A numerical sink of axial angular momentum in CAM-FV
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1 A numerical sink of axial angular momentum in CAM-FV Thomas Toniazzo, Peter Lauritzen, Christiane Jablonowski, Mats Bentsen, Helge Drange, Trond Iversen AMWG meeting, Boulder 9 Februrary 2016
2 CAM-FV likes easterlies Held and Suarez (1994) high-top simulations by Yao and Jablonowski (2015) with CAM and different dycores shows peculiarity of FV case.
3 CAM, superrotation and Titan Lebonnois et al. 2012, JGR 117/E12004 Lauritzen et al. 2014, J.Adv.Model.Earth Syst. 6/129 [...]
4 CAM FV and angular momentum CAM (4/5) FV dycore appears not to conserve momentum at 1.9x2.5 degree resolution Going to 0.9x1.25 degrees, the problem seems mitigated
5 CAM FV and angular momentum CAM (4/5) FV dycore appears not to conserve momentum at 1.9x2.5 degree resolution Going to 0.9x1.25 degrees, the problem seems mitigated Increased net torque appears associated with stronger and wider easterlies, poleward and weaker Westerlies
6 CAM FV and angular momentum Imbalance is confirmed in AP mode Doubling the resolution halves the error
7 CAM FV and angular momentum
8 CAM FV and angular momentum Imbalance is confirmed in AP mode Doubling the resolution halves the error T85 Comparison with spectral (EUL) dycore confirms weak westerlies & strong easterlies. F19 T42
9 CAM FV and angular momentum Relative error is Proportional to grid-spacing (blue/green) Insensitive to time-step (blue) Insensitive to explicit diffusion or damping (blue) Circulation dependent (magenta, solid) Insensitive to physics (magenta, broken)
10 Stress-free simulations
11 CAM-FV biases Double ITCZ Hadley circulation too symmetric and too intense Trade winds too wide and strong
12 An aside: systematic biases in CAM
13 Einstein (1926), Schneider (1977), Held & Hou (1980) momentum conservation Dissipation of axial momentum and (resolved) overturning circulation are in balance with each other
14 CAM4-FV biases Hadley circulation too strong, symmetric Double ITCZ, amplified by coupling AMIP
15 CAM4-FV biases Hadley circulation too strong, symmetric Double ITCZ, amplified by coupling AMIP SST biases
16 CAM4-FV biases Hadley circulation too strong, symmetric Double ITCZ, amplified by coupling SST biases AMIP Precip biases
17 CAM4-FV biases Hadley circulation too strong, symmetric Double ITCZ, amplified by coupling SST biases AMIP How about the width?... Precip biases
18 Schneider (1977), Held & Hou (1980) model a) momentum conservation b) thermal wind balance R*(aΩ) R²(HΔH/CτΔv)(aΩ)
19 Effects of axial momentum loss on equilibrium solution Assume a loss or export of axial momentum near the edge of the Hadley Cell: In other words: the drop off of the thermal-wind T field occurs further poleward, thus expanding the Hadley Cell
20 Interim summary CAMx-FV (x 3) has a non-physical sink of axial momentum large: 40% of the physical fluxes in FV19 (but circulation dependent) requires compensation by unbalanced easterly surface stress results in excessively strong and wide trade winds physically linked with over-active overturning (Hadley) circulation, and may contribute to the double ITCZ problem insensitive to physics or to time-step, but proportional to horizontal grid spacing compares unfavourably with other non-conserving dycores, e.g. ~8% spurious source in non-mass-conserving HadGAM3 to our knowledge, worst case in CMIP5 but GFDL and GISS come close
