Microphysics’ evolution,

Past, ongoing and foreseen

-----

Part a: principles, structure, some details and past problems’ solutions

J.-F. Geleyn, R. Brožková

A1WD, Ljubljana, Slovenia, 13-15/06/2012

Principles The ALARO microphysical package treats the time-

evolution of prognostically handled hydrometeors. It delivers precipitation fluxes and tendencies (or equivalently pseudo-fluxes) for local (Eulerian view) phase changes.

However the condensation/evaporation processes within clouds are supposed to have happened upstream (an unavoidable choice in 3MT where condensation/evaporation rates are the sums of the ones of separated processes) and thus cannot interact with all the rest, built then around the treatment of the sedimentation process of falling species.

The separation between snow and graupel (thermodynamically transparent anyhow) is currently treated diagnostically, but a prognostic version is under development.

Structure A quite general, quasi stand-alone, routine (named

APLMPHYS) handles:– (1) the sedimentation of the three kinds of precipitating

species; – (2) the distinction for each layer between four sub-grid areas

[cloudy area seeded from above by precipitations originating from cloud fractions higher-up, non-seeded cloudy area, seeded clear-air area, non-seeded clear-air area];

– (3) the redistribution of fluxes’ intensities and areas’ extensions from each layer to the one just below, according to geometrical options (random-, maximum-random- and mixed-type for the overlap).

APLMPHYS calls 3 routines where the actual physical processes are calculated (with as many grouped options as one wishes)– ACACON for auto-conversion-type processes (called once per

layer);– ACCOLL for collection-type processes (called twice per layer); – ACEVMEL for phase changes for falling hydrometeors (called

thrice per layer, but one time only for the melting/freezing).

Structure (bis)

Structure (ter) The apparent complexity of APLMPHYS is

sometimes considered as a handicap. But this targetted choice allows a lot of flexibility and efficiency:– One may very simply go from one type of auto-

conversion (or collection, or evaporation, …) to another formulation; the same applies for the parametric formulae of the three probability functions P1/2/3(Z) of our ‘statistical sedimentation algorithm’; each time the alternatives arec compact and localised together.

– The geometrical choices (how the grid-mesh is subdivided) and the geometrical consequences (see next viewgraphs) are handled easily in a vertical loop (respectively for each layer and at their interfaces). Explanation in the ‘b’ part of the lecture.

Geometry of clouds and rain

Random overlap of parts separated by clear air, maximum overlap of adjacent parts (schematic view)

Processes (1) The partition between water and ice phases at the

time of their creation/destruction by cloud condensates’ evolution follows a statistical partition law based only on temperature T (for the case it is smaller than the treble point temperature Tt):

Tx is the temperature of the maximum distance between the ice and liquid water saturation pressure curves.

fi is 1 in ALARO but may be tuned to any other value.

i is of course the resulting proportion of the created/destroyed ice phase

2

2

))((2

)),min((exp1)(

xti

tti TTf

TTTT

Processes (2) The direct auto-conversion between either cloud

liquid droplets and rain or cloud ice crystals and snow follows Lopez (2002), but with the threshold curve of Kessler (1969) replaced by the continuous formula of Sundquist (1978), at equal integral.

In ALARO: l=500s; qlcr=3.E-04; ct

*=0.0231K-1; i0=500s;

(qicr)min=8.E-07; (qi

cr)max=5.E-05.

The fip function (not to be confused with fi) will be used for all similar T dependencies (while there are 5 independent values in Lopez, within +/-12% of ct

*).

)1(2

// )/(4

/

/_

/cr

ilil qq

il

ilconvauto

il eq

dt

dq

))](exp(,1min[)( *ttip TTcTf

)(/)( 0 TfT ipii )())()(()()( minmaxmin TfqqqTq ip

cri

cri

cri

cri

Processes (3) The Wegener-Bergeron-Findeisen process is

parameterised in ALARO as one auto-conversion process between cloud liquid droplets and graupel (one ‘jumps over’ the brief ice cristal phase, owing to the strong intensity of the process). The formulation follows Van der Hage (1995) and the latter’s analysis made by Luc Gerard at the beginning of ALARO-0.

