Texas Tech University

Atmospheric Science Group

Ibrahim SONMEZ

Ph.D Canditate

Validation of the Proposed Texas Mesonet

from the aspect of site spacing density.

Overview

Observation System over Texas

Proposed Texas Mesonet Project

Literature Review

Observational Error Estimation

Spatial correlation analysis

Power Spectrum Analysis

Error estimation in true Fourier coefficients

Conclusion & Suggestions

NWS Sites:

Coop Sites:

West Texas Mesonet sites

The Others:

What is wrong with the current network?

Not every parameter is observed in every site

Time resolution

The available surface observations are few and far away

– Surface site spatial resolution:150-200 km

– Upper air site spatial resolution: 400-500 km

– Only 1 of every 5 county is monitored

– Difficult to detect mesoscale phenomena

Very poor data from Gulf of Mexico

Literature Review:

Presented by Gandin(1963) and refined by Huss(1971), Theibaux(1973,1975) and Schlatter(1975)

Principle: To minimize the interpolation error at grid points

Requirement: Statistical structure (time & space covariance function)

Assumption: Domain is homogenous and isotrop

Aplications: Upper air network expantion by Gandin et. al.(1967), and Gandin(1970)

1. Statistical Approach:

Literature Review:

Based on Shanon (1949) information theory

Entropy is defined as a measure of uncertainty associated

with the probability of occurrence of an event

Aplications:Hydrological network design Caselton and

Husain (1980), optimum air monitoring network design

Husain and Khan (1983), meteorological network

expansion (Husain and Ukayli 1983; Husain et al. 1984;

Husain et al. 1986)

2. Entropy Approach:

Literature Review:

Numerical models are used to determine the observational density due to the error growth rate of the model

Limitations: evaluates the whole network, effected by the network configuration & time of the run

Aplications: Alaka and Lewis, (1967,1968), Kasahara (1972), Kasahara and Williamson (1972)

3. Dynamical Approach:

Proposed Texas Mesonet sites

Expected benefits of Mesonet:

Weather information: Improvement in the performance

of nowcasting and forecasting

Energy: Saving in energy use & exploring new energy

sources such as, wind and solar energy

Air Quality: Provide better input for models & reduce

medical costs

Agriculture: Recommendations about planting, watering

and harvesting

Forest & Grassland fire management:

Determination of the accurate fire weather conditions

Water Management: Accurate determination of rainfall,

flood control & power use

Education: Opportunity for using a scientific data &

research

Analysis over Texas

Parameters Number of

stations

Data

Period

Total

period

Pressure 14 1970-1994 25

Temperature 15 1970-1994 25

R. Humidity 15 1970-1994 25

Wind 15 1971-1993 23

Parameters: Pressure, Temperature, Rel. Humidity, Wind

Observations: 3 hourly

Dataset:

STATION NAME

STATION

WBAN #

LATITUDE

LONGITUDE

ELEVATION (M)

DALLAS/FT WORTH AP

3927

N32:54

W097:02

167.6

VICTORIA REGIONAL AP

12912

N28:51

W096:55

31.7

PORT ARTHUR JEFFERSN

12917

N29:57

W094:01

4.9

BROWNSVILLE INTL AP

12919

N25:54

W097:26

5.8

SAN ANTONIO INTL AP

12921

N29:32

W098:28

241.7

CORPUS CHRISTI INTL

12924

N27:46

W097:30

13.4

HOUSTON INT'CNTNL AP

12960

N29:58

W095:21

29.3

AUSTIN MUNICIPAL AP

13958

N30:17

W097:42

178.9

WACO MADISN COOPRAP

13959

N31:37

W097:13

152.4

ABILENE MUNI AP

13962

N32:25

W099:41

543.8

WICHITA FALLS MUN AP

13966

N33:58

W098:29

302.9

MIDLAND REGIONAL TER

23023

N31:57

W102:11

870.8

SAN ANGELO MATHIS FD

23034

N31:22

W100:30

579.4

LUBBOCK REGIONAL AP

23042

N33:39

W101:49

991.8

AMARILLO INTL ARPT

23047

N35:14

W101:42

1092.9

List of the stations

Site locations over Texas

Observational Error Estimation

Assumptions:

Errors are symmetric (the average is zero). Errors are not intercorrelated. Errors are not correlated with the true values of the quantity

HOUSTON (TEMPERATURE, F)

y = 1E-08x3 - 4E-05x

2 - 0.0081x + 57.094

0

10

20

30

40

50

60

70

0 200 400 600 800 1000

Distance (km)

Co

vari

an

ce (

F**

2)

Cov~(f,f)=Cov(f,f)+σ2E σ

2E =Cov~(f,f)-Cov(f,f)

(Gandin, 1969)

