pressure level, certain parts of the images have less detail. Additionally, water vapor quantities generally decrease in mass content as altitude increases.
Pairs of representative sample water vapor images, taken 10 min apart, are shown for three pressure levels (850, 500, and 300 hPa), along with the differences between each pair. These images are part of a simulated water vapor dataset that captures Hurricane Harvey in the Gulf of Mexico during its Harvey EDS on 23/24 Aug 2017.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Pairs of representative sample water vapor images, taken 10 min apart, are shown for three pressure levels (850, 500, and 300 hPa), along with the differences between each pair. These images are part of a simulated water vapor dataset that captures Hurricane Harvey in the Gulf of Mexico during its Harvey LDS on 24 Aug 2017.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figures 8 and 9 display the wind speeds and wind vectors from the simulations, as well as the AMVs obtained using both the feature matching and optical flow algorithms. As with the prior case, the feature matching algorithm does not compute AMVs near domain boundaries and fails to produce matches for portions of the grid, as indicated by the white regions in Figs. 8 and 9. The feature matching algorithm also tends to generate oversmoothed and erratic vector fields in some areas, while producing regionally constant speed maps with less structure in others. This behavior is similar to that observed for the tropical convection dataset. Our analysis also reveals that while the optical flow algorithm produces coherent and dense flow fields that closely resemble the wind field pattern from the simulations, it struggles to capture the strong winds around the southern and eastern sides of the hurricane. This observation aligns with the challenges the optical flow method faces in regions with significant circulation, such as hurricanes. Recognizing that applying optical flow to all water vapor points may not optimally represent the dynamics of rapidly rotating systems like hurricanes, future studies might benefit from exploring the application of optical flow to cloud fields or radiance fields for potentially improved results in such scenarios.
Wind speed and wind vector fields from the simulation are displayed for reference, along with those derived by both the FM and OF algorithms for a sample pair of images from the Hurricane Harvey (EDS) dataset taken 10 min apart. The white pixels represent regions where FM does not produce matches.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Wind speed and wind vector fields from the simulation are displayed for reference, along with those derived by both the FM and OF algorithms for a sample pair of images from the Hurricane Harvey (LDS) dataset taken 10 min apart. The white pixels represent regions where FM does not produce matches.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figure 10 shows RMSVD errors obtained using feature matching and optical flow methods for the Harvey EDS and Harvey LDS datasets at 2-, 6-, and 10-min time intervals and at 850-, 500-, and 300-hPa pressure levels. Compared to the feature matching algorithm, the optical flow algorithm improves AMV accuracy by 50.3% on average for the Harvey EDS dataset and by 51.0% on average for the Harvey LDS dataset.
RMSVD errors obtained using FM and OF methods are presented for the Hurricane Harvey datasets in their EDS on the left and LDS on the right, across various time intervals and pressure levels. Compared to the FM algorithm, the OF algorithm exhibits an average improvement in AMV accuracy of 50.3% for the Harvey EDS dataset and 51.0% for the Harvey LDS dataset.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
In the left column of Fig. 11, the line plots display the RMS magnitude of simulated wind vectors, the RMS deviation from mean wind vector, as well as the RMSVD of the results from feature matching and optical flow, averaged across all time intervals. These are plotted against pressure levels for both the Harvey EDS (top) and Harvey LDS (bottom) datasets. The RMS magnitude of simulated wind vectors line plot shows a decrease in wind speed with increasing altitude. Moreover, wind speeds are lower for the Harvey EDS dataset compared to the Harvey LDS dataset. The errors in AMVs for both feature matching and optical flow are lowest at the 500-hPa pressure level. When comparing the plot of the RMS deviation from mean wind vector to that of the retrieved vector field, it is evident that optical flow retrieval provides a substantial amount of information.
(left) Line plots representing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of FM and OF results are plotted against pressure levels for the (top) Harvey EDS dataset and (bottom) Harvey LDS dataset. (right) Line plots showing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of FM and OF results are plotted against time intervals for the Harvey EDS dataset (top) and Harvey LDS dataset (bottom).
