precipitation? Data description, Introduction, Motivation ... · PDF fileData description, Introduction, Motivation Research presentation . ... NSEP Reanalysis ... Physics options

Why do we seek help from “big data” in nowcasting of precipitation?

Data description, Introduction, Motivation

Research presentation

Radar Data Used here: 17 years of quasi-continuous records. Reflectivity at a resolution 4x4 km2, every 15min.

0.00

0.05

0.10

0.15

Prob

. Pre

cipi

tatio

n [Z

> 1

5dBZ

]

PLUS NSEP Reanalysis Data every 3h

Description of the CAPS SSEF ensembles. All ensemble members, except one, assimilate radar data.

Physics options used in the ensemble: MP-Thompson (Thompson et al.,2008), Ferrier (Ferrier et al.,2002),WSM6 (Hong and Lim,2006), WDM6 (Lim and Hong, 2010), Morrison (Morrison et al.,2009), M-Y (Milbrandt and Yau,2005); PBL-MYJ (Janji 1994),YSU (Hong et al.,2006),QNSE (Sukoriansky et al.,2005), MYNN (Nakanishi and Niino, 2006), ACM2 (Pleim,2007);LSM-Noah (Tewari et al.,2004), RUC (Benjamin et al.,2004); SW -Dudhia(Dudhia,1989), RRTMG (Iacono et al.,2008), Goddard (Chou and Suarez,1999); lsls LW-RRTM (Mlawer et al.,1997),RRTMG (Iacono et al.,2008).

The NWP model data Year Forecast

lengthIC/LBC/PHYS MP only PB L only Miscellaneous

2008 30h 8 members;MP : Thompson,Ferrier, WSM6;

SW : Dudhia, Goddard;PBL : MYJ, YSU.

;2.2VWRA-FRW--CN :MP : Thompson,

SW -G oddard, PBL - MYJ;all : LW -R RTM;

LSM -Noah.2009 30h --

2010 30h

2011 36h

2012 36h

2013 48h

WRF-ARW V3.0.1.1;CN :MP: Thompson,

SW -G oddard, PBL -MYJ,

all : LW -R RTM.LSM -Noah;

SW -G oddard;

WRF-ARW V3.2.1;CN :MP -Th ompson,

all : LW -R RTM,PBL -MYJ, LSM -Noah;

Rad ar-D A cycl ed member(CC).

SW -G oddard;

WRF-ARW V3.1.1;CN :MP: Thompson,,


2 I C-o nly memb ers .

SW -G oddard;



1 SK EB memb er.

SW -RR TMG;


all : LW -R RTMG,PBL -MYJ, LSM -Noah;

1 m embe r M P coupled to radiation.

LSM : Noah, RUC.

8 members;MP : Thompson,Ferrier, WSM6;

SW : Dudhia, Goddard;PBL : MYJ, YSU;

LSM : Noah.

3 members;MP : WDM6,

Ferrier, WSM6, Morr ison;PBL : MYJ;

LSM : Noah, RUC.

9 members;MP : Thompson, WDM6,Ferrier, WSM6, Morrison;

PBL : MYJ, YSU,QNSE, MYNN;

LSM : Noah.

2 members;MP : Thompson;

PBL : MYNN, QNSE;

LSM : Noah, RUC.

17 members;MP : Thompson, WDM6,

Ferrier (+) , WSM6,

PBL : MYJ, YSU,QNSE, MYNN, ACM2;

Morri son, M -Y;

LSM : Noah.

10 members,MP : Thompson-v31,

Ferrier ( 2), WSM 6 ( 5),

PBL : MYJ;Morri son, M -Y , WDM6;

LSM : Noah.

10 members;MP : Thompson,

PBL : MYJ (4) , YSUQNSE, MYNN,

ACM2 ( 3), YSU-Thom pson;

LSM : Noah.

3 m embers,MP : Morrison,

PBL : MYJ;M-Y , WD M6;

LSM : Noah.

4 m embers;

MP : Thompson;

PBL : ACM2, YSU,QNSE, MYNN;

LSM : Noah, RUC.

13 members;MP : Thompson, WDM6,

PBL : MYJ, YSU,QNSE, MYNN, ACM2;

Morrison, M -Y;

LSM : Noah.

6 m embers,MP : WDM6, NSS L, Morrison, M -Y , WSM 6;

PBL : MYJ;LSM : Noah.