21 Aside #2: risk of bad science with biased CAM (& possibly others?...)
22 TRAC-MIP: a model intercomparison based on ML-AP integrations Voigt et al Bjerknes Centre (i.e. TT) participating with CAM5Oslo (NorESM-2 set-up) 1. Energetically closed 2. Thermodynamically coupled
23 TRAC-MIP: a model intercomparison based on ML-AP integrations Groups and model currently participating: Sarah Kang and Jeongbin Seo from UNIST (GFDL AM2) Elizabeth Maroon from UW (GFDL AM2) Juergen Bader and Jong-yeon Park from MPI (ECHAM6.3) Aiko Voigt from LDEO (ECHAM6.1) Nick Klingaman from University of Reading (MetUM GA6.0) Masakazu Yoshimori from Hokkaido (MIROC) Thomas Toniazzo from Uni Climate, Bergen (CAM5, FV19) Brian Rose from SUNY Albany (CAM4, FV19) Ross Dixon from U. Wisconsin (CAM3, T42) Simona Bordoni from CalTech (Moist Idealized GCM) Ruby Leung and Jian Lu from PNNL (MPAS with CAM5 physics) Francis Codron from UPMC (LMDZ) Joy Singarayer from University of Reading (HadCM3) Sonali McDermid from NASA GISS (ModelE)
24 TRAC-MIP: a model intercomparison based on ML-AP integrations Groups and model currently participating: Sarah Kang and Jeongbin Seo from UNIST (GFDL AM2) Elizabeth Maroon from UW (GFDL AM2) Juergen Bader and Jong-yeon Park from MPI (ECHAM6.3) Aiko Voigt from LDEO (ECHAM6.1) Nick Klingaman from University of Reading (MetUM GA6.0) Masakazu Yoshimori from Hokkaido (MIROC) Thomas Toniazzo from Uni Climate, Bergen (CAM5, FV19) Brian Rose from SUNY Albany (CAM4, FV19) Ross Dixon from U. Wisconsin (CAM3, T42) Simona Bordoni from CalTech (Moist Idealized GCM) Ruby Leung and Jian Lu from PNNL (MPAS with CAM5 physics) Francis Codron from UPMC (LMDZ) Joy Singarayer from University of Reading (HadCM3) Sonali McDermid from NASA GISS (ModelE)
25 Centennialscale variability in NorESM Long PI-control and LM integrations show centenntial-scale variability and is the subject of current studies. It is coupled with anomalous surface torque and may be entirely spurious.
26 Diagnostic assessment of AM source S M = t L R D L T x C dp L R= p u a cos a cos d g p 1 dp D L= uv a cos a cos d p a g T x = x a cos a cos d ptop top C = a sin 2 t 0 p a cos ' d d ' 2
27 SM T42,85 show balanced apparent source consistent with diffusion F19,09 show M sink everywhere, esp. subtropics
28 SM T42,85 show balanced apparent source consistent with diffusion F19,09 show M sink everywhere, esp. subtropics
29 SM
30 SM
31 SM
32 Angular-momentum streamfunction ptop M = p ΨM dp uv a cos v a cos a cos d g Differences between FV and spectral dycore simulations highlight M advection towards two areas of low M ΨM [kpa km²] and u [m/s], F09 - T85
33 Interim Summary #2 Localisation of spurious sink of axial momentum apparently governed by physics broadly colocated with baroclinic zones of momentum convergence Investigation proposed to find causes (NFR Frinatek submission) got great marks, wonderful praise, and no money We keep at it anyway
34 Speculations... Possible causes of numerical AM sink in the FV dycore: 1. representation of the pressure gradient terms, especially its departure from Simmons and Burridge (1981) 2. C-D grid discretisation and related interpolations (Skamarock 2008) 3. Lin and Rood s (1996) FFSL extension of Colella and Woodward s (1984) PPM algorithm 4. Arakawa-Lamb (1981) momentum source in discretisation of kinetic energy term 5. Suarez-Takacs (1994) upwinding for Hollingworth-Kållberg instability.
35 ...and next steps Possible causes of numerical AM sink in the FV dycore: 1. Test a S&B-like implementation of pressure-gradient terms (a la UKMO UM) 2. Leave dummy C-D grid interpolations in H&S set-up, applying (T,u) tendencies on the dycore grid 3. Test FV³ for AM dissipation.
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