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
In the right column of Fig. 11, the line plots depict the RMS magnitude of simulated wind vectors, the RMS deviation from mean wind vector, and the RMSVD of results from feature matching and optical flow, averaged across all pressure levels. These are plotted against time intervals for the Harvey EDS (top) and Harvey LDS (bottom) datasets. There is a noticeable dependence of the feature matching results on the time interval, with smaller errors occurring at a 6-min interval. Conversely, the optical flow errors do not show a significant dependence on time interval and are much smaller compared to those obtained using the feature matching method.
c. ETC dataset
We now examine a simulated water vapor dataset that captures an extratropical cyclone, specifically a winter storm, over the Western Atlantic from 0002 to 1200 UTC 22 November 2006 (Posselt et al. 2019). This dataset comprises 360 images, each with dimensions of 1440 × 1440 grid points. It has a spatial resolution of 4000 m and a temporal resolution of 120 s, covering a 12-h period. The dataset is defined across three pressure levels: 850, 500, and 300 hPa. In our study, we analyze the entire dataset at three different time intervals: 2, 6, and 10 min.
Pairs of sample water vapor images from the ETC multiframe dataset, along with the differences between them, are depicted in Fig. 12 for all three pressure levels. The time interval between the images in each pair is 10 min. It can be observed that the data have more structure at higher pressure levels compared to lower pressure levels. Additionally, water vapor quantities generally decrease in mass content with increasing altitude. It is important to note that, compared to the three datasets previously analyzed in this paper, the ETC dataset exhibits lower moisture content in most parts of the images, especially at the 300- and 500-hPa pressure levels.
Pairs of representative sample water vapor images, taken 10 min apart, are shown for three pressure levels (850, 500, and 300 hPa), along with the differences between each pair. These images are part of a simulated water vapor dataset that captures an ETC over the Western Atlantic on 22 Nov 2006. The white pixels represent regions that have been masked due to topography. The color scale ranges differ between each layer.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figure 13 presents the corresponding wind speeds and wind vectors from the simulations, as well as AMVs obtained using both the feature matching and optical flow algorithms. Notably, wind speeds tend to increase with altitude. Compared to the three datasets analyzed earlier in this paper, it should be noted that the wind speeds from the simulations in the ETC dataset are of higher magnitudes at the higher altitude pressure levels (500 and 300 hPa) and that the water vapor amounts and contrast are generally lower. As in the previous three cases, the feature matching algorithm is unable to compute AMVs near domain boundaries or near areas where the data are masked due to topography. In contrast, the optical flow algorithm computes dense AMVs for every pixel in each pair of images. While the optical flow algorithm captures the general direction and pattern of the storm, it faces challenges in accurately reproducing the highest wind speeds. Conversely, the feature matching algorithm presents different characteristics in its performance. It generates vector fields that show evidence of oversmoothing in certain regions and unpredictable fluctuations in others. Additionally, the feature matching algorithm results in speed maps that are regionally constant, thus providing less detailed information.
Wind speed and wind vector fields from the simulation are displayed for reference, along with those derived by the FM and OF algorithms for a sample pair of images taken 10 min apart from the ETC dataset. The white pixels represent areas masked due to topography or regions where FM does not produce matches.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Figure 14 shows the RMSVD errors obtained using feature matching and optical flow methods for the ETC dataset at 2-, 6-, and 10-min time intervals and at 850-, 500-, and 300-hPa pressure levels. Compared to the feature matching algorithm, the optical flow algorithm improves AMV accuracy by 29.6% on average.
RMSVD errors obtained using the FM and OF methods are presented for the ETC dataset at various time intervals and pressure levels. The OF algorithm demonstrates an average improvement of 29.6% in AMV accuracy compared to the FM algorithm.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
The line plots in Fig. 15 (left) display the RMS magnitude of simulated wind vectors and the RMS deviation from mean wind vector, as well as the RMSVD of the results from feature matching and optical flow methods, averaged over all time intervals. These are plotted against pressure levels for the ETC dataset. The RMS magnitude of simulated wind vectors line plot reveals an increase in wind speed with increasing altitude. The errors in AMVs appear to be proportional to the wind speed. While the errors are larger for the ETC case than for the tropical cases, a comparison between the plot of the RMS deviation from mean wind vector and that of the retrieved vector field indicates that the optical flow retrieval provides a substantial degree of information.
(left) Line plots representing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of the results from FM and OF are plotted against pressure levels for the ETC dataset. The figure suggests that OF retrieval is highly informative. (right) Line plots showing RMS magnitude of simulated wind vectors, RMS deviation from mean wind vector, and RMSVD of the results from FM and OF are plotted against time intervals for the ETC dataset.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
An important observation regarding the ETC dataset is that, due to the higher winds and lower moisture content in this dataset compared to the three datasets previously analyzed in this paper, the RMSVD errors for both feature matching and optical flow results are larger. This illustrates the challenge faced by any algorithm for weather regimes characterized by high winds and low moisture content. The dependence of errors on water vapor content and gradient was documented in Posselt et al. (2019) and indicates that neither the feature matching algorithm nor the optical flow algorithm is immune to systematic state-dependent errors.
