Journal of Advances in Modeling Earth Systems最新文献

{"title":"The Ensemble Kalman Inversion Race","authors":"Rebecca Gjini,&nbsp;Matthias Morzfeld,&nbsp;Oliver R. A. Dunbar,&nbsp;Tapio Schneider","doi":"10.1029/2025MS005629","DOIUrl":"https://doi.org/10.1029/2025MS005629","url":null,"abstract":"<p>Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As hybrid physics and machine-learning models advance, the number of parameters and complexity of parameterizations in climate models will continue to grow. To fully realize these advances, we must move from laborious hand-tuning to calibration-driven model development in rapid iteration cycles. Thus, robust calibration of these parameters plays an increasingly important role. We focus on learning climate model parameters by minimizing the misfit between modeled and observed climate statistics in an idealized setting. Ensemble Kalman methods are a natural choice for this problem because they are derivative-free, scalable to high dimensions, and robust to noise caused by statistical observations. Given the many variants of ensemble methods proposed, an important question is: <i>Which ensemble Kalman method should be used for climate model calibration</i>? To answer this question, we perform systematic numerical experiments to explore the relative computational efficiencies of several ensemble Kalman methods. The numerical experiments involve statistical observations of Lorenz-type models of increasing complexity, frequently used to represent simplified atmospheric systems, with some featuring neural network parameterizations. For each test problem, several ensemble Kalman methods and a derivative-based method “race” to reach a specified accuracy, and we measure the computational cost required to achieve the desired accuracy. We investigate how prior information and the parameter or data dimensions define the computational costs of the various methods.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005629","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148860075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Riverine Nitrate Fate and Transport in the Great Lakes Basin Using the Community Land Model","authors":"Farshid Felfelani,&nbsp;Yadu Pokhrel,&nbsp;Mantha S. Phanikumar,&nbsp;David M. Lawrence","doi":"10.1029/2025MS005595","DOIUrl":"https://doi.org/10.1029/2025MS005595","url":null,"abstract":"<p>Agriculture and urbanization have profoundly altered the terrestrial nitrogen cycle, leading to widespread water quality degradation. Nitrogen leached from managed soils is transported and transformed through river networks, influencing downstream nutrient dynamics and ecosystem functioning. Limited knowledge of riverine nitrogen transport highlights the need for improved modeling of nitrogen transport and transformation in land models. This study presents first-order estimates of large-scale stream nitrate transport and reaction by using a newly implemented nitrogen routing scheme in the Model for Scale Adaptive River Transport (MOSART), the river routing scheme in the Community Land Model version 5 (CLM5). The new scheme explicitly simulates nitrate-nitrogen concentrations in rivers by resolving the one-dimensional advection-dispersion-reaction equation. The model is tested over the Great Lakes Basin (GLB) with fertilizer applications prescribed based on two different data sets. Results indicate that the model promisingly reproduces the observed magnitude and temporal variability of riverine nitrate concentrations. Further, nitrate delivery from lake-specific contributing subbasins to the Great Lakes shorelines is quantified across fertilizer application scenarios. When normalized by lake volume, nitrate delivery was highest in Lakes Erie and Ontario, with concentrations of approximately 9.5 and 2.2 tons km⁻³, respectively. An analysis of simulation minus observation reveals a modest bias toward underestimating nitrate concentrations across observation sites, partly driven by low streamflow bias and elevated numerical dispersion inherent in the transport scheme. Overall, the implemented nitrate routing framework provides a physically-based representation of large-scale riverine nitrate transport and transformations and establishes a basis for future model development and nutrient assessments within CLM5-MOSART.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005595","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assimilation of Velocity Data for Tidal Hydrodynamics Model Calibration","authors":"Connor Jordan,&nbsp;Athanasios Angeloudis","doi":"10.1029/2025MS005399","DOIUrl":"https://doi.org/10.1029/2025MS005399","url":null,"abstract":"<p>Assessing tidal stream energy resource typically involves the application of numerical models calibrated against sparse Acoustic Doppler Current Profiler (ADCP) data. This introduces significant challenges in energetic sites which are prone to significant spatiotemporal variations, like the Pentland Firth, Scotland, which is home to the world's highest capacity commercial tidal array. This study investigates the implications of limited calibration data and examines different approaches for constructing an appropriate friction field in tidal hydrodynamics model calibration. We compare performances between models using uniform and sediment-based friction coefficient fields and introduce the first application of adjoint-based calibration for optimizing a resource assessment model based on velocity data. The adjoint approach is applied iteratively and adjusts the friction