References

Toro2013
Eleuterio F Toro (2013), Riemann solvers and numerical methods for fluid dynamics: a practical introduction, Springer Science & Business Media, 2013.
BrooksCorey1964
R. J. Brooks , A. T. Corey (1964), Hydraulic properties of porous media, Hydrology Papers, 3, 1964.
Rutledge1983
Desai2019
Neel Desai , KK Chandrakar , G Kinney , W Cantrell , RA Shaw (2019), Aerosol-Mediated Glaciation of Mixed-Phase Clouds: Steady-State Laboratory Measurements, Geophysical Research Letters, 46(15), 9154--9162, 2019.
Ralston1962
Anthony Ralston (1962), Runge-Kutta methods with minimum error bounds, Mathematics of computation, 16(80), 431--437, 1962.
Stevens2005
Bjorn Stevens , Chin-Hoh Moeng , Andrew S Ackerman , Christopher S Bretherton , Andreas Chlond , Stephan de Roode , James Edwards , Jean-Christophe Golaz , Hongli Jiang , Marat Khairoutdinov , others (2005), Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus, Monthly weather review, 133(6), 1443--1462, 2005.
Berrut2004
Jean-Paul Berrut , Lloyd N Trefethen (2004), Barycentric lagrange interpolation, SIAM review, 46(3), 501--517, 2004.
Kaul2015
Colleen M Kaul , Jo { \~a } o Teixeira , Kentaroh Suzuki (2015), Sensitivities in large-eddy simulations of mixed-phase Arctic stratocumulus clouds using a simple microphysics approach, Monthly Weather Review, 143(11), 4393--4421, 2015.
Ronchi1996
C. Ronchi , R. Iacono , P. S. Paolucci (1996), The ``cubed sphere``: a new method for the solution of partial differential equations in spherical geometry, Journal of Computational Physics, 124(1), 93--114, 1996.
Bonan19a
G. Bonan (2019), Climate Change and Terrestrial Ecoystem Modeling, Cambridge Univ. Press, Cambridge , UK , and New York , NY , USA, 2019.
KnothWolke1998
Oswald Knoth , Ralf Wolke (1998), Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows, Applied Numerical Mathematics, 28(2), 327--341, 1998.
CarslawJaeger
H. Carslaw , J. Jaeger (1959), Conduction of heat in solids, Clarendon Press Oxford, 1959.
Vreugdenhil2018
Catherine A Vreugdenhil , John R Taylor (2018), Large-eddy simulations of stratified plane Couette flow using the anisotropic minimum-dissipation model, Physics of Fluids, 30(8), 085104, 2018.
KurylykWatanabe2013
B. Kurylyk , K. Watanabe (2013), Review: The mathematical representation of freezing and thawing processes in variably-saturated , non-deformable soils., Advances in Water Resources, 60, 160-177, 2013.
Vreman2004
AW Vreman (2004), An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications, Physics of fluids, 16(10), 3670--3681, 2004.
Carpenter1990
Richard L Carpenter Jr , Kelvin K Droegemeier , Paul R Woodward , Carl E Hane (1990), Application of the piecewise parabolic method (PPM) to meteorological modeling, Monthly Weather Review, 118(3), 586--612, 1990.
Koshyk2001
John N Koshyk , Kevin Hamilton (2001), The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM, Journal of the atmospheric sciences, 58(4), 329--348, 2001.
Mizoguchi1990
M. Mizoguchi (1990), Water , heat and salt transport in freezing soil, Ph.D Thesis , University of Tokyo, , 1990.
giraldoRestelli2008a
Light2016
Nair2005
Ramachandran D Nair , Stephen J Thomas , Richard D Loft (2005), A Discontinuous Galerkin Transport Scheme on the Cubed Sphere, Monthly Weather Review, 133(4), 814--828, 2005.
Cosby1984
Painter2011
Baer1972
Ferdinand Baer (1972), An alternate scale representation of atmospheric energy spectra, Journal of the Atmospheric Sciences, 29(4), 649--664, 1972.
Wyngaard1975
John C Wyngaard (1975), Modeling the planetary boundary layer—extension to the stable case, Boundary-Layer Meteorology, 9(4), 441--460, 1975.
KnothWensch2014
Oswald Knoth , Joerg Wensch (2014), Generalized split-explicit Runge–Kutta methods for the compressible Euler equations, Monthly Weather Review, 142(5), 2067--2081, 2014.
