Recent Progress of Improving

Model Physics in NCEP GFS

Yu-Tai Hou

NOAA/NCEP/EMC

(yu-tai.hou@noaa.gov)

TWPAC Workshop, May 2013

1

Physics Modeling – the Frontier line for

Advanced Environmental Prediction Models

• Extremely complex nature and wide range of disciplines

interacting to each others – A constant challenge to the

limit of our knowledge and resource capability.

• Focus on NCEP GFS activities of the following topics:

- Convection and PBL

- Cloud microphysics

- Atmospheric aerosols

- Land surface modeling

- Radiative transfer process under cloudy condition

- Neural-Network Emulation of radiation models

2

NCEP GFS Cumulus Convection and

PBL schemes

(Courtesy of Jongil Han)

3

Shallow convection scheme :

• using mass-flux (MF) approach to increase stratocumulus clouds in the west coasts of South America and Africa

PBL scheme:

• enhancing stratocumulus-cloud-top-driven turbulence mixing and using local diffusion for nighttime stable PBL

Deep convection scheme:

• making cumulus cloud deeper and stronger to reduce unrealistic grid point storms (bull’s eyes precip pattern)

• including the effect from convection-induced pressure gradient force to reduce convective momentum transport, and in turn, to significantly improve hurricane intensity forecasts

4

Convection and PBL(operational GFS - Han and Pan, 2010)

• Reducing drag coefficient over the oceans in high wind conditions to help improving hurricane intensity and track forecasts especially in the Eastern-Pacific.

• New EDMF (Eddy-Diffusivity Mass-Flux) scheme for the convective boundary layer (the current EDCG scheme over-predicts PBL growth when wind is strong, but under-predicts the growth for the convection-dominated PBL).

• An universal cumulus convection scheme applicable to any horizontal resolution (the assumption that an updraft area is negligibly small in a model grid won't hold for very high resolution models).

5

Convection and PBL(Ongoing Research and Development)

AT 2008 (00Z) EP 2008 (00Z)

P12H: Opr

PD21: Shal+Concv

PD29: Shal+Concv+RedCd

6

AT 2008 (00Z) EP 2008 (00Z)

P12H: Opr

PD21: Shal+Concv

PD29: Shal+Concv+RedCd

7

NCEP GFS Cloud Microphysics Scheme

(Courtesy of Ruiyu Sun)

8

Cloud Microphysics(operational GFS)

Zhao and Carr (1996), Sundqvist et al. (1989):

• prognostic cloud condensate (water or ice) and specific

humidity, considering partial cloudy situations, separation of

cloud water and ice based on temperature alone

Moorthi et al. (2001):

• Diagnostic cloud cover from relative humidity and cloud

condensate

- Cloud cover produced in microphysics (Sundqvist) and used

in radiation (Xu and Randall) are calculated differently and

have different values

9

• Unified PDF based cloud cover scheme

• Condensation/evaporation based on the unified PDF cloud

cover scheme.

• Homogeneous nucleation of ice. Improved conversion of

cloud water to rain.

• Testing other cloud microphysics such as Ferrier’s scheme,

and Thompson’s scheme, etc.

10

Cloud Microphysics(Working in progress)

Vector wind RMSE

11

Precipitation skills (60-84h)

12

NOAA Environmental Modeling System

(NEMS) GFS Aerosol Component

(NGAC)

(Courtesy of Sarah Lu)

13

• 5-day dust forecast once per day (at 00Z), output

every 3 hour, at T126 L64 resolution

• Same physics and dynamics as operational T574

L64 GFS with the following exceptions:

• Lower resolution (T126 L64)

• Use Relaxed Arakawa-Schubert scheme

[Moorthi and Suarez, 1999] with convective

transport and tracer scavenging

• Turn off aerosol-radiation feedback

• ICs: Aerosols from previous day forecast and

meteorology from operational GDAS

Near-Real-Time NGAC Configuration

Configuration:

• GFS based on NOAA Environmental Modeling System (NEMS)

• NASA Goddard Chemistry Aerosol Radiation and Transport Model (GOCART)