The line plots in Fig. 15 (right) depict the RMS magnitude of simulated wind vectors, the RMS deviation from mean wind vector, and the RMSVD of feature matching and optical flow results, averaged across all pressure levels. These are plotted against time intervals for the ETC dataset. There is a strong dependence of the feature matching results on the time interval. However, as in the tropical cases, the optical flow results do not exhibit a significant dependence on time interval. The errors in optical flow are not only smaller but are also robust to changes in time interval.
We now examine in more detail how the errors in retrieved clear-air water vapor AMVs, measured as magnitude of wind vector differences between feature matching and optical flow AMVs versus the simulation reference wind field, relate to the atmospheric state. Specifically, we focus on the dependency of AMV error on water vapor content and wind speed and their relationship. Results are presented in terms of wind vector difference (WVD) magnitude, defined as
As shown in Fig. 16a, which plots wind vector difference magnitude as a function of water vapor mass mixing ratio, the feature matching algorithm struggles to generate an AMV in regions of low water vapor content. Errors are highest at very low water vapor content (less than 1 g kg−1) and decrease as water vapor values rise above 1 g kg−1, beyond which wind vector difference magnitude generally stays within ±3 m s−1. Figure 17a demonstrates that the optical flow algorithm produces more accurate AMVs at very low water vapor content, despite some errors. The smallest error occurs at water vapor values above 1 g kg−1, where the wind vector difference magnitude is largely within ±2 m s−1. Figure 18a illustrates the error distribution of the differences between OF and FM errors (OF-FM). In this figure, solid lines indicate positive differences and dashed lines represent negative differences. More samples with large negative differences highlight the superior performance of the optical flow method. Furthermore, more samples with small and near-zero positive differences suggest that where feature matching outperforms optical flow, the differences in accuracy are minimal.
Difference between FM and simulation (SIM) winds for the ETC image pair at the 850-hPa pressure level, taken 10 min apart, depicted as a function of (a) water vapor content, (b) wind speed, (c) water vapor gradient, and (d) the angle between wind direction and water vapor gradient. The color shading indicates the percentage of total grid points with a specific wind vector difference magnitude. Black vertical lines in (d) denote positions of the ±90° angles.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Difference between OF and SIM winds for the ETC image pair at the 850-hPa pressure level, taken 10 min apart, depicted as a function of (a) water vapor content, (b) wind speed, (c) water vapor gradient, and (d) the angle between wind direction and water vapor gradient. The color shading indicates the percentage of total grid points with a specific wind vector difference magnitude. Black vertical lines in (d) denote positions of the ±90° angles.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Error distribution for the ETC image pair at the 850-hPa pressure level, taken 10 min apart. Differences between OF-FM are depicted in contours. Solid lines represent positive values, while dashed lines represent negative values.
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Both feature matching and optical flow demonstrate a dependence of wind vector difference magnitude on wind speed, with larger errors found at greater wind speeds. This pattern is shown in Fig. 16b for feature matching and in Fig. 17b for optical flow. However, errors are more significant for feature matching, while optical flow shows a concentration of samples with near-zero error. The superiority of optical flow, especially at certain wind speeds, is further confirmed by Fig. 18b, where dashed lines indicate instances where optical flow significantly outperforms feature matching.
A dependence of wind vector difference magnitude on the water vapor gradient is observed for both feature matching and optical flow. As shown in Fig. 16c for feature matching and Fig. 17c for optical flow, the largest errors are concentrated at the smallest gradients. This pattern aligns with expectations, given that feature matching requires distinct features for a reliable match and optical flow needs a certain level of detail to accurately advance a flow. However, errors are significantly smaller for optical flow, as confirmed by Fig. 18c.
Finally, we display the wind vector difference magnitude as a function of the angle between the wind direction and the gradient in the water vapor field in Fig. 16d for feature matching and Fig. 17d for optical flow. Angles of ±90° suggest that the wind is following paths where the water vapor content is constant. In such conditions, where there are no substantial changes in water vapor content for the AMV algorithms to detect or track, the outcome can be an underestimation of wind speeds or even assigning near-zero wind speeds when, in truth, the winds are considerably stronger. As evidence of this, the highest errors occur for wind-gradient angles of ±90° for both feature matching and optical flow. However, the errors from optical flow are less than those from feature matching, as evidenced by Fig. 18d.