10 members;

MP : Thompson;

PBL : YSU, ACM2,QNSE, MYNN;

-

Ming Xue

Mesoscale nowcasting in the past (1 to 500 km) (forecasting for 0 to 6h)

In the beginning there were analogues: “BIG DATA” was in a forecaster’s memory (accumulated experience for

situations analogous to the present) and the processing algorithms were

conceptual models.

Conceptual models: a complex problem reduced to a system with few proxy variables.

Best example in my memory:

Hector Grandoso forecasting occurrence of hailstorms in Mendoza

Then computers became more and more powerful: NWP became the future.

Models became better, numerical methods improved, more and more physics

was added…

Then, deterministic chaos cast a shadow, model errors became an issue,

physical parameterizations are always poor approximations to reality,

nature is constantly perturbed at the smaller scales and runs away from

model predictions….

Ensemble forecast accounted for uncertainties, dada assimilation would

correct the drift the NWP shortcomings.

Forecast improved continuously over time (at least at 500mb)!

AND ALL THE WHILE, MESOSCALE PRECIPITATION STUBBORNLY REFUSED TO BE WELL PREDICTED QUANTITATIVELY

WHAT IS THE PRESENT SITUATION?

Surcel, M , et al, 2015: A study on the scale-dependence of the predictability of precipitation patterns, J. Atmos. Sci., 72, 216-235.

Madalina Surcel

Methodology in a nutshel: 1- take 1-h accumulations of precipitation patterns, form radar and model forecasts 2- decompose by scale, λ 3- compare these patterns scale by scale (band-pass) 4- from this comparison determine λ0, the scale at which predicability is totally lost as a function of lead time:

That is, at λ0 forecast and verification are totally decorrelated.


Madalina Surcel

PHVR�њ

0 5 10 15 20 25Lead time [h]

10

100

1000

h 0 [km

] PHVR�ћ

PHVR�ќ




Madalina Surcel

NWP wthout Radar Data Assim. veryfied by observations PHVR�њ

0 5 10 15 20 25Lead time [h]

10

100

1000

h 0 [km

] PHVR�ћ

PHVR�ќ




Madalina Surcel

NWP wthout Radar Data Assim. veryfied by observations

NWP with Radar Data Assim. veryfied by observations

PHVR�њ

0 5 10 15 20 25Lead time [h]

10

100

1000

h 0 [km

] PHVR�ћ

PHVR�ќ




Madalina Surcel


NWP with Radar Data Assim. veryfied by NWP (intrinsic)


PHVR�њ

0 5 10 15 20 25Lead time [h]

10

100

1000

h 0 [km

] PHVR�ћ

PHVR�ќ




Madalina Surcel


NWP with Radar Data Assim. veryfied by NWP (intrinsic)


PHVR�њ

0 5 10 15 20 25Lead time [h]

10

100

1000

h 0 [km

] PHVR�ћ

PHVR�ќ



Observations contribution from errors in observations

Limits to Mesoscale Predictability

Summary of model validation with radar data: With no radar data assimilation scales smaller than ~300km are not predictable

Effect of Radar Data Assimilation lasts forever, but the improvement in skill (small) lasts up to ~4h lead time (roughly as the spin-up time)

Madalina Surcel


Limit to intrinsic model predicability When an ensemble member is used as truth there is some

predictability for 12h at λ>200km



Madalina Surcel


Limit to intrinsic model predicability When an ensemble member is used as truth there is some

predictability for 12h at λ>200km



Madalina Surcel

FOR PRECIPITATION, BEYOND THESE SHORT LIMITS AND SMALLER SCALES THERE CAN ONLY BE PROBABILISTIC FORECASTING / NOWCASTING.

Can we improve short term forecasting of precipitation with the available long term radar records and model outputs?

Isztar Zawadzki, McGill University, Presenting work of:

Aitor Atencia Ruiz de Gopegui Bernat Puigdomènech Treserras

And many thanks to M.K. Yau and F. Fabry for comments and support

BACK TO ANALOGUES (but now with data instead of subjective experience)

__________________________

Probabilistic Nowcasting of Precipitation Using “Analogues” (Similar Patterns);

Preliminary Comparison with NWP.

