snow micro-structure to micro-wave...

Microsnow August 2014

Snow micro-structure to

micro-wave modelling

G. Picard

L. Brucker, F. Dupont, A. Roy, N. ChampollionL. Arnaud, M. Fily,

A. Royer, A. Langlois, H. Löwe, B. Bidegaray-Fesquet

Snow micro-structure is complex- granular/porous medium, anisotropy- wide distribution of characteristic lengths (=”grain size”)- sometime liquid water- …Only basic metrics (Dmax, optical grain size) are easily measurable in the field (excl. X-ray tomo) or predicted by snowpack models.

The snowpack is complex- plane parallel layers with rough interfaces (air-snow, snow-soil, internal layering) to 3D structure (e.g. sastrugi)- soil (or ice) is “part” of snowpack: incl. water, ice, mineral scatterers- vegetation, …

The electromagnetic problem is complex - electromagnetically dense medium (fractional volume f >0 and <1)- “grain size” ~ wavelength- ice has high permittivityConsequences: internal field is significant / multiple scattering / near field / resonance or interferences

No perfect multi-purpose model

Context

What do “we” want to do ?

Ultimate goal: retrieve snowpack properties of interest (SWE, temperature, density, stratification, soil state, …). In general, these properties are well-defined and easy to measure in the field.

Intermediate step: retrieve/estimate other snowpack properties (grain size, …) to regularize/initialize the retrieval.

1. We need a “good” EM model

EM model

Snowpack properties:- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt)- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Brightness temperaturesat several frequencies (max 10)and polarisations (2 to 4)

Backsacttering coefficientat several frequencies (max 2)and polarisations (2 to 16)

Context

The retrieval is under-determined problem

2. We need inverse method and prior information

EM modelBrightness temperatureObservations at several frequencies and polarisations

residual

Inverse method

- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt)- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Weak constrain on grain size and micro-structure properties as they are used by and estimated from the EM model (self-consistent variable): e.g. Globsnow (SWE retrieval, effective snowpack grain size estimated)

→ “we” only need an EM model with a good frequency-dependence (e.g. C. Mätzler, L. Tsang)

Context

adaptation

2alter. Prior information comes from a snowpack model


residual

Inverse method

- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt) and information on the location of liquid water- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Snowpackevolution

model

Strong constrain on grain size and micro-structure properties as the snowpack model and the EM model have to use the same variables

→ “we” need well defined snow grain size and a “good” EM model

Context

Objective:

Validate EM models with accurate/well defined measurements of grain size

Outline of this talk:

1 – Validation of DMRT-ML using SSA measurements

2 – The micro-structure in EM models

Limit this talk: to “fast models”, i.e. scattering and absorption coefficients have an analytical formulation. Exclude e.g. numerical exact solutions of Maxwell equations

3 - Perspectives

Context

The characteristics of DMRT-ML are presented by L. Brucker this afternoon

Successive steps of the validation performed at LGGE:

1- Brucker at al. 2011: DMRT-ML development and first application to Dome C with SSA derived from NIR photography

2- Picard et al. 2014: second application at Dome C with SSA measured with POSSSUM

3- Roy et al. 2013: soil is implemented in DMRT-ML , application to seasonal snow

4- Dupont et al. 2014: DMRT-ML applied to bubbly-ice

Validation of DMRT-ML with SSA measurements

L. Arnaud and H. Brunjail: trained by M. SchneebeliNIR photography at Dome C in December 20061 snowpit: 3x 1m

First validation at Dome C, Antarctica - Brucker et al. 2011

NIR refectance SSA Optical radius:→ → ropt=3

ρSSA

Measurements of density, every 2-3 cm

Another density profile 0 – 20m from a previous campaign

Measurements of temperature profile every 1h (40 probes from 0 to 20m)

First validation at Dome C - Brucker et al. 2011

Direct run: optical radius is used as input of the monodisperse none-sticky QCA-CP DMRT (Shih et al. 1997)

