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Title: Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress

Abstract

© 2018 American Meteorological Society. Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently.Once development ismature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model.As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherentmodel are here termed physics-dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problemwith references to examples in the literature, to show howthe problem can be analyzed, and to create awareness of the issue acrossmore » the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/ormodels use variable resolutions.« less

Authors:
 [1];  [2];  [2];  [3];  [4];  [5];  [6];  [6];  [7];  [7];  [8];  [7];  [9];  [9];  [10];  [11];  [12];  [4];  [13];  [4] more »;  [2];  [2] « less
  1. Departamento de Oceanografía Física, Centro de Investigación Científica y Educación Superior de Ensenada, Ensenada, Baja California, México
  2. Pacific Northwest National Laboratory, Richland, Washington
  3. Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California
  4. National Center for Atmospheric Research, Boulder, Colorado
  5. Hans Ertel Center for Weather Research, Deutscher Wetterdienst, Offenbach, Germany
  6. Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan
  7. Met Office, Exeter, United Kingdom
  8. CEMPS, Exeter University, Exeter, United Kingdom
  9. INRIA, University of Grenoble–Alpes, LJK, CNRS, Grenoble, France
  10. ECMWF, Shinfield Park, Reading, United Kingdom
  11. Royal Meteorological Institute of Belgium, Brussels, Belgium, Department of Physics and Astronomy, Ghent University, Ghent, Belgium
  12. IAP Kühlungsborn, Leibniz–Institut für Atmosphärenphysik e.V. an der Universität Rostock, Kühlungsborn, Germany
  13. Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, California
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Univ. of Michigan, Ann Arbor, MI (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Univ. Grenoble Alpes (France)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); PNNL Laboratory Directed Research and Development (LDRD) Program; National Research Agency (ANR) (France)
OSTI Identifier:
1475245
Alternate Identifier(s):
OSTI ID: 1502013; OSTI ID: 1507739; OSTI ID: 1563976
Report Number(s):
LLNL-JRNL-756718; PNNL-SA-137579
Journal ID: ISSN 0027-0644
Grant/Contract Number:  
AC52-07NA27344; AC05-76RL01830; SC0006684; SC0003990; AC02-05CH11231; ANR-14-CE23-0010
Resource Type:
Published Article
Journal Name:
Monthly Weather Review
Additional Journal Information:
Journal Name: Monthly Weather Review Journal Volume: 146 Journal Issue: 11; Journal ID: ISSN 0027-0644
Publisher:
American Meteorological Society
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; 58 GEOSCIENCES; coupled models; model comparison; model errors; model evaluation/performance; numerical analysis/modeling; parameterization

Citation Formats

Gross, Markus, Wan, Hui, Rasch, Philip J., Caldwell, Peter M., Williamson, David L., Klocke, Daniel, Jablonowski, Christiane, Thatcher, Diana R., Wood, Nigel, Cullen, Mike, Beare, Bob, Willett, Martin, Lemarié, Florian, Blayo, Eric, Malardel, Sylvie, Termonia, Piet, Gassmann, Almut, Lauritzen, Peter H., Johansen, Hans, Zarzycki, Colin M., Sakaguchi, Koichi, and Leung, Ruby. Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress. United States: N. p., 2018. Web. doi:10.1175/MWR-D-17-0345.1.
Gross, Markus, Wan, Hui, Rasch, Philip J., Caldwell, Peter M., Williamson, David L., Klocke, Daniel, Jablonowski, Christiane, Thatcher, Diana R., Wood, Nigel, Cullen, Mike, Beare, Bob, Willett, Martin, Lemarié, Florian, Blayo, Eric, Malardel, Sylvie, Termonia, Piet, Gassmann, Almut, Lauritzen, Peter H., Johansen, Hans, Zarzycki, Colin M., Sakaguchi, Koichi, & Leung, Ruby. Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress. United States. https://doi.org/10.1175/MWR-D-17-0345.1
Gross, Markus, Wan, Hui, Rasch, Philip J., Caldwell, Peter M., Williamson, David L., Klocke, Daniel, Jablonowski, Christiane, Thatcher, Diana R., Wood, Nigel, Cullen, Mike, Beare, Bob, Willett, Martin, Lemarié, Florian, Blayo, Eric, Malardel, Sylvie, Termonia, Piet, Gassmann, Almut, Lauritzen, Peter H., Johansen, Hans, Zarzycki, Colin M., Sakaguchi, Koichi, and Leung, Ruby. Thu . "Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress". United States. https://doi.org/10.1175/MWR-D-17-0345.1.
@article{osti_1475245,
title = {Physics–Dynamics Coupling in Weather, Climate, and Earth System Models: Challenges and Recent Progress},
author = {Gross, Markus and Wan, Hui and Rasch, Philip J. and Caldwell, Peter M. and Williamson, David L. and Klocke, Daniel and Jablonowski, Christiane and Thatcher, Diana R. and Wood, Nigel and Cullen, Mike and Beare, Bob and Willett, Martin and Lemarié, Florian and Blayo, Eric and Malardel, Sylvie and Termonia, Piet and Gassmann, Almut and Lauritzen, Peter H. and Johansen, Hans and Zarzycki, Colin M. and Sakaguchi, Koichi and Leung, Ruby},
abstractNote = {© 2018 American Meteorological Society. Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently.Once development ismature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model.As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherentmodel are here termed physics-dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problemwith references to examples in the literature, to show howthe problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/ormodels use variable resolutions.},
doi = {10.1175/MWR-D-17-0345.1},
journal = {Monthly Weather Review},
number = 11,
volume = 146,
place = {United States},
year = {Thu Nov 01 00:00:00 EDT 2018},
month = {Thu Nov 01 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1175/MWR-D-17-0345.1