7. Discussion and conclusions
The results we present are meant to illustrate the differences among feature matching and the TV-L1 optical flow algorithm across various weather regimes. While we use high-resolution and realistic simulations to conduct the analysis, the results are somewhat idealized since real observing systems will be unable to retrieve water vapor in all conditions. Specifically, for operational satellite datasets, water vapor retrievals are unavailable in cloudy regions for hyperspectral infrared sounding and unavailable in precipitating regions for microwave sounding. Additionally, water vapor retrievals will contain AMV retrieval errors due to instrument noise and image navigation and registration errors, which are not captured in this analysis. The relatively coarse vertical and horizontal resolution of passive sounders will also introduce errors into the retrieved wind fields (Posselt et al. 2019). As such, our results may be viewed as the best we might possibly expect to obtain for the two algorithms given a perfect AMV observing system.
This study has utilized four simulated datasets, each with hundreds of time snapshots, data defined at various altitudes, high spatial resolution, and extensive areal coverage, to analyze the performance of the optical flow method compared to the feature matching technique in retrieving AMVs. We used a high-resolution WRF numerical weather prediction model to generate simulations of diverse weather scenes, including tropical convection, the early and late stages of a tropical cyclone, and a winter storm. We evaluated the performance of AMV methods at three pressure levels and across three distinct time intervals.
For the feature matching algorithm, we employed three sequential images for AMV retrieval. In contrast, our robust and efficient optical flow approach derives AMVs from only two images and does not require initial guesses for any configuration or pressure level. These features significantly enhance flexibility in planning future missions.
The feature matching algorithm cannot compute AMVs near domain boundaries or near areas where data are masked due to topography. Conversely, the optical flow algorithm generates dense AMVs for every pixel in a pair of images, yielding smaller errors compared to the feature matching method. The wind speeds and AMVs derived from the optical flow algorithm closely resemble the wind fields from the simulations, though the algorithm does underrepresent the strongest wind speeds. Conversely, the feature matching algorithm yields vector fields that demonstrate oversmoothing in certain areas and erratic behavior in others, while generating speed maps that are regionally constant and less detailed. Our work plays a critical role in determining the mission architecture and projected instrument performance for future satellite missions designed to retrieve atmospheric winds.
In terms of computational efficiency, it is crucial to understand the disparities between feature matching and optical flow. The exhaustive search in feature matching, particularly in texture-rich scenes, can be time consuming. On the other hand, the optical flow method consistently processes every pixel and employs the efficient techniques outlined in the paper. Our empirical evaluations showed that optical flow computed wind fields from 76 to 1500 times faster than feature matching.
The key findings of our study may be summarized as follows:
-
Optical flow systematically outperforms feature matching, generating dense AMVs with significantly smaller errors for all weather conditions, at all pressure levels, and at different time intervals. Compared to the feature matching algorithm, the optical flow algorithm improves AMV accuracy by 30%–50%.
-
The performance of AMV algorithms depends on the state of the atmosphere. The uncertainties in AMVs generally appear to be proportional to wind speed. Data featuring more structure, which usually occurs at lower altitudes, are associated with smaller errors. The algorithms produce larger errors for weather regimes characterized by high winds and low moisture content.
-
There is relative invariance of the results to time intervals for the optical flow algorithm. In contrast, feature matching results exhibit a strong dependence on time intervals. The consistency of optical flow errors across time intervals offers greater flexibility in the planning of future missions.
In future work, we will extend the analysis of Posselt et al. (2019) to explore the relative trades among observing system types for realistic infrared and microwave sounders. We will account for the inability of infrared to see through clouds and the inability of microwave to provide measurements in regions with heavy precipitation. We will consider various vertical resolutions, the role of wind shear, and the impact of instrument noise on AMV retrieval. Additionally, we will focus on enhancing quality control measures and incorporating additional information sources, such as active wind measurements (e.g., Doppler wind lidar) to correct systematic errors in AMVs.
In addition, we plan to extend our analyses to incorporate high-resolution, three-dimensional data for reconstructing fully 3D winds. Acknowledging the challenge in accurately retrieving vertical motions, we aim to enhance the optical flow algorithm’s sensitivity and accuracy for 3D applications. This will involve integrating advanced algorithmic design and data processing techniques, including additional constraints and physical models. In particular, image registration models based on the theory of elasticity (Yanovsky et al. 2008) and viscous fluid flow (Yanovsky et al. 2007, 2009), with additional constraints, have proven successful in tensor-based morphometry and related fields. By adapting the optical flow algorithm to three dimensions, we strive to improve its capability for retrieving vertical motions, despite their typically smaller scale compared to horizontal winds.
