1. Slide 1 Montreal, May 2015 ©ECMWF Representing 3D radiative effects in weather and climate models Robin Hogan ECMWF and University of Reading Contributions from: Sophia Schäfer, Christine Chiu (University of Reading) Carolin Klinger, Bernhard Mayer (LMU Munich) Susanne Crewell (University of Cologne) Maike Ahlgrimm (ECMWF)

2. Slide 2 Montreal, May 2015 ©ECMWF Motivation and overview ● No current radiation scheme that represents all 3D effects in shortwave and longwave is fast enough to use in weather and climate models ● Therefore, we have no reliable estimates of their impact on fluxes globally, or the impact on temperature and other model variables ● Solar energy industry requires forecasts of direct and diffuse solar radiation separately, which can be significantly biased when 3D effects are neglected ● This talk introduces a radiation scheme that can fill this gap ● Matrix-exponential method for solving a new form of two-stream equations ● How important are longwave 3D effects? ● Observational evidence for 3D effects in direct/diffuse ratio ● What is the effective cloud edge length for 3D radiation? ● Outlook

3. Slide 3 Montreal, May 2015 ©ECMWF Shortwave 3D radiative effects ● Useful to consider mechanisms for 3D effects (Varnai and Davies 1999) ● The two main mechanisms give errors of opposite sign (Hogan & Shonk 2013): ● Side Illumination –Direct-beam effect –Can be captured to some extent by modifying cloud overlap (Tompkins & DiGiuseppe 2007) ● Side escape –Diffuse effect –Cannot be captured by modifying cloud overlap

4. Slide 4 Montreal, May 2015 ©ECMWF Longwave 3D radiative effects ● Very little literature; most radiation people seem to assume it’s negligible ● Heidinger & Cox (1995) estimated 30% increase in surface cloud forcing at 11  m ● Thought experiment: consider a cubic isothermal optically thick cloud in vacuum ● Each face emits same, and half of radiation from horizontal faces goes down ● Therefore surface downwelling radiation must be three times what would be calculated neglecting 3D effects ● What about more realistic clouds with absorption by atmospheric gases?

5. Slide 5 Montreal, May 2015 ©ECMWF SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides SPARTACUS!

6. Slide 6 Montreal, May 2015 ©ECMWF SPARTACUS approach a a c bc b a Source terms Shortwave: direct solar beam Longwave: Planck function New terms Exchange between regions Hogan & Shonk provided formulas for f xy in terms of cloud edge length a uaua vava ubub vbvb

7. Slide 7 Montreal, May 2015 ©ECMWF Matrix solution in a single layer (shortwave) ● Define diffuse upwelling, diffuse downwelling and direct downwelling as vectors u, v and s: ● Write two-stream equations as: where 9x9 matrix is composed of known terms analogous to  1 -  4 in the standard two-stream equations: (coupled linear homogeneous ODEs) ● Solution for layer of thickness z 1 : Matrix exponential Waterman (1981), Flatau & Stephens (1998) Can compute using Padé approximant plus scaling & squaring method (Higham 2005)

8. Slide 8 Montreal, May 2015 ©ECMWF Reflection and transmission matrices ● We want relationships between fluxes of the form: ● Transmission matrix for 2 regions given by and likewise for R and S ± ● If matrix exponential is decomposed as: then reflection and transmission matrices given by: ● For scalars, we get same answer as Meador & Weaver (1980) formulas ● For speed, only use matrix exponential for partially cloudy layers u(0) u(z1)u(z1) v(0) s(0)

9. Slide 9 Montreal, May 2015 ©ECMWF Extension to multiple layers: the adding method A aa A bb A ba A ab

10. Slide 10 Montreal, May 2015 ©ECMWF How do we deal with cloud overlap? V aa V ba V bb V ab Half-level Extension to longwave

11. Slide 11 Montreal, May 2015 ©ECMWF Broadband shortwave SPARTACUS vs MYSTIC (I3RC case 4) ● SPARTACUS coded up in Fortran 90 with RRTM-G for gas absorption –Use “ellipsified” cloud edge length (see later) ● Compare to full 3D Monte Carlo calculation from MYSTIC in cumulus –Mean of 4 solar azimuths, error bar indicates standard deviation due to sun orientation ● Good match! ● 3D effect up to 20 W m -2, similar to inhomogeneity effect ● Large difference in direct surface flux at large solar zenith angle