Citation Metrics:
Cited by: 44 works
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Figures / Tables:

FIG. 1 FIG. 1: Schematic representation of physics–dynamics coupling. (a) Two models: an ocean model and an atmosphere model. Both of these have spatial scales (here indicated by the plane with red lines) and temporal scales (indicated by the blue axis). These are coupled (thick lines); that means one domain in themore » spatial plane maps into the spatial plane of the other model (thick red line) and similarly in the temporal axis (thick blue line). In the spatial plane, aspects such as grid type, fixed vs variable resolution, one-dimensional vs three-dimensional, and fine vs coarse are shown as some of the aspects of the spatial resolution that can vary between models and do not necessarily have a straightforward mapping. Then, each of these models has its ecosystem of parameterizations (an arbitrary set of processes was chosen here for illustration only), which interact with the model and themselves via coupling. These parameterizations also occupy potentially—or almost certainly—different areas on the spatial plane and temporal axis. All of this exists in front of a background problem of thermodynamics, which ultimately governs them all (or ought to, anyhow). (b) Four-tier scheme of investigation, ranging from (by necessity) abstract analysis via reduced equation sets (with less necessity for abstraction) to simplified physics tests and finally full model runs. The complexity of the analysis increases from one to the other. The manner in which the results and conclusions from the experimentation can inform the production runs ranges from ‘‘difficult’’ (results are expected in the form of guidance or informing a choice that needs to be made in the design phase) to ‘‘direct’’ (a benefit can be demonstrated straightaway by producing an improved forecast).« less

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Precipitation distributions for explicit versus parametrized convection in a large-domain high-resolution tropical case study
journal, March 2012

  • Holloway, C. E.; Woolnough, S. J.; Lister, G. M. S.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 138, Issue 668
  • DOI: 10.1002/qj.1903

An evaluation of the variable‐resolution CESM for modeling California's climate
journal, January 2016

  • Huang, Xingying; Rhoades, Alan M.; Ullrich, Paul A.
  • Journal of Advances in Modeling Earth Systems, Vol. 8, Issue 1
  • DOI: 10.1002/2015MS000559

On the mathematical stability of stratified flow models with local turbulence closure schemes
journal, September 2008


Horizontal grids for global weather and climate prediction models: a review
journal, November 2011

  • Staniforth, Andrew; Thuburn, John
  • Quarterly Journal of the Royal Meteorological Society, Vol. 138, Issue 662
  • DOI: 10.1002/qj.958

A Moist Benchmark Calculation for Atmospheric General Circulation Models
journal, October 2008

  • Lee, Myong-In; Suarez, Max J.; Kang, In-Sik
  • Journal of Climate, Vol. 21, Issue 19
  • DOI: 10.1175/2008JCLI1891.1

Sensitivity of Simulated Climate to Horizontal and Vertical Resolution in the ECHAM5 Atmosphere Model
journal, August 2006

  • Roeckner, E.; Brokopf, R.; Esch, M.
  • Journal of Climate, Vol. 19, Issue 16
  • DOI: 10.1175/JCLI3824.1