Acknowledgments.
This work was supported by a grant from the National Oceanic and Atmospheric Administration (NOAA) Broad Agency Announcement (BAA) on Measuring the Atmospheric Wind Profile (BAA-NOAA-3DWinds-2022). This work was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with National Aeronautics and Space Administration (80NM0018D0004). Government sponsorship acknowledged. We would like to express our sincere gratitude to the three anonymous peer reviewers for their invaluable contributions to this paper. Their insightful comments and constructive suggestions have significantly enhanced the quality and clarity of our work. We deeply appreciate their expertise and the time they dedicated to reviewing our manuscript.
Data availability statement.
All data used to create the results presented in this manuscript have been archived on NASA’s high performance computing system and are available upon request.
APPENDIX
Details on Optical Flow Methods
a. Horn–Schunck method
b. TV-L1 method
In our analyses, the water vapor data were not normalized prior to input into the TV-L1 algorithm. The weighting parameter λ varies smoothly with the pressure level, as demonstrated in Fig. A1 for the ETC case. Although the minimization in Eq. (A7) is convex, due to the linearization introduced in Eq. (A6), it is valid only for small displacements. For large displacements, pyramid schemes are employed. These schemes use a coarse-to-fine strategy in the energy minimization procedure, guiding convergence toward the global minimum and avoiding local minima (Zach et al. 2007; Wedel et al. 2009). For implementation details, we refer readers to Pérez et al. (2013), van der Walt et al. (2014).
Parameter vs pressure (hPa).
Citation: Journal of Applied Meteorology and Climatology 63, 10; 10.1175/JAMC-D-23-0169.1
Numerous efficient methods have been proposed to solve the subproblem defined by the functional in Eq. (A8). These methods typically either transform the problem into a convex optimization problem or employ iterative techniques that exploit the semiconvex properties of the energy function. A vast body of literature exists on these subjects. Examples of methods that could be used or adapted to solve Eq. (A8) include primal-dual algorithms (Chambolle and Pock 2011), alternating minimization methods (Wang et al. 2007; Yanovsky and Davis 2015), split-Bregman methods (Goldstein and Osher 2009; Yanovsky et al. 2015), and the alternating direction method of multipliers (ADMM) (Boyd et al. 2011; Qin et al. 2015; Yanovsky and Dragomiretskiy 2018).
REFERENCES
Alliney, S., 1992: Digital filters as absolute norm regularizers. IEEE Trans. Signal Process., 40, 1548–1562, https://doi.org/10.1109/78.139258.
Apke, J. M., J. R. Mecikalski, K. Bedka, E. W. McCaul Jr., C. R. Homeyer, and C. P. Jewett, 2018: Relationships between deep convection updraft characteristics and satellite-based super rapid scan mesoscale atmospheric motion vector-derived flow. Mon. Wea. Rev., 146, 3461–3480, https://doi.org/10.1175/MWR-D-18-0119.1.
Apke, J. M., Y.-J. Noh, and K. Bedka, 2022: Comparison of optical flow derivation techniques for retrieving tropospheric winds from satellite image sequences. J. Atmos. Oceanic Technol., 39, 2005–2021, https://doi.org/10.1175/JTECH-D-22-0057.1.
Bajcsy, R., and S. Kovacic, 1989: Multiresolution elastic matching. Comput. Vision Graphics Image Process., 46 (1), 1–21, https://doi.org/10.1016/S0734-189X(89)80014-3.
Bedka, K. M., and J. R. Mecikalski, 2005: Application of satellite-derived atmospheric motion vectors for estimating mesoscale flows. J. Appl. Meteor., 44, 1761–1772, https://doi.org/10.1175/JAM2264.1.
Bertalmio, M., G. Sapiro, V. Caselles, and C. Ballester, 2000: Image inpainting. Proc. of the 27th Annual Conf. on Computer Graphics and Interactive Techniques (SIGGRAPH), New York, NY, ACM Press/Addison-Wesley Publishing Co., 417–424, https://doi.org/10.1145/344779.344972.