coefficient with successive ADCP surveys. Our results demonstrate that the most widely applied approach employing a uniform friction coefficient fails to deliver adequate predictive performance across multiple data sets, even at close proximity. In turn, initial adjoint-based calibrations are prone to overfitting, which is rectified only with additional data acquisition. Simultaneously, calibration to solely the channel of interest could lead to significant inaccuracy in kinetic energy fluxes and thus greatly impact upper bound estimates on the resource and array-array interactions. These findings highlight the critical need for extensive and strategic ADCP data collection, which significantly reduces uncertainty and enhances model reliability, advancing the fidelity of coastal ocean models as in the tidal energy application we consider in this study.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005399","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148785115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient Emulation, Uncertainty Quantification, and Sensitivity Analysis for a Land Surface Model Using Evidential Deep Learning","authors":"Kachinga Silwimba,&nbsp;Alejandro N. Flores,&nbsp;Linnia R. Hawkins,&nbsp;Charles Becker,&nbsp;Katherine Dagon,&nbsp;David John Gagne,&nbsp;Jodi Mead,&nbsp;Daniel Kennedy,&nbsp;Irene Cionni,&nbsp;Stanley Akor,&nbsp;Pamela L. Sullivan,&nbsp;Sharon A. Billings,&nbsp;Hoori Ajami,&nbsp;Daniel R. Hirmas,&nbsp;Li Li,&nbsp;Jesse B. Nippert","doi":"10.1029/2025MS005587","DOIUrl":"https://doi.org/10.1029/2025MS005587","url":null,"abstract":"<p>Land surface models (LSMs), such as the Community Land Model version 5 (CLM5), represent complex vegetation processes; however, systematic biases persist between modeled and observed leaf area index (LAI) because of parameter uncertainties and knowledge gaps. The high computational cost of CLM5 is a barrier to extensive sensitivity analyses and ensemble simulations at the global scale. This study addresses these limitations by training an evidential deep neural network (EDNN) emulator on a 500-member CLM5 perturbed parameter ensemble generated via Latin hypercube sampling of 32 key plant physiological parameters. The EDNN employs cyclic temporal encoding to preserve seasonal periodicity and to predict LAI anomalies, thereby emphasizing variability. It also quantifies predictive uncertainty by jointly learning aleatoric and epistemic components in a single forward pass, yielding well-calibrated probabilistic outputs without requiring computationally intensive ensembles. Across the contiguous United States, the EDNN reproduces CLM5-simulated LAI with a median <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>≈</mo>\u0000 <mn>0.8</mn>\u0000 </mrow>\u0000 <annotation> ${R}^{2}approx 0.8$</annotation>\u0000 </semantics></math> on held-out members and years while requiring substantially less computation. The EDNN emulator captures seasonal cycles, interannual variability in LAI, and uncertainties (aleatoric and epistemic) in a single pass. The sensitivity analysis highlights photosynthetic capacity and the leaf carbon-to-nitrogen ratio as dominant controls on LAI variability, with seasonal shifts in their influence reflecting phenological dynamics. These capabilities enable comprehensive parameter-sensitivity studies and more efficient calibration and tuning of land surface models by supporting rapid probabilistic forecasting and adaptive model refinement, thereby paving the way for scalable Earth-system modeling, robust parameter exploration, and uncertainty-informed projections of land-surface processes.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005587","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantifying Numerical Energy Dissipation in Implicit Large Eddy Simulations","authors":"J. Thuburn","doi":"10.1029/2026MS005938","DOIUrl":"https://doi.org/10.1029/2026MS005938","url":null,"abstract":"<p>A novel methodology, using energy tracers, is introduced with the aim of diagnosing numerical energy dissipation, both globally and locally, in numerical models of the atmosphere. Energy dissipation might correspond to some physical process, such as the cascade of kinetic energy to unresolved scales if that energy is not restored as heat. Energy dissipation might also arise as an artifact of the numerical methods used; for example, in the current study the model used conservatively transports entropy, neglecting entropy sources due to mixing, resulting in a spurious energy loss. The energy tracer methodology is applied to Implicit Large Eddy Simulation of several canonical atmospheric boundary layer flows. The method is found to produce plausible local estimates of kinetic energy dissipation that are correlated with the local rate of strain. However, it does not yield useful estimates of the local spurious internal energy loss due to numerical mixing; possible reasons are discussed. The energy tracer method does produce useful estimates of the global kinetic energy dissipation and internal energy loss. For simple cases, the global internal energy loss estimates are confirmed by an independent method based on changes in the pdf of specific entropy or total specific humidity. The spurious global internal energy loss can be reduced by conservatively transporting, instead of entropy, a thermodynamic variable that is more nearly linearly mixing. This idea is analyzed theoretically, and is demonstrated in simulations that transport a quantity approximating the ice-liquid water potential temperature.