Phased Implementation:

• Dust-only guidance is established in Q4FY12 (NCEP-GSFC collaboration)

• Full-package aerosol forecast after real-time global smoke emissions are available and

tested (NCEP-NESDIS-GSFC collaborative activities funded by JCSDA)

14

Noah Land Surface Model (LSM)(Courtesy of Helin Wei)

16

Noah model has realistic land physics & is coupled with NCEP

short-range NAM, medium-range GFS, and seasonal CFS, and run

“uncoupled”, i.e. NLDAS, and GLDAS (in Climate Forecast

System)

Noah LSM Physics• Four soil layers (10, 30, 60, 100 cm thick)

• Prognostic Land States

– Surface skin temperature

– Total soil moisture at each layer (volumetric)

• total of liquid and frozen (bounded by saturation value depending on soil type)

– Liquid soil moisture each layer (volumetric)

• can be supercooled

– Soil temperature at each layer

– Canopy water content

• dew/frost, intercepted precipitation

– Snowpack water equivalent (SWE) content

– Snowpack depth (physical snow depth)

• Above prognostic states require initial conditions

– Provided by WRF Preprocessing System (WPS) (former SI and REAL)

Noah LSM Physics : Soil Prognostic Equation

Soil Moisture

-“Richard’s Equation for soil water movement

- D, K functions (soil texture, soil moisture)

represents sources (rainfall) and sinks (evaporation)

Soil Temperature

- C, tK functions (soil texture, soil moisture)

- Soil temperature information used to compute ground heat flux

Noah LSM Physics: Surface Evaporation

E = Edir + Et + Ec + Esnow

Noah LSM Physics: Surface Water Budget

dS = P - R - E

• Et represents evaporation of water from plant canopy via uptake from roots in the soil, which can be parameterized in terms of “resistances” to the “potential” flux

Flux = Potential/Resistance

• Potential evaporation: amount of evaporation that would occur if a sufficient water source were available. Surface and air temperatures, insolation, and wind all affect this

Noah LSM Physics: Vegetation Transpiration (Et)

17

18

- Radiative process is one of the most complex and computational intensive part of all model physics. As an essential part of model physics, it directly and indirectly connects all physics processes with model dynamics, and regulates the overall earth-atmosphere energy exchanges and transformations.

- Development of modern radiation model is driven by thepressing needs from the rapidly advancement of other model physics, such as cloud-microphysics, aerosols, land model, chemistry model, convection, etc.; as well as by ever increasing specific requests from community users (government agencies, forecasts, environmental studies, agriculture/energy/communication industries, health, …).

Atmospheric Radiative Process in

Numerical Weather/Climate Prediction

Models

19

20

Neural Network Emulations of

GFS/CFS Radiations(V. Krasnopolsky et al.)

Sample Distribution of Computation time in NCEP CFS T126L64

Radiation Dynamics Other

~60%

~20%

~20%

21

NN Emulations of Model Physics ParameterizationsLearning from Data

GCM

X Y

Original Radiation parameterization

F

X Y

NN Emulation

FNN

TrainingSet …, {Xi, Yi}, … Xi Dphys

FRAD

22

NN Approximation Accuracy and Performance vs. Original Parameterization

(on independent data set)

Parameter Model Bias RMSE RMSEt RMSEb Performance

LWR(K/day)

NCEP CFSAER rrtm

2. 10-3 0.40 0.09 0.64 12

times faster

NCAR CAMW.D. Collins

3. 10-4 0.28 0.06 0.86 150

times faster

SWR(K/day)