Schlegel2012
M Schlegel , O Knoth , M Arnold , R Wolke (2012), Implementation of multirate time integration methods for air pollution modelling, Geoscientific Model Development, 5(6), 1395--1405, 2012.
Kennedy2019
Christopher A Kennedy , Mark H Carpenter (2019), Higher-order additive Runge–Kutta schemes for ordinary differential equations, Applied Numerical Mathematics, 136, 183--205, 2019.
Dai2019a
Yongjiu Dai al. (2019), Evaluation of Soil Thermal Conductivity Schemes for Use in Land Surface Modeling, arXiv:1908.04579 [physics.ao-ph].
Schlegel2009
Martin Schlegel , Oswald Knoth , Martin Arnold , Ralf Wolke (2009), Multirate Runge-Kutta schemes for advection equations, Journal of Computational and Applied Mathematics, 226(2), 345--357, 2009.
Straka1993
Jerry M Straka , Robert B Wilhelmson , Louis J Wicker , John R Anderson , Kelvin K Droegemeier (1993), Numerical solutions of a non-linear density current: A benchmark solution and comparisons, International Journal for Numerical Methods in Fluids, 17(1), 1--22, 1993.
Ullrich2014
Paul A Ullrich , Thomas Melvin , Christiane Jablonowski , Andrew Staniforth (2014), A proposed baroclinic wave test case for deep-and shallow-atmosphere dynamical cores, Quarterly Journal of the Royal Meteorological Society, 140(682), 1590--1602, 2014.
Kopriva2006
David A Kopriva (2006), Metric identities and the discontinuous spectral element method on curvilinear meshes, Journal of Scientific Computing, 26(3), 301, 2006.
Chen2013
Xi Chen , Natalia Andronova , Bram Van Leer , Joyce E. Penner , John P. Boyd , Christiane Jablonowski , Shian-Jiann Lin (01 Jul. 2013), A Control-Volume Model of the Compressible Euler Equations with a Vertical Lagrangian Coordinate, Monthly Weather Review, 141(7), 2526 - 2544, 01 Jul. 2013.
Byun1990
Daewon W Byun (1990), On the analytical solutions of flux-profile relationships for the atmospheric surface layer, Journal of Applied Meteorology, 29(7), 652--657, 1990.
Smagorinsky1963
Joseph Smagorinsky (1963), General circulation experiments with the primitive equations: I. The basic experiment, Monthly weather review, 91(3), 99--164, 1963.
Businger1971
Joost A Businger , John C Wyngaard , Yꎬ Izumi , Edward F Bradley (1971), Flux-profile relationships in the atmospheric surface layer, Journal of the atmospheric Sciences, 28(2), 181--189, 1971.
Wood2005
R Wood (2005), Drizzle in stratiform boundary layer clouds. Part II: Microphysical aspects, Journal of the atmospheric sciences, 62(9), 3034--3050, 2005.
Johanson1975
O. Johanson (1977), Thermal conductivity of soils, Ph.D Thesis , Cold Regions Research and Engineering Laboratory, , 682-690, 1977.
Lundin1990
L.C. Lundin (1990), Hydraulic properties in an operational model of frozen soil, J. Hydrol., 118, 289--310, 1990.
Woodward00a
Vogl2019
Christopher J Vogl , Andrew Steyer , Daniel R Reynolds , Paul A Ullrich , Carol S Woodward (2019), Evaluation of Implicit-Explicit Additive Runge-Kutta Integrators for the HOMME-NH Dynamical Core, Journal of Advances in Modeling Earth Systems, 11(12), 4228--4244, 2019.
Wang2006
Lian-Ping Wang , Charmaine N Franklin , Orlando Ayala , Wojciech W Grabowski (2006), Probability distributions of angle of approach and relative velocity for colliding droplets in a turbulent flow, Journal of the atmospheric sciences, 63(3), 881--900, 2006.
Sandu2019
Adrian Sandu (2019), A class of multirate infinitesimal gark methods, SIAM Journal on Numerical Analysis, 57(5), 2300--2327, 2019.
Williamson1992
David L Williamson , John B Drake , James J Hack , R { \ " u } diger Jakob , Paul N Swarztrauber (1992), A standard test set for numerical approximations to the shallow water equations in spherical geometry, Journal of Computational Physics, 102(1), 211--224, 1992.