Bertalmio, M., A. L. Bertozzi, and G. Sapiro, 2001: Navier-stokes, fluid dynamics, and image and video inpainting. Proc. 2001 IEEE Computer Society Conf. on Computer Vision and Pattern Recognition. CVPR 2001, Kauai, HI, Institute of Electrical and Electronics Engineers, I, https://doi.org/10.1109/CVPR.2001.990497.
Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein, 2011: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn., 3, 1–122, https://doi.org/10.1561/2200000016.
Broit, C., 1981: Optimal registration of deformed images. Ph.D. thesis, University of Pennsylvania, 24 pp., https://www.proquest.com/openview/caa61be896faae8f9146eb96e3f8c78d/1?pq-origsite=gscholar&cbl=18750&diss=y.
Chambolle, A., 2004: An algorithm for total variation minimization and applications. J. Math. Imaging Vision, 20, 89–97, https://doi.org/10.1023/B:JMIV.0000011325.36760.1e.
Chambolle, A., and T. Pock, 2011: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vision, 40, 120–145, https://doi.org/10.1007/s10851-010-0251-1.
Chan, T. F., and J. Shen, 2001: Nontexture inpainting by curvature-driven diffusions. J. Vision Commun. Image Representation, 12, 436–449, https://doi.org/10.1006/jvci.2001.0487.
Christensen, G. E., R. D. Rabbitt, and M. I. Miller, 1996: Deformable templates using large deformation kinematics. IEEE Trans. Image Process., 5, 1435–1447, https://doi.org/10.1109/83.536892.
Chui, C. K., and H. N. Mhaskar, 2010: MRA contextual-recovery extension of smooth functions on manifolds. Appl. Comput. Harmon. Anal., 28, 104–113, https://doi.org/10.1016/j.acha.2009.04.004.
Cordoba, M., S. L. Dance, G. A. Kelly, N. K. Nichols, and J. A. Waller, 2017: Diagnosing atmospheric motion vector observation errors for an operational high-resolution data assimilation system. Quart. J. Roy. Meteor. Soc., 143, 333–341, https://doi.org/10.1002/qj.2925.
D’Agostino, E., F. Maes, D. Vandermeulen, and P. Suetens, 2003: A viscous fluid model for multimodal non-rigid image registration using mutual information. Med. Image Anal., 7, 565–575, https://doi.org/10.1016/S1361-8415(03)00039-2.
Damelin, S. B., and N. S. Hoang, 2018: On surface completion and image inpainting by biharmonic functions: Numerical aspects. Int. J. Math. Math. Sci., 2018, 1–8, https://doi.org/10.1155/2018/3950312.
Dann, R., J. Hoford, S. Kovacic, M. Reivich, and R. Bajcsy, 1989: Evaluation of elastic matching system for anatomic (CT, MR) and functional (PET) cerebral images. J. Comput. Assist. Tomogr., 13, 603–611, https://doi.org/10.1097/00004728-198907000-00009.
Donoho, D. L., and I. M. Johnstone, 1995: Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Stat. Assoc., 90, 1200–1224, https://doi.org/10.1080/01621459.1995.10476626.
Goldstein, T., and S. Osher, 2009: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci., 2, 323–343, https://doi.org/10.1137/080725891.
Gottlieb, S., and C.-W. Shu, 1998: Total variation diminishing Runge-Kutta schemes. Math. Comput., 67, 73–85, https://doi.org/10.1090/S0025-5718-98-00913-2.
Harten, A., 1983: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys., 49, 357–393, https://doi.org/10.1016/0021-9991(83)90136-5.
Hong, S.-Y., 2010: A new stable boundary-layer mixing scheme and its impact on the simulated East Asian summer monsoon. Quart. J. Roy. Meteor. Soc., 136, 1481–1496, https://doi.org/10.1002/qj.665.
Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF Single-Moment 6-class microphysics scheme (WSM6). Asia-Pac. J. Atmos. Sci., 42, 129–151.
Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341, https://doi.org/10.1175/MWR3199.1.
Horn, B. K. P., and B. G. Schunck, 1981: Determining optical flow. Artif. Intell., 17, 185–203, https://doi.org/10.1016/0004-3702(81)90024-2.
Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, 2008JD009944, https://doi.org/10.1029/2008JD009944.
Lewis, W. E., C. S. Velden, and D. Stettner, 2020: Strategies for assimilating high-density atmospheric motion vectors into a regional tropical cyclone forecast model (HWRF). Atmosphere, 11, 673, https://doi.org/10.3390/atmos11060673.