12. Slide 12 Montreal, May 2015 ©ECMWF 3D effects in observations of direct/total downwelling flux Troccoli & Morcrette (2014) reported biases in ECMWF direct solar radiation from, important for solar energy industry Bin observations and model by solar zenith angle and cloud fraction, considering only cases of boundary-layer clouds: Next step: apply new 3D radiation scheme to the ECMWF cloud fields to verify that differences are due to 3D effects ECMWF model ARM SGP (13 yrs)

13. Slide 13 Montreal, May 2015 ©ECMWF What about cloud edge length? ● SPARTACUS takes cloud edge length per unit area of gridbox as input ● Will need to be parameterized in the GCM as an effective cloud size –E.g. use shallow/deep cumulus schemes to diagnose when clouds with strongest 3D effect are present ● For cubes, longwave SPARTACUS matches SHDOM/MYSTIC well, but not for realistic clouds ● Hypotheses: –Small-scale structure of a cloud does not matter for radiation; the effective edge length is that of an ellipse with the same area and aspect ratio –Clouds tend to cluster, but SPARTACUS assumes random distribution Horizontal cross section through a cloud “Ellipsified” cloud

14. Slide 14 Montreal, May 2015 ©ECMWF Four experiments manipulating the I3RC cumulus field… Isolated cloud Original Original “Ellipsified” clouds

15. Slide 15 Montreal, May 2015 ©ECMWF Longwave downwelling flux: SPARTACUS versus SHDOM ● Excellent match with ICA, but SPARTACUS overestimates 3D effect ● SPARTACUS overestimation is removed for isolated, ellipsified clouds ● Parameterization will need to account for clustering and effective edge length Independent column approx3D radiation

16. Slide 16 Montreal, May 2015 ©ECMWF Longwave presents additional challenges To compute exchange between cloud and clear-sky, shortwave SPARTACUS assumes cloud-edge flux equal to in-cloud mean flux In optically thick clouds, scattering reduces emitted flux below black-body value (emissivity effect) In optically thin clouds, lateral flux builds up towards cloud edge FF Using thought experiment for a cube, we have parameterized these effects Parameterization strictly only applicable for clouds with an aspect ratio of around 1

17. Slide 17 Montreal, May 2015 ©ECMWF ● SPARTACUS uses ellipsified edge length but no proximity/lateral effects yet ● 3D effects increase surface CRF by 29% in MYSTIC and 36% in SPARTACUS –Also differences in 1D calculations that need to be investigated ● Surface 3D effect of 4 W m-2 smaller than shortwave maximum –Partly just because cumulus clouds have smaller CRF in longwave than shortwave ● But constant over diurnal cycle so might integrate to a larger effect? Broadband longwave SPARTACUS vs MYSTIC (I3RC case) DownUp

18. Slide 18 Montreal, May 2015 ©ECMWF Summary ● SPARTACUS is a promising method for representing 3D effects efficiently in a GCM radiation scheme ● Radiatively effective cloud edge length is approximately equal to perimeter of a fitted ellipse, although cloud clustering is important as well ● Longwave 3D effects systematically increase CRF and shouldn’t be neglected ● Incorporate longwave parameterizations ● Implement online in the ECMWF model ● How can we parameterize cloud edge length from model fields? ● What is the impact of 3D radiation on global fluxes and temperatures? Next steps

20. Slide 20 Montreal, May 2015 ©ECMWF Shortwave results Coded up in Fortran 90 with RRTM-G for gas absorption Good match with cumulus case of Pincus et al. (2005): cloud cover 0.22, edge length calculated from aspect ratio of 0.7 3D effect similar size to inhomogeneity effect Large difference in direct surface flux at large solar zenith angle

21. Slide 21 Montreal, May 2015 ©ECMWF Impact on flux and heating rate profiles Longwave Shortwave,  0 =70° Heating rate Downwelling Upwelling