The global aerosol-climate model ECHAM-HAM, version 2: sensitivity to improvements in process representations
journal, January 2012

  • Zhang, K.; O'Donnell, D.; Kazil, J.
  • Atmospheric Chemistry and Physics, Vol. 12, Issue 19
  • DOI: 10.5194/acp-12-8911-2012

Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I
journal, April 1974


How does subgrid-scale parametrization influence nonlinear spectral energy fluxes in global NWP models?: NONLINEAR SPECTRAL ENERGY FLUXES IN NWP
journal, May 2016

  • Malardel, Sylvie; Wedi, Nils P.
  • Journal of Geophysical Research: Atmospheres, Vol. 121, Issue 10
  • DOI: 10.1002/2015JD023970

Seamless Stratocumulus Simulation across the Turbulent Gray Zone
journal, April 2014


Using aquaplanets to understand the robust responses of comprehensive climate models to forcing
journal, May 2014


A Combined Eddy-Diffusivity Mass-Flux Approach for the Convective Boundary Layer
journal, April 2007

  • Siebesma, A. Pier; Soares, Pedro M. M.; Teixeira, João
  • Journal of the Atmospheric Sciences, Vol. 64, Issue 4
  • DOI: 10.1175/JAS3888.1

Effects of Deforestation on Spatiotemporal Distributions of Precipitation in South America
journal, April 2011

  • Medvigy, David; Walko, Robert L.; Avissar, Roni
  • Journal of Climate, Vol. 24, Issue 8
  • DOI: 10.1175/2010JCLI3882.1

Exploring the impacts of physics and resolution on aqua-planet simulations from a nonhydrostatic global variable-resolution modeling framework: IMPACTS OF PHYSICS AND RESOLUTION
journal, November 2016

  • Zhao, Chun; Leung, L. Ruby; Park, Sang-Hun
  • Journal of Advances in Modeling Earth Systems, Vol. 8, Issue 4
  • DOI: 10.1002/2016MS000727

Context and Aims of the Aqua-Planet Experiment
journal, January 2013

  • Blackburn, Michael; Hoskins, Brian J.
  • Journal of the Meteorological Society of Japan. Ser. II, Vol. 91A, Issue 0
  • DOI: 10.2151/jmsj.2013-A01

Multiphysics simulations: Challenges and opportunities
journal, February 2013

  • Keyes, David E.; McInnes, Lois C.; Woodward, Carol
  • The International Journal of High Performance Computing Applications, Vol. 27, Issue 1
  • DOI: 10.1177/1094342012468181

A compatible and conservative spectral element method on unstructured grids
journal, August 2010


A New Moist Turbulence Parameterization in the Community Atmosphere Model
journal, June 2009


A PDF-Based Model for Boundary Layer Clouds. Part II: Model Results
journal, December 2002


The Impact of the Time Step on the Intensity of ITCZ in an Aquaplanet GCM
journal, November 2008

  • Mishra, Saroj K.; Srinivasan, J.; Nanjundiah, Ravi S.
  • Monthly Weather Review, Vol. 136, Issue 11
  • DOI: 10.1175/2008MWR2478.1

Toward Quantifying the Climate Heat Engine: Solar Absorption and Terrestrial Emission Temperatures and Material Entropy Production
journal, May 2017

  • Bannon, Peter R.; Lee, Sukyoung
  • Journal of the Atmospheric Sciences, Vol. 74, Issue 6
  • DOI: 10.1175/JAS-D-16-0240.1

The Aqua-Planet Experiment (APE): CONTROL SST Simulation
journal, January 2013

  • Blackburn, Michael; Williamson, David L.; Nakajima, Kensuke
  • Journal of the Meteorological Society of Japan. Ser. II, Vol. 91A, Issue 0
  • DOI: 10.2151/jmsj.2013-A02

The Monte Carlo Independent Column Approximation: an assessment using several global atmospheric models
journal, July 2008

  • Barker, H. W.; Cole, J. N. S.; Morcrette, J. -J.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 134, Issue 635
  • DOI: 10.1002/qj.303

A “Vertically Lagrangian” Finite-Volume Dynamical Core for Global Models
journal, October 2004


Evaluation of Global Atmospheric Solvers Using Extensions of the Jablonowski and Williamson Baroclinic Wave Test Case
journal, September 2013

  • Park, Sang-Hun; Skamarock, William C.; Klemp, Joseph B.
  • Monthly Weather Review, Vol. 141, Issue 9
  • DOI: 10.1175/MWR-D-12-00096.1

