three-dimensional radiative transfer in clouds

Three-Dimensional Radiative Transfer in Clouds

Warren WiscombeNASA Goddard

3D Rad Transf in Clouds 2

See new book, edited by Marshak and Davis, published late 2004

mainly shortwave (sunlight)

dedicated to Gerry Pomraning and Georgii Titov


A motivation: Clouds cause 2–5 C range in predicted global average temperature increase for 2xCO2

1979 Report on CO2 and Climate, Woods Hole:

“... the equilibrium surface global warming due to 2xCO2 will be in the range 1.5 to 4.5 C”.

2001 IPCC: Essentially the same as above.

temperature range is pretty uniformly filled!


99% of atmospheric radiative transfer approximate{d,s} 3D clouds as 1D slabs

Constraints were: slow computers, and inability to (a) specify cloud in 3D, (b) test models (cloud or radiation)


There’s an approximately 1D world overhead on a mountaintop on a clear day


But the real world of cloud radiation looks nothing like the tame, peaceful 1D world


What are the unique aspects of Earth atmospheric radiative transfer?

Clouds & vegetation — extreme 3D, big scale range

Strong, dense absorption lines

Forward-peaked scattering phase function

Surface BRDF importantspecular reflection, hot spot!

Polarization — Rayleigh, aerosol, glint

Beams from inside, outside

Rapid variation — turbulent


Real cloud radiation looks turbulent, with occasional excursions above the 1D envelope


and it still looks intermittent for a 3–hr subset of total flux!


1D radiative transfer history in the atmospheric sciences

Chandrasekhar (1950):– polarized radiative transfer

Sekera & students (1950s) inspired by Chandrasekhar to study Rayleigh scattering atmosphere w. aerosol– polarized r.t. survived only in microwave until POLDER

reinvigorated field

van de Hulst, Twomey (1960s): adding-doubling

Dave and others: spherical harmonics w. polarization– 1968 code still survives in UV project at Goddard!

Dave: Mie scattering


Peaks of 1D theory were reached withGrant-Hunt version of adding-doubling (1969)

Stamnes et al. discrete ordinates (DISORT, 1988)

k-distributions (Lacis/Hansen and others, 1980s)

Atmospheric radiative transfer field focused on the wavelength rather than the x-y spatial dimension. Lab spectroscopy measurements led to an hubris that models were correct without testing them in the open air. Thus the field became largely an indoor activity...


Thus, when theoreticians emerged into the open air, they were puzzled...

“What is this strange alien object?”


I started in 3D and 1D-spherical r.t., devolved to 1D-slab...

In 1970, the 3D world I entered was dominated by– Monte Carlo methods– discretize everything– spectral-expand some things, discretize others– diffusion, Eddington methods & variants

First two were severely computer-constrained– random number generators were mediocre– linear algebra algorithms for large matrices were poor

(this was even before LINPACK!)

Atmospheric science inherited these methods but eventually improved on them considerably


then I rode the 1D to 3D transition in cloud radiation, mainly funded by ARM

In radiative transfer methodology, the transition was somewhat predictable:

– more photons in Monte Carlo (finally, enough!)

– various stews of discrete vs. spectral for both angle and space dimensions, with some computationally hopeless, now-dead methods

– avoidance of brute force methods because matrices can become so large (a small problem of 100x100x20 w. 80 discrete angles could lead to matrices of 16Mx16M)


The full range of 3D radiative transfer options are now used in cloud studiesDiffusion and other approximations

Analytical-numerical (quintessence: SHDOM, 1998)

Monte Carlo

Cases:- step cloud- 2D field from ARM radar- 3D field derived from Landsat- Sc and shallow Cu, Large Eddy model


Emerging subject, cloud micro-3D radiative transfer, challenges “elementary-volume” assumption embodied in phase function p

Monochromatic Radiative Transfer Equation


What assumptions are being challenged?

According to high-time-resolution aircraft data, above a critical radius of ~14 m:

(1) NumberOfDrops(radius r) = c(r) x VolumeD(r)

where 0 < D(r) < 1

(2) the larger drops are, the more they cluster

NumberOfDrops(radius r) = c x Volume


This is a numerical simulation of drop clustering based on aircraft data


But if we give up “elementary volume”, what can we do, radiative transfer-wise?First-principles Monte Carlo: each photon interacts with actual drops at specific spatial locations, rather than with a fictitious elementary volume.

(At the outermost limit of what we can do computationally)

Fractional differential equations: in the very simplest case of pure transmission through a fractal-clustered drop distribution, must solve:

dI(x) =−σ small I (x) dx−σ largeγlarge(x) I (x) (dx)D

0 < D <1, γlarge(x) =0 no large drop at x1 large drop at x

⎧⎨⎩


Many details of 3D radiative transfer will be covered in the following talks, so because the 1D to 3D transition in cloud structure modeling was more unexpected, I will focus instead on:

(1) cloud structure — theoreti-empirical, and instruments for measuring it

(2) tentative steps toward incorporating 3D into routine activities of our field


Clouds are highly variable in x, y, z & t“Immense chaos amid immense order” (turbulence produces chaos, reigned in by overall physical controls that create & sustain large cloud systems)

Clouds are the tip of the water vapor iceberg! – Typically <3% of water vapor in column condenses.

