Obukhov Length Computation using simple measurements from weather stations and AXYS Wind Sentinel Buoys

Transcription

1 Obukhov Length Computation using simple measurements from weather stations and AXYS Wind Sentinel Buoys Peter Taylor, Daniel Laroche, Zheng-Qi Wang and Robert McLaren : York University WWOSC, Montreal, Aug 2014

2 York weather station Cabauw mast

3 York weather staion data. Station/index.asp

4 AXYS Wind Sentinel buoy: lidar wind profiler plus in situ Air (3.4m) and water T and wind speed and direction (4.1m).

5 Obukhov Length (L) Dimension of Length (m) Related to ratio of TKE production through shear and buoyancy.

6 Solving for the Obukhov Length u s and θ s cannot be directly measured on a simple weather station. Assume velocity and temperature profiles are known functions of ζ =z/l Assume - Surface roughness length - Horizontal Homogeneity u s,θ s and L can then be determined from measurement of T and U.

7 Velocity and Temperature profiles Stable Stratification ( T >0) (2) (3)

8 Velocity and Temperature profiles Unstable Stratification ( T <0) (4) (5) Where (6)

9 Computing the Obukhov Length (L) Stable Stratification Rearranging (2) and (3)

10 Computing the Obukhov Length (L) FOR UNSTABLE SITUATIONS Using (4), (5) and (6) initialize with M=0 to find initial approximation of u s and θ s, then compute a new M. Iterate until M converges FOR STABLE OR UNSTABLE SITUATIONS OVER WATER Over water can use Charnock relation for z 0m = u s2 /(ag), and empirical expressions for z 0h (from Brutsaert) This involves another iteration cycle.

11 1.2 Profile Method ( 1/L 1 ) Flux Method ( 1/L 2 ) Wind Speed 8 Inverse of Calculated Obukhov Length, 1/L (m -1 ) Wind Speed (ms -1 ) /6/13 0: /6/ : /6/ : /6/13 0:00 Date Sample comparisons with Cabauw flux measurements of L - Summer

12 0.4 Profile Method ( 1/L 1 ) Flux Method ( 1/L 2 ) Wind Speed 15 Inverse of Calculated Obukhov Length, 1/L (m -1 ) Wind Speed (ms -1 ) /1/14 0: /1/ : /1/ : /1/14 0:00 Date Sample comparisons with Cabauw flux measurements of L - Winter

13 Calculated Obukhov Length (m) Calculated Obukhov Length (m) Wind Speed (ms -1 ) T (K) Ucrit (ms -1 ) Wind Speed (ms -1 ), T (K), Ucrit (ms -1 ) : : : : : :00 12: : :00 18: : :00 0: January 6, 2010 Sample data from York Weather Station, Winter

14 300 Calculated Obukhov Length (m) Wind Speed (ms -1 ) T (K) Ucrit (ms -1 ) 8 Calculated Obukhov Length (m) Wind Speed (ms -1 ), T (K), Ucrit (ms -1 ) : :00 4: : :00 10: : :00 16: : :00 22: :00-2 July 1, 2010 Sample data from York Weather Station, Summer

15 Histogram of 1/L York - winter month

16 Summer at York

17 WindSentinelResults (Stable Stratification) Roughness Length (m) z 11 x 0h and z 0m z 0h z 0m U (ms -1 ) U Measured validated Obhokov Length (m) Obhokov Length (L) T Measured validated U s s T (K) 0.3 U s (ms -1 ) s (K)

18 WindSentinel Results (Unstable Stratification) Roughness Length (m) z 11 x 0h and z 0m z 0h z 0m U (ms -1 ) U Measured validated Obhokov Length (m) Obhokov Length (L) T (K) T Measured validated U s (ms -1 ) U s s (K) s

19 0.2 Inverse Obukhov Length (m -1 ) Wind Speed (ms -1 ) T (K) Inverse Obukhov Length (m -1 ) Wind Speed (ms -1 ), T (K) : : :00 12: :00 12: :00 12: :00-8 December 1, December 4, 2013 (UTC) Sample WindSentinel data from Lake Michigan Grand Valley State University

20 Future Work Compare WindSentinel over water results with flux measurements on a tall mast in the Taiwan Strait. Apply to wind energy resource assessment studies and profile extrapolation. References Brutsaert, W. (1982). Evaporation Into the Atmosphere Theory, History, and Applications. 1st ed. Dordrecht: D. Reidel Publishing Company. Foken, T. (2003). Angewandte Meteorologie. 1st ed. New York: Springer. Laroche, D., Wang, Z. and Taylor, P. (2014). Estimation of the Obukhov length from wind speed and temperature measurements. Submitted to Boundary-Layer Meteorology. Taylor, P. (1970). A model of airflow above changes in surface heat flux, temperature and roughness for neutral and unstable conditions. Boundary-Layer Meteorology, 1(1), pp Taylor, P. (1971). Airflow above changes in surface heat flux, temperature and roughness; an extension to include the stable case. Boundary-Layer Meteorology, 1(4), pp