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Precipitation Statistical Characterization Series in Bogotá towards the
Implementation of Mathematical Models for Completing Missing Data
using WEATHER RADAR and SATELLITEL TECHNOLOGY


Julio Alberto Garcia Leal

Ing. Automatización Electrónica

Esp
. Telemática

Est.

MsC.

Hidrosistemas

Tutora: Eddy Herrera Daza

MsC.

Estadistica

Candidata
PhD

Ingenieria



Pontificia Universidad Javeriana


Bogotá Colombia
-


Fortaleza 01
-

12
November

2010


Introduction


Presentation on research project under
my PhD tutor. Eddy Herrera Daza
-
Precipitation Statistical Characterization
Series in Bogotá towards the
Implementation of Mathematical Models
for Completing Missing Data using
WEATHER RADAR and SATELLITEL
TECHNOLOGY


Objetives




Regionalization of rainfall fields through satellite images and
weather radar


Previous analysis of 1D profiles to full 2D image processing


Forecasting of rainfall field using satellite image and weather
radar

Precipitation

is

the

key

hydrologic

variable

linking

the

atmosphere

with

land

surface

processes,

and

playing

a

dominant

role

in

both

weather

and

climate
.

.

Additionally,

many

international

research

programs

have

placed

high

priority

on

the

development

of

reliable

global

precipitation

observation
.


During

the

past

few

decades,

satellite

sensor

technology

has

facilitated

the

development

of

innovative

approaches

to

global

precipitation

observations
.

Clearly,

satellite
-
based

technologies

have

the

potential

to

provide

improved

precipitation

estimates

for

large

portions

of

the

world

where

gauge

observations

are

limited
.

Recently

many

satellite
-
based

precipitation

algorithms

have

been

developed

(
Ba

and

Gruber,

2001
;

Huffman

et

al
.
,

2002
;

Joyce

et

al
.
,

2004
;

Negri

et

al
.
,

2002
;

Sorooshian

et

al
.
,

2000
;

Tapiador

et

al
.
,

2002
;

Turk

et

al
.
,

2002
;

Vicente

et

al
.
,

1998
;

Weng

et

al
.
,

2003
)
.

These

algorithms

generate

precipitation

products

consisting

of

higher

spatial

and

temporal

resolution

with

potential

to

be

used

in

hydrologic

research

and

water

resources

applications
.

Evaluation

of

recently

developed

precipitation

products

over

various

regions

is

ongoing

(Ebert,

2004
;

Kidd,

2004
;

Janowiak
,

2004
)
.

I

N

T

R

O

D

U
C

T

I

O

N


Clouds, which are at the source of the hydrological
cycle, are the most obvious manifestation of the
earth's turbulent atmospheric dynamics (Lovejoy, s.
1982)(Wilkinson, J.
&
Kanellopoulos
, J. eta 1995).



By modulating the input of solar radiation, they play
a critical role in the maintenance of the earth's
climate .


They are also one of the main sources of uncertainty
in current climate
modelling
.

B

E

C

A

U

S

E


C
L

O

U

D

S


I

M

A

G

E

S

Study

Area

Department
: Cundinamarca

City: Bogotá D.C


In 2005, the city had a population of 7.881 .156
people in its urban area, 6.778 .691 people in
the city and a population density of approx.
3,912 inhabitants per square kilometer
according to figures presented by the National
Bureau of Statistics (DANE) of the 2005
census



