ROTATE: A Coordinate System for Analyzing Atmospheric Rivers

This study introduces the ROTated Atmospheric river coordinaTE (ROTATE) system — a novel storm‐centric coordinate system designed specifically for analyzing atmospheric rivers (ARs). It effectively preserves key AR signals in the time mean that may be lost or obscured in simple averaging due to diverse AR orientations and shapes. By applying the ROTATE system, we compared climatological characteristics for northern hemisphere ARs. Composites of four key meteorological variables, integrated vapor transport, integrated water vapor, precipitation, and windspeed, indicate distinct and clearer patterns of ARs compared to the conventional non‐rotated AR centroid‐based compositing approach. Moreover, the ROTATE system improves precipitation rates, particularly around the AR center and its head and tail regions, providing more distinct delineations of the precipitation signals between landfalling and oceanic ARs. Overall, the ROTATE system has the potential to serve as a valuable tool for better comparing and understanding the characteristics, processes, and impacts of ARs across different regions.


Introduction
Atmospheric rivers (ARs; American Meteorological Society, 2017; Ralph et al., 2018) are a distinct meteorological phenomenon that exerts a notable influence on the Earth's weather, climate, ecosystem, and human inhabitability.In the early stages of research conducted by Zhu and Newell (1994, among others), it was discovered that ARs are responsible for more than 90% of the transport of water vapor toward the poles beyond approximately 30°latitude.Remarkably, despite this significant contribution, ARs only occupy around 10% of the Earth's circumference at midlatitudes.These findings highlight the fundamental importance of ARs in shaping the distribution of water vapor on a global scale, consequently influencing the spatial and temporal patterns, including extreme events, of the planet's energy and water cycles.
AR events have gathered considerable scientific and public attention in recent years due to their occurrences and impacts in densely inhabited coastal regions.An illustration of this is the heightened frequency of AR events experienced along the west coast of the United States during the winter of 2022-2023, during which California experienced two times the average number of ARs and got some relief from the recent multi-year drought.Highimpact ARs have also been witnessed in various other locations across the globe over the past few years.For instance, the amplification of favorable atmospheric conditions at Yellowstone National Park, driven by the moisture associated with an AR, resulted in significant rainfall over the region.This became pronounced to the extent that evacuations were required in specific areas of the park.In August 2022, a severe flooding event occurred in the southern provinces of Pakistan.This event was linked to the presence of two ARs that transported substantial moisture from the Arabian Sea (Nanditha et al., 2023).The scientific importance of ARs in high-latitude research, particularly when studying polar ARs, is noteworthy.Recent research (Zhang et al., 2023) employing observations and climate model simulations revealed that the frequent occurrence of ARs in early winter is associated with a 34% reduction in Arctic sea-ice coverage in the Barents-Kara Seas and central Arctic region.These ARs amplify radiation, precipitation, and ice melting, hindering the sea-ice recovery over the region.
In AR studies, particularly when conducting systematic analyses of AR processes using numerous AR instances, there is a common interest to create spatial composites that delineate the characteristics of ARs themselves and the corresponding large-scale environments (Guo et al., 2020;Zhang et al., 2019).However, due to the varied orientations and shapes exhibited by ARs, employing a straightforward temporal average (e.g., based on ARs on the conventional geographic coordinates) can potentially diminish crucial distinguishing features, especially for areas where we do not already have a comprehensive understanding of the AR structure.Moreover, most composite studies conducted thus far have been based on the longitude and latitude of the AR centroid.This approach might overlook crucial AR signals if the shape of the AR is not linear.
In this paper, we propose a method inspired by techniques frequently utilized in cyclone tracking (e.g., Naud et al., 2012).This technique aims to isolate, center, and rotate each distinct AR by an amount determined by a desired alignment condition.Through this procedure, we establish a storm-centric AR coordinate system that facilitates the co-location of crucial variables pertaining to AR characteristics, processes, and impacts.