NCEP CFSAER rrtm 5. 10-3 0.20 0.21 0.22

~45

times faster

NCAR CAM W.D. Collins

-4. 10-3 0.19 0.17 0.43 20

times faster

NCEP GFS/CFS Radiation Models

23

A Quick Review – Timeline

1990 2000 2010

V1

GFDL-LW

GFDL-SW

V2

GFDL-LW

CHOU-SW

V3

RRTM-LW

CHOU-SW

V4

RRTM-LW

RRTM-SW

V5

RRTM_McICA-LW

RRTM_McICA-SW

MRF

ETA

MRF/

GFS

CFSv1

ETA/

NAM

GFS GFS

CFSR

CFSv2

GFS

NAM *

NMMB*

CFSv3*

1985 1995 2005 2015

24

1. Driver Module - prepares astronomy parameters, atmospheric profiles

(aerosols, gases, clouds), and surface conditions

2. Astronomy Module - observed/derived form sun-spot cycle, annual/monthly

mean solar constant tables (5w/m2 difference in TSI absolute and TIM scales)

3. Aerosol Module - clim/GOCART aerosol schemes + historical stratospheric

volcanic data set

4. Gas Module - progn/clim O3, 2-D hist obs CO2, fixed other GH gases

5. Cloud module - 2 progn cloud mic-phys, legacy diagn cloud scheme

6. Surface module - veg type based clim/Modis surface albedo and emissivity

7. SW radiation module – RRTMG/RRTMG-McICA + (early schemes with plug-

in compatible common module and interface structure)

8. LW radiation module – RRTMG/RRTMG-McICA + (early schemes with plug-

in compatible common module and interface structure)

NCEP Unified Radiation Module Structures:

Features:Standardized component modules, General plug-in compatible, Simple to use, Easy to upgrade, Efficient, and Flexible in future expansion.

25

Schematic Radiation Module Structure

•Driver Module

Init/update

main driver

Astronomy Module

Init/update

mean coszen

Gases Module

Init/update

ozone

co2

Cloud Module

initialization

prog cld1

prog cld2

diag cld

Aerosol Module

Init/update

clim aerosols

Derived Type :aerosol_type

Surface Module

initialization

SW albedo

LW emissivity

Derived Type :sfcalb_type

SW Param Module

SW Data Table Module

SW Main Moduleinitialization

sw radiation

Outputs :total sky heating ratessurface fluxes (up/down)toa atms fluxes (up/down)

Optional outputs:clear sky heating ratesspectral band heating rates fluxes profiles (up/down)surface flux components

LW Param Module

LW Data Table Module

LW Main Moduleinitialization

lw radiation

Outputs :total sky heating ratessurface fluxes (up/down)toa atms fluxes (up/down)

Optional outputs:clear sky heating ratesspectral band heating rates fluxes profiles (up/down)

rare gases

GOCART aerosols

26

Global Annual Mean of Raditiative Fluxes

(S.K. Yang et al.)

TOA

OLR

TOA

CS

OLR

TOA

RSW

TOA

CSRSW SFC SW DN

SFC

SW UP

SFC

LW DN

SFC

LW UP

Jul00-Jun05 CFSR 228.1 248.2 101.8 65.2 167.6 36.9 304.2 356.4

CERES

(EBAF/SARB) 224.1 249.7 102.7 61.7 165.7 32.9 304.7 354.7

Diff (RMSD) 4.1(6.74) -1.5(6.12) -0.9(16.30) 3.5(10.54) 1.9(18.02) 4.0(9.05) -0.5(10.3) 1.6(10.14)

Spatial

Correlatn 0.9 0.87 0.72 0.88 0.76 0.91 0.92 0.92

Jan85-Dec86 R1 237.1 267.8 115.3 54.9 207.5 333

ERBE 234 266.7 102.7 53.1 184 349.5

Dif 3.1 1.7 12.6 1.8 23.5 -16.5

27

• Clouds are products from chaotic turbulence process that leaves a hallmark of highly inhomogeneous in both spatial and temporal distributions. The complexity of cloud components (gas/liquid/ice/snow/rain …) produce a wide range of radiative spectral responses.

• Even for a very high resolution NWM, it is still hardly capable to capture the details of the complexity and randomness of cloud structure and distribution.

