Vapor Kinetic Energy for the Detection and Understanding of Atmospheric Rivers

Atmospheric rivers (ARs) are narrow, low-level jets that transport large amounts of moisture and often accompany extratropical cyclones, leading to strong winds and heavy precipitation in coastal regions. Prior AR research has emphasized detection and statistics (frequency, intensity, duration) using integrated vapor transport (IVT), but a prognostic understanding that links humidity and wind evolution has been lacking because a conservation or budget equation for IVT is difficult to derive. The study asks: can a new framework that couples winds and moisture with an explicit governing equation reveal the physical processes that drive AR growth, decay, and eastward propagation? The authors propose vapor kinetic energy (VKE), defined from humidity-weighted momentum, and its column-integrated form (IVKE), to both detect ARs and diagnose their evolution. They hypothesize that IVKE can identify ARs comparably to IVT while enabling a physically grounded budget that quantifies energy sources, sinks, and transport underlying AR dynamics.

The community has developed numerous AR detection algorithms (e.g., ARTMIP intercomparison) and largely relied on IVT for identification. Because deriving an IVT conservation law is challenging, many studies have analyzed the column water vapor budget, finding that horizontal moisture convergence supplies AR moisture while condensation and precipitation remove it. These approaches implicitly treat wind evolution as secondary. Other work documents the association of ARs with extratropical cyclones and low-level jets and highlights that ARs can be moisture- or wind-dominated. However, previous frameworks have not jointly treated humidity and wind within a single prognostic equation that can attribute AR growth, decay, and movement to specific physical processes, such as potential energy to kinetic energy conversion, turbulence, and condensation.

• Define vapor kinetic energy (VKE) as the kinetic energy of horizontal winds weighted by the square of specific humidity; define integrated VKE (IVKE) by vertically integrating VKE over pressure. Derive a prognostic equation for VKE and, by vertical integration, for IVKE by combining the moisture and momentum equations. The VKE tendency consists primarily of horizontal and vertical advection of VKE, conversion of potential energy (PE) to kinetic energy (KE), turbulent KE dissipation, and condensation effects; other terms are shown negligible for this analysis.
• AR detection comparison: Apply two independent detection algorithms to MERRA-2 reanalysis (1980–2019)—TempestExtremes (Laplacian-based thresholds) and the Mundhenk et al. method (geometric and intensity thresholds). For each, replace IVT with IVKE using tuned thresholds to match global AR frequency, and compare detection frequencies and event captures.
• Composite analysis: Use an Eulerian, regression-based composite centered on locations with maximum IVKE variance (North Pacific primary; also North Atlantic and South Atlantic). Compute an IVKE time series averaged over a 1°×1° box and regress anomalies of VKE/IVKE and all IVKE-budget terms at each grid point on this index. Reconstruct composite fields by scaling with one standard deviation of the index. Assess statistical significance with a two-tailed t-test accounting for autocorrelation. Analyze vertical cross-sections to resolve vertical structure.
• Projection diagnostics: Quantify contributions of each physical term to AR growth/decay by projecting each IVKE-tendency component onto the IVKE anomaly, yielding an inverse-timescale measure (rate). Quantify contributions to AR movement by projecting each term onto the total IVKE tendency. Verify budget closure and compute residuals.
• Datasets and numerics: Primary fields from MERRA-2 (3-hourly, pressure- and model-level products) with tendencies for winds and moisture; supplementary calculations with ERA5 (1-hourly pressure-level fields). Spatial derivatives via central differencing; vertical integration via the Boer scheme; tendencies computed with staggered time steps consistent with time averaging. Where ERA5 does not provide certain subgrid terms (e.g., condensation and KE dissipation), estimate them diagnostically from supplementary relations.
• Robustness and case study: Repeat composites in North Atlantic and South Atlantic; repeat diagnostics with ERA5 for 2010–2019. Analyze a January 2023 AR event with 3-hourly evolution to illustrate lifecycle stages (intensification and decay).