V-polarisation

DMRT-ML

AMSR-E

DMRT-ML modelropt(z)ρ(z)T(z,t)

TB(37V)(t)

TB(19V)(t)

• Over-estimation of the emissivity

• Over-estimation of the penetration depth

Under-estimation of the grain size



DMRT-ML model

ropt(z)ρ(z)T(z,t)

TB(37V)(t)

TB(19V)(t)

Adaptation was required: Optimise 2 parameters Φ and ropt(z>3m)

rDMRT=Φ ropt

Optimisation

19 GHz

37 GHz


Partial validation:

4 independent variables are well predicted with only 2 optimised parameters:emissivity and penetration depth at two frequencies.

What is really validated here: - absorption coefficient and density profile. κe=κs+κa ω=κs/(κs+κa)- RT solutionNote: It was not possible to get as good results with MEMLS

What is not validated here:- the absolute value of the scattering coefficient predicted by DMRT theory (because of Φ)

Important result:

Possible error sources: Calibration of NIR photography, satellite footprint, … but 2.8 is a large value

rDMRT=2.8 ropt

Up to ~ 8 m deep, ~2-3 h ~20 min for 8 mincluding snow core logging

Second validation at Dome C - Picard et al. 2014Better SSA profiles

Drill a hole (~100 mm in diameter) POSSSUM (Arnaud et al. 2011)

Second validation at Dome C - Picard et al. 2014Density profile from the snow core extracted for POSSSUM / SSA measurements

5 cm resolution

Second validation at Dome C - Picard et al. 2014Ground-based radiometers at 19 and 37 GHz in two points

2012-13 at Dome C with A. Royer, U. Sherbrooke

2 points near Concordia chosen for their contrasted TB

Second validation at Dome C - Picard et al. 2014

8 m profiles

Snowpit 1 and 2



TB(37V)(t)

TB(19V)(t)

Optimise 1 parameter: Φ(one for all freq, pola, angle, snowpits)

rDMRT=Φ ropt

V-pol

H-pol

Color : snowpit


Stronger validation:

8 independent variables are well predicted with only 1 optimised parameter

What is really validated here:

- grain size and density profiles (note: difference between snowpits is explain by the density)- frequency dependence- polarization dependence

- Φ is a micro-structure parameter (ie indep of EM parameters) or potential deficiency of DMRT theory

From 2.8 to 2.3, this is a 20 % difference (SSA accuracy?)

rDMRT=2.3 ropt

DMRT “ice” validation - Dupont et al. 2014Bubbly ice

Barnes ice cap in Baffin Island, 2011A. Langlois, U. Sherbooke

Adélie Land 2012 – 13with A. Royer

DMRT “ice” validation - Dupont et al. 2014

Adélie Land results : bare ice

37 GHz 19 GHz

11 GHz

Pure ice

Bubbly ice

Mesured densityOptimize bubble size (0.68 mm)Measured bubble size (0.6 mm)

rDMRT=1 rbubble


Barnes ice cap results : 80-cm snow over bare ice

37 GHz 19 GHz

Both density and bubble size are optimized. Again optimised value ~ real bubble size (i.e. Φ=1)

DMRT is for spherical scatterers and it works without scaling when scatterers are truely spherical!

It can be excluded that Φ was necessary to compensate potential DMRT errors

Validation for seasonal snow - Roy et al. 2013

How Φ is variable among snow types ?

A. Roy (U. Sherbrooke) implemented soil refection in DMRT-ML.Application to 20 snowpits in 3 locations in Canada where SSA was measured with IRIS.One Φ optimised for all the sites at 37 GHz, V-pol. Soil parameters optimized using 19 GHz,V/H polarisation

Φ=3.3

Conclusion: Empirical micro-structure parameter

ΦPicard et al. 2014 2.3Brucker et al. 2.8Roy et al. 2013 3.3Dupont et al. 2014 3.5Others ?

Are they really different ?

Potentiel bais :- SSA measurements (different methods were used)- Soil parameters (large uncertainty!)- Radiometer measurements (second order)

Future :1- More accurate measurements are required. Uncertainty analysis.2- Scaling grain size Φ is not satisfactory. What the theory says ?