AR Detection Algorithm
In the current study, an advanced AR tracking algorithm of global scale is employed.Initially proposed by Guan and Waliser (2015), the algorithm has undergone subsequent improvements and validations by Guan et al. (2018).Further enhancements were introduced by Guan and Waliser (2019), which included the implementation of lifecycle tracking and other modifications.This algorithm serves the purpose of detecting ARs in conventional gridded datasets and subsequently delineating basic AR characteristics such as AR intensity and frequency.The MERRA2-based AR database (Guan, 2022) is used.The reanalysis AR database generated using this algorithm has been extensively evaluated and utilized in various studies and remains the only database that has been validated against dropsonde observations for fundamental AR characteristics such as AR width and total integrated water vapor transport (IVT) across the AR (Guan et al., 2018).While the database covers the entire MERRA2 period, the data utilized in this paper specifically spans a 2-year period (2019-2020), aligning with other data products detailed further in the data section.

A New AR Coordinate System
The mathematical solution to compositing ARs with varying orientations involves a series of coordinate transformations.Initially, the latitudinal and longitudinal grid of each AR (within a range of ± 40°from the AR centroid or center) on Earth's spherical coordinates, is converted into Cartesian coordinates (x, y).These Cartesian coordinates are then further converted into polar coordinates (r, φ).The variables r and φ are generic variables (i.e., independent of ARs).Here "r" is the radial coordinate, representing radial distance of a point from the origin, and "φ" is the angular coordinate, indicating the polar angle of a point from the origin.To align all ARs into a specific direction (in the current study, with IVT directed toward the east), the polar coordinate is rotated by adding a chosen angle to φ, considering the unique orientation of each individual AR.Note that in current analysis, the orientation refers to the direction of mean IVT within an AR, with the IVT direction defined in the algorithm as the number of degrees going clockwise from northward (northward ARs have an orientation of 0°, eastward ARs have an orientation of 90°, and so on).Since the ARs we considered in this study are constrained to be northward/eastward in the northern hemisphere (i.e., orientations within 0-90°), the rotation involves subtracting the IVT direction from 90°to align it from west to east.The center of rotation and the origin of the coordinate systems are both located at the AR center.This AR center is determined by the highest IVT along the transect line that crosses the centroid (i.e., the average longitude and latitude weighted by IVT) of the AR.Once the rotation is completed, the polar coordinates are converted back into Cartesian coordinates.To represent each rotated AR, we utilize an N × M matrix, where N represents the number of grid cells along the direction of mean water vapor transport in the AR, and M represents the number of grid cells across that direction.Figure 1 provides an illustration of this rotation technique.After isolating and rotating each individual AR, we create composite maps based on the centered and directionally aligned ARs.Using this ROTated Atmospheric river coordinaTE (ROTATE) system, we combine key variables related to ARs obtained from satellite observations with their Geophysical Research Letters 10.1029/2023GL106736 corresponding data from reanalysis products.For the current analysis, the rotation has been carried out for every AR in the northern hemisphere spanning from 2019 to 2020.The majority of AR instances exhibit rotation angles between 20 and 40°, covering both short and long types of ARs (Figure S2 in Supporting Information S1).Important to emphasize that Guan andWaliser (2015, 2019) extensively detail the basic AR characteristics and statistics of AR geometry, including aspects like length, width, orientation, and lifecycles.In our current study, the AR sample size is limited to 2 years and constrained to the first quadrant (i.e., 0-90°IVT direction).Despite these limitations, the median IVT direction values (55.6°fromNorth) align well with the climatological longerterm mean values documented in Guan and Waliser's (2015) study.