For every radar map similar patterns were searched in 17 years of radar archives. Similarity is defined by a decision-tree comprising the following criteria:

1. Spatial cross-correlation between Rainfall patterns

2. Location to account for Geographical factors

3. Temporal correlation to select for similarity of Motion & Evolution of patterns

4. Time of the day and year to account for the Diurnal and Annual cycles

Analogue selection criteria

5- Synoptic situation to account for influence of Large scale forcing

There are three main factors needed for rainfall occurrence: instability, moisture and forcing.

The variables more appropriate were found to be:

temperature, Τ at 50 kPa, specific humidity at 70 kPa and

pressure vertical velocity, ω at 85 kPa.


5- Synoptic situation to account for influence of Large scale forcing

There are three main factors needed for rainfall occurrence: instability, moisture and forcing.

The variables more appropriate were found to be:

temperature, Τ at 50 kPa, specific humidity at 70 kPa and

pressure vertical velocity, ω at 85 kPa.


Why these 7 parameters? Because this is the conceptual model framework to which we are used and we understand, and black-box approach like SOM did

not work for precipitation patters. Surely it can be refined.

For all criteria the degree of similarity between the observation and the analogue candidate is determined by the desired ensemble number of “analogues” available in the records.

The number of “analogues” can be adjusted so that the ensemble is not over nor under-dispersive. The latter can be evaluated by the nowcast of the previous time.

Thus, the procedure can be made adaptable to the situation.


10.0

17.5

25.0

32.5

40.0

47.5

55.0

62.5

70.0

Ref

lect

ivity

[dBZ

]

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50

Latit

ude

OBSERVATION

10.0

17.5

25.0

32.5

40.0

47.5

55.0

62.5

70.0

Ref

lect

ivity

[dBZ

]

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50

Latit

ude

CANDIDATE

Example of Analogues

Example of Analogues

From these 26 patterns we determine a map of probability of precipitation occurrence

Example of 22 May 2013

Comparison of Probability of PrecipitationMaps of probability of precipitation derived from 26 members ensembles.

Green contours are radar verification

Analogues ensemble OU model ensemble

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50

Latit

ude

0.0

0.2

0.4

0.6

0.8

1.0

Prob

. Ana

logs

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50

Latit

ude

0.0

0.2

0.4

0.6

0.8

1.0

Prob

. NW

P

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50La

titud

e

0.0

0.2

0.4

0.6

0.8

1.0

Prob

. NW

P

-100 -95 -90 -85 -80 -75Longitude

30

35

40

45

50

Latit

ude

0.0

0.2

0.4

0.6

0.8

1.0

Prob

. Ana

logs

Example of 10 May 2013

and they are either 1 or 0 depending whether an event occurred or not.280

• ROC area score: This score is the area under the ROC curve. ROC stands for Relative281

Operating Characteristic and it is a plot of the Probability of Detection (POD) versus282

the False Alarm Rate (FAR). These two scores are contingency-table scores that are283

based on dichotomous forecasts (Dobryshman 1972). A dichotomous forecast indicates284

whether an event has occurred or not at each point of the grid and it is specified by285

the exceedance of a certain threshold. In this study 15 dBZ (0.3 mm) is the selected286

threshold. The four combinations of forecasts (yes or no) and observations (yes or no)287

are hit, miss, false alarm and correct negative. The two scores used to define the ROC288

curve are computed as:289

POD =hit

hit + miss(3)

290

FAR =false alarm

false alarm + correct negatives(4)

These indices are computed by using a set of increasing probability thresholds (for291

example, 0.05, 0.15, 0.25, etc.) to make the yes/no decision for the ensemble forecast.292

The ROC area score’s range takes values from 0 to 1. 1 stands for a perfect forecast293

and values lower than 0.5 indicate no forecast skill.294

• The spread of an ensemble of members at a particular forecast time step is measured295

as:296

Spread =

vuut 1

Np

(Nm

� 1)·

NpX

i=1

NmX

j=1

(fij

� f̂i

)2 (5)

where Np

is the total number of points of the domain, Nm

is the number of ensemble297

members, fij

stand for i pixel of the jth ensemble member (Fj

) and f̂i

is the mean of298

the ensemble members at a given pixel i.299

12

Answers the question: What is the ability of the forecast to discriminate between precipitation events and non-events?

