Nonlinear Balance at Mesoscale: Balanced vertical motion with respect to model convection temperature tendencies

Transcription

1 Motivations and Methodology Results Summary Nonlinear Balance at Mesoscale: Balanced vertical motion with respect to model convection temperature tendencies Christian Pagé Peter Zwack Acknowledgements: Luc Fillion, Amin Erfani, Sylvie Gravel, Michel Desgagné WWRP Symposium on Nowcasting and Very Short Range Forecasting (WSN05) 5-9 September 2005 / Toulouse, France

2 Motivations and Methodology Results Summary Outline Motivations and Methodology Related work Numerical models Importance of divergence information to short-term convective forecasts NLB omega equation Results Quality of NLB omega diagnostics NLB omega equation terms Comparison NLB vs digitally filtered omega Divergent winds and analysis

3 Motivations and Methodology Results Summary Related work Models Divergence/convection NLB ω Higher-order balance in variational data assimilation Adiabatic balanced omega (QG) in the control variable (4DVAR) at ECMWF (synoptic scale) by Fisher (2003). Incorporate diabatic forcing terms in the QG omega equation (Fillion, 2004a-b): temperature tendencies from model s convection (parameterized /explicit). Is it possible to extend the method: Models at 1-10 km resolution Yes! Are there higher-order terms necessary? Not necessarily Are divergent winds important for short-term convective forecasts? Yes!

4 Motivations and Methodology Results Summary Related work Models Divergence/convection NLB ω Experiments Canadian GEM model: regional (REG) operational and Limited-Area (LAM) configurations (Côté at al., 1998). Multi-nested mesoscale model simulations Pilot model: REG 15 km. Nested model: LAM 2.5 km. LAM Model Integration timestep: 1 minute. Non-hydrostatic, explicit convection. Real case study Model initialization: July 7th UTC. Almost purely convective. No synoptic-scale baroclinic and upper level forcings.

5 Motivations and Methodology Results Summary Related work Models Divergence/convection NLB ω Importance of divergence information to short-term convective forecasts Nesting a LAM inside the LAM simulation of the case study. Two simulations where initial temperature, humidity, rotational winds and pressure : from pilot LAM. Div. winds from pilot VS div. winds removed Mean correlation ω hpa ω at 750 hpa after 45 min. 1 Initial divergence = correlation vs reference time (min.)

6 Motivations and Methodology Results Summary Related work Models Divergence/convection NLB ω NLB omega equation Diagnostic equation Nonlinear Balance (NLB) omega equation diagnostics: diabatic forcing terms from model s convection. Vertical motion of Ensembles of individual convective elements Comparison NLB omega vs digitally-filtered and unfiltered omega. Relative importance of the various terms in the NLB omega equation. R p 2 Sω + f (f + ζ) 2 ω p 2 f ω 2 ζ p 2 f [ ω v p x p ω ] u y p = R [ p 2 V T ] R q p 2 f [ V c p p (f ] + ζ) f [ ] k F + f [ ] ζag calculated using NLB p p t

7 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ NLB diagnostics vs model Results shown are valid after 5h of LAM forecasts (17 UTC) LAM Model and NLB diagnosed vertical motions Correlation: 0.92; Ratio of RMS: At 750 hpa. Contours 50 to 50 Pa/s (interval 5). Many of the ensembles of storm cells are old: close to balance.

8 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Relative magnitude of NLB omega equation terms In diabatic regions f p Nonlinear Balanced omega R p 2 Sω +f (f + ζ) 2 ω p 2 f ω 2 ζ [ ω x p 2 v p ω y u p ] = R p [ 2 V T ] f p R p 2 q c p [ V (f ] + ζ) ] +f p [ ζag t Up to All terms with f are negligible, except ageo. vort. tendency term

9 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Comparison NLB vs digitally filtered omega Results shown are valid after 1h30 of LAM forecasts (12h30 UTC) LAM Model and NLB diagnosed vertical motions Model vertical motion: no digital filter. Correlation: 0.87; Ratio of RMS: At 750 hpa. Contours 50 to 50 Pa/s (interval 5).

10 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Comparison NLB vs digitally filtered omega Results shown are valid after 1h30 of LAM forecasts (12h30 UTC) LAM Model and NLB diagnosed vertical motions Model vertical motion: digital filter 1h cut-off (3h time span). Correlation: 0.84; Ratio of RMS: At 750 hpa. Contours 50 to 50 Pa/s (interval 5).

11 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Comparison NLB vs digitally filtered omega Results shown are valid after 1h30 of LAM forecasts (12h30 UTC) LAM Model and NLB diagnosed vertical motions Model vertical motion: digital filter 3h cut-off (3h time span). Correlation: 0.70; Ratio of RMS: At 750 hpa. Contours 50 to 50 Pa/s (interval 5).

12 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Impact of divergent winds on a 1h30 forecast: experiment Nesting a LAM inside the LAM simulation of the case study. Two simulations where temperature, humidity, rotational winds and pressure : from pilot LAM. Div. winds from pilot VS balanced div. winds Mean correlation ω hpa ω at 750 hpa after 45 min. 1 Initial divergence = 0 Initial divergence = Nonlinear Balance 0.8 correlation vs reference time (min.)

13 Motivations and Methodology Results Summary Quality NLB diags NLB eqn terms NLB vs DF Div. winds/ Impact of divergent winds on a 1h30 forecast: experiment Two simulations where initial temperature, humidity, rotational winds and pressure : from pilot LAM. After 45 mins of forecasts (initial divergence from pilot LAM in black) initial divergence = 0 correlation=0.13 (0.21 after 30 min.) initial divergence = balanced correlation=0.70 (0.81 after 30 min.)

14 Motivations and Methodology Results Summary Summary This case study suggests that : NLB omega equation is valid for mesoscale convective ensembles as small as 15 km using model s diabatic temperature tendencies; Some spatial and temporal filtering is needed; Rotational effects are generally not significant; The term R p 2 Sω balances R p 2 q c p. Diagnosed balanced divergent winds contains useful information for the evolution of convection. Results not shown in this presentation : Model mass field is highly contaminated by high frequency oscillations. It is possible to calculate the balanced part of the mass field from the rotational winds using NLB equation. Questions?

15 Motivations and Methodology Results Summary Summary This case study suggests that : NLB omega equation is valid for mesoscale convective ensembles as small as 15 km using model s diabatic temperature tendencies; Some spatial and temporal filtering is needed; Rotational effects are generally not significant; The term R p 2 Sω balances R p 2 q c p. Diagnosed balanced divergent winds contains useful information for the evolution of convection. Results not shown in this presentation : Model mass field is highly contaminated by high frequency oscillations. It is possible to calculate the balanced part of the mass field from the rotational winds using NLB equation. Questions?