Validation of the Proposed Texas Mesonet from the aspect of site spacing density. Ibrahim SONMEZ Ph.D Canditate Texas Tech University Atmospheric Science Group
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: 1. Statistical Approach: 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)
Literature Review: 2. Entropy Approach: 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)
Literature Review: 3. Dynamical Approach: 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)
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 Dataset: Parameters: Pressure, Temperature, Rel. Humidity, Wind Observations: 3 hourly 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
List of the stations 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
Site locations over Texas
Covariance (F**2) 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 Cov ~ (f,f)=cov(f,f)+σ 2 E σ 2 E =Cov ~ (f,f)-cov(f,f) (Gandin, 1969) 70 60 50 40 30 20 10 0 HOUSTON (TEMPERATURE, F) y = 1E-08x 3-4E-05x 2-0.0081x + 57.094 0 200 400 600 800 1000 Distance (km)
cavariance (F**2) 80 70 60 50 40 30 20 10 0 TEXAS TEMPERATURE y = 6E-08x 3-9E-05x 2-0.0044x + 62.45 R 2 = 0.7882 0 200 400 600 800 1000 1200 distance (km) Variance (at x=0) Intercepting point 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
Spatial Correlation Analysis r 1,2 = N 1 i= 1 N å ( x 1i - x s x 1 1 ) ( x s x 2 2i - x 2 ) Thiebaux,1974 Candidate analytic correlation functions. Equation Form Fixed Parameter F1 g a Cos( wx) exp( - lx ) none F2 g a Cos( wx) exp( - lx ) g =2.0 F3 g a exp( - lx ) none
Parameter analysis Par. Eq. α ω λ γ AES 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 2.4 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 3.56 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 3.15 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 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 8.6 Press. Temp. Humid. Wind_U Wind_V
correlation coeff. correlation coeff. correlation coeff. correlation coeff. correlation coeff. Spatial Correlation Scatter & Functions Pressure Temperature Humidity 1.2 1 0.8 0.6 0.4 0.2 0 y=0.99*exp(-1.02e-06x^1.9) 0 250 500 750 1000 1250 distance (km) y=0.98*cos(8.98e-04x)*exp(-3.33e-04x^1.1) 1 0.8 0.6 0.4 0.2 0 0 250 500 750 1000 1250 distance (km) 1 y=0.99*exp(-1.05e-03x^1.1) 0.8 0.6 0.4 0.2 0 0 250 500 750 1000 1250 distance (km) Wind_U y=0.73*cos(1.44e-03x)*exp(-1.57e-03x^1.0) 0.8 0.6 0.4 0.2 0 0 250 500 750 1000 1250-0.2 distance (km) Wind_V y=0.87*cos(1.70e-03x)*exp(-1.24e-04x^1.3) 1 0.8 0.6 0.4 0.2 0-0.2 0 250 500 750 1000 1250 distance (km)
Power Spectrum ï î ï í ì = ò - - function ariance Auto u C Spectrum Power m S number Wave m du e u C m S T T T m u i cov : ) ( : ) ( : where, ) ( ) ( 2p 2 ) ( ) ( s r u C u = Spectral density function: ò - - = T T T m u i du e u m S p r s 2 2 ) ( ) (
Pow er density Pow er density Pow er density Pow er density Pow er density Power Spectrum of parameters: 0.3 0.25 0.2 0.15 0.1 0.05 0 Pressure 0 5 10 15 20 25 30 w ave number (m) Temperature 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5 10 15 20 25 30 w ave number (m) Humidity 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5 10 15 20 25 30 wave number (m) Wind_U 0.1 0.08 0.06 0.04 0.02 0 0 5 10 15 20 25 30 w ave number (m) Wind_V 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5 10 15 20 25 30 w ave number (m)
Cumulative power spect. Cumulative Power Spectrum 100 90 80 70 60 50 40 30 20 10 0 0 2 4 6 8 10 12 14 16 18 20 wave number (m) P T H W_U W_V
Error estimation in true Fourier coefficients - to - Assumption: True field stretching from 2 2 x i2pm ìy( x) : True field Y = å L ( x) ane í - îan : True( coplex) coefficients L L a n = L 1 2 - x i2pn L L ò Y ( x) e L - 2 dx However, observation are taken at grid spacing of Dx where Dx = L N
Error estimation in true Fourier coefficients 1 (x ) 1 ˆ 2 N-1 0 j 2 N-1 0 j j x e M L x e L a L x n i j L x n i n j j D + D Y = - = - = å å p p î í ì error t Measuremen : M a of Estimation : â where j n n m m m a a ˆ - = e [ ] N ) (.. ˆ 2 2 2 2 M m N m N m m m m S S a a s e e + + = - = - +
Error square/sm Error Square term variation with wave # Temperature 3.0 2.0 1.0 200 km 150 km 100 km 75 km 50 km 0.0 0 5 10 15 20 Wave number (m)
Error square/sm Error square/sm Error square/sm Errror squre/sm Error Square term variation with wave # Pressure Humidity 2.0 1.5 1.0 200 km 150 km 100 km 75 km 50 km 2.0 1.5 1.0 200 km 150 km 100 km 75 km 50 km 0.5 0.5 0.0 0 2 4 6 8 10 Wave number (m) 0.0 0 5 10 15 20 25 Wave number (m) Wind_U Wind_V 6.0 5.0 4.0 3.0 2.0 200 km 150 km 100 km 75 km 50 km 4.0 3.5 3.0 2.5 2.0 1.5 200 km 150 km 100 km 75 km 50 km 1.0 1.0 0.0 0.5 0 5 10 15 20 Wave number (m) 0.0 0 5 10 15 20 25 30 Wave number (m)
Critical Wave numbers for parameters Spacing Δ x(km) Pressure Temperature Humidity Wind_U Wind_V 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
Sm, e**2 True field error variance estimation Sm error square Sm =1 e**2 0 0 k m
Error variance Error variance(m/s^2) Error variance (m/s^2) Error variance(mb^2) Error variance (C^2) True field error variance variation Pressure Temperature 3.3 3.2 3.1 5.5 5 3 2.9 2.8 4.5 4 2.7 2.6 2.5 2.4 0 50 100 150 200 250 Site spacing (km) 3.5 3 0 50 100 150 200 250 Site spacing (km) Relative Humidity Wind_U Wind_V 160 150 140 130 120 110 100 90 80 0 50 100 150 200 250 5.4 5.2 5 4.8 4.6 4.4 4.2 4 0 50 100 150 200 250 4.3 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.7 2.5 0 50 100 150 200 250 Site Spacing (km) Site spacing (km) Site spacing (km)
True field error variance decrement Parameter Error variance at 200 km spacing Error variance at 50 km spacing Decrement in error variance (%) 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 Parameter Error variance at 200 km spacing Error variance at 50 km spacing Decrement in error variance (%) 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
Conclusions & Suggestions 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
Acknowledgments Dr. Tim Doggett (advisor) Dr. John Nielsen-Gammon (ex advisor) Dr. Gerald North (Dept. Head) Grad students in Atm. Science Group Others.