For ALARO: FaWBF=1600; Fb

WBF=4. It is important to note the maximum efficiency of the

process for equal ql and qi values as well as its quasi-saturated intensity then (Fa

WBF has a very high value).

)1()²(

. ))(..]/([).((4

2 TqqFqq

il

il

l

laWBFWBF

lcri

crl

bWBFil

eqq

qqqF

dt

dq

Processes (4) The various collection processes all scale with

respect to the one of cloud liquid water by rain (fluxes R, G and S for rain, graupel and snow respectively).

For ALARO: CrE=0.067; Cs

E=0.274 (both in SI units). On the basis of Lopez (2002) the ratio of the two

coefficients takes a lot of effects into account: fall-speeds, numbers of small droplets (respectively crystals), slopes of spectral laws, temperature dependencies, collection efficiencies and a geometrical factor.

NB: because of a differing way of scaling, the fluxes’ exponent is implicitly 6/7 (and not 4/5) in Lopez.

isE

coll

S

iipl

sE

coll

S

l

ipirE

coll

G

il

rE

coll

G

l

ipirE

coll

R

il

rE

coll

R

l

qGSSCdt

dqTfqGSSC

dt

dq

TfqGSGCdt

dqqGSGC

dt

dq

TfqRCdt

dqqRC

dt

dq

.)(.)(/.)(.

)(..)(..)(.

)(.....

5/15/1

5/15/1

5/45/4

Processes (5) The sedimentation is treated following the so-called

‘PDF-based’ method (instead of using classical advective algorithms). One computes for each layer 3 probabilities:– P1, for a falling specie present in the layer at the beginning of

the time step to go through the bottom before the end;– P2, for a falling specie to fully cross the layer during the time

step;– P3, for a falling specie created (or -mathematically indifferently-

depleted) during the time step within the layer to leave it at the bottom during the same spell of time.

We know 2 consistent ways of doing such a computation (fixed mean fall-speeds and Lagrangian displacement / variable mean fall-speeds and dispersed displacement). ALARO uses the second method which writes:

))(1/())()(()(

/))(2/1()(

/))(1()(

)())./((

3322

33

01

00

ZPZPZEZP

ZZEZP

ZZPZP

eZPtwzP Z E2/3 second and third exponential integrals (approximated); Z inverse of the Courant number.

Processes (6) The three basic fall-speeds scale with respect to the

one of rain water.

For ALARO: r=13.4; s=3.4 (both in SI units). On the basis of Lopez (2002) the ratio of the two

coefficients takes several effects into account: numbers of small droplets (resp. crystals), slopes of spectral laws, temperature dependencies.

NB: because of a differing way of scaling, the fluxes’ exponent is implicitly 1/7 (and not 1/6) in Lopez. The air density exponent is also differing. Nevertheless, for standard atmospheric conditions, both curves of resulting fall-speeds are very close to each other.

6/1

4

6/1

4

6/1

4

)(.

;

GSTfw

GSw

Rw

ipss

rgrr

Processes (7) The evaporation of falling species is treated in

ALARO by a strict application of the Kessler (1969) method around the single Marshall-Palmer (1948) formula, but with an in-depth revisit of the basic data (this revisit also indirectly explains some of the above-mentioned small differences with Lopez (2002)).

The basic result is obtained for the rain evaporation. It is then applied ‘as is’ for the other species. The idea here is that a change (essentially) of fall speed has two opposite consequences: more turbulence favours evaporation in case of quicker fall but there is less time to let this act (and vice-versa for a slower fall).

For ALARO: Fevap=4.8E+06 (in SI units).

One uses qw (and not qsat) as target because of the induced cooling on the air temperature. p for pressure.