TODO: Other 'almost equivalent Φ' could be deduced from several recent studies with HUT, radiometer and SSA measurements (e.g. CoReH2O), fitting with DMRT scattering

Micro-structure in the models

The representation of snow micro-structure in the snow emission models is the key.

Micro-structure in three snow emission models

DMRT*Shih et al. 1997

DISORTJin, 1994

IBA(Wahl=12)

6-fux

Empirical KsSemi-empirical Ka

2-fux

HUTDMRT-ML (and others) MEMLS

Maximum extent(aka traditional grain size)

Dmax

Autocorrelation functionA(x)

Sphere radius (distribution), stickiness: a, τ

κs,κa,P(Θ) κs,κa,P(Θ)

e.g. exponentialpex correlation length

W98(Wahl<12)

Empirical relationship between 'micro-structure' and scatt/abso/ext coefficients

Derived from Maxwell Eqs + many approx considering a collection of scatterers

* DMRT-ML uses qca-cp, small spherical scatterers, short range. Other options: qca, long range, and qca-Mie, spheroids, ..


Poly-disperse grain size distribution should provide a better description of the snow

Motivation: Scattering cross section is driven by radius^3 in the Rayleigh approximation (small scatterers w/r wavelength).

Bigger grains have a MUCH larger contribution to scattering.

Good news: equivalent grain (function of the density) (Jin, 1994 with DMRT QCA)

Assumption here: Rayleigh distribution sharply decreasing upper tail = convergence

Factor x 1.5 at 300 kg/m3

Highly dependent on the shape of the distribution / upper tail !


Phenomenological approach of scattering

Sparse medium, f<< 1 % (e.g. vegetation): For the calculation of Ks and Ka, scatterers are supposed independent

Incident field an internal field→The internal field absorption→The internal field radiate scattered wave→ →

Important : Other scatterers are very far and randomly positioned. Total scattered energy is linear with the number density of scatterers (no position dependent)

Incident electric fieldScat

tered electric fi

eld

Internal field


Phenomenological approach

dense medium, f~30 % (e.g. snow)

1

Incident electric field

Scattered

electric fi

eld by 1

2

The field “received” by scatterer 2, is the sum of the incident field and the field scattered by scatterer 2. Because 2 is close to 1, the scattered field is intense and the phase is not random →coherent effect. The scattering diagram of 1+2 is not the sum of the scattering diagrams. In addition: near field effect.The internal field is different from the independent case which affects the absorption.


In practice: the scattering coefficient is reduced w/r to 'independent scatterers'. The absorption is slightly larger. The extinction is either smaller or larger than 'independent scatterers' depending on the scattering/absorption domination.

DMRT (constant radius)qca-cp none-sticky

IBA (constant radius)

Indep.

DMRT

Abs

Scatt

Indep.

IBA

Scatt

Abs


The precise relative position of scatterers with respect to each others is very important in dense media.

fractional volume f = 35%

Both media have ~ the same density and SSA but different electromagnetic behaviour

Freely positioned sphere(100% random position)

Hard sphere(100% random position + non-overlapping)


Hard sphere is not the only option: stickiness

f = 20%

Hard sphere (2D) + stickiness

More voids

Cluster eq. big scatterer⬇

Increased scattering


f = 20%

++ stickiness + stickiness

Increase stickiness (decrease τ → 0.1) increase clustering → → more scattering at constant SSA and density

Terrible consequence: SSA+density measurements or predictions by snowpack models is insufficient to characterize snow for electromagnetic calculations


Large infuence of the stickiness in DMRT on the scattering coefficient(absorption is not marginally affected)

x5 factor on Ks for τ=0.2

(could go down to τ=0.09, but not with DMRT-ML)

Coupling between stickiness and density Impact of stickiness depends on density→(very dense no alternative to stick to neighbours)→

None-sticky

Very sticky


Stickiness clustering, but is not equivalent to bigger grains →(even with weaker dielectric constant)