Clouds represent only the tail of the relative humidity probability distribution; this already ensures high variability.


Real regularity in clouds happens when waves overpower turbulence, and is rare


This deep tropical convection from Shuttle is more typical of the “immense chaos”


Coast of Holland shows how surface variability adds to cloud variability

These cloud waves would cause mild bump in power spectrum

Landsat image


Nevertheless, following Occam’s Razor, clouds were modeled as cubes, 1975-90


the ultimate Euclidean cloud...


Lovejoy (1982) showed that clouds have a fractal not Euclidean character

if Euclidean:

area perim 2

the data show:

area perim 1.5


What other evidence of fractality was found?

Cloud liquid water power spectra from field campaigns:

- scaling behavior over a range 10 m to ~50 km!

- no preferred scale


How was the idea of modeling clouds as fractals received?

Euclidean cloud papers survived into the early 1990s

Fractal models not taken seriously until extended:

– beyond the monofractals in Mandelbrot’s book

– beyond cloud geometry, to cloud liquid water

Two attractive features finally won the day: – simpler than Euclidean models (fewer

parameters) – better connected to the underlying scaling

physics exemplified in Kolmogorov approach to turbulence


Nowadays we routinely model statistical clouds using empirical information


Scaling analysis for Landsat cloud radiances revealed a scale break at ~0.5 km...

not seen in cloud optical depth.


3D radiative smoothing has three regimes

Analysis of the Landsat scale break led to the basic ideas underlying multiple scattering lidar


Another way to specify a cloud is to use a “cloud-resolving model”

Dynamical and dynamical/microphysical cloud models were mainly for thunderstorms.

Models for more horizontally extensive cloud forms remained primitive through the 1980s, but have matured since then and are now routinely used to provide input to 3D radiative transfer models.

Most 3D radiation modelers use both fractal and cloud-resolving models for specifying clouds, according to the situation.


Ron Welch, Bill Hall and I pioneered radiation-cloud physics collaboration

Hall/Clark model:- 2D thunderstorm!- explicit drop size

categories

We horizontally averaged Hall’s results to use in a 1D radiation model — ugh...


I3RC (Intercomparison of 3D Radiation Codes) uses cloud-resolving model input for some cases

http://i3rc.gsfc.nasa.gov/


What simple ways have been put forward to deal with or account for 3D variability in climate models?


1D error has two very different natures depending on pixel size

Independent Column Plane-Parallel


Cubic clouds gave an extreme view of the perils of ignoring 3D

cloudy cubes have optical depth 50


The simplest and oldest method for dealing with 3D is “cloud fraction”

Cloud fraction (“oktas”) has sentimental and historical value in meteorology.

Cloud fraction Ac is used as a linear weight:I =Ac I cloudy

(1D) + (1−Ac) I clear(1D)


So what’s wrong with cloud fraction?

Stephens (1988), showed that

Ac (radiative) ≠Ac(true)(equality only when no correlations between fluctuations in the radiation and cloud fields)

This inequality makes it impossible to test retrievals of Ac(radiative) against an alternative, non-radiative definition. (done still)

Sometimes Ac(radiative) < 0 to get the radiation right!


The next band-aid beyond cloud fraction was cloud overlap

random, maximum, and max-random were all tried...but none seem to work well


The first decent 1D approximation to 3D was the Independent Column Approximation (ICA)

Requires the probability distribution of optical depth

pdf()in the cloudy part of the scene, instead of just the mean optical depth.

Since the low- part of pdf() is very hard to get, in practice we still fall back on cloud fraction...


Application to Global Climate Models

100-500 km

Approximations to incorporate 3D effects into a 1D framework:-Cahalan, -Barker/Oreopoulis, -Cairns, -Pincus/Barker.


Serious limitation of slab model is partitioning of space into two disjoint half-spaces, one containing Sun, other the Earth

so from any point, can view reflected or transmitted light, not both

Davis has proposed a spherical cloud model more in accord with everyday experience


Davis uses illuminated and shaded sides of each cloud to retrieve “optical diameter”

eff =2χ

1− g

Robs

Tobs

generalization of familiar 2-stream theory with redefintion of R, T,


How do 3D effects impact typical 1D retrievals of cloud properties?