28

Difficulties of Presenting Clouds in

Radiation Computations

Resolve sub-grid cloud structures in NWCMs

• Nested 2-D cloud resolving model (CRM) – O(N)

very expansive, (N: number of sub-grid profiles, full

RT computation for each sub-grid profile)

• Independent column approximation (ICA) – O(N)

very expensive, (N: number of sub-grids, full RT

computation for each sub-grid)

• Monte-Carlo independent column approximation

(McICA) – O(~1) considerably less expensive (partial RT for each sub-grid)

29

Advantages of McICA

• Providing a vibrant while efficient way to mimic the random nature of cloud distributions. (also useful for ensemble applications)

• A complete separation of optical characteristics from RT solver and is proved to be unbiased against ICA (Barker et al. 2002, Barker and Raisanen 2005)

• In addition of cloudiness, the same concept can be used to treat cloud condensate as well.

• Currently implemented on CFSv2 and tested on GFS with a simple cloud vertical overlapping assumption (e.g. random or maximum-random), more elaborate scheme (e.g. de-correlation length) is under study.

• Shown significant impact on climate-scale, moderate impact on medium to short-range forecast. Impact might grow when other physics advances.

30

31

Preliminary GFS Test Results(GFS T574 RRTM vs. RRTM-McICA+modified cloud cover)

32

Preliminary GFS Test Results(GFS T574 RRTM vs. RRTM-McICA+modified cloud cover)

33

Preliminary GFS Test Results(SL T1148 RRTM vs. RRTM_McICA)

34

Preliminary GFS Test Results(SL T1148 RRTM vs. RRTM_McICA)

35

Preliminary GFS Test Results(SL T1148 RRTM vs. RRTM_McICA)

36

Looking Forward

Operational GFS Working in progress

Main radiation

RT model RRTMG RRTMG_McICA + NN-emulator

Frequency One-hour LW and SW More frequent (reduced horz-res, NN)

Clouds

Overlapping Max-random De-correlation overlap

Homogeneity Homogeneous Inhomogeneous

Components Liquid/Ice Liquid/Ice/Rain/Snow…

Green-House Gases

CO2 Obs/estim 15 deg h-res, vrtcl well mix Updated, vertical varying profofile

Other GHGs Prescribed global clim Obs/estim CH4, N2O, CFC, …

Carbon cycle Not included Experimental carbon-cycle model (CFS)

Solar Constant

Magnitude Mean at 1366 w/m2 Mean at 1361 w/m2

11-Yr Cycle (1944-2006) annual mean Updated annual/monthly tables

Aerosols

Tropospheric 5 deg horiz res, monthly clim GOCART interactive aerosol model

Stratospheric Historical Obs. In 4-zonal bands Updated + vertical profile

Surface

Land albedo Sfc veg type based monthly clim MODIS retrieval based monthly clim

Ocean albedo Fixed+empirical cosz adjustment Func of ocean salinity/sfc wind/cosz

Emissivity Sfc veg type based fixed values Updated, spectral varying 37

Final Remarks

• Experiencing a great period of discovering and advancing of a wide range of physics processes for environmental prediction models.

• Treatment of model physics (parameterization) has been gradually shifting from macro-scale description of mean phenomenon towards micro-scale presentation of detailed physics process.

• At NCEP/EMC, we are building a solid foundation for advanced environmental prediction models through both in-house effort and close collaborations with academia community and research institutes.

38

Thank You

39

Supplementary Materials

40

Radiation_Astronomy Module(Revised Total Solar Irradiance Values)

Solar constant value : (Control parameter - ISOL)ISOL=0: prescribed value = 1366 w/m2 (old), =1361 w/m2 (new)ISOL=1: NOAA old scale yearly solar constant table with 11-year cycle (1944-2006)**ISOL=2: NOAA new scale yearly solar constant table with 11-year cycle (1850-2019)**ISOL=3: CMIP5 yearly solar constant table with 11-year cycle (1610-2008)ISOL=4: CMIP5 monthly solar constant table with 11-year cycle (1882-2008)**tabulated by H. Vandendool

Old

TSI

in a

bso

lute

sca

le New

TSI in TIM

scale

41

Radiation_Gases Module

CO2 Distribution : (Cntl parm - ICO2) ICO2=0: use prescribed global annual mean value (currently set as 380ppmv)