TEXAS TEMPERATURE

y = 6E-08x3 - 9E-05x

2 - 0.0044x + 62.45

R2 = 0.7882

0

10

20

30

40

50

60

70

80

0 200 400 600 800 1000 1200

distance (km)

cavari

an

ce (

F**

2)

Difference

Parameter Average

variance

95 % Confid.

interval

Average

intercepting

95 % Confid.

interval

Error

Variance

Pressure (mb^2) 31.27 31.27±3.89 28.8 28.8±0.98 2.47

Temperature (C^2) 20.88 20.88±2.00 17.88 17.88±0.73 3

Relative Humidity 251.68 251.68±41.72 176.04 176.04±15.71 75.64

Wind_u (m/s^2) 6.93 6.93±1.47 3.16 3.16±0.38 3.77

Wind_v (m/s^2) 15.78 15.78±2.17 13.3 13.3±0.71 2.48

Variance (at x=0) Intercepting point

Spatial Correlation Analysis

21

)( )(1 1

2211

2,1

xx

N

i

ii xxxx

Nr

ss

å=

--

=

Candidate analytic correlation functions.

Equation Form Fixed Parameter

F1 )exp()( glwa xxCos - none

F2 )exp()( glwa xxCos - g =2.0

F3 )exp( gla x- none

Thiebaux,1974

Parameter analysis

Par. Eq. α ω λ γ AES

Press

. F1 0.99 9.11E-05 5.29E-07 2 2.45

F2 0.99 9.11E-05 5.29E-07 2 2.45

F3 0.99 --- 1.02E-06 1.9 2.4Pre

ss.

Temp. F1 0.98 8.98E-04 3.33E-07 1.1 3.49

F2 0.89 1.59E-04 1.17E-06 2 3.78

F3 0.98 --- 1.32E-04 1.3 3.56Tem

p.

Hum

id. F1 0.99 8.73E-04 1.69E-03 1 3.17

F2 0.75 9.17E-05 2.57E-06 2 4.05

F3 0.99 --- 1.05E-03 1.1 3.15H

umid

.

Win

d_U F1 0.73 1.44E-03 1.57E-03 1 4.85

F2 0.56 1.89E-04 3.15E-06 2 4.94

F3 0.78 --- 1.28E-03 1.1 5.07

Win

d_V

Win

d_U

F1 0.87 1.70E-03 1.24E-04 1.3 7.75

F2 0.84 1.68E-03 1.60E-06 2 7.82

F3 0.95 --- 1.52E-04 1.4 8.6Win

d_V

Spatial Correlation Scatter & Functions

Pressure

0

0.2

0.4

0.6

0.8

1

1.2

0 250 500 750 1000 1250distance (km)

co

rre

lati

on

co

eff

.

y=0.99*Exp(-1.02E-06X^1.9)

Temperature

0

0.2

0.4

0.6

0.8

1

0 250 500 750 1000 1250

distance (km)

co

rre

lati

on

co

eff

.

y=0.98*Cos(8.98E-04X)*Exp(-3.33E-04X^1.1)

Humidity

0

0.2

0.4

0.6

0.8

1

0 250 500 750 1000 1250

distance (km)

co

rre

lati

on

co

eff

. y=0.99*Exp(-1.05E-03X^1.1)

Wind_U

-0.2

0

0.2

0.4

0.6

0.8

0 250 500 750 1000 1250

distance (km)

co

rre

lati

on

co

eff

.

y=0.73*Cos(1.44E-03X)*Exp(-1.57E-03X^1.0)

Wind_V

-0.2

0

0.2

0.4

0.6

0.8

1

0 250 500 750 1000 1250

distance (km)

co

rre

lati

on

co

eff

.

y=0.87*Cos(1.70E-03X)*Exp(-1.24E-04X^1.3)

Power Spectrum

ïî

ïí

ì

= ò-

-

functionarianceAutouC

SpectrumPowermS

numberWavem

dueuCmS

T

T

T

mui

cov:)(

:)(

:

where,)()(2p

2

)()(

sr

uCu =

Spectral density function: ò-

-

=

T

T

T

mui

dueumS p

rs

2

2)(

)(

Power Spectrum of parameters:

Pressure

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20 25 30

wave number (m)

Po

we

r d

en

sit

y

Temperature

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 5 10 15 20 25 30

wave number (m)

Po

we

r d

en

sit

y

Wind_U

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 30

wave number (m)

Po

we

r d

en

sit

y

Wind_V

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25 30

wave number (m)

Po

we

r d

en

sit

y

Humidity

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25 30

wave number (m)

Po

we

r d

en

sit

y

Cumulative Power Spectrum

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

wave number (m)

Cu

mu

lati

ve

po

we

r sp

ect.