Range: 0 to 1. 0.5 = no skill. Perfect score: 1

ROC Area = POD d(FAR)∫Relative Operating Characteristic, ROC:

Skill Comparison (probability)

0 2 4 6 8 10Lead-time [h]

0.4

0.6

0.8

1.0

ROC

Area

No Skill

Model Analogues

(For 26 events from 31st April to 12th June and 26 members ensembles)











POD =hit

hit + miss(3)

290

FAR =false alarm







as:296

Spread =

vuut 1

Np

(Nm

� 1)·

NpX

i=1

NmX

j=1

(fij

� f̂i

)2 (5)

where Np



members, fij


) and f̂i

is the mean of298


12





Even though the patterns were different, the probability map have a reasonable performance with both techniques.

0 2 4 6 8 10Lead-time [h]

0.4

0.6

0.8

1.0

ROC

Area

No Skill

Model Analogues












POD =hit

hit + miss(3)

290

FAR =false alarm







as:296

Spread =

vuut 1

Np

(Nm

� 1)·

NpX

i=1

NmX

j=1

(fij

� f̂i

)2 (5)

where Np



members, fij


) and f̂i

is the mean of298


12





Even though the patterns were different, the probability map have a reasonable performance with both techniques.

0 2 4 6 8 10Lead-time [h]

0.4

0.6

0.8

1.0

ROC

Area

No Skill

Model Analogues

The differences are statistically significative.


Answers the question: What is the magnitude of the probability forecast errors?

Range: 0 to 1 Perfect score: 0

Brier Score = 1N

1Nm

f jj=1

Nm∑⎛

⎝⎜⎞

⎠⎟− oi

⎡

⎣⎢⎢

⎤

⎦⎥⎥

2

i=1

N

∑


indicates points in space (N); indicates members (Nm) is forecast value: 0, miss; 1, hit is observation: 0, miss; 1, hit

ijfoi

0 2 4 6 8 10Lead-time [h]

0.00

0.02

0.04

0.06

0.08

0.10

Brie

r Model Analogues


Answers the question: What is the magnitude of the probability forecast errors?

Range: 0 to 1 Perfect score: 0

Brier Score = 1N

1Nm

f jj=1

Nm∑⎛

⎝⎜⎞

⎠⎟− oi

⎡

⎣⎢⎢

⎤

⎦⎥⎥

2

i=1

N

∑


indicates points in space (N); indicates members (Nm) is forecast value: 0, miss; 1, hit is observation: 0, miss; 1, hit

ijfoi

0 2 4 6 8 10Lead-time [h]

0.00

0.02

0.04

0.06

0.08

0.10

Brie

r Model Analogues



0 2 4 6 8 10Lead-time [h]

0.0

0.5

1.0

1.5

2.0

2.5

RM

SE [S

kill]

Model Analog

0

5

10

15

20

25

Even

t

Skill Comparison (RMS)



RMSE = 1N

(Roi=1

N

∑ − f )2

indicates point (N); is observation is average of members

iR0f

0 2 4 6 8 10Lead-time [h]

0.0

0.5

1.0

1.5

2.0

2.5

RM

SE [S

kill]

Model Analog

0

5

10

15

20

25

Even

t

Skill Comparison (RMS)



Analogues have more information on the probability and intensity of precipitation.

RMSE = 1N

(Roi=1

N

∑ − f )2

indicates point (N); is observation is average of members

iR0f

Do analogues ensembles forecasts cover observations? Skill-Spread Ratio


0 2 4 6 8 10Lead-time [h]

0.2

1.0

10

RM

SE -

Skill

SD o

f Ens

embl

e Sp

read

Analogues

Over-dispersive

Under-dispersiveSpread = 1

N(Nm −1)( f j − f )2

j=1

Nm

∑i=1

N

∑

indicates point (N); indicates members (Nm) is average of members

ijf

Do analogues ensembles forecasts cover observations? Skill-Spread Ratio

The small under-dispersivity is perhaps due to the limited number of ensemble members


0 2 4 6 8 10Lead-time [h]

0.2

1.0

10

RM

SE -

Skill

SD o

f Ens

embl

e Sp

read

Analogues

Over-dispersive

Under-dispersiveSpread = 1

N(Nm −1)( f j − f )2

j=1

Nm

∑i=1

N

∑


ijf

Do model ensembles forecasts cover observations? Skill-Spread Ratio

(For 26 events from 31st April to 12th June. For 26 members ensembles,

and for 15 most dispersive members)

0 2 4 6 8 10Lead-time [h]

0.2

1.0

10

OU model RM

SE -

Skill

SD o

f Ens

embl

e Sp

read

Over-dispersive

Under-dispersive

1526Spread = 1

N(Nm −1)( f j − f )2

j=1

Nm

∑i=1

N

∑


ijf

Do model ensembles forecasts cover observations? Skill-Spread Ratio

(For 26 events from 31st April to 12th June. For 26 members ensembles,

and for 15 most dispersive members)

And it is not bias. It is hard to get model ensembles sufficiently dispersive.