τ=0.2 and at density of 200 kg/m3 factor → x1.6 is required



Conclusion:

+ Stickiness: τ=0.2 and at density of 300 kg/m3 factor → x1.9+ Poly-disperse grain size distribution: Rayleigh dist. at 300 kg/m3 factor → x1.5

= It seems that with these two factors, the experimental micro-structure factor Φ in the range 2-4 can be explained. Variations of could be explained by variations of Φstickiness or upper tail of the distribution

Stickiness is not strictly equivalent to scaling grain sizeTheoretical incompatibility between and stickinessΦ

Implications:

1- The calculation of DMRT sticky grains with size distribution remains to be done (to my knowledge). Work in progress with Brigitte Bidegaray-Fesquet, LJK, Grenoble

2- Which stickiness values and distribution shape should we use in practice ?Work conducted by Henning Löwe, SLF, Davos

Should we really focus on stickiness and size distribution shape ?



DISORTJin, 1994

IBA(Wahl=12)

6-fux


2-fux


Maximum diameterDmax





W98(Wahl<12)





Maxwell equations Collection of discrete scatterers

Response of scatterers to incident field,polarisability (=scatterer shape)

Electromagnetic approximations

Position of the scatterers

Parameters

DMRT IBA

Same

Almost the same: spheres

In fact IBA: Field factor K can be chosenMEMLS uses empirical K, not exactly spheres

DMRT exists also for spheroids

Almost the same in the low freq approx ??

Probability of distance between centres

Probability of distance of mass (eq. dielectric value)

Are DMRT and IBA different ?

Hard spheres (PY pair-distribution)Radius, stickiness

Exponential correlation functionpex

DMRT QCA-CPStickiness=0.75

IBA Sphereconstant radius


Comparison of DMRT and IBA: Surprise !!

it's IBA with spherical scatterers and independent sphere correlation function at 0-order, assuming pc=2/3*(1-f)*D (Maetzler, 1998)Not IBA with K-empirical scatterers and exponential correlation function (as in MEMLS, Mätzler and Wiesmann, 1999)

To learn more see Henning Löwe presentation


Which representation of snow should we use ?

● Spheres (~), hard sphere packing is physical (+), radius (++) (easy to understand, →SSA measurements, snowpack models), stickiness and size distribution (--)

● Exponential autocorrelation function is physically incompatible with spherical hard scatterers (-) overlapping scatterers, difficult to measure (~) snow slice or X-tomo, → →only one parameter (corr length) accounts for “SSA+density+stickiness” (+).

● Recent alternative: bicontinuous medium (Ding et al. 2010), two micro-structure parameters, see Leung Tsang presentation this afternoon

● The real autocorrelation function can be obtained from X-Ray tomo (++), but is more difficult to use than a few parameters (-)


One slide from H. Löwe, Snow Grain Size Workshop, Grenoble, 2013

Microwave wavelength

- SSA is the first derivative of the autocorrelation at r=0 (Debye, 1957 ; r=0 means few microns for optical measurements or X-tomo) whereas microwaves are sensitive over the wavelength range- Exponential function (blue and red curve) is not suitable in the presented case.

Only SSA or only correlation length is insufficient for snow

Perspectives

Practical recommendations for the future regarding micro-structure:

1- learn more about the autocorrelation function of natural snow using X-Ray tomoHow variable with snow type ? impact of metamorphism ?

2- choose the most versatile/best autocorrelation function (maybe from existing ones) with max ONE measurable parameter to describe the “stickiness/grain size distribution”- effect of the medium in complement with SSA and density. We could call it Ф, Cyrillic “ef” looks like sticky grains (as

Greek capital Φ from which it comes from is already used for grain size scaling).