Grachev2007
Andrey A Grachev , Edgar L Andreas , Christopher W Fairall , Peter S Guest , P Ola G Persson (2007), SHEBA flux–profile relationships in the stable atmospheric boundary layer, Boundary-layer meteorology, 124(3), 315--333, 2007.
Seifert2006
Axel Seifert , Klaus Dieter Beheng (2006), A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description, Meteorology and atmospheric physics, 92(1-2), 45--66, 2006.
Lauritzen2012
Peter Hjort Lauritzen , William C Skamarock , MJ Prather , MA Taylor (2012), A standard test case suite for two-dimensional linear transport on the sphere, Geoscientific Model Development, 5(3), 887--901, 2012.
Watanabe2011
K. Watanabe al. (2011), Freezing experiments on unsaturated sand , loam , and silt loam., Annals of Glaciology, 52, 2011.
Mason2010
Basil John Mason (2010), Physics of clouds, Clarendon Press, 2010.
Taylor1937
G. I. Taylor , A. E. Green (1937), Mechanisms of production of small eddies from large ones, Proc. Roy. Soc. A, 158(895), 1937.
Schar2002
Christoph Sch { \ " a } r , Daniel Leuenberger , Oliver Fuhrer , Daniel L { \ " u } thi , Claude Girard (2002), A new terrain-following vertical coordinate formulation for atmospheric prediction models, Monthly Weather Review, 130(10), 2459--2480, 2002.
Atkinson2011
Kendall Atkinson , Weimin Han , David E Stewart (2011), Numerical solution of ordinary differential equations, John Wiley \& Sons, 2011.
Doms2011
G { \ " u } nther Doms , M Baldauf (2011), A Description of the Nonhydrostatic Regional COSMO model. Part I: Dynamics and Numerics, Deutscher Wetterdienst , Offenbach, -1, 2011.
Beare2006
Robert J Beare , Malcolm K Macvean , Albert AM Holtslag , Joan Cuxart , Igor Esau , Jean-Christophe Golaz , Maria A Jimenez , Marat Khairoutdinov , Branko Kosovic , David Lewellen , others (2006), An intercomparison of large-eddy simulations of the stable boundary layer, Boundary-Layer Meteorology, 118(2), 247--272, 2006.
Spiteri2002
Raymond J Spiteri , Steven J Ruuth (2002), A new class of optimal high-order strong-stability-preserving time discretization methods, SIAM Journal on Numerical Analysis, 40(2), 469--491, 2002.
Lilly1962
Douglas K Lilly (1962), On the numerical simulation of buoyant convection, Tellus, 14(2), 148--172, 1962.
Muhlbauer2013
Andreas Muhlbauer , Wojciech W Grabowski , Szymon P Malinowski , Thomas P Ackerman , George H Bryan , Zachary J Lebo , Jason A Milbrandt , Hugh Morrison , Mikhail Ovchinnikov , Sarah Tessendorf , others (2013), Reexamination of the state of the art of cloud modeling shows real improvements, Bulletin of the American Meteorological Society, 94(5), ES45--ES48, 2013.
Rutledge1984
Saad1986
Youcef Saad , Martin H Schultz (1986), GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on scientific and statistical computing, 7(3), 856--869, 1986.
BallandArp2005
V. Balland , P. A. Arp (2005), Modeling soil thermal conductivities over a wide range of conditions, J. Env. Eng. Sci., 4, 549--558, 2005.
Corey1977
A. T. Corey (1977), Mechanics of Heterogeneous Fluids in Porous Media, Water Resources Publication, Fort Collins , CO, 1977.
vanGenuchten1980
M. Th. Genuchten (1980), A Closed form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils, Soil Science Society of America Journal, 44(5), 892, 1980.
Shu1988
Chi-Wang Shu , Stanley Osher (1988), Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of computational physics, 77(2), 439--471, 1988.
Bull2014
J.R. Bull , A. Jameson (2014), Simulation of the Compressible { Taylor Green } Vortex using High-Order Flux Reconstruction Schemes, AIAA Aviation 7th AIAA theoretical fluid mechanics conference, , 2014.
