Entrapment An important mechanism for shortwave 3D cloud radiative effects and its inclusion in the SPARTACUS radiative transfer model Robin Hogan, Mark Fielding (ECMWF) Howard Barker (Environment & Climate Change Canada) Najda Villefranque (University of Toulouse) r.j.hogan@ecmwf.int

Frequently claimed, never backed up with evidence: “Shortwave 3D effects of clouds are negligible because the sign of the effect depends on sun angle so cancels across the diurnal cycle” “Longwave 3D effects of clouds are negligible because I don’t know of any papers that say otherwise” European Centre for Medium-Range Weather Forecasts

3D effects in the ECMWF radiation scheme “ecRad” SPARTACUS solver: add extra terms to the two-stream equations: 𝑑 𝑣 𝑎 𝑑𝑧 = 𝛽 𝑒 − 𝛾 1 𝑎 𝑣 𝑎 + 𝛾 2 𝑎 𝑢 𝑎 + 𝑠 𝑎− − 𝑓 𝑎𝑏 𝑣 𝑎 + 𝑓 𝑏𝑎 𝑣 𝑏 Rate of exchange between regions is: Write two-stream equations in matrix form including direct solar flux s: where Solution per layer in terms of matrix exponentials: Solve for flux profile using matrix version of the Adding Method SPARTACUS solver is 5.7 times slower than McICA (OK for research) New terms representing exchange between regions Length of cloud perimeter per unit gridbox area (related to cloud size) 𝑓𝑎𝑏= 𝐿𝑎𝑏 2𝑐𝑎 Fraction of gridbox occupied by clear skies (region a) Speedy Algorithm for Radiative Transfer through Cloud Sides a ua va ub vb Matrix exponential Waterman (1981), Flatau & Stephens (1998) a b c a b c a Hogan et al., Schafer et al. (JGR 2016)

SPARTACUS applied to cumulus cloud scene Lower reflectance… why? ? Compare independent column approximation with fully 3D Excellent agreement between SPARTACUS and (far slower) Monte Carlo Higher reflectance due to cloud edges Hogan et al. (JGR 2016)

Mechanisms for 3D shortwave effects What about multi-level clouds? Entrapment! Upward trapping Downward trapping Upward escape Downward escape ≈ Side illumination Side escape = Varnai & Davies (1999) Hogan & Shonk (2013) European Centre for Medium-Range Weather Forecasts

Idealized calculation: what is the albedo of this scene? R R* R 0 Surface albedo = 0 Reflectance of each cloud: R No absorption so transmittance T = 1 – R R/2 Independent column approximation Reflectance of 2 non-absorbing clouds Adding method with R* = 2R/(1+R) Reflectance of scene Weighted average Rscene = R/2 + R*/4 = R(1+R/2)/(1+R) Optically thick limit: Rscene = 3/4 Horizontal transport in regions Mean reflectance of layer = R/2 Reflectance of scene Random overlap so apply adding method to mean reflectances: Rscene = 2(R/2)/(1+R/2) = 2R/(2+R) Optically thick limit: Rscene = 2/3

Representing three extremes of “entrapment” in SPARTACUS We need albedo matrix A at layer interfaces 𝛼 𝑏𝑎 No 3D effects requires matrix to be diagonal Better approach: compute RMS horizontal migration distance of light paths beneath cloud 2016 SPARTACUS: full horizontal homogenization of radiation under clouds 𝐀= 𝛼 𝑎𝑎 𝛼 𝑏𝑎 𝛼 𝑎𝑏 𝛼 𝑏𝑏 = 𝛼 0 0 𝛼 𝐀= 𝛼/2 𝛼/2 𝛼/2 𝛼/2

Computing horizontal migration distances within SPARTACUS xdiff(z) ARM cumulus case At each height z, estimate mean horizontal distance travelled by reflected light xdiff(z) and xdir(z) Given cloud effective size, we can estimate fraction of radiation that is reflected into the base of another region First comparison of mean horizontal distances to Monte Carlo shows promise but refinements needed (Najda Villefranque) direct diffuse z xdir(z) European Centre for Medium-Range Weather Forecasts

Broadband testing against Monte Carlo Howard Barker has run Monte Carlo calculations on 59 varied scenes from Canadian and Met Office models at ~200 m resolution Minimum entrapment Computed entrapment Maximum entrapment Entrapment changes 3D effect by a factor of three for overhead sun!

3D impact in 4x one-year coupled simulations with ECMWF model 3D effect on LW surface downwelling: +1.6 W m-2 Minimum (no) entrapment SW surface: +0.1 W m-2 SW TOA: +0.3 W m-2 Computed entrapment SW surface: +0.8 W m-2 SW TOA: +1.2 W m-2 Maximum entrapment SW surface: +2.2 W m-2 SW TOA: +3.1 W m-2

European Centre for Medium-Range Weather Forecasts Summary Shortwave 3D radiative effects traditionally considered to be about transport through cloud sides Significant biases when sun is low in the sky Led to development of SPARTACUS solver in ECMWF radiation scheme “ecRad” Near-cancellation in global impact between side illumination & side escape (~0.2 W m-2) We find that horizontal transport within clear or cloudy regions has a larger effect Systematically reduces scene albedo due to the “entrapment” mechanism Added to SPARTACUS solver and being evaluated using Monte Carlo simulations Estimate of global SW radiative effect: warming of around +1 W m-2 Remaining questions (see Mark Fielding’s presentation tomorrow) Can we derive the effective cloud size from observations? What is the impact of 3D radiative effects in long coupled climate simulations? What is the relative importance of longwave and shortwave 3D effects? European Centre for Medium-Range Weather Forecasts