Effect of SST Variation on ITCZ in APE Simulations
journal, January 2013

  • Rajendran, Kavirajan; Kitoh, Akio; Srinivasan, Jayaraman
  • Journal of the Meteorological Society of Japan. Ser. II, Vol. 91A, Issue 0
  • DOI: 10.2151/jmsj.2013-A06

A New Boundary Layer Mixing Scheme. Part I: Scheme Description and Single-Column Model Tests
journal, September 2000


An Approach for Convective Parameterization with Memory: Separating Microphysics and Transport in Grid-Scale Equations
journal, November 2007

  • Piriou, Jean-Marcel; Redelsperger, Jean-Luc; Geleyn, Jean-François
  • Journal of the Atmospheric Sciences, Vol. 64, Issue 11
  • DOI: 10.1175/2007JAS2144.1

Toward unification of the multiscale modeling of the atmosphere
journal, January 2011

  • Arakawa, A.; Jung, J. -H.; Wu, C. -M.
  • Atmospheric Chemistry and Physics, Vol. 11, Issue 8
  • DOI: 10.5194/acp-11-3731-2011

50 Years of the Monin–Obukhov Similarity Theory
journal, June 2006


Entropy Production and Climate Efficiency
journal, August 2015


A Variable-Resolution Finite-Element Technique for Regional Forecasting with the Primitive Equations
journal, April 1978


Recent developments in variable-resolution global climate modelling
journal, August 2013


Evolution of a subgrid deep convection parametrization in a limited-area model with increasing resolution
journal, July 2005

  • Gerard, L.; Geleyn, J. -F.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 131, Issue 610
  • DOI: 10.1256/qj.04.72

NCAR_Topo (v1.0): NCAR global model topography generation software for unstructured grids
journal, January 2015

  • Lauritzen, P. H.; Bacmeister, J. T.; Callaghan, P. F.
  • Geoscientific Model Development, Vol. 8, Issue 12
  • DOI: 10.5194/gmd-8-3975-2015

The Dry-Entropy Budget of a Moist Atmosphere
journal, December 2008


Toward Numerical Modeling in the “Terra Incognita”
journal, July 2004


Stability of algorithms for a two domain natural convection problem and observed model uncertainty
journal, December 2010


A Unified Convection Scheme (UNICON). Part I: Formulation
journal, November 2014


Coupling technologies for Earth System Modelling
journal, January 2012


Impact of horizontal resolution on simulation of precipitation extremes in an aqua-planet version of Community Atmospheric Model (CAM3)
journal, January 2011


Regional Climate Modeling: Progress, Challenges, and Prospects
journal, January 2004

  • Wang, Yuqing; Leung, L. Ruby; McGREGOR, John L.
  • Journal of the Meteorological Society of Japan. Ser. II, Vol. 82, Issue 6
  • DOI: 10.2151/jmsj.82.1599

Variable resolution general circulation models: Stretched-grid model intercomparison project (SGMIP)
journal, January 2006

  • Fox-Rabinovitz, Michael; Côté, Jean; Dugas, Bernard
  • Journal of Geophysical Research, Vol. 111, Issue D16
  • DOI: 10.1029/2005JD006520

Validating weather and climate models at small Rossby numbers: including a boundary layer
journal, July 2016

  • Beare, Robert J.; Cullen, Michael J. P.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 142, Issue 700
  • DOI: 10.1002/qj.2852

Predicting Small-Scale, Short-Lived Downbursts: Case Study with the NWP Limited-Area ALARO Model for the Pukkelpop Thunderstorm
journal, February 2015


Assessing the CAM5 physics suite in the WRF-Chem model: implementation, resolution sensitivity, and a first evaluation for a regional case study
journal, January 2014

  • Ma, P. -L.; Rasch, P. J.; Fast, J. D.
  • Geoscientific Model Development, Vol. 7, Issue 3
  • DOI: 10.5194/gmd-7-755-2014

Impact of Coupling with an Ice–Ocean Model on Global Medium-Range NWP Forecast Skill
journal, April 2018

  • Smith, Gregory C.; Bélanger, Jean-Marc; Roy, François
  • Monthly Weather Review, Vol. 146, Issue 4
  • DOI: 10.1175/MWR-D-17-0157.1

Evaporation and Precipitation Surface Effects in Local Mass Continuity Laws of Moist Air
journal, October 2006