• AR detection: IVKE-based detection is as effective as IVT-based detection. The difference in AR frequency between IVT and IVKE is on the order of 1–2 days per year using TempestExtremes and about 4 days per year using the Mundhenk algorithm, much smaller than differences across algorithms themselves (~10 days per year). Spatial patterns and maxima match ARTMIP ensemble characteristics.
• Governing physics from the IVKE budget:
  • Eastward movement is dominated by horizontal advection of VKE; decomposition shows horizontal advection of vapor contributes more to movement than horizontal advection of KE.
  • Growth and maintenance are primarily driven by conversion of potential energy to kinetic energy (PE→KE), which is in phase with the IVKE anomaly and reflects ageostrophic low-level wind components accelerating the jet. Vertical advection of VKE also contributes positively near the AR core.
  • Decay is dominated by turbulent dissipation of KE and condensation of vapor, which produce negative IVKE tendencies over the AR core.
  • Other terms in the full budget are negligible in magnitude for AR dynamics in this framework. The IVKE budget closes with a residual of only 0.6% of the sum of sources.
• Vertical structure: VKE maximizes near 950 hPa due to strong low-level jets and high humidity and decreases aloft with decreasing moisture. PE→KE conversion and turbulent dissipation are concentrated between 1000–800 hPa. Condensation-related negative tendencies extend roughly from 900 to 500 hPa. Vertical advection increases VKE above ~950 hPa and decreases it below, with the vapor component increasing VKE and the KE component decreasing it.
• Dataset robustness: ERA5 reproduces the MERRA-2 composite results for growth/decay and movement contributions; small discrepancies are likely due to ERA5 hourly instantaneous vs MERRA-2 3-hourly time-averaged sampling. Where ERA5 lacks direct subgrid tendencies, diagnostic estimates yield consistent overall balances.
• Case study (North America landfall, 4 Jan 2023): During intensification (18–21 UTC 3 Jan), the growth rate was 0.91 ± 0.02 day⁻¹ (≈12% intensity increase in 3 hours), followed by another ~10% increase in the next 3 hours. During decay after landfall (18–21 UTC 4 Jan), the growth rate was −0.75 ± 0.01 day⁻¹ (≈9% decrease in 3 hours). Throughout, PE→KE conversion and vertical advection of vapor are prominent positive contributors, while condensation and turbulent dissipation are the dominant negative contributors. The sum of horizontal advection of KE and vapor tends to be negative in the growth/decay projection, while horizontal advection remains the leading contributor to movement in the composite diagnostics.

By introducing VKE and IVKE, the study unifies humidity and wind within a single prognostic framework that both detects ARs and quantitatively attributes their evolution to physical processes. The diagnosis reveals that AR intensity is sustained by PE→KE conversion associated with ageostrophic low-level jets, directly connecting AR dynamics to baroclinic energetics. Horizontal advection primarily translates ARs eastward, with both moisture and wind contributions, emphasizing that AR evolution depends on their coupled thermodynamic and dynamic structure. The framework goes beyond column water vapor budgets by explicitly incorporating kinetic energy processes absent from moisture-only analyses, thereby clarifying the roles of jets, turbulence, and condensation. Agreement between independent reanalyses and algorithms supports robustness. The results highlight that accurate simulation and prediction of ARs require realistic representation of boundary layer turbulence and moist convection, as these unresolved processes significantly influence IVKE sources and sinks.

The paper introduces IVKE as a detection and diagnostic framework for atmospheric rivers that is comparably effective to IVT for identification while enabling a closed, quantitative budget. Key contributions include: (1) a derived governing equation for IVKE; (2) demonstration that PE→KE conversion predominantly sustains AR intensity, balanced by turbulent dissipation and condensation; and (3) identification of horizontal VKE advection as the primary driver of eastward movement, with moisture advection leading. The framework captures the vertical structure of AR energetics and is robust across datasets and detection methods. Future work proposed includes seasonal stratification of IVKE budgets, examination of regional and flavor-dependent AR dynamics (e.g., “windy” vs “wet” ARs), development of an AR-following (Lagrangian) diagnostic frame to track lifecycle evolution, and targeted study of subgrid processes to improve model representation and forecasts.

• The analysis is Eulerian and location-centered; an AR-following (Lagrangian) framework is noted as future work and could alter interpretation of movement mechanisms along AR tracks.
• Reliance on reanalysis products (MERRA-2, ERA5) introduces uncertainties from data assimilation and parameterized physics; some subgrid tendencies (e.g., condensation, KE dissipation) are not directly available in ERA5 and are diagnostically estimated.
• Detection results depend on chosen thresholds when substituting IVKE for IVT; while tuned to match global frequencies, sensitivity to parameter choices may affect counts regionally.
• Seasonal and flavor-specific variations (winter vs summer; windy vs wet ARs; regional differences) are not analyzed here and could modify relative term magnitudes in the IVKE budget.
• Unresolved boundary layer turbulence and moist convection, shown to be important in the IVKE budget, may be imperfectly represented, affecting quantitative attribution.