Data
The primary meteorological variables utilized in our study are IVT, integrated water vapor (IWV), and precipitation.These variables are extensively employed in AR-related climate and weather research.The first two variables were obtained from the NASA Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2), as documented by Gelaro et al. (2017).The dataset's horizontal resolution is 0.625°l ongitude × 0.5°latitude.In this analysis, we have incorporated an additional quantity MERRA2 vertical velocity (omega) at 500 hPa, and equivalent wind speed, which is essentially a ratio between IVT and IWV.
For precipitation, we relied on satellite-based products, namely the NASA level-3 Global Precipitation Mission (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG) products, as described at https://disc.gsfc.nasa.gov/datasets/GPM_3IMERGHH_06/summary.Specifically, we utilized the Final Run (GPM_3IMERGHH) gridded precipitation with a horizontal resolution of 0.1°× 0.1°and a temporal resolution of 0.5 hr.The data product is further refined by converting it into 6-hourly intervals within the Guan and Waliser (2019) AR database, followed by application of bilinear spatial interpolation onto the MERRA2 grid.

Results and Discussion
Figure 2 illustrates the composite averages of the four key variables related to ARs using the original unrotated fields (based on AR centroid and AR center) and rotated fields.In the unrotated scenario, the AR variables centered around the AR centroid are relatively weaker than those centered around the AR center.For example, the peak average value for IVT is about 607 kg m 1 s 1 , whereas it is 542 kg m 1 s 1 for the centroid-based approach (Figure 3).The pattern of significantly increasing values in the AR center over the AR centroid is also observed for IWV, Equivalent Windspeed, and Precipitation variables.The distinct and amplified signals in the AR-centerbased approach can be attributed to the fact that the shapes of ARs are not strictly oriented as straight lines in most cases.Instead, their shapes can vary and take different forms, deviating from the aligned shape.This introduces the potential for the centroid and the true AR center not to align.As a result, when creating a composite of AR variables, the signals are more likely to diminish when using the centroid-based approach.In contrast, the ARcenter-based approach consistently captures the true AR center, leading to a more meaningful composite even when the geometries of ARs vary over time.
Rotation results in a concentration of generally high values in all variables around the AR center due to the alignment of the AR structure after rotation (e.g., ∼642 kg m 1 s 1 for the IVT variable).Notably, in regions outside the proximity of the AR footprints, the IVT signals appear faded, which can be attributed to the sharp gradients in IVT near the AR boundaries (Figure 2).The IWV exhibits notable values (35-40 kg m 2 ) near the AR tail toward the lower left quadrants, indicating the canonical pattern of AR moisture transport out of the tropical moisture reservoir.Much like the case with IVT, rotation results in an elevation of high IWV values, consistent with a better alignment of the AR structure after rotation.
Similar to IVT and IWV, the results demonstrate that the precipitation features are better concentrated after the rotation (Figure 2).While the precipitation differences between the AR centroid and ROTATE are more prominent on the tail side of the AR, the most intense rainfall is concentrated just north of the AR center, oriented toward the AR head.In this, the influence of warm frontal impact on the distribution of precipitation patterns at the AR head side is a significant aspect to consider, especially considering the common embedding of ARs within the circulation of extratropical cyclones (Ralph et al., 2020).The warm conveyor belt in these cyclones frequently acts as the forward extension of an AR, resulting in an ascent at the warm front that significantly affects precipitation occurrence and rates.To qualitatively confirm any influence stemming from frontal ascent, we added MERRA2 vertical velocity at 500 hPa as a variable subjected to both averaging and rotation, as illustrated in Figure S3 in Supporting Information S1.A negative omega value represents the upward motion.Notably, there is a prominent negative (upward) omega value in the AR composites, extending from the near center to the head of the AR, with these negative values being more prevalent in the ROTATE system.This upward motion aligns with anomalously higher precipitation rates extending from the center to the AR head.In the non-rotated composite, this asymmetric precipitation pattern relative to the ROTATE system is less discernible (Figures 2 and 3).
Within the AR region, the ROTATE system exhibits more distinct spatial features in the equivalent winds compared to the unrotated AR centroid.The peak winds within the AR centroid are slightly shifted more from the center in comparison to the other two methods (see the spatial plot Figure 2 and the cross-section plot Figure 3).Remarkably, in the ROTATE system, the peak wind values are approximately 1.0 m s 1 higher than those in the non-rotated centroid-based AR.These values seem to be attenuated when averaging over the non-unidirectional ARs within the AR centroid.