3- develop instruments for field measurements and evolution equations for snowpack models for this parameter

This talk focuses on Ks, but anisotropy and phase function are also to be considered

DMRT-MLropt

ρT

TB(37V)(t)

TB(19V)(t)

rDMRT=Φ ropt

Snow emission model

ropt

ФρT

TB(37V)(t)

TB(19V)(t)

Perspectives

Other (more important?) priorities:

● soil parametrisation is major uncertainty (snow micro-structure is second-order in many cases)

● air/snow surface roughness (e.g. sastrugi, polarimetric radiometry)

● extend the validity range of DMRT QCA for large density: f>0.3(Liang et al. 2006, Dierking et al. 2012)

● For high frequency (AMSU-B), DMRT model (public version) for large clusters and/or for large scatterers (+ computationally efficiency)

● For low frequency (SMOS, Aquarius), wave approach and stratification is required, see Marion Leduc-Leballeur's talk.

● Passive / active models

Micro-structure matters

Macro-structure matters too

Thank you for your attention

Microsnow August 2014

Snow micro-structure to

micro-wave modelling

G. Picard

L. Brucker, F. Dupont, A. Roy, N. ChampollionL. Arnaud, M. Fily,

A. Royer, A. Langlois, H. Löwe, B. Bidegaray-Fesquet

Snow micro-structure is complex- granular/porous medium, anisotropy- wide distribution of characteristic lengths (=”grain size”)- sometime liquid water- …Only basic metrics (Dmax, optical grain size) are easily measurable in the field (excl. X-ray tomo) or predicted by snowpack models.

The snowpack is complex- plane parallel layers with rough interfaces (air-snow, snow-soil, internal layering) to 3D structure (e.g. sastrugi)- soil (or ice) is “part” of snowpack: incl. water, ice, mineral scatterers- vegetation, …

The electromagnetic problem is complex - electromagnetically dense medium (fractional volume f >0 and <1)- “grain size” ~ wavelength- ice has high permittivityConsequences: internal field is significant / multiple scattering / near field / resonance or interferences

No perfect multi-purpose model

Context

What do “we” want to do ?

Ultimate goal: retrieve snowpack properties of interest (SWE, temperature, density, stratification, soil state, …). In general, these properties are well-defined and easy to measure in the field.

Intermediate step: retrieve/estimate other snowpack properties (grain size, …) to regularize/initialize the retrieval.

1. We need a “good” EM model

EM model

Snowpack properties:- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt)- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Brightness temperaturesat several frequencies (max 10)and polarisations (2 to 4)

Backsacttering coefficientat several frequencies (max 2)and polarisations (2 to 16)

Context

The retrieval is under-determined problem

2. We need inverse method and prior information


residual

Inverse method

- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt)- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Weak constrain on grain size and micro-structure properties as they are used by and estimated from the EM model (self-consistent variable): e.g. Globsnow (SWE retrieval, effective snowpack grain size estimated)

→ “we” only need an EM model with a good frequency-dependence (e.g. C. Mätzler, L. Tsang)

Context

adaptation

2alter. Prior information comes from a snowpack model


residual

Inverse method

- temperature profile- density profile- grain size profile and other micro-structure information- ice dielectric constant- liquid water content profile, impurities (salt) and information on the location of liquid water- surface and interface roughness- soil EM properties (dielectric constant or scattering/absorption)

Snowpackevolution

model

Strong constrain on grain size and micro-structure properties as the snowpack model and the EM model have to use the same variables

→ “we” need well defined snow grain size and a “good” EM model

Context

Objective:

Validate EM models with accurate/well defined measurements of grain size

Outline of this talk:

1 – Validation of DMRT-ML using SSA measurements

2 – The micro-structure in EM models

Limit this talk: to “fast models”, i.e. scattering and absorption coefficients have an analytical formulation. Exclude e.g. numerical exact solutions of Maxwell equations

3 - Perspectives

Context

The characteristics of DMRT-ML are presented by L. Brucker this afternoon

Successive steps of the validation performed at LGGE:

1- Brucker at al. 2011: DMRT-ML development and first application to Dome C with SSA derived from NIR photography

2- Picard et al. 2014: second application at Dome C with SSA measured with POSSSUM

3- Roy et al. 2013: soil is implemented in DMRT-ML , application to seasonal snow