Lu, X., B. Davis, and X. Wang, 2022: Improving the assimilation of enhanced atmospheric motion vectors for hurricane intensity predictions with HWRF. Remote Sens., 14, 2040, https://doi.org/10.3390/rs14092040.
Meyer, Y., 2001: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, 122 pp.
Mueller, K., C. Moroney, V. Jovanovic, M. J. Garay, J.-P. Muller, L. D. Girolamo, and R. Davies, 2013: MISR level 2 cloud product algorithm theoretical basis. JPL Tech. Doc. D-73327, 51 pp., https://eospso.gsfc.nasa.gov/sites/default/files/atbd/MISR_L2_CLOUD_ATBD-1.pdf.
National Academies of Sciences, Engineering, and Medicine, 2018: Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space. The National Academies Press, 716 pp., https://doi.org/10.17226/24938.
Osher, S., and S. Chakravarthy, 1984: High resolution schemes and the entropy condition. SIAM J. Numer. Anal., 21, 955–984, https://doi.org/10.1137/0721060.
Osher, S., and L. I. Rudin, 1990: Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal., 27, 919–940, https://doi.org/10.1137/0727053.
Ouyed, A., X. Zeng, L. Wu, D. Posselt, and H. Su, 2021: Two-stage artificial intelligence algorithm for calculating moisture-tracking atmospheric motion vectors. J. Appl. Meteor. Climatol., 60, 1671–1684, https://doi.org/10.1175/JAMC-D-21-0070.1.
Oyama, R., 2017: Relationship between tropical cyclone intensification and cloud-top outflow revealed by upper-tropospheric atmospheric motion vectors. J. Appl. Meteor. Climatol., 56, 2801–2819, https://doi.org/10.1175/JAMC-D-17-0058.1.
Pérez, J. S., E. Meinhardt-Llopis, and G. Facciolo, 2013: TV-L1 optical flow estimation. Image Process. Line, 2013, 137–150, https://doi.org/10.5201/ipol.2013.26.
Posselt, D. J., and Coauthors, 2019: Quantitative assessment of state-dependent atmospheric motion vector uncertainties. J. Appl. Meteor. Climatol., 58, 2479–2495, https://doi.org/10.1175/JAMC-D-19-0166.1.
Posselt, D. J., L. Wu, M. Schreier, J. Roman, M. Minamide, and B. Lambrigtsen, 2022: Assessing the forecast impact of a geostationary microwave sounder using regional and global OSSEs. Mon. Wea. Rev., 150, 625–645, https://doi.org/10.1175/MWR-D-21-0192.1.
Qin, J., I. Yanovsky, and W. Yin, 2015: Efficient simultaneous image deconvolution and upsampling algorithm for low-resolution microwave sounder data. J. Appl. Remote Sens., 9, 095035, https://doi.org/10.1117/1.JRS.9.095035.
Rudin, L. I., S. Osher, and E. Fatemi, 1992: Nonlinear total variation based noise removal algorithms. Physica D, 60, 259–268, https://doi.org/10.1016/0167-2789(92)90242-F.
Shen, J., and T. F. Chan, 2002: Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math., 62, 1019–1043, https://doi.org/10.1137/S0036139900368844.
Shen, J., S. H. Kang, and T. F. Chan, 2003: Euler’s elastica and curvature-based inpainting. SIAM J. Appl. Math., 63, 564–592, https://doi.org/10.1137/S0036139901390088.
Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.
Stettner, D., C. Velden, R. Rabin, S. Wanzong, J. Daniels, and W. Bresky, 2019: Development of enhanced vortex-scale atmospheric motion vectors for hurricane applications. Remote Sens., 11, 1981, https://doi.org/10.3390/rs11171981.
Teixeira, J. V., H. Nguyen, D. J. Posselt, H. Su, and L. Wu, 2021: Using machine learning to model uncertainty for water vapor atmospheric motion vectors. Atmos. Meas. Tech., 14, 1941–1957, https://doi.org/10.5194/amt-14-1941-2021.
Telea, A., 2004: An image inpainting technique based on the fast marching method. J. Graphics Tools, 9, 23–34, https://doi.org/10.1080/10867651.2004.10487596.
van der Walt, S., and Coauthors, 2014: Scikit-image: Image processing in Python. PeerJ, 2, e453, https://doi.org/10.7717/peerj.453.
Velden, C., W. E. Lewis, W. Bresky, D. Stettner, J. Daniels, and S. Wanzong, 2017: Assimilation of high-resolution satellite-derived atmospheric motion vectors: Impact on HWRF forecasts of tropical cyclone track and intensity. Mon. Wea. Rev., 145, 1107–1125, https://doi.org/10.1175/MWR-D-16-0229.1.