0 2 4 6 8 10Lead-time [h]

0.2

1.0

10

OU model RM

SE -

Skill

SD o

f Ens

embl

e Sp

read

Over-dispersive

Under-dispersive

1526Spread = 1

N(Nm −1)( f j − f )2

j=1

Nm

∑i=1

N

∑


ijf

NEXT True analogues: close states on an attractor.

The Lorenz attractor

As a 3-D trajectory with 2-D projections

o

The X-Y projection of a sparse attractor

101

102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)

Projection on the X,Y plane)

LABasin

The X-Y projection of the full attractor: high density of

trajectories (points)

Dimension (fraction of phase space occupied by the attractor)

Correlation Dimension: 1-take a circle of radius r and count the total nº of points within the circle for all

positions in the domain, Cr 2- Repeat for all r and plot log Cr vs log r The slope is the CD0 2 4 6 8

log(r)

18

20

22

24

log(

Cr)

XY Projection

Slope=Corr. Dim

=1.215

dxdt

=σ (y − x); dydt

= x(ρ − z)− y; dzdt

= xy − βz σ = 10; ρ = 28 ; β = 83

The trajectory of the LA attractor is obtained by solving three differential

equations.

If the time of each point of the trajectory is recorded the equations are no

longer needed. The attractor is “DATA”

Starting from the red point we can obtain the future trajectories (red) of all

the analogues within the point. This is the analogues ensemble forecast.

Forecasting with the attractor

-20 -10 0 10 20X(t)

0

10

20

30

40

50

Z(t)


equations.






-20 -10 0 10 20X(t)

0

10

20

30

40

50

Z(t)

An ensemble forecast of x at time tf is made by choosing a set of close values on the

attractor around x(t0), y(t0), z(t0), the ANALOGUES, and then following the evolution of

the ensemble average of x as well as their spread in time until the forecast time tf.


equations.





If the equations for a system are known it may be more practical to get a solution

every time a forecast is needed than have the huge table for all the solutions.

But, for the atmosphere we ignore the exact equations. Moreover, we cannot

compute all the solutions from the equations we have.


-20 -10 0 10 20X(t)

0

10

20

30

40

50

Z(t)

An ensemble forecast of x at time tf is made by choosing a set of close values on the

attractor around x(t0), y(t0), z(t0), the ANALOGUES, and then following the evolution of

the ensemble average of x as well as their spread in time until the forecast time tf.

What happens if we only have a reduced dimension?

101

102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin

0Climatology:

RMS of the LA

0.1 1.0Time [s]

33 Analogues on the 3-D attractor

10 1000.01

0.10

1.0

10

100 0

x-R

MS

of th

e An

alog

ues

Ense

mbl

e Sp

read

The value of the forecast by analogues-ensemble is measured by

the distance of the curve to the RMS of climatology.


101

102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin

0Climatology:

RMS of the LA

0.1 1.0Time [s]


10 1000.01

0.10

1.0

10

100 0

x-R

MS

of th

e An

alog

ues

Ense

mbl

e Sp

read

Even if the dimension of the attractor is reduced (from 3 to 2

in this case) the information may have practical value.

141 analogues on the 2_D attractor(Reduc. dim. anal.)




101

102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin

0Climatology:

RMS of the LA

The analogues ensemble forecast from the reduced dimension attractor

contains a greater amount of information than climatology.

0.1 1.0Time [s]


10 1000.01

0.10

1.0

10

100 0

x-R

MS

of th

e An

alog

ues

Ense

mbl

e Sp

read

Even if the dimension of the attractor is reduced (from 3 to 2

in this case) the information may have practical value.

141 analogues on the 2_D attractor(Reduc. dim. anal.)



Must we know the exact variables of the phase space?

