A statistical nowcasting method for an urban wind field at rooftop - PowerPoint PPT Presentation

A statistical nowcasting method for an urban wind field at rooftop level Ziv Klausner, Eyal Fattal Applied mathematics department 1

Urban wind field: varying homogeneity 15-8-98 2100 15-8-98 0800 2

Ongoing network of weather stations Ideal Reality Therefore, our approach: – Define a distribution – Choose a representative sample – Nowcasting using statistical inference

Population ’s spatial distribution Define the wind vector, in time t , at a point (x, y) U t , x y as a random variable The population of wind vectors in time t : wind in all possible points (x, y) in a given area A       U ; , F x y A P t x , y Parameters:  • Expectancy (2D vector) t  • Covariance (2x2 matrix) t 4

A sample of the spatial distribution Given the population, a representative sample can be chosen. It consists of n weather stations:    F U , U , ..., U S t t t x , x x , x x , x 1 1 2 2 n n From it, the following statistics are calculated:   u •   spatial average t  U t   v t       var u cov u v , •   covariance matrix t t t  S     t cov u v , var v   t t t   These are estimators for and t t 5

Tolerance region In terms of repeated sampling, for the i -th sample: • R i - tolerance region constructed to assure: E[ p i ] = P • p i - actual proportion contained in R i We choose to use elliptic R t in u, v space:            T   1 2 S U ; U U U U R D P t t t t t t t x , y x , y D 2 – Mahalanobis distance for P 6

D 2 (P) for the case of bivariate normal distribution   For a population ( and are known): t t        2 2 1 , 2 D P P For a sample (around for E[ P ]): U t           1   2 n 1 n 1 F 1 P ; 2 , n 2  2 D P , n    n n 2 Chew, Journal of American Statistical Association,1966 7

Application for the metropolitan area of Tel-Aviv Photographs by Yan Nasonov, Felix Rubinstein, Remi Jouan, EdoM, Paul Simpson, Cccc3333, 8 distributed under a CC-BY 2.0 license.

Stages 1. Choosing a sample 2. Sample’s representativeness examination 3. Tolerance region estimation: D 2 = f (E[ P ]) 9

Choosing a sample Available DB: • metropolitan Tel-Aviv • ~20 weather stations • rooftop level Based on meteorological considerations - entry of climatic phenomena to the area: • sea breeze • slope winds • weather fronts Therefore, weather stations on the area’s perimeter (“ fence ”) 10

Sample’s representativeness examination For each t we’ve calculated:   u •   t spatial average  U t   v t       var u cov u v , •   covariance matrix t t t  S     t cov u v , var v   t t t For every U t we’ve calculated:          T  2 1 S D U U U U U t t t t t t x , y x , y x  x  Once for and another for U F U F t P t S , y , y 11

Sample’s representativeness examination – D 2 distributions 12

Tolerance region: D 2 (E[P]) ─── D 2 =2.5, E[P] = 52% ─── D 2 =5.1, E[P] = 69% ─── D 2 =7.7, E[P] = 79% 13

Tolerance region: Empirical vs theoretical  Winter  Spring  Summer  Autumn 14

Learning: 2 months of each season R 2 = 0.9039 R 2 = 0.96086  0400  0800  1200  2100 15

Validation: on the remaining month  0400  0800  1200  2100 16

Discussion The model: • Inherent wind speed- direction correlation • Includes a distinct directionality ─── D 2 =2.5, E[P] = 52% ─── D 2 =5.1, E[P] = 69% ─── D 2 =7.7, E[P] = 79% 17

Summary • Wind field is represented by 4 perimeter stations • Nowcasting based on O/L measurements Advantages: • No need for further historical data • Relevant for all the area (rooftop level) • Speed-direction correlation, distinct directionality 18

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