ICO2=1: use observed global annual mean value

ICO2=2: use observed monthly 2-d data table in 15° horizontal resolution

O3 Distribution : (Cntl parm – NTOZ)

NTOZ=0: seasonal climatology ozone

NTOZ>0: prognostic ozone

Rare Gases : (currently use global mean climatology values, historical observational database will be developed in near future)

CH4 - 1.50 x 10-6 N2O - 0.31 x 10-6 O2 - 0.209

CO - 1.50 x 10-8 CF11 - 3.52 x 10-10 CF12- 6.36 x 10-10

CF22 - 1.50 x 10-10 CF113- 0.82 x 10-10 CCL4- 1.40 x 10-10

** all units are in ppmv

42

Radiation_Clouds Module

Cloud prediction scheme: Prognostic 1: based on Zhao/Carr/Sundqvist prognostic cloud-microphysics,

Moorthi/Pan/Xu&Randell diagnostic cloud cover

Prognostic 2: based on Ferrier/Moorthi cloud-microphysics

Prognostic x: next gen microphysics

Diagnostic : legacy diagnostic scheme based on RH-table lookups

Cloud overlapping method: (Cntl parm – IOVR_SW/IOVR_LW)IOVR = 0: randomly overlapping vertical cloud layers

IOVR = 1: maximum-random overlapping vertical cloud layers

IOVR = x: other types of overlapping scheme

Sub-grid cloud approximation: (Cntl parm – ISUBC_SW/ISUBC_LW)

ISUBC=0: no sub-grid cloud approximation

ISUBC=1: use McICA sub-grid approximation (testing mode with prescribed

permutation seeds)

ISUBC=2: use McICA sub-grid approximation (random permutation seeds)

43

Radiation_aerosols Module

Aerosol model: (Cntl parm – IAER_MDL)Troposphere: IAER_MDL=0: monthly global aerosol climatology in 15° horizontal

resolution

IAER_MDL>0: GOCART aerosol scheme (climatology, interactive)

Stratosphere: historical recorded volcanic forcing in four zonal mean bands (1850-2000)

Aerosol radiative effect: (Cntl parm – IAER)

IAER – a 3-digit integer flag, abc, for Volcanic, LW, and SW, respectively

a=0: use background stratospheric aerosol if b and/or c ≠ 0, otherwise no effect

=1: include historical stratospheric volcanic aerosol effect (* no current data)

b=0: no tropospheric LW aerosol effect

=1: include tropospheric LW aerosol effect

c=0: no tropospheric SW aerosol effect

=1: include tropospheric SW aerosol effect

44

Radiation_surface Module

SW surface albedo: (Cntl parm – IALB)

IALB = 0: vegetation type based climatology scheme (monthly data in 1 degree

horizontal resolution)

IALB = 1: MODIS retrievals based monthly mean climatology

LW surface emissivity: (Cntl parm – IEMS)

IEMS = 0: black-body emissivity (=1.0)

IEMS = 1: vegetation type based climatology in 1 degree horizontal resolution

45

V1- NCEP adaptations of GFDL LW, GFDL (L-H) SW

Model background:

- Limited understanding & modeling knowledge of many physics

processes, low spatial-temporal resolution, tight computer power, …

- Prescribed 3-fixed layers, zonal clouds, prescribed cloud optical

properties, fixed CO2 LW transmission table, omitted many G-H

gases, no aerosol effect, black-body emissivity, prescribed surface,

albedo, 12-hour calling frequency, zonal mean cosine of zenith angle,…

Related development and upgrades:

- Diagnostic, interactive cloud cover scheme

Eta model: developed prognostic cloud microphysics (Zhao, Carr) with

fixed cloud radiative properties

- Optimization of GFDL radiation code

- Approximation of surface downward SW fluxes components

- Seasonal climatology surface albedo with simple cosz adjustment

Evolutions of NCEP Radiation Models

A Quick Review – V1

46

V2- NCEP adaptations of GFDL LW and CHOU SW

Model background:

- Increased model spatial resolution (MRF – T62, T126)

- Improved radiation-physics-dynamics interactions (a basic cloud

model and more frequent radiation computations)

