9 th annual CMAS conference Downscaling Comparison by

9 th annual CMAS conference Downscaling Comparison by WRF between Spectral and Grid Nudging Peng Liu, Alexandra P. Tsimpidi, Yongtao Hu, Armistead G. Russell, Athanasios Nenes Georgia Institute of Technology, Atlanta, GA, 30332 10 -13 -2010

Nudging Techniques and their issues Nudging: to bring the solution of model (Q) to the observed results or results from global model(Q*) Q= Q – f ×(Q – Q*) (f: nudging coefficient) Lateral nudging: Method and Goal: nudging only conducted in a zone near boundaries to smooth results near boundaries Issue: downscale results can hardly maintain large scale features provided by global model Grid nudging: Method and Goal: nudging conducted at every grid cell point of the whole domain to enforce downscaling results close to global model results Issue: include global model information of all scope of spectrum, in which the shortwave information are not as reliable as that of regional model

Nudging Techniques and their issues Spectral nudging: Method and Goal: only account for longwaves of the global model information to avoid the downscaling results from over-enforced by global model Issue: appropriate parameters need to be determined, such as nudging coefficient ---- common in all nudging techniques wave number ---- unique

Objectives To determine wave number and evaluate the choice, which includes: (1) compare with grid nudging technique (2) compare with different wave number choices or sensitivity to wave number

Part 1: Evaluation of Grid and Spectral Nudging Performance: similarity at different scales Design of Experiment NCEP/NCAR Reanalysis Data 2. 5*2. 5 deg. Jul 2009 Oct 2009 Jan 2010 Apr 2010 Grid nudging Spectral nudging wave number (3, 3) Based on (a)regional domain size and (b) reliable large-scale features provided by global model: >1500 km WRF domain: 6000 km × 4600 km Resolution 36 km Evaluation similarity Scale : 2000 km and 300 km Variables: water vapor mixing ratio, U and V of first vertical layer

Part 1: Evaluation of Grid and Spectral Nudging Performance: similarity at different scales Calculation of Similarity at Certain Scale Step 1 Divide the WRF domain into new cells in certain scale, e. g. 2000 km or 300 km Step 2 By Von Storch et at (2000) ψ*: input NCEP/NCAR field of a new cell, derived by calculating the spatial average of all original grid cells in the new cell ψ : WRF output field of a new cell, derived by calculating the spatial average of all original grid cells in the new cell < >: spatial average Meaning of Similarity t : time ---- at certain scale, how output keep the features of input field ---- higher similarity, stronger ability to keep input features

Part 1: Continued Similarity of Kinetic Energy at different scales (a) similarity of kinetic energy of Jul 2009 similarity 1 1 (b)similarity of kinetic energy of Jan 2010 similarity 0, 96 0, 92 0, 88 0, 84 0, 8 1 21 41 61 81 time series (every 6 h) With tested wave number(3, 3) 101 1 21 41 61 81 time series (every 6 h) 101 grid nudging at scale 2000 km spectral nudging at scale 2000 km grid nudging at scale 300 km spectral nudging at scale 300 km at large scale: spectral nudging performs better by giving higher similarity at small scale: spectral nudging performs better by giving lower similarity

Part 1: Continued Similarity of Water Mixing Ratio at different scales (a) similarity of water vapor mixing ratio of Jul 2009 1 1 similarity (b)similarity of water vapor mixing ratio of Jan 2010 similarity 0, 99 0, 98 0, 97 0, 96 0, 95 1 21 41 61 81 time series (every 6 h) 101 0, 95 1 21 41 61 81 Time series (every 6 h) 101 grid nudging at scale 2000 km spectral nudging at scale 2000 km grid nudging at scale 300 km spectral nudging at scale 300 km

Part 1: Continued Relative Difference between gird and spectral nudging of 36 km resolution WRF output Evaluated by Root Mean Square Error (RMSE): Where N is the total number of grid cell points and p is the results by spectral nudging and o is by grid nudging. u and v subscripts denote the U and V wind. for Qv: for wind vector: Result By Anthes(1983) (a) RMSE of Qv and wind vector of Jul 2009 normalized 0, 6 RMSE (b) WRMSE of Qv and wind vector of Jan 2010 0, 6 0, 5 0, 4 0, 3 0, 2 0, 1 0 QV wind vector 0 1 21 41 61 81 time series (every 6 h) 101 1 21 41 61 81 101 time series (every 6 h)

Part 2: Sensitivity Tests to Wave Numbers in Spectral Nudging Similarity of Kinetic Energy of 3 sets wave number at different scales (a) similarity of kinetic energy in scale 2000 km of Jan 2010 (b)similarity of kinetic erengy in scale 300 km of Jan 2010 1 0, 95 similarity 0, 99 0, 98 0, 97 0, 96 0, 85 0, 94 0, 93 0, 8 1 21 41 61 81 time series (every 6 h) 101 1 wave number(2, 2) 21 41 61 81 time series (every 6 h) wave number(3, 3) 101 wave number(6, 6) at large scale: Not sensitive; wave number (2, 2) gives extreme low similarity at small scale: A little more sensitive; wave number(6, 6) gives higher similarity

Part 2: Sensitivity Tests to Wave Numbers in Spectral Nudging Difference of WRF 36 km Resolution Output with wave number ( 2, 2) and (6, 6) with respect to output with wave number (3, 3) Evaluated by Root Mean Square Error (RMSE): (a) RMSE of Qv between different wavenumbers normallized RMSE 0, 16 0, 14 0, 12 0, 1 0, 08 0, 06 0, 04 0, 02 0 1 21 41 61 81 time series (every 6 h) 101 (b) WRMSE of wind speed between different wavenumbers normalized WRMSE 0, 45 0, 4 0, 35 0, 3 0, 25 0, 2 0, 15 0, 1 0, 05 0 1 21 41 61 81 time series (every 6 h) wavenumber(3, 3)-(2, 2) 101 wavenumber(3, 3)-(6, 6)

Conclusions: • In downscale spectral nudging performs better to meet the need at different scales • In the case studied, the choice of wave number is appropriate. • Generally, smaller wave numbers preferred, under the condition that large-scale features can be well captured • Results not sensitive to wave number, so no strict constrains when choose wave number; but if want to modify downscaling results, the change of wave number would be less possible to work.