0

We can taylor the attractor to fit our needs. Say, we want to

forecast the mean of x,y,z, the eccentricity of x,z, [z2/(x2+z2)]½, and

the euclidian distance between x and y. From the original attractor

we can construct an attractor in these coordinates:

0.001 0.01 0.1 1 10 10010-8

10-6

10-4

10-2

100

0.001 0.01 0.1 1 10 100Radius

10-8

10-6

10-4

10-2

100

Cr

Cor. Dim: 2.08

The attractor conserves all its characteristic.

WE CAN USE PROXY VARIABLES TO DEFINE THE PHASE SPACE

101

102

103

104

105

106

107

Den

sity

[# p

oint

s]

5 10 15 20 25 30d(x,y)

-5

0

5

10

15

20

25

Mea

n (x

,y,z

)

Is this low order system relevant for Nowcasting of such a high order system as precipitation?

Consider the attractor as the climatology of the

system represented as the joint probability of

the phase-space variables, p(x|y|(z). The

number of variables can be reduced, or use

proxy variables, and still the ensemble of

analogues will have predictive value. 101

102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin








102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin

OUR GOAL IS TO EXPLORE THE USE OF RADAR DATA, TOGETHER

WIH OTHER DATA, TO CONSTRUCT A CLIMATOLOGY OF THE JOINT

PROBABILITY OF RELEVANT VARIABLES, WHICH WE WILL CALL

“RAIN ATTRACTOR” AND STUDY ITS NOWCASTING POTENTIAL








102

103

104

105

106

107

108

Den

sity

[# p

oint

s]

-20 -10 0 10 20X (t)

-20

-10

0

10

20

Y (t)


LABasin

OUR GOAL IS TO EXPLORE THE USE OF RADAR DATA, TOGETHER

WIH OTHER DATA, TO CONSTRUCT A CLIMATOLOGY OF THE JOINT

PROBABILITY OF RELEVANT VARIABLES, WHICH WE WILL CALL

“RAIN ATTRACTOR” AND STUDY ITS NOWCASTING POTENTIAL

What are “RELEVANT VARIABLES”?

Here we go back to conceptual models and Hector Grandoso.

A first attempt at a “Rain Attractor”

From 17 years of continental composites of precipitation patterns we

can construct a 5-D (sparce) RAIN ATTRACTOR. The phase space we

use is comprised of one thermodynamic variable and 4 statistical

properties of the pattern:

70-50 kPa thickness (every 3h, from reanalysis),

Area of precipitation,

its Eccentricity,

Marginal Mean reflectivity,

Decorrelation time.

Here we will use all variables or a smaller dimension subset of them.

105 1062.4

2.5

2.6

2.7

1 10Decorrelation time [h]

0.0 0.2 0.4 0.6 0.8 1.0Eccentricity

20 25 30Marginal mean [dBZ]

1

2

7

18

50

132

Area [km2]2.4

2.5

2.6

2.7

2.4

2.5

2.6

2.7

(50-

70) k

Pa th

ickn

ess

[km

]

2.4

2.5

2.6

2.7

Nº o

f poi

nts

(50-

70) k

Pa th

ickn

ess

[km

]

(50-

70) k

Pa th

ickn

ess

[km

]

(50-

70) k

Pa th

ickn

ess

[km

]

Density Projections of a 5-D Rain Attractor

-1.5 -1.0 -0.5 0.0 0.5 1.0log(r)

-10

-8

-6

-4

-2

0

log(

Cr)

Phase space:Area - M.M. - Ecc. - Dec Time - Thickness

corr. dimension = 4.81

The other Projections of the Rain Attractor

For this 4-D attractor:

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0log(r)

-10

-8

-6

-4

-2

0

log(

Cr)

corr. dimension = 3.74

Phase space:Area - M.M. - Ecc. - Dec Time

2 7 19 51 136 364Nº of points

1

20 25 30Marginal Mean [dBZ]

105

106

Area

[km

2 ]


1

10D

ecor

rela

tion

time

[h]

0.0 0.2 0.4 0.6 0.8 1.0Eccentricty

105

106

Area

[km

2 ]

0.0 0.2 0.4 0.6 0.8 1.0Eccentricty

1

10

Dec

orre

latio

n tim

e [h

]

105 106

Area [km2]

1

10

Dec

orre

latio

n tim

e [h

]