1D retrieval of cloud optical depth at increasingly oblique angles shows 3D effect


Remote retrieval of cloud optical depth using 1D algorithms incurs considerable bias

Each dot corresponds to a 50x50 km area with averaged separately over all illuminated vs all shaded pixels


Cahalan inhomogeneity parameter is rough measure of 3D bias in optical depth

=exp(lnτ )

τ

where is cloudoptical depth


What instruments do we currently use to probe and characterize clouds?Major categories are passive & active (probes)

We must extrapolate 1D or 2D data into 4D:

– ground-based probes: t-z

– aircraft-based probes: mix of t–z and x–z

– space-based probes: x-z

– all are dimensionally challenged!


Current aircraft cloud sampling probes

PMS 2D-P optical array probe

King liquid water probe

Rosemount total temperature probe

PMS FSSP-100 (Forward Scattering Spectrometer Probe)


Aircraft cloud probes sample cm3 volumesRemote sensing instruments sample much bigger volumes:

– > m3 for radars– approaching km3 for satellites

Other problems:– aircraft fly horizontally ; cloud radars point vertically– clouds evolve while aircraft fly through them

To match aircraft scale with radar and/or satellite scale (both time and space!), aircraft would need to perform “long-range scans”!


ARM Oklahoma:A “Field of Beams”


ARM let theoreticians do things like...

help lead field programs (“IOPs”)

suggest new instruments

and take observations!


Lidar can detect cloud base but usually not cloud top (except for cirrus)

Micropulse lidar (Spinhirne) inside trailer at ARM Oklahoma site


We prefer to remote-sense in the microwave spectrum because clouds are relatively transparent there...

and also because

(a) gases do not dominate absorption;

(b) scattering, except by ice, is relatively negligible.


Passive microwave radiometers can retrieve cloud liquid water path directly

Microwaves satisfy a simple radiative transfer equation with only thermal emission, but:

– ice is invisible– clouds of low optical depth are invisible– rte-based retrieval has been less successful than

empirical


mm radar can see through most clouds but is confused by drizzle and insects

MilliMeter Cloud Radar at ARM Oklahoma site (35 GHz ~ 1 cm wavelength)

2D time-height slice but not whole 4-D cloud field


In sum, active cloud-probing instruments struggle to characterize a single 4-D cloud

Lidars and radars are “dimensionally challenged”

Lidars can’t see deeply into a cloud

Space lidar beams are ~100 m wide at cloud level; creates multiple scattering artifacts

Passive microwaves can’t see ice or thin clouds

Cloud radars are sensitive to drizzle, insects, ...


Only by combining different kinds of instru-ments can we hope to characterize clouds

IR thermometer atop microwave radiometer

Whole Sky Imager

Experimental Nephelo; rotates to scan sky


Some new instruments and methods to capitalize on advances in 3D radiative transfer understanding


Now: Two-channel 3D cloud optical depth retrieval uses these two instruments

Cimel (French); designed for aerosol but now has added a “cloud mode”; over 100 deployed in global network

Two-channel NFOV (Narrow Field of View)


Now: THOR lidar shoots lidar straight down then measures time-resolved scattered photons in bulls-eye rings around central spot

THOR was based on advances in Green’s function theory and radiative smoothing in 3D clouds

THOR retrieves geometric thickness of op. thick clouds


Now: IceSat lidar getting Equator to pole cloud topography & some internal structure

(and apparently IceSat is showing cloud fraction ~ 70%


European 4-D Clouds Project: 2–mm cloud radar and 22–channel microwave radiometer can scan clouds fast, simultaneously


Future: Understand EOS 1D cloud property retrievals from a 3D perspective

1D cloud optical depth from two solar channels (MODIS)


Future: In situ lidar senses extinction in expanding spheres around aircraft

One of new class of instruments designed using extensive Monte Carlo simulations

curve steepenswhen light bubblehits edge of cloud


Future: CloudSat radar will see cloud drops (not just rain drops like TRMM)

with complementary measurements from other cars on “the A-train”:

- CALIPSO: lidar

- PARASOL: polarized radiances (French)

- Aqua, Aura: last great multi-instrument Eos platforms

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Future: Cloud tomography was pioneered by cloud physicist Warner in the 1980s


Warner’s 1986 tomography from two surface microwave radiometers


In summary, 3D cloud radiative transfer exploded in the 1990s and has many applicationsPublicly available 3D models like SHDOM and Pincus or

Mayer Monte Carlo build on a solid foundation of 1D models like DISORT, SBDART, CHARTS, etc.

Can simulate realistic cloud structures using fractals, wavelets, and statistical methods from turbulence

Quantum leaps in dynamical/microphysical cloud models

A new breed of cloud experiments: SUCCESS, SHEBA, ARM, 4D Clouds,...

New instrumental concepts exploiting the time dimension and multiple scattering (Davis WAIL, Cahalan THOR lidars)

Instruments and measurement strategies for field campaigns simulated in advance with 3D radiation models

Discussion time!

three-dimensional radiative transfer in clouds

Documents

d envelope3d rad transf

d world3d rad transf

d clouds

d transition

d theory

d slabsconstraints

radiation3d rad transf

considerably3d rad transf