Representing 3D radiative effects in weather and climate mo - PowerPoint Presentation

Slide1

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)Slide2

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?

OutlookSlide3

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 overlapSlide4

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 vacuumEach face emits same, and half of radiation from horizontal faces goes downTherefore surface downwelling radiation must be three times what would be calculated neglecting 3D effects

What about more realistic clouds with absorption by atmospheric gases?Slide5

SPeedy

Algorithm for

Radiative

TrAnsfer

through

CloUd Sides

SPARTACUS!Slide6

SPARTACUS approach

Follows from Hogan &

Shonk

(2013), but:

Represents

longwave

3D effects, including longwave scatteringRepresents cloud inhomogeneity using “Tripleclouds” approachA

more elegant and accurate solver using matrix exponentialsClouds represented by three regions at each height Sufficient to represent cloud structure (Shonk & Hogan 2008)Extra terms added to two-stream equations:

a

a

c

b

c

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

u

a

v

a

u

b

v

bSlide7

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 g1-g4 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)Slide8

Reflection and

t

ransmission 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

(

z

1

)

v

(0)

s

(0)Slide9

Extension to multiple layers: the adding method

The adding method (e.g.

Lacis

and Hansen 1974) can be used to combine the reflectance and transmittance matrices of pairs of layers

In

N-stream radiative transfer (e.g. N

=16), the elements of the flux vector would represent different streams, but the method works just as well for different regionsWe work up from the surface and compute the albedo of the whole atmosphere below each half-levelAlbedo

After this we can head back down again to compute the fluxes

For one region, this is exactly the same as solving a tridiagonal system with forward elimination followed by backsubstitution

A

aa

A

bb

A

ba

A

abSlide10

How do we deal with cloud overlap?

Following Edwards-

Slingo

code method: overlap matrices

Downward overlap

(similarly for upward overlap

U

)Matrix elements calculated from a decorrelation length following Shonk et al. (2010)Albedo just above a half level (

A) is related to albedo just below a half level (B) by A=UBVTwo-stream equations now look like this:

V

aa

V

ba

V

bb

V

ab

Half-level

Extension to

longwaveSlide11

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 effectLarge difference in direct surface flux at large solar zenith angleSlide12

3D effects in observations of direct/total downwelling flux

Troccoli

&

Morcrette

(2014

) reported biases in ECMWF direct solar radiation from, important

for solar energy industryBin 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 effectsECMWF modelARM SGP (13 yrs

)Slide13

What about cloud edge length?

SPARTACUS takes

cloud edge length per unit area of

gridbox

as inputWill need to be parameterized in the GCM as an effective cloud sizeE.g. use shallow/deep cumulus schemes to diagnose when clouds with strongest 3D effect are presentFor cubes, longwave

SPARTACUS matches SHDOM/MYSTIC well, but not for realistic cloudsHypotheses: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

” cloudSlide14

Four experiments manipulating the I3RC cumulus field…

Isolated cloud Original

Original “

Ellipsified

” cloudsSlide15

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 approx 3D radiationSlide16

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



Using thought experiment for a cube, we have parameterized these effects

Parameterization strictly only applicable for clouds with an aspect ratio of around 1Slide17

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 shortwaveBut constant over diurnal cycle so might integrate to a larger effect?

Broadband longwave SPARTACUS vs MYSTIC (I3RC case)Down

UpSlide18

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 parameterizationsImplement online in the ECMWF modelHow can we parameterize cloud edge length from model fields?What is the impact of 3D radiation on global fluxes and temperatures?N

ext stepsSlide19
Slide20

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 0.73D effect similar size to inhomogeneity effectLarge difference in direct surface flux at large solar zenith angleSlide21

Impact on flux and heating rate profiles

Longwave

Shortwave,

q

0

=70°

Heating rate

Downwelling Upwelling