Landfall and Oceanic ARs
We compared the performance of the ROTATE and unrotated systems in composite datasets of landfall ARs and oceanic ARs.Note that the AR detection algorithm includes a landfall AR flag option, while oceanic ARs are identified when the AR head, centroid, and tail are all over the ocean, determined by the land/sea mask.Given the significance of precipitation in the context of ARs, our analysis is specifically focused on this particular variable.
Both landfall and oceanic ARs exhibit uniformity in rainfall patterns, featuring an asymmetric distribution along the AR axis near its center (Figure 4).However, landfall ARs display more dispersed precipitation compared to oceanic ARs.The differences between landfall and oceanic ARs can be attributed to distinct angles and standard deviations of the IVT axes (Figure S1 in Supporting Information S1), resulting in diverse outcomes when these composites are compared.The precipitation signal becomes somewhat distorted when not adjusted for rotation in both scenarios.For example, there is a considerable loss in rainfall amounts around the AR center and toward the head and tail of the AR.In particular, the precipitation signals in the AR centroid for landfall ARs show a significant reduction.On the other, applying rotation helps unveil weaker features that might not be as evident in the non-rotated case.There is an apparent precipitation enhancement near the AR head than tail for both landfalling and oceanic ARs.This observation is further corroborated by examining the cross-sectional profile of the composite map (Figure 5), revealing that rainfall in the ROTATE system is approximately 0.3-0.4mm hr 1 Geophysical Research Letters 10.1029/2023GL106736 higher that in the unrotated centroid ARs.The asymmetric distribution of rain is wider in the AR centroid compared to the other two methods (refer to Figure 5).The advantage of rotation is even more pronounced for landfalling ARs compared to oceanic ARs.The omega plot at 500 hPa (Figure S4 in Supporting Information S1) further substantiates the involvement of frontal ascent activity in the precipitation process for both landfall and oceanic ARs.This activity is more pronounced in oceanic ARs than in landfall ARs.Considering the common association of ARs with the warm conveyor belt, which features strong ascent in the proximity of extratropical cyclones and their fronts over the ocean (Ralph et al., 2020), the substantial precipitation pattern near the head of oceanic ARs exhibits a more noticeable upward curve when contrasted with landfall ARs.On the other hand, when an AR makes landfall, the moisture-laden air is forced to rise over the terrain, potentially enhancing precipitation, especially in regions with conducive topography like mountains.These subtle details in precipitation and vertical motion become more apparent following the rotation process.Important to mention that the amount

Geophysical Research Letters
10.1029/2023GL106736 of precipitation associated with landfall ARs versus oceanic ARs can vary and is influenced by multiple factors.Generalizing that one induces significantly more precipitation than the other is not straightforward without considering specific circumstances and conditions.