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2026MS005938","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disentangling Internal Tides From Balanced Motions With Deep Learning and Surface Field Synergy","authors":"Han Wang,&nbsp;Jeffrey Uncu,&nbsp;Kaushik Srinivasan,&nbsp;Nicolas Grisouard","doi":"10.1029/2025MS005617","DOIUrl":"https://doi.org/10.1029/2025MS005617","url":null,"abstract":"<p>A fundamental challenge in ocean dynamics is disentangling balanced motions and internal waves. Extracting internal tidal (IT) imprints from surface data is a central part of this challenge. Traditional harmonic analysis fails under strong incoherence and poor temporal sampling, as in global satellite observations. New wide-swath satellites provide two-dimensional spatial coverage, allowing IT extraction to be reformulated as image translation. Building on our earlier deep-learning approach for extracting IT signatures from sea surface height (SSH) in an idealized turbulent simulation, we show that a simpler, computationally cheaper algorithm performs comparably in our experiments when the learning rate is annealed during training. Using this algorithm, we test different combinations of surface inputs: SSH, surface temperature, and surface velocity. All fields contribute synergistically to disentanglement in our deterministic benchmark, with surface velocity by far the most informative. These findings underscore the value of coordinated multi-platform observations and highlight the importance of surface velocity for separating balanced motions and internal waves. Additional analysis shows that both wave-signature information and scattering-medium information aid IT extraction. To exploit large-scale, mesoscale-reaching information in the scattering medium, the algorithm must be highly nonlocal. Residual errors concentrate at small spatial scales near mode-2 tidal wavelengths, likely reflecting incomplete input information, uncertainty in the simulation-derived reference fields, including possible Doppler-shift contamination, and limitations of the present deterministic architecture.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005617","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Overview of Aerosols in the E3SM Version 3: New Model Features and Their Impacts","authors":"Hailong Wang,&nbsp;Mingxuan Wu,&nbsp;Ziming Ke,&nbsp;Yan Feng,&nbsp;Manish Shrivastava,&nbsp;Qi Tang,&nbsp;Hui Wan,&nbsp;Xiaohong Liu,&nbsp;Richard C. Easter,&nbsp;Wuyin Lin,&nbsp;Balwinder Singh,&nbsp;Christopher R. Terai,&nbsp;Susannah M. Burrows,&nbsp;Jiwen Fan,&nbsp;Po-Lun Ma,&nbsp;Naser Mahfouz,&nbsp;Johannes Mülmenstädt,&nbsp;Yun Qian,&nbsp;Yunpeng Shan,&nbsp;Kai Zhang,&nbsp;Yuying Zhang,&nbsp;L. Ruby Leung,&nbsp;Philip J. Rasch,&nbsp;Shaocheng Xie","doi":"10.1029/2025MS005733","DOIUrl":"https://doi.org/10.1029/2025MS005733","url":null,"abstract":"<p>Accurate and comprehensive representation of aerosols in Earth system models (ESMs) is critical for modeling radiative forcing and seasonal-to-decadal variability. With increasing computing power, detailed physical and chemical processes representing aerosols and their interactions with other components of the Earth system can be treated more explicitly and accurately in ESMs. Like many other ESMs, the U.S. DOE Energy Exascale Earth System Model (E3SM) versions 1 and 2 have a state-of-the-art treatment of major aerosol species but crudely treat or even neglect some aerosol components that become increasingly important in the future with decreasing sulfur emissions. Several science-driven model developments of new aerosol features, including an explicit treatment of nitrate and ammonium aerosol species using MOSAIC coupled with the chemUCI gas chemistry scheme, explicit secondary organic aerosol (SOA) formation and loss, prognostic stratospheric sulfate (using chemical, microphysical and optical treatments instead of prescribing optical properties for volcanic aerosol), improved convective wet removal, improved numerical coupling of aerosol processes (i.e., emission, dry deposition, and turbulent mixing), and a new dust particle emission scheme, have been included in E3SM version 3 (E3SMv3) to better capture their roles in the Earth system. These new aerosol developments also require coupling with relatively comprehensive atmospheric chemistry to represent the reactions involving precursor gases and oxidants. Besides the new modeling capabilities, the aerosol improvements (e.g., SOA and dust lifetime and spatial distribution) contribute to E3SMv3's better performance in reproducing the historical temperature trends and enable the model to better project near-future Earth system changes.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2025MS005733","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Replacing Tunable Parameters in Weather and Climate Models With State-Dependent Functions Using Reinforcement Learning","authors":"Pritthijit Nath,&nbsp;Sebastian Schemm,&nbsp;Henry Moss,&nbsp;Peter Haynes,&nbsp;Emily Shuckburgh,&nbsp;Mark J. Webb","doi":"10.1029/2026MS005745","DOIUrl":"https://doi.org/10.1029/2026MS005745","url":null,"abstract":"<p>Weather and climate models rely on parameterizations to represent unresolved sub-grid processes. Traditional schemes rely on fixed coefficients that are weakly constrained and tuned offline, contributing to persistent biases that limit their ability to adapt to underlying physics. This study presents a framework that learns components of parametrization schemes online as