0.0

0.2

0.4

0.6

0.8

1.0

Ecce

ntric

ty

Trajectories on the Rain Attractor

1

2

7

19

50

136

363

Den

sity


105

106

Area

[km

2 ] 1

1

2

6

18

47

125

331

Den

sity

105 106

Area [km2]

1

10

Dec

orre

latio

n tim

e [h

]

1

26/10/1995 - 28/02/2014 374286 files scale 1 - 4x4km - point 1 - Z average t=0 t=100 days

Forecast and Ensemble Spread on the Rain Attractor

How does it work? Say, at the present time we have only marginal mean (MM). 1-Select in the 1-D attractor 250 cases with the closest MM

We see that there is a skill better than climatology for ~2 days.

ForecastEnsemble spread

Marginal mean,M.M

10-2

Lead-Time [days]

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

SD

Spr

ead

of M

argi

nal M

ean

10 100Lead-Time [days]

22

25M

argi

nal M

ean

[dBZ

]

250 analogues26

24

23

27

0.1 10.1 1 10 100

climatology of the season

2-Make the ensemble forecast

3-Measure the ensemble spread


1-Select in this 4-D attractor 250 cases with the closest values of these 4 parameters 2-Make the average ensemble forecast 3-Measure the ensemble spread


10-2

Lead-Time [days]

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

SD

Spr

ead

of M

argi

nal M

ean


22

25M

argi

nal M

ean

[dBZ

]

250 analogues26

24

23

27

0.1 10.1 1 10 100


Marginal mean,M.MM.M + Area + Ecc. + Dec-Time

Now add to MM the Area, Eccentricity and Decorrelation Time of the pattern.

We see that the skill is much better than climatology for ~10 days.


1-Select in this 3-D attractor 250 cases with the closest values of the 3 parameters 2-Make the average ensemble forecast 3-Measure the ensemble spread


10-2

Lead-Time [days]

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

SD

Spr

ead

of M

argi

nal M

ean


22

25M

argi

nal M

ean

[dBZ

]

250 analogues26

24

23

27

0.1 10.1 1 10 100


Marginal mean,M.MM.M + Area + Ecc. + Dec-Time

Thickness + M.M. + Dec-Time

Now we take the 50-70 kPa Thickness, MM, and Decorrelation Time.

We see that the skill is much better than climatology for ~30 days and longer.

Comparison of Performance

30/04/2013 00:00 - 26 analogues

0 2 4 6 8 10Lead-Time [h]

18

20

22

24

26

28

Mar

gina

l Mea

n [d

BZ]

Area: 4.07e5 [km2]Marginal Mean: 24.69 [dBZ]Decorrelation time: 2.74 [h]Eccentricity: 0.86

Starting time ((2h): 00:00 [UTC] Similar pattern analogues4D attractor analogues

Verification

0 2 4 6 8 10Lead-Time [h]

105

5x105

Area

[km

2 ]

Area: 4.07e5 [km2]Marginal Mean: 24.69 [dBZ]Decorrelation time: 2.74 [h]Eccentricity: 0.86

Starting time ((2h): 00:00 [UTC] Similar pattern analogs4D attractor analogs

Verification

Not surprisingly, attractor analogues are better at predicting Area and

Marginal Mean that similar patterns. They were tailored for this purpose!

And the average of 24 days:24 days x 26 analogues

0 2 4 6 8 10Lead-Time [h]

20

22

24

26

28

Mar

gina

l Mea

n [d

BZ]

Similar pattern analogues 4D attractor analogues

Verification

0 2 4 6 8 10Lead-Time [h]

105

106

Area

[km

2 ]


Verification

0 2 4 6 8 10Lead-Time [h]

20

22

24

26

28M

argi

nal M

ean

[dBZ

]


Verification

0 2 4 6 8 10Lead-Time [h]

105

106

Area

[km

2 ]


Verification

Comparison of Performance

This attractor approach is now moving to Switzerland where it became part

of an SNSF AMBIZIONE project (Urs German, Loris Foresti).

Combination with satellite data, surface data, orography;

Search for the smallest most effective phase space (principal components?)

State dependence

…..

A PhD position available

This was a first exploration of the “Rain Attractor”. It looks promising.

NEXT:

THANK YOU

precipitation? Data description, Introduction, Motivation ... · PDF fileData description, Introduction, Motivation Research presentation . ... NSEP Reanalysis ... Physics options

Documents