Related development and upgrades:

- Empirical RH table look-up for diagnostic cloud scheme

- Empirical cloud-radiative properties

- Multi-component seasonal climatology surface albedo

- Localized astronomy calculation and corresponding surface flux

diurnal adjustment

- Developed/tested on MRF/GFS with prognostic cloud microphysics

NAM model: developed/tested with a new type of prognostic cloud

microphysics (Ferrier) for the GFDL LW/SW (as in V1 package)

A Quick Review – V2

47

V3- NCEP adaptations of RRTM LW and CHOU SW

Model background:

- Higher model spatial resolution (MRF/GFS –T254)

- Improved model physics (convection, cloud microphysics, simple land

surface model)

Related development and upgrades:

- Cloud microphysics: prognostic cloud condensate, diagnostic cloud

cover

- Cloud radiative properties based on cloud condensates (liquid, ice)

- Improved cloud vertical overlapping approximation for radiative fluxes

calculations

- Global distributed seasonal (monthly) climatology of aerosols and

radiative properties

- NOAH land model

- Tested an optional RAS convection scheme

A Quick Review – V3

48

A Quick Review – V4

V4- NCEP adaptations of RRTM LW and RRTM SW

Model background:

- Increased model spatial resolution (GFS –T382/T574)

- Improved model physics (land model, deep/shallow convection, PBL, …)

Related development and upgrades:

- A globally distributed historical CO2 2-D database from observations,

extrapolated for model forecast

- Unified, spectrally distributed aerosol radiative property model

- Non-Blackbody surface type based LW emissivity

- Optional Ferrier cloud microphysics in GFS

- ARM data based surface albedo-zenith angle dependency

- Developed/tested with a prototype of MODIS retrieval based surface

albedo

- Developed/tested with NASA GOCART aerosol model

- Developed/tested with a fast Neural-Net Emulator for radiation

calculations

49

V5- NCEP adaptations of RRTM-McICA LW and RRTM-McICA SW

Model background:

- Increasing model spatial resolution (SL-GFS –T787/T1148/T15xx/…)

- Advanced model physics (convection, cloud microphysics, PBL,

coupled land/ocean/ice model, …)

Related development and upgrades:- Stochastic, sub-grid cloud approach to cloud-radiation interactions(CFSv2 contains an early version of RRTM-McICA started in 2010)

- Updated solar constant table (Vandendool), and improved cosz calculations- Improved cloud microphysics, snow-optical prop, cloudiness- Improved GOCART prognostic and climatology aerosol models- MODIS based surface albedo- Optimized code, streamlined interfaces, improved portability- Developing advanced BL model, convection schemes, multi-tracer cloud-

microphysics- Developing stochastic Neural-Net Emulator- Developing advanced ocean surface albedo scheme- Developing advanced cloud-radiative processes (decorrelation-length,

inhomogeneity, …)

A Quick Review – V5

50

51

GFDL0 GFDL1 NASA RRTM RRTMG RRTMG-McICA(1989) (2000) (2001) (2002) (2003) (2009)

RT Scheme: (tran-tables) (Kdis/tran) ( --- Corr-kdis --- )No. Bands: 15* 48* 10 16 16 16 Gen Terms: 163* 300* 130 256 140 140

Maj Gases: --- Same for all schemes include O3, H2O, CO2 ---

Min Gases: No CH4,N2O CH4,N2O ( --- CH4,N2O,O2,CO --- )4 CFCs 3 CFCs 4 CFCs

Aerosols: No ( --- Capable of including aerosol effect --- )

Cld OVLP: Random Random 3-domain Random/Max-Ran/otherMax-Ran

Cld Opt: Bulk ( --- CLW/CIW based in polynomial forms --- )

Surface: (-- B-B emis --) ( --- variable emissivity --- )

Spd Factor: Fast Slow Slow Slow Fast Fast(L64) ~1.5 ~5 ~5-8 ~2-5 1 1.2

Note: (fixed co2 tran-tb) prescribed multi-ang 1-ang McICA( B-B sfc emiss ) 3-domain