Webb2017
M. J. Webb , T. Andrews , A. Bodas-Salcedo , S. Bony , C. S. Bretherton , R. Chadwick , H. Chepfer , H. Douville , P. Good , J. E. Kay , S. A. Klein , R. Marchand , B. Medeiros , A. P. Siebesma , C. B. Skinner , B. Stevens , G. Tselioudis , Y. Tsushima , M. Watanabe (2017), The Cloud Feedback Model Intercomparison Project (CFMIP) contribution to CMIP6, Geoscientific Model Development, 10(1), 359--384, 2017.
Nishizawa2018
S Nishizawa , Y Kitamura (2018), A Surface Flux Scheme Based on the Monin-Obukhov Similarity for Finite Volume Models, Journal of Advances in Modeling Earth Systems, 10(12), 3159--3175, 2018.
Kessler1995
Edwin Kessler (1995), On the continuity and distribution of water substance in atmospheric circulations, Atmospheric research, 38(1-4), 109--145, 1995.
Niegemann2012
Jens Niegemann , Richard Diehl , Kurt Busch (2012), Efficient low-storage Runge–Kutta schemes with optimized stability regions, Journal of Computational Physics, 231(2), 364--372, 2012.
DallAmico2011
M. Dall'Amico al. (2011), A robust and energy-conserving model of freezing variably-saturated soil., The Cryosphere, 5, 469-484, 2011.
LockWoodWeller2014
S.-J. Lock , N. Wood , H. Weller (2014), Numerical analyses of Runge–Kutta implicit–explicit schemes for horizontally explicit , vertically implicit solutions of atmospheric models, Quarterly Journal of the Royal Meteorological Society, 140(682), 1654-1669, 2014.
Arabas2015
Sylwester Arabas , Anna Jaruga , Hanna Pawlowska , Wojciech W Grabowski (2015), libcloudph++ 1.0: a single-moment bulk , double-moment bulk , and particle-based warm-rain microphysics library in C++, Geoscientific Model Development, 8(6), 1677--1707, 2015.
Giraldo2013
Francis X Giraldo , James F Kelly , Emil M Constantinescu (2013), Implicit-explicit formulations of a three-dimensional nonhydrostatic unified model of the atmosphere ( { NUMA } ), SIAM Journal on Scientific Computing, 35(5), B1162--B1194, 2013.
Karrer2020
M Karrer , A Seifert , C Siewert , D Ori , A von Lerber , S Kneifel (2020), Ice Particle Properties Inferred from Aggregation Modelling, Journal of Advances in Modeling Earth Systems, -1, e2020MS002066, 2020.
Roberts2018
Steven Roberts , Arash Sarshar , Adrian Sandu (2019), Coupled Multirate Infinitesimal GARK Schemes for Stiff Systems with Multiple Time Scales, arXiv preprint arXiv:1812.00808, -1, 2019.
Boyd1996
JP Boyd (1996), The erfc-log filter and the asymptotics of the Euler and Vandeven sequence accelerations, In Proceedings of the Third International Conference on Spectral and High Order Methods, 267--276, 1996.
Bank1985
R. E. Bank , W. M. Coughran , W. Fichtner , E. H. Grosse , D. J. Rose , R. K. Smith (1985), Transient simulation of silicon devices and circuits, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 4(4), 436-451, 1985.
Grabowski1998
Wojciech W Grabowski (1998), Toward cloud resolving modeling of large-scale tropical circulations: A simple cloud microphysics parameterization, Journal of the Atmospheric Sciences, 55(21), 3283--3298, 1998.
Durran1982
Dale R Durran , Joseph B Klemp (1982), On the effects of moisture on the Brunt-V { \ " a } is { \ " a } l { \ " a } frequency, Journal of the Atmospheric Sciences, 39(10), 2152--2158, 1982.
Heun1900
Gryanik2020
Vladimir M Gryanik , Christof L { \ " u } pkes , Andrey Grachev , Dmitry Sidorenko (2020), New modified and extended stability functions for the stable boundary layer based on SHEBA and parametrizations of bulk transfer coefficients for climate models, Journal of the Atmospheric Sciences, -1, 2020.
WickerSkamarock2002
Louis J. Wicker , William C. Skamarock (2002), Time-Splitting Methods for Elastic Models Using Forward Time Schemes, Monthly Weather Review, 130(8), 2088--2097, 2002.
Wiin1967
Aksel WIIN-NIELSEN (1967), On the annual variation and spectral distribution of atmospheric energy 1, Tellus, 19(4), 540--559, 1967.