Conclusions
Our study introduces a unique coordinate system (ROTATE) specifically designed for ARs that effectively preserves the mean signals, which may otherwise be lost due to the diverse orientations and shapes exhibited by AR phenomena.Although commonly employed in cyclone tracking (e.g., Naud et al., 2012), this method has not been extensively utilized in AR studies until now.By using the ROTATE system, this study focused on analyzing and comparing AR composites in the northern hemisphere, revealing distinctive patterns across different meteorological variables.The central point to note is that the signals associated with ARs in the variables we used are more pronounced in the ROTATE system compared to the unrotated approach and the conventional approach based on the AR centroid.
When analyzing precipitation composites for landfall and oceanic ARs, we consistently observed higher precipitation values on the AR head side compared to the AR tail side in both the ROTATE and unrotated systems.This is likely due to the significant influence of embedded large-scale weather dynamics, such as the common association of the warm conveyor belt within extratropical cyclones linked with oceanic ARs, or the orographic interaction, as observed in the context of a landfalling AR event.However, the differences between the nonrotated AR centroid and ROTATE are more pronounced within landfall ARs than for oceanic ARs.This discrepancy can be attributed to a greater standard deviation in the AR orientation (e.g., the IVT direction) for landfall ARs compared to oceanic ARs.The findings imply that rotation plays a substantial role in highlighting the precipitation enhancement near the head of ARs.
In conclusion, the ROTATE system provides a valuable tool for analyzing ARs and their interactions with the environment.By centering and rotating each individual AR, one can create accurate composite analyses that capture the essential characteristics of these phenomena.This approach facilitates a comprehensive understanding of ARs, improves predictions of associated extreme weather events, and contributes to weather/ climate modeling efforts.Furthermore, while ARs are typically associated with high-latitude regions, there has been a growing interest in exploring their impacts in tropical areas and their unique behaviors upon landfall compared to those occurring at higher latitudes (Reid et al., 2021(Reid et al., , 2022)).Notably, recent findings by Reid et al. (2022) shed light on how rainfall patterns in Australia are influenced by both extratropical and tropical ARs.With ARs continuing to exert their influence on various regions globally, the adoption of the new AR-centric coordinate system is poised to be instrumental in deepening our understanding and readiness for these significant meteorological phenomena.

Figure 1 .
Figure 1.An example of the ROTATE system for ARs: non-rotated (left panel) and rotated (right panel) grid for an AR event tracked by the Guan and Waliser (2019) algorithm.The shading shows MERRA-2 IVT magnitudes (kg m 1 s 1 ).The X-and Y-axis represent the distance (km) from the center of rotation (AR center).Solid and dashed black lines are IVT direction and transect, respectively.The center of rotation is determined by the highest IVT along the transect line that crosses the centroid (i.e., the average longitude and latitude weighted by IVT) of the AR.

Figure 2 .
Figure 2. Composite means of integrated vapor transport (IVT), integrated water vapor (IWV), equivalent winds (i.e., IVT divided by IWV), and precipitation using the original, non-rotated AR centroid (top row), non-rotated AR center (middle row) and rotated AR center (bottom row) methods based on ARs across the entire northern hemisphere during 2019-2020.The contour line (leftmost column) represents the IVT value of 250 kg m 1 s 1 .The X and Y axes show the distance (in kilometers) from the AR center.The point where the thin horizontal and vertical black lines intersect at 0 km marks the AR's center.The thin red lines in first column denote a set of cross-profiles, evenly spaced at 50 km intervals and extending 1,000 km in length, that traverse orthogonally to the median IVT direction of whole population.A and B (top-left panel) are the end points of the profile line.

Figure 3 .
Figure3.Cross-sectional profile of mean integrated vapor transport (IVT), integrated water vapor (IWV), equivalent winds (i.e., IVT divided by IWV), and precipitation using the original, non-rotated AR centroid, non-rotated AR center and rotated AR center methods based on ARs across the entire northern hemisphere during 2019-2020.The mean stacking of cross-profiles, as shown in Figure2, generates the cross-sectional profile, with the shaded light pink area indicating the 2-sigma confidence bounds on the stacked mean profile.Red dashed lines indicate the difference between the rotated center and the non-rotated AR centroid methods; blue dashed lines represent the difference between the non-rotated AR center and the non-rotated AR centroid methods.The right y-axis, symmetrically centered around zero, displays the difference values.

Figure 4 .
Figure 4. Composite mean values of IMERG precipitation rate for the landfall (top row) and oceanic (bottom row) ARs are depicted for 2019-2020.The contour line represents an IVT value of 250 kg m 1 s 1 .The X and Y axes represent kilometers from the AR center, with the intersection point of the thin horizontal and vertical black lines at 0 km denoting the AR's center.The thin red lines denote a set of cross-profiles, evenly spaced at 50 km intervals and extending 1,000 km in length, that traverse orthogonally to the median IVT direction of whole population.A and B are the end-points of the profile line.

Figure 5 .
Figure 5. Same as Figure 3, but for the landfall ARs (left panel) and oceanic ARs (right panel).