4- Dupont et al. 2014: DMRT-ML applied to bubbly-ice

Validation of DMRT-ML with SSA measurements

L. Arnaud and H. Brunjail: trained by M. SchneebeliNIR photography at Dome C in December 20061 snowpit: 3x 1m

First validation at Dome C, Antarctica - Brucker et al. 2011

NIR refectance SSA Optical radius:→ → ropt=3

ρSSA

Measurements of density, every 2-3 cm

Another density profile 0 – 20m from a previous campaign

Measurements of temperature profile every 1h (40 probes from 0 to 20m)


Direct run: optical radius is used as input of the monodisperse none-sticky QCA-CP DMRT (Shih et al. 1997)

V-polarisation

DMRT-ML

AMSR-E


TB(37V)(t)

TB(19V)(t)

• Over-estimation of the emissivity

• Over-estimation of the penetration depth

Under-estimation of the grain size



DMRT-ML model

ropt(z)ρ(z)T(z,t)

TB(37V)(t)

TB(19V)(t)

Adaptation was required: Optimise 2 parameters Φ and ropt(z>3m)

rDMRT=Φ ropt

Optimisation

19 GHz

37 GHz


Partial validation:

4 independent variables are well predicted with only 2 optimised parameters:emissivity and penetration depth at two frequencies.

What is really validated here: - absorption coefficient and density profile. κe=κs+κa ω=κs/(κs+κa)- RT solutionNote: It was not possible to get as good results with MEMLS

What is not validated here:- the absolute value of the scattering coefficient predicted by DMRT theory (because of Φ)

Important result:

Possible error sources: Calibration of NIR photography, satellite footprint, … but 2.8 is a large value

rDMRT=2.8 ropt

Up to ~ 8 m deep, ~2-3 h ~20 min for 8 mincluding snow core logging

Second validation at Dome C - Picard et al. 2014Better SSA profiles

Drill a hole (~100 mm in diameter) POSSSUM (Arnaud et al. 2011)

Second validation at Dome C - Picard et al. 2014Density profile from the snow core extracted for POSSSUM / SSA measurements

5 cm resolution

Second validation at Dome C - Picard et al. 2014Ground-based radiometers at 19 and 37 GHz in two points

2012-13 at Dome C with A. Royer, U. Sherbrooke

2 points near Concordia chosen for their contrasted TB


8 m profiles

Snowpit 1 and 2



TB(37V)(t)

TB(19V)(t)

Optimise 1 parameter: Φ(one for all freq, pola, angle, snowpits)

rDMRT=Φ ropt

V-pol

H-pol

Color : snowpit


Stronger validation:

8 independent variables are well predicted with only 1 optimised parameter

What is really validated here:

- grain size and density profiles (note: difference between snowpits is explain by the density)- frequency dependence- polarization dependence

- Φ is a micro-structure parameter (ie indep of EM parameters) or potential deficiency of DMRT theory

From 2.8 to 2.3, this is a 20 % difference (SSA accuracy?)

rDMRT=2.3 ropt

DMRT “ice” validation - Dupont et al. 2014Bubbly ice

Barnes ice cap in Baffin Island, 2011A. Langlois, U. Sherbooke

Adélie Land 2012 – 13with A. Royer


Adélie Land results : bare ice

37 GHz 19 GHz

11 GHz

Pure ice

Bubbly ice

Mesured densityOptimize bubble size (0.68 mm)Measured bubble size (0.6 mm)

rDMRT=1 rbubble


Barnes ice cap results : 80-cm snow over bare ice

37 GHz 19 GHz

Both density and bubble size are optimized. Again optimised value ~ real bubble size (i.e. Φ=1)

DMRT is for spherical scatterers and it works without scaling when scatterers are truely spherical!

It can be excluded that Φ was necessary to compensate potential DMRT errors

Validation for seasonal snow - Roy et al. 2013

How Φ is variable among snow types ?