Wang, Y., W. Yin, and Y. Zhang, 2007: A fast algorithm for image deblurring with total variation regularization. CAAM Tech. Rep. TR07-10, 19 pp., https://www.cmor-faculty.rice.edu/∼zhang/reports/tr0710.pdf.
Wedel, A., T. Pock, C. Zach, H. Bischof, and D. Cremers, 2009: An improved algorithm for TV-L1 optical flow. Statistical and Geometrical Approaches to Visual Motion Analysis, D. Cremers et al., Eds., Springer, 23–45.
Wu, Q., H.-Q. Wang, Y.-J. Lin, Y.-Z. Zhuang, and Y. Zhang, 2016: Deriving AMVs from geostationary satellite images using optical flow algorithm based on polynomial expansion. J. Atmos. Oceanic Technol., 33, 1727–1747, https://doi.org/10.1175/JTECH-D-16-0013.1.
Xie, Q., D. Li, Y. Yang, Y. Ma, X. Pan, and M. Chen, 2023: Impact of assimilating atmospheric motion vectors from Himawari-8 and clear-sky radiance from FY-4A GIIRS on binary typhoons. Atmos. Res., 282, 106550, https://doi.org/10.1016/j.atmosres.2022.106550.
Yanovsky, I., and A. B. Davis, 2015: Separation of a cirrus layer and broken cumulus clouds in multispectral images. IEEE Trans. Geosci. Remote Sens., 53, 2275–2285, https://doi.org/10.1109/TGRS.2014.2352319.
Yanovsky, I., and B. H. Lambrigtsen, 2016: Enhancing the temporal resolution of image sequences capturing evolving weather phenomena. Remote Sens. Lett., 7, 239–248, https://doi.org/10.1080/2150704X.2015.1128130.
Yanovsky, I., and K. Dragomiretskiy, 2018: Variational destriping in remote sensing imagery: Total variation with L1 fidelity. Remote Sens., 10, 300, https://doi.org/10.3390/rs10020300.
Yanovsky, I., P. M. Thompson, S. Osher, and A. D. Leow, 2007: Topology preserving log-unbiased nonlinear image registration: Theory and implementation. 2007 IEEE Conf. on Computer Vision and Pattern Recognition, Minneapolis, MN, Institute of Electrical and Electronics Engineers, 1–8, https://doi.org/10.1109/CVPR.2007.383144.
Yanovsky, I., C. Le Guyader, A. Leow, A. W. Toga, P. M. Thompson, and L. Vese, 2008: Unbiased volumetric registration via nonlinear elastic regularization. Second MICCAI Workshop on Mathematical Foundations of Computational Anatomy, New York, NY, HAL Open Science, 13 pp., https://inria.hal.science/inria-00629762v1/file/mfca08_1_1.pdf.
Yanovsky, I., A. D. Leow, S. Lee, S. J. Osher, and P. M. Thompson, 2009: Comparing registration methods for mapping brain change using tensor-based morphometry. Med. Image Anal., 13, 679–700, https://doi.org/10.1016/j.media.2009.06.002.
Yanovsky, I., B. H. Lambrigtsen, A. B. Tanner, and L. A. Vese, 2015: Efficient deconvolution and super-resolution methods in microwave imagery. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens., 8, 4273–4283, https://doi.org/10.1109/JSTARS.2015.2424451.
Yanovsky, I., B. Holt, and F. Ayoub, 2020: Deriving velocity fields of submesoscale eddies using multi-sensor imagery. IGARSS 2020 – 2020 IEEE Int. Geoscience and Remote Sensing Symp., Waikoloa, HI, Institute of Electrical and Electronics Engineers, 1921–1924, https://doi.org/10.1109/IGARSS39084.2020.9323797.
Zach, C., T. Pock, and H. Bischof, 2007: A duality based approach for realtime TV-L1 optical flow. Pattern Recognition, F. A. Hamprecht, C. Schnörr, and B. Jähne, Eds., Springer, 214–223.
Zhao, J., J. Gao, T. A. Jones, and J. Hu, 2021: Impact of assimilating high-resolution atmospheric motion vectors on convective scale short-term forecasts: 1. Observing System Simulation Experiment (OSSE). J. Adv. Model. Earth Syst., 13, e2021MS002484, https://doi.org/10.1029/2021MS002486.