a function of the evolving model state using reinforcement learning (RL) and evaluates policy-driven parameter updates across idealized testbeds spanning a simple climate bias correction (SCBC), a radiative-convective equilibrium (RCE), and a zonal mean energy balance model (EBM) with single-agent and federated multi-agent settings. Across nine RL algorithms, Truncated Quantile Critics (TQC), Deep Deterministic Policy Gradient (DDPG), and Twin Delayed DDPG (TD3) achieved the highest skill and stable convergence, with performance assessed against a static baseline using area-weighted RMSE, temperature and pressure-level diagnostics. For the EBM, single-agent RL outperformed static parameter tuning with the strongest gains in tropical and mid-latitude bands, while federated RL on multi-agent setups enabled specialized control and faster convergence, with a six-agent DDPG configuration using frequent aggregation yielding the lowest area-weighted RMSE across the tropics and mid-latitudes. The learned corrections were also physically meaningful as agents modulated EBM radiative parameters to reduce meridional biases, adjusted RCE lapse rates to match vertical temperature errors, and stabilized heating increments to limit drift. Overall, results show that RL can learn skillful state-dependent parametrization components in idealized settings, offering a scalable pathway for online learning within numerical models and a starting point for evaluation in weather and climate models.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2026MS005745","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Enhanced Langmuir Turbulence Parameterization With Nonlocal Momentum and Scalar Fluxes","authors":"Peng Wang","doi":"10.1029/2026MS005854","DOIUrl":"https://doi.org/10.1029/2026MS005854","url":null,"abstract":"<p>Langmuir turbulence plays a critical role in the oceanic surface boundary layer by efficiently transporting momentum, heat, gases, and nutrients. Since its characteristic scale (meters to tens of meters) is far smaller than typical grid cells of ocean general circulation models, it must be parameterized. A key limitation of existing Langmuir schemes is the omission of Langmuir-induced nonlocal fluxes. While these schemes reproduce scalar fields reasonably well, the lack of nonlocal momentum flux results in velocity simulations with excessive vertical shear and unrealistic near-surface values. To overcome this limitation, we introduce an enhanced Langmuir turbulence parameterization that incorporates a unified formulation for both Langmuir and convective nonlocal fluxes of momentum and scalars into the K-profile parameterization framework. When evaluated against large-eddy simulation benchmarks, the new scheme demonstrates significant improvement in velocity simulations while maintaining excellent accuracy for scalar fields. These results underscore the necessity of including nonlocal fluxes for accurate modeling of Langmuir turbulence effects.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2026MS005854","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Introducing the Coincidence Index: A Novel Diagnostic and Production-Based Framework for Water Body Interaction Analysis and Its Application to Study the Interaction of River Plumes","authors":"Xiangyu Li,&nbsp;Knut Klingbeil,&nbsp;Hans Burchard","doi":"10.1029/2026MS005737","DOIUrl":"https://doi.org/10.1029/2026MS005737","url":null,"abstract":"<p>Quantifying interactions between distinct water bodies is critical yet challenging for understanding ocean and estuarine dynamics. We introduce the coincidence index (CI), defined as the product of two arbitrary tracers (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 </mrow>\u0000 <annotation> $a$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 <annotation> $b$</annotation>\u0000 </semantics></math>), to diagnose where two water masses coexist and mix. By deriving a transport equation for the CI, we identify a single active production term, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 <mo>∇</mo>\u0000 <mi>a</mi>\u0000 <mo>⋅</mo>\u0000 <mi>K</mi>\u0000 <mo>⋅</mo>\u0000 <mo>∇</mo>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 <annotation> ${P}_{ab}=-2nabla acdot mathbf{K}cdot nabla b$</annotation>\u0000 </semantics></math>, that pinpoints physical mixing locations, while advection and diffusion only redistribute CI. We apply this method in two numerical models: Oceananigans for a Large-Eddy simulation of river confluence, and General Estuarine Transport Model for the analysis of the interaction of water masses from the Elbe and Weser river plumes in the German Bight. In both, the CI accurately highlights mixing interfaces; for example, the CI pattern from the river confluence simulation matches observations from the Lancang River. In the German Bight, the CI reveals a narrow, persistent interface between river plumes, with vertical diffusion dominating production. Artificial numerical production of CI, arising from the discretization of advection, is also diagnosed but found to be less significant. The CI method thus enables precise, quantitative diagnostics of water mass mixing from laboratory to realistic estuarine systems, advancing our understanding of transport and mixing processes central to aquatic environments.</p>","PeriodicalId":14881,"journal":{"name":"Journal of Advances in Modeling Earth Systems","volume":"18 8","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1029/2026MS005737","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}