  • Wacker, Ulrike; Frisius, Thomas; Herbert, Fritz
  • Journal of the Atmospheric Sciences, Vol. 63, Issue 10
  • DOI: 10.1175/JAS3754.1

Experimental Tropical Cyclone Forecasts Using a Variable-Resolution Global Model
journal, October 2015

  • Zarzycki, Colin M.; Jablonowski, Christiane
  • Monthly Weather Review, Vol. 143, Issue 10
  • DOI: 10.1175/MWR-D-15-0159.1

Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part I: Maximum Work and Frictional Dissipation
journal, January 2002


Effects of time step size on the simulation of tropical climate in NCAR-CAM3
journal, January 2011


A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids
journal, May 2010

  • Ringler, T. D.; Thuburn, J.; Klemp, J. B.
  • Journal of Computational Physics, Vol. 229, Issue 9
  • DOI: 10.1016/j.jcp.2009.12.007

On the Land Surface–Atmosphere Coupling and Its Impact in a Single-Column Atmospheric Model
journal, March 2001


Comparison of dynamical cores for NWP models: comparison of COSMO and Dune
journal, April 2012

  • Brdar, Slavko; Baldauf, Michael; Dedner, Andreas
  • Theoretical and Computational Fluid Dynamics, Vol. 27, Issue 3-4
  • DOI: 10.1007/s00162-012-0264-z

Sources and sinks of climate entropy
journal, July 2000

  • Goody, Richard
  • Quarterly Journal of the Royal Meteorological Society, Vol. 126, Issue 566
  • DOI: 10.1002/qj.49712656619

A multi-layer land surface energy budget model for implicit coupling with global atmospheric simulations
journal, January 2016

  • Ryder, J.; Polcher, J.; Peylin, P.
  • Geoscientific Model Development, Vol. 9, Issue 1
  • DOI: 10.5194/gmd-9-223-2016

On Constraining Estimates of Climate Sensitivity with Present-Day Observations through Model Weighting
journal, December 2011

  • Klocke, Daniel; Pincus, Robert; Quaas, Johannes
  • Journal of Climate, Vol. 24, Issue 23
  • DOI: 10.1175/2011JCLI4193.1

The effect of time steps and time-scales on parametrization suites
journal, August 2012

  • Williamson, David L.
  • Quarterly Journal of the Royal Meteorological Society, Vol. 139, Issue 671
  • DOI: 10.1002/qj.1992

Observed Scaling in Clouds and Precipitation and Scale Incognizance in Regional to Global Atmospheric Models
journal, December 2013


Bulk Mass-Flux Perturbation Formulation for a Unified Approach of Deep Convection at High Resolution
journal, October 2015


Analysis of Ocean-atmosphere Coupling Algorithms: Consistency and Stability
journal, January 2015


The Impact of Noisy Physics on the Stability and Accuracy of Physics–Dynamics Coupling
journal, December 2013

  • Hodyss, Daniel; Viner, Kevin C.; Reinecke, Alex
  • Monthly Weather Review, Vol. 141, Issue 12
  • DOI: 10.1175/MWR-D-13-00035.1

The Art and Science of Climate Model Tuning
journal, March 2017

  • Hourdin, Frédéric; Mauritsen, Thorsten; Gettelman, Andrew
  • Bulletin of the American Meteorological Society, Vol. 98, Issue 3
  • DOI: 10.1175/BAMS-D-15-00135.1

Sources and pathways of the upscale effects on the Southern Hemisphere jet in MPAS-CAM4 variable-resolution simulations: UPSCALE EFFECTS IN MPAS-CAM4
journal, November 2016

  • Sakaguchi, Koichi; Lu, Jian; Leung, L. Ruby
  • Journal of Advances in Modeling Earth Systems, Vol. 8, Issue 4
  • DOI: 10.1002/2016MS000743

Multiscale Performance of the ALARO-0 Model for Simulating Extreme Summer Precipitation Climatology in Belgium
journal, October 2013


Exploring a Multiresolution Approach Using AMIP Simulations
journal, July 2015


Characterizing Sierra Nevada Snowpack Using Variable-Resolution CESM
journal, January 2016

  • Rhoades, Alan M.; Huang, Xingying; Ullrich, Paul A.
  • Journal of Applied Meteorology and Climatology, Vol. 55, Issue 1
  • DOI: 10.1175/JAMC-D-15-0156.1