A. Roy (U. Sherbrooke) implemented soil refection in DMRT-ML.Application to 20 snowpits in 3 locations in Canada where SSA was measured with IRIS.One Φ optimised for all the sites at 37 GHz, V-pol. Soil parameters optimized using 19 GHz,V/H polarisation

Φ=3.3

Conclusion: Empirical micro-structure parameter

ΦPicard et al. 2014 2.3Brucker et al. 2.8Roy et al. 2013 3.3Dupont et al. 2014 3.5Others ?

Are they really different ?

Potentiel bais :- SSA measurements (different methods were used)- Soil parameters (large uncertainty!)- Radiometer measurements (second order)

Future :1- More accurate measurements are required. Uncertainty analysis.2- Scaling grain size Φ is not satisfactory. What the theory says ?

TODO: Other 'almost equivalent Φ' could be deduced from several recent studies with HUT, radiometer and SSA measurements (e.g. CoReH2O), fitting with DMRT scattering


The representation of snow micro-structure in the snow emission models is the key.



DISORTJin, 1994

IBA(Wahl=12)

6-fux


2-fux


Maximum extent(aka traditional grain size)

Dmax





W98(Wahl<12)





Poly-disperse grain size distribution should provide a better description of the snow

Motivation: Scattering cross section is driven by radius^3 in the Rayleigh approximation (small scatterers w/r wavelength).

Bigger grains have a MUCH larger contribution to scattering.

Good news: equivalent grain (function of the density) (Jin, 1994 with DMRT QCA)

Assumption here: Rayleigh distribution sharply decreasing upper tail = convergence

Factor x 1.5 at 300 kg/m3

Highly dependent on the shape of the distribution / upper tail !


Phenomenological approach of scattering

Sparse medium, f<< 1 % (e.g. vegetation): For the calculation of Ks and Ka, scatterers are supposed independent

Incident field an internal field→The internal field absorption→The internal field radiate scattered wave→ →

Important : Other scatterers are very far and randomly positioned. Total scattered energy is linear with the number density of scatterers (no position dependent)

Incident electric fieldScat

tered ele

ctric fi

eld

Internal field


Phenomenological approach

dense medium, f~30 % (e.g. snow)

1

Incident electric field

Scatter

ed electr

ic field by 1

2

The field “received” by scatterer 2, is the sum of the incident field and the field scattered by scatterer 2. Because 2 is close to 1, the scattered field is intense and the phase is not random →coherent effect. The scattering diagram of 1+2 is not the sum of the scattering diagrams. In addition: near field effect.The internal field is different from the independent case which affects the absorption.


In practice: the scattering coefficient is reduced w/r to 'independent scatterers'. The absorption is slightly larger. The extinction is either smaller or larger than 'independent scatterers' depending on the scattering/absorption domination.

DMRT (constant radius)qca-cp none-sticky

IBA (constant radius)

Indep.

DMRT

Abs

Scatt

Indep.

IBA

Scatt

Abs


The precise relative position of scatterers with respect to each others is very important in dense media.

fractional volume f = 35%

Both media have ~ the same density and SSA but different electromagnetic behaviour

Freely positioned sphere(100% random position)

Hard sphere(100% random position + non-overlapping)


Hard sphere is not the only option: stickiness

f = 20%

Hard sphere (2D) + stickiness

More voids

Cluster eq. big scatterer⬇

Increased scattering


f = 20%

++ stickiness + stickiness

Increase stickiness (decrease τ → 0.1) increase clustering → → more scattering at constant SSA and density

Terrible consequence: SSA+density measurements or predictions by snowpack models is insufficient to characterize snow for electromagnetic calculations


Large infuence of the stickiness in DMRT on the scattering coefficient(absorption is not marginally affected)

x5 factor on Ks for τ=0.2

(could go down to τ=0.09, but not with DMRT-ML)

Coupling between stickiness and density Impact of stickiness depends on density→(very dense no alternative to stick to neighbours)→

None-sticky

Very sticky


Stickiness clustering, but is not equivalent to bigger grains →(even with weaker dielectric constant)