Marshall1948
John S Marshall , W Mc K Palmer (1948), The distribution of raindrops with size, Journal of meteorology, 5(4), 165--166, 1948.
Hansson2004
K. Hansson al. (2004), Water Flow and Heat Transport in Frozen Soil: Numerical Solution and Freeze–Thaw Applications, Vadose Zone Journal, 3, 693-704, 2004.
Rancic1996
M. Ran\v { c } i\' { c } , R. J. Purser , F. Mesinger (1996), A global shallow-water model using an expanded spherical cube: Gnomonic versus conformal coordinates, Quarterly Journal of the Royal Meteorological Society, 122(532), 959--982, 1996.
Skilling2004
John Skilling (2004), Programming the Hilbert curve, In AIP Conference Proceedings, 381--387, 2004.
Tomita2008
Hirofumi Tomita , Koji Goto , Masaki Satoh (2008), A New Approach to Atmospheric General Circulation Model: Global Cloud Resolving Model { NICAM } and its Computational Performance, { SIAM } Journal on Scientific Computing, 30(6), 2755--2776, 2008.
Khvorostyanov2002
Vitaly I Khvorostyanov , Judith A Curry (2002), Terminal velocities of droplets and crystals: Power laws with continuous parameters over the size spectrum, Journal of the atmospheric sciences, 59(11), 1872--1884, 2002.
Kosovic2000
Branko Kosovi { \'c } , Judith A Curry (2000), A large eddy simulation study of a quasi-steady , stably stratified atmospheric boundary layer, Journal of the atmospheric sciences, 57(8), 1052--1068, 2000.
WenschKnothGalant2009
J. Wensch , Knoth O. , A. Galant (2009), Multirate infinitesimal step methods for atmospheric flow simulation, BIT Numerical Mathematics, 49(2), 449--473, 2009.
Kennedy2001
Christopher Alan Kennedy (2001), Additive Runge-Kutta schemes for convection-diffusion-reaction equations, National Aeronautics and Space Administration , Langley Research Center, 2001.
GolubVanLoan2013
Gene H. Golub , Charles F. Van Loan (2013), Matrix Computations, Johns Hopkins University Press, Baltimore , MD , USA, 2013.
Rafei2018
M.E. Rafei , L. K\ " on\ " oszy , Z. Rana (2018), Investigation of Numerical Dissipation in Classicaland Implicit Large Eddy Simulations, Aerospace, , 2018.
Ogura1971
Yoshimitsu Ogura , Tsutomu Takahashi (1971), Numerical simulation of the life cycle of a thunderstorm cell, Mon. Wea. Rev, 99(12), 895--911, 1971.
KennedyCarpenter2016
C. A. Kennedy , M. H. Carpenter (2016), Diagonally implicit Runge-Kutta methods for ordinary differential equations. A review, Technical Report NASA/TM–2016–219173, National Aeronautics and Space Administration, Langley Research Center , Hampton , VA, 2016.
Eisenstat1983
Stanley C Eisenstat , Howard C Elman , Martin H Schultz (1983), Variational iterative methods for nonsymmetric systems of linear equations, SIAM Journal on Numerical Analysis, 20(2), 345--357, 1983.
Grabowski1996
Wojciech W Grabowski , Piotr K Smolarkiewicz (1996), Two-time-level semi-Lagrangian modeling of precipitating clouds, Monthly weather review, 124(3), 487--497, 1996.
Held1994
Isaac M Held , Max J Suarez (1994), A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models, Bulletin of the American Meteorological society, 75(10), 1825--1830, 1994.
Morrison2008
Siebesma2003
A Pier Siebesma , Christopher S Bretherton , Andrew Brown , Andreas Chlond , Joan Cuxart , Peter G Duynkerke , Hongli Jiang , Marat Khairoutdinov , David Lewellen , Chin-Hoh Moeng , others (2003), A large eddy simulation intercomparison study of shallow cumulus convection, Journal of the Atmospheric Sciences, 60(10), 1201--1219, 2003.
Harrington1995
Jerry Y Harrington , Michael P Meyers , Robert L Walko , William R Cotton (1995), Parameterization of ice crystal conversion processes due to vapor deposition for mesoscale models using double-moment basis functions. Part I: Basic formulation and parcel model results, Journal of the atmospheric sciences, 52(23), 4344--4366, 1995.