)()/1()(2

1

)/1()(2

1

)/1( vwevap qqFpd

dG

GSpd

dS

GSpd

Rd

Processes (8) The melting of falling ice-type species is treated in

parallel to the one of evaporation (including the identification between all kind of species). The computations concern this time the proportion of the ice phase rather than the absolute fluxes and the related constants for the ratio of the synthetic coefficients are thus the molecular diffusivities of respectively heat and water vapour, the heat capacity of air and the latent heat of fusion.

ms and mg are the snow and graupel proportions of the total precipitation flux (mi=ms+mg).

For ALARO: Fmelt=2.4E+04 (in SI units).

GSTTFpd

md

m

m

pd

md

m

mtmelt

g

g

is

s

i /)()/1()/1(

Processes (9) The (re-)freezing of rain is treated symmetrically to

the one of snow/graupel metling. But the process is arbitrarily assumed (from a rough litterature survey) to be eighty times less efficient. The resulting specie is graupel.

For ALARO: Ffreez=3.0E+02 (in SI units).

RTTFpd

mdtfreez

i /)()/1(

Past algorithmic problems (1/3)

Since APLMPHYS, ACACON, ACCOLL and ACEVMEL took their stable shape, back in 2007, we discovered (and cured) three important problems:– (A) With small or big Courant number values the

PDF-based sedimentation computations became detrimentally unprecise (no example shown)

– We introduced two limitations at 0.04 (!) and 1.E+10.

– (B)– (C)

Past algorithmic problems (2/3)

Since APLMPHYS, ACACON, ACCOLL and ACEVMEL took their stable shape, back in 2007, we discovered (and cured) three important problems:– (A)– (B) Despite the care taken to exclude any prognostic

consideration from such computations, two partly extrapolating algorithms (for the computation of the graupel proportion’s influence on fall speeds and collection efficiencies & for the anticipated precipitation flux in the middle of the current layer) entered in resonance to create a 4. wave in the ice water budget (see diagrams in the next viewgraph).

– The cure: applying a recursive filter (depth 90. hPa) in the first case and extrapolating from full level to full level in the second case (ignoring the ‘budget flux’).

– (C)

The 4. syndrome & its correction

Spoiled budget Corrective step

Of course the correction has a global impact as well (~20%). On the other hand, the formulae at stake are quite empirical (process 4

&6)

Past algorithmic problems (3/3) Since APLMPHYS, ACACON, ACCOLL and

ACEVMEL took their stable shape, back in 2007, we discovered (and cured) three important problems:– (A)– (B)– (C) It was found that there existed a quite devilish

feed-back in the handling of the diagnostic graupel sedimentation.The latter was supposed to happen with the same probabilities P1/2/3 than for rain, even for very different amounts. But the induced strong sedimentation reduced the effective graupel amounts drastically, increasing thus the contradiction.

– The cure is a separate computation of the graupel’s probability functions. The total of snow and graupel is used as input for both ‘snow’ and ‘rain’ formulae, the latter giving the graupel’s result.

Signature of the graupel’s runaway

The impact of what could be expected as a minor correction is quite spectacular, at least on the mass field. Sedimentation is a key issue!

Change in Phi-biases The bug ‘stretched’ the atmosphere

before

after

Conclusions The ‘APLMPHYS’ microphysical code was developed in order to

be economical and nevertheless compatible with several alternative scientific solutions at each of the following levels:– Sedimentation;– Number of ice-phase falling species;– Geometry of the clouds and ‘seeded’ grid-box fractions;– Basic processes (auto-conversion type, collection type, water phase

changes during fall). Part of its structure is still influenced by the original ‘3MT drive’,

but this may be easily corrected at the occasion of future steps. The current nominal solution in ALARO is of intermediate

complexity, sometimes directly inspired by the work of Lopez (2002), sometimes not.

In order to be able to sustain long time-steps, continuity and compactness have been privileged when choosing the analytical representation (9 generic sets of equations -with various declinations- but only 15 tuning constants!).

On three occasions we faced diagnosed delicate algorithmic behaviours, but each time an appropriate solution could be found.