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Probability Density Functions of Liquid Water Path and Total Water Content of Marine Boundary Layer Clouds. Hideaki Kawai Japan Meteorological Agency Joao Teixeira Jet Propulsion Laboratory, Caltech. Today’s Talk. 1. Data - PowerPoint PPT Presentation
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Probability Density Functions of Liquid Water Path and Total
Water Content ofMarine Boundary Layer Clouds
Hideaki Kawai Japan Meteorological AgencyJoao Teixeira Jet Propulsion Laboratory Caltech
1 Data
2 Relationships between PDFs of LWP and PDFs
of total water content
3 Impact of inhomogeneity on precipitation and
radiation processes
4 PDFs for various types of marine boundary layer
Todayrsquos Talk
1 Data
bull Data GOES visible channel data (055-075microm) spatial resolution 1km mesh temporal resolution less than 30 minutesbull Location GPCI line 20S line 88W line
(Each line consists of 8 locations)bull Area size 200km x 200kmbull Period 1999-2001 (Jan Apr Jul Oct) bull Number of used snapshots
~ 100000 (3 (lines) x 8 (locations) x 3 (years) x 4 (months) x 30 (daysmonth) x 10-20 (timesday))
GPCI line
20S line
88W line
EPIC Buoy
Homogeneity
Skewness S
Kurtosis K
2)(cLWP
LWPc
Wood and Hartmann (2006)
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
1 Data
2 Relationships between PDFs of LWP and PDFs
of total water content
3 Impact of inhomogeneity on precipitation and
radiation processes
4 PDFs for various types of marine boundary layer
Todayrsquos Talk
1 Data
bull Data GOES visible channel data (055-075microm) spatial resolution 1km mesh temporal resolution less than 30 minutesbull Location GPCI line 20S line 88W line
(Each line consists of 8 locations)bull Area size 200km x 200kmbull Period 1999-2001 (Jan Apr Jul Oct) bull Number of used snapshots
~ 100000 (3 (lines) x 8 (locations) x 3 (years) x 4 (months) x 30 (daysmonth) x 10-20 (timesday))
GPCI line
20S line
88W line
EPIC Buoy
Homogeneity
Skewness S
Kurtosis K
2)(cLWP
LWPc
Wood and Hartmann (2006)
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
1 Data
bull Data GOES visible channel data (055-075microm) spatial resolution 1km mesh temporal resolution less than 30 minutesbull Location GPCI line 20S line 88W line
(Each line consists of 8 locations)bull Area size 200km x 200kmbull Period 1999-2001 (Jan Apr Jul Oct) bull Number of used snapshots
~ 100000 (3 (lines) x 8 (locations) x 3 (years) x 4 (months) x 30 (daysmonth) x 10-20 (timesday))
GPCI line
20S line
88W line
EPIC Buoy
Homogeneity
Skewness S
Kurtosis K
2)(cLWP
LWPc
Wood and Hartmann (2006)
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
GPCI line
20S line
88W line
EPIC Buoy
Homogeneity
Skewness S
Kurtosis K
2)(cLWP
LWPc
Wood and Hartmann (2006)
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Homogeneity
Skewness S
Kurtosis K
2)(cLWP
LWPc
Wood and Hartmann (2006)
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
2 PDFs of LWP and PDFs of total water content
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Relationship among PDFs of total water content liquid water content and liquid water path
Assumptions
(1) Average of Total Water Content is constant in the mixed layer
(2) PDF of total water content is the same through the mixed layer
(3) Saturation specific humidity decreases linearly upward
(4) Spatial fluctuation of total water content is vertically coherent (Structure of overlap of PDF is correlated completely
tq
sq
)( tq qPt
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
2 )(
2
1))((
2
1)(
2
1topst
ss
topsttopsttopst qqq
z
q
zqqqqhqqLWP
Liquid Water Path
212
1A
q
z
s
topst qLWPAq
)(2)(
)()( topsqt
tqLWP qLWPAPLWP
A
LWPd
dqqPLWPP
tt
)(LWPPLWP
LWP
Under the assumptions what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be
PDF of LWP
depth of cloud just below the cloud toph topsq sq
using the substitution
(1)
As a result this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997)
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
PDF of total water content
GaussianUniform Triangular
PDF of liquid water content(at the cloud top)
corresponding PDF of liquid water path
Examples of PDFs of and corresponding PDFs of tq LWP
( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1 )
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and skewness of LWP PDFs
Cloud Amount
Ske
wne
ss
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
3 Impact of inhomogeneity on precipitation process and radiation process
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Correction ratio for autoconversion rate
lClP auau )(
)( )(model_
lClPP auauau
lllPlPR auauau )()(
Often used equation of autoconversion rate
Calculation used usually in GCMs
Correction ratio for autoconversion rate
More appropriate calculation
)()(model_ lPRlPP auauauau
l LWC
Want to know this ratio
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
PDF of total water content is assumed to be Gaussian
Correction ratio for Autoconversion rate
Cloud Amount []
Cor
rect
ion
Rat
io
auR
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
)( LWP
))(( 1 LWPffLWPeff
Effective Thickness Approach (ETA)
To get the factor
Effective LWP
))(( RffLWP
Want to know this factor
Reduction factor for LWP used in radiation process
eff
LWPLWPeffeff
f a function to convert reflectance to LWPRf
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Reduction factor used in radiation processes