P

T

H

W_U

W_V

Error estimation in true Fourier coefficients

Assumption: True field stretching from 2

2

Lto

L--

However, observation are taken at grid spacing of xD

where N

Lx =D

îíìY

=Y å¥

¥- tscoefficiencoplexTruea

fieldTruexeax

n

L

xmi

n )(:

:)( )(

2p

dxexL

a L

xni

L

L

n

p22

2

)(1 -

-

òY=

Error estimation in true Fourier coefficients

1

)(x1

ˆ21-N

0j

21-N

0j

j xeML

xeL

a L

xni

jL

xni

n

jj

D+DY=-

=

-

=

ååpp

îíì

error tMeasuremen :M

a of Estimation :a where

j

nn

mmm aa ˆ-=e [ ]

N)(

.

.ˆ

22

22

MmNmNm

mmm

SS

aa

se

e

++=

-=

-+

Error Square term variation with wave #

Temperature

0.0

1.0

2.0

3.0

0 5 10 15 20

Wave number (m)

Err

or

sq

uare

/Sm

200 km

150 km

100 km

75 km

50 km

Error Square term variation with wave #

Pressure

0.0

0.5

1.0

1.5

2.0

0 2 4 6 8 10

Wave number (m)

Err

or

sq

uare

/Sm

200 km

150 km

100 km

75 km

50 km

Humidity

0.0

0.5

1.0

1.5

2.0

0 5 10 15 20 25

Wave number (m)

Err

ror

sq

ure

/Sm

200 km

150 km

100 km

75 km

50 km

Wind_U

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 5 10 15 20

Wave number (m)

Err

or

sq

uare

/Sm 200 km

150 km

100 km

75 km

50 km

Wind_V

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 5 10 15 20 25 30

Wave number (m)

Erro

r s

qu

are

/Sm

200 km

150 km

100 km

75 km

50 km

Critical Wave numbers for parameters

Spacing

Δ x(km)

200 5 9 9 5 10

150 5 10 11 6 11

100 6 13 14 7 12

75 6 14 16 8 14

50 7 18 19 10 16

Wind_VPressure Temperature Humidity Wind_U

True field error variance estimation

0

0

m

Sm

, e

**2

Sm

error square

k

Sm

=1

e**2

True field error variance variation

Pressure

2.4

2.5

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

0 50 100 150 200 250

Site spacing (km)

Err

or

va

ria

nc

e(m

b^

2)

Temperature

3

3.5

4

4.5

5

5.5

0 50 100 150 200 250

Site spacing (km)

Erro

r v

aria

nc

e (

C^

2)

Relative Humidity

80

90

100

110

120

130

140

150

160

0 50 100 150 200 250

Site Spacing (km)

Err

or

va

ria

nc

e

Wind_U

4

4.2

4.4

4.6

4.8

5

5.2

5.4

0 50 100 150 200 250

Site spacing (km)

Err

or

va

ria

nc

e(m

/s^

2)

Wind_V

2.5

2.7

2.9

3.1

3.3

3.5

3.7

3.9

4.1

4.3

0 50 100 150 200 250

Site spacing (km)

Err

or

va

ria

nc

e (

m/s

^2

)

True field error variance decrement

Pressure (mb^2) 0.73 0.27 63.00

Temperature (C^2) 2.23 1.04 53.25

Relative Humidity 61.60 28.85 53.16

Wind_u (m/s^2) 1.56 0.76 51.45

Wind_v (m/s^2) 1.67 0.71 57.48

Decrement in error

variance (%)

Parameter Error variance at

200 km spacing

Error variance at

50 km spacing

Pressure (mb^2) 3.20 2.74 14.39

Temperature (C^2) 5.23 4.04 22.69

Relative Humidity 137.24 104.49 23.86

Wind_u (m/s^2) 5.33 4.53 15.06

Wind_v (m/s^2) 4.15 3.19 23.15

Error variance at

200 km spacing

Error variance at

50 km spacing

Decrement in error

variance (%)

Parameter

Large scale variations are governing most of the parameter variation

Large scale variation was highest in the pressure, temperature and humidity

Small scale variations are relatively important in the u component of the wind, humidity and v component of the wind

Error square term is very sensitive to site spacing amounts

Almost a linear decreasing trend in error variance is observed by smaller spacing amounts

14.39-23.86 % decrement in error variance is observed between 200 and 50 km spacing

Conclusions & Suggestions

Useful curves are obtained to identify the site spacing

amount depending on the desired error variance or to

identify the error variance depending on the desired site

spacing amount

Financial aspect of the problem also has to be considered

Same analysis may be repeated by considering the East-

West & North-South variation of the spatial correlation

Some other Agricultural parameter might be interesting to

analyze in the same sense

Conclusions & Suggestions

Acknowledgments

Dr. Tim Doggett (advisor)

Dr. John Nielsen-Gammon (ex advisor)

Dr. Gerald North (Dept. Head)

Grad students in Atm. Science Group

Others ….