Comparison of LW Radiation Schemes

52

GFDL0 GFDL1 NASA NCEP/Chou RRTM RRTMG RRTMG-McICA(1988) (2000) (1999) (1995) (2002) (2004) (2009)

RT Scheme: Kdis ESF (--- Kdis/tran ---) (--- Corr–kdis ---) No. Bands: 2 25 11 9 14 14 14 Gen Terms: 12 72 38 18 224 112 112

Maj Gases: ( --- Same for all the schemes, O3,H2O, --- )

Min Gases: ( --- CO2, O2 --- ) ( -- CO2,CH4,N2O,O2 -- )

Aerosols: No ( --- Capable of including aerosol effect --- )

Cld OVLP: (-- Random --) 3-domain Random ( Random/Max-Ran/other ) Max-Ran*

Cld Opt: Bulk ( --- CLW/CIW based in polynomial forms --- )

Surface: Bulk ( --- dir/dif, spectral distributed albedo --- )

Spd Factor:V-Fast V-Slow Slow Fast V-Slow Slow Slow(L64) ~0.6 ~11 ~5 1 ~8 ~4 ~5

Note: no dir/dif prescribed McICAseparations 3-domain

Comparison of SW Radiation Schemes

A model grid column is divided into N sub-columns, each onerepresents either a cloud-free or an overcast column.

For each sub-column, randomly generated numbers, Ri,k (infractions), are assigned to every model vertical layer.

Cloud random overlapping can be easily realized explicitly by:

for k=1, N

if Ri,k > (1 – Ck) Ci,k = 1 (cloudy layer) otherwise Ci,k = 0 (cloud-free layer)

i - sub-column, k- vertical layer*** Note: in ICA, scattering between columns is ignored

How an ICA Sub-Column Clouds Generator

Simulates a Random Overlap Scheme

53

Two Examples of ICA Distributions of

Random Overlapping for Thin Layered CloudsIn

ced

ence

-1In

ced

ence

-2C

olu

mn

clou

ds

Co

lum

n clo

ud

s

54

Two Examples of ICA Distributions of

Random Overlapping for Very Thick CloudC

olu

mn

clou

ds

Co

lum

n clo

ud

sIn

ced

ence

-1In

ced

ence

-2

55

To achieve explicit max-random cloud overlapping, need to track previous layers’ status.

First, generate layered random number, Ri,k, and find the trackingprobability, Pi,k, based on previous layer condition.set Pi,1=Ri,1

for k=2, Nif Ri,k-1 > (1 – Ck-1) Pi,k=Pi,k-1 (use previous layer P)otherwise Pi,k=Ri,k ∙ (1–Ck-1) (P is adjusted by Ck-1)

Then assign layer cloudiness similar in the random case, but by replacing R with P.for k=1, Nif Pi,k > (1 – Ck) Ci,k = 1 (cloudy layer) otherwise Ci,k = 0 (cloud-free layer)

How an ICA Sub-Column Clouds Generator

Simulates a Maximum-Random Overlapping scheme

56

Two Examples of ICA Distributions of

Max-Random Overlapping for Thin Layered Cloud

Co

lum

n clo

ud

sC

olu

mn

clou

ds

Ince

den

ce-1

Ince

den

ce-2

57

General expression of 1-D radiation flux calculation:

where Fk are spectral corresponding fluxes, and thetotal number, Κ, depends on different RT schemes

Independent column approximation (ICA):

where N is the number of total sub-columns ineach model grid

That leads to a double summation:

that is too expensive for most applications!

Monte-Carlo independent column approximation (McICA):

McICA sub-grid cloud approximation

In a correlated-k distribution (CKD) approach, if the number of quadrature points (g-points) are sufficient large and evenly treated, then one may apply the McICA to reduce computation time.

≈

where k is the number of randomly generated sub-columns

58

Two Examples of ICA Distributions of

Max-Random Overlapping for Very Thick CloudC

olu

mn

clou

ds

Co

lum

n clo

ud

sIn

ced

ence

-1In

ced

ence

-2

59