Cloud Amount []
Red
uctio
n F
acto
r
PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
4 PDFs for various types of marine boundary layer
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Relationship between cloud amount and skewness of LWP PDFs
Ske
wne
ss
Cloud Amount []Four ABL types categorized using h850-h1000
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Summary 0 Subgrid-scale variability of marine boundary layer cloud
LWPs is investigated using GOES visible channel data
1 Generally speaking Gaussian function seems to represent PDFs of total water content well under the set of our assumptions
2 Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount
3 When the ABL is strongly or moderately stable PDFs of total water content is triangular or Gaussian On the other hand when the ABL is unstable the shape of the PDFs is almost unique with low homogeneity and high skewness amp kurtosis
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
The End
Thank you
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Supplemental Slides
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Processing
bull Elimination of Middle amp High Clouds Using infrared channel (IR1 102-112microm) Criterion TbbltTsea-Toffset-15 -gt M-CL or H-CL More than 1 -gt The snapshot is not usedbull Cloud Threshold threshold albedo = 013 (LWP=5[gm2])
bull Count Data -gt Radiance post launch calibration solar zenith angle calibrationbull Radiance -gt Reflectancebull Reflectance -gt Liquid water path Using the relationship by Han et al (1998) (re MODIS)
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Comparison between LWP from GOES and EPIC LWP
6 days data is used
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Comparison between HomogeneitySkewness from GOES and MODIS
Homogeneity
Skewness
Hom
o (MO
DIS
)S
kew (M
OD
IS)
Skew (GOES)
Homo (GOES)
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
GPCI line
Each dot median of 30 (daysmonth) x 3 (years) daily-averaged dataBars 90 confidence intervals from bootstrap method
Larger γ smaller S and K toward sea coast
Largest γ smallest S and K are in NH summer
Spatial variation is larger than seasonal variation
Along SH line results are similar
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
20S line
Largest γ smallest S and K are in SH winter and spring
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
88W line
Largest γ smallest S and K are in SH winter and spring
Seasonal variation is larger than spatial variation
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
sensible heat flux latent heat flux Psea U10m V10m10m wind speed temperature advection near surface T2m lifting condensation level ω700 ω850 U850 V850 Wind shear (850-1000) RH850 RH925 RH1000 θ700minusθ1000 θv700minusθv1000 h700minush1000 EIS (Wood amp Bretherton 2006) θ775minusθ1000 θv775minusθv1000 h775minush1000 θ850minusθ1000 θv850minusθv1000 h850minush1000(h850minush1000) minus kL (q850minusq1000) (k=070 053 023) h850minush1000 Buoyancy of plume Tplume(850lt-1000)minusT850 Tv plume(850lt-1000)minusTv850
bull Used meteorological data ERA40bull Parameters examined
bull Used Metric Spearmanrsquos rank correlation Kendallrsquos rank correlation Pearsonrsquos correlation
bull Above Metrics are calculated for monthly-based data daily data
daily anomaly data to each month data
Δθe minus k(LCp) Δqt
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
As an example if CGLMSE (k=070) is plotted in X axishellip
Each color consists of 8 locations x 4 seasons
Location closest to the land
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
These conventional functions seem not to be able to represent PDFs of Liquid Water Path
(The case that PDFs of LWP themselves are conventional functions)
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Points Observation data median 25th amp 75th percentile values All the original data (~100000 snapshots ) are used for this statistics
Lines Theoretical Curves Two lines correspond to two mimicked detection limits (10 or 20 of
average liquid water path)
Relationship between cloud amount and homogeneity of LWP PDFs
Cloud Amount
Hom
ogen
eit
y
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
When PDFs of total water content are assumed to be Gaussian the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well
Cloud AmountCloud Amount
Kur
tosi
s
Ske
wne
ss
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
When ABL is strongly stable the PDFs of total water content tend to be similar to Triangular distribution When ABL is unstable the PDFs have a unique shape with low homogeneity high skewness and high kurtosis regardless of the cloud amount
Relationship between cloud amount and skewnesskurtosis of LWP PDFs
Cloud Amount []
Cloud Amount []
Kur
tosi
s
Ske
wne
ss
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
ll
Production of Precipitation
)()( lPlP auau )()( lPlP auau
Effect of inhomogeneity on conversion of cloud water to precipitation
l l
)(lPR auau
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Shortwave Reflectance
Effect of inhomogeneity on shortwave reflectance
)( eff eff
)()()( rfleffrflrfl FFF )()()( rfleffrflrfl FFF Optical Thickness
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
Four ABL types categorized using h850-h1000
US Unstable WS Weakly StableMS Moderately Stable SS Strongly Stable
SSMSWSUS SSMSWSUS