Weather

Stations

Stations


GEOGRAPHICAL COORDINATES

ESCUELA

LA

UNIÓN

04
°
20’33.5”N
-

74
°
11’01.7” W

PASQUILLA

04
°
26’46.4”N
-

74
°
09’17.5” W

LA

ESPERANZA


04
°
27

4
.
8
”N

-

74
°
06

40
”W

USME
. U
. A.NARIÑO

04
°
28’53.2”N
-

74
°
07’37.0” W

DOÑA

JUANA

04
°
30’02.9”N
-

74
°
08’14.6” W

STA

MARÍA

MICAELA

04
°
30’2.0”N
-

74
°
05’10.6” W

JUAN

REY

04
°
31’7.0”N
-

74
°
05’18.7” W

QUIBA

04
°
32’34.6”N
-

74
°
09’21” W

SAN

BENITO

04
°
33’52.3”N
-

74
°
08’15.6” W

SIERRA

MORENA

04
°
34’29.8”N
-

74
°
10’14.4” W

DECANTADOR

04
°
34’18.0”N
-

74
°
04’6.8” W

VITELMA

04
°
34’31.0”N
-

74
°
04’18.8” W

GUADALUPE

04
°
35’31.1”N
-

74
°
03’16.1”W

TANQUE

PARAÍSO

04
°
37’40.8”N
-

74
°
03’30.2” W

CIRCUNVALAR U
. A. NARIÑO

04
°
38’11.9”N
-

74
°
03’36.1” W

CERRO

CAZADORES

04
°
39’56.6”N
-

74
°
01’42.5” W

16
Weather

Stations

River

upstream

Bogota

for

DEPAE

Study

Area

(
Weather

Stations
)

Methodology

Adquisition

informatión

Radar
image

satellite images of
cloudy scenes

Image

Processing

Parameter

Extraction

as:

contours

of
the

Clouds

Reflectivies


Segmentation

Image


through

Colombia does not have weather radar

Weather

radar
image


Sampling time: every 10 minutes

Location: Bogota D.C

Image Creation: From Time Series


Movie:

Different

Scales

Consider

Correlation

Image

between

Radar
image

Satellite

Image

Classification


Support

Vector
Machine (SVM)

Cluster

Two

or

more
classes

the correlation must be equal to 1

methods of supervised or unsupervised
classification

Path


Wavelet (
Space

-

Time)

Fourier (
Rotation

and
Translation
)

Kalman

Filter

Prediction

Tracking Storm

Rainfall

The

Mellin

transform

is

an

integral

transform

that

may

be

regarded

as

the

multiplicative

version

of

the

two
-
sided

Laplace

transform
.

This

integral

transform

is

closely

connected

to

the

theory

of

Dirichlet

series,

and

is

often

used

in

number

theory

and

the

theory

of

asymptotic

expansions
.

It

is

closely

related

to

the

Laplace

transform

and

the

Fourier

transform,

and

the

theory

of

the

gamma

function

and

allied

special

functions
.


Kalman

Filter

0
100
200
300
400
500
600
700
800
900
1000
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Threshold in witch I am certain that the plant state is at a given time


real plant behavior
observations over this plant
he Kalman filter prediction over the plant
original thought of the plant
Ground

gauge

and

radar

data

are

used

in

the

evaluation

to

provide

an

overview

of

daily

as

well

as

seasonal

statistics

of

satellite

and

ground
-
based

precipitation

observation
.


Several

regional

evaluation

studies

of

satellite

high
-
resolution

precipitation

were

applied

to

the

validation

of

results

and

calibration

C

A

L

I

B

R

T

I

O

N


A

N

D


V

A

L

I

D

A

T

I

O

N

E

X

P

E

C

T
E

D


R

E

S

U

L

T

S



Regionalization of rainfall fields


analysis of 1D and 2D image


Regionalization based on a
methodology that complements the
forecasting

R.F.
Cahalan
, in
Advances in Remote Sensing and

Retrieval Methods, edited by A. Deepak, H. Fleming,
J.
Theon

(Deepak Pub, Hampton, 1989), p. 371.

Fractals in
Geoscience

and Remote Sensing, Image
Understanding

Research Series, vol. 1, ECSC
-
EC
-
EAEC,

edited by G. G. Wilkinson, J.
Kanellopoulos
, J.
Megier

(Brussels, Luxemburg, 1995).

B
I
B
L
I
O
G
R
A
P
H
Y

Thanks