Does increasing model stratospheric resolution improve. extended-range forecast skill?

Does increasing model stratospheric resolution improve extended-range forecast skill? 0 Greg Roff, David W. J. Thompson and Harry Hendon (email: G.Roff@bom.gov.au) Centre for Australian Weather and Climate Research (CAWCR), Melbourne, Australia Department of Atmospheric Science, Colorado State University, Fort Collins, USA Submitted to Geophys. Res. Letters

0 Abstract The effect of stratospheric resolution on extended-range forecast skill at high latitudes in the Southern Hemisphere is explored. Ensemble forecasts are made for two model configurations that differ only in vertical resolution above 00 hpa. An ensemble of 0-day forecasts is made from mid November initial conditions for each year -00. November is when the Southern Hemisphere stratosphere is most variable. As expected, the high resolution model is associated with better forecast skill in the stratosphere throughout the 0 day integration. Surprisingly, the high resolution model is also associated with better forecast skill in the troposphere ~- weeks after the initialization date. The mean-square error of the tropospheric forecast is reduced ~-% in the high resolution model between forecast days ~0-, and the reduction in error is statistically significant. The results suggest extended-range forecast skill can be improved in current forecast schemes by increasing model stratospheric resolution.

0 0. Introduction Observations suggest that stratospheric processes play a demonstrable role in driving extratropical tropospheric climate variability on intraseasonal timescales [Baldwin and Dunkerton,, 00]. Stratosphere/troposphere coupling thus provides a mechanism whereby relatively long-lived intraseasonal stratospheric variability contributes to tropospheric climate variability on timescales beyond the ~0 day limit of deterministic weather prediction [e.g., Thompson et al., 00; Baldwin et al., 00]. It also provides a mechanism whereby anthropogenic forcing at stratospheric levels is communicated to tropospheric levels [e.g., Thompson and Solomon, 00]. The implications of stratosphere/troposphere coupling for weather prediction have been estimated in three ways: ) by examining the observed linkages between stratospheric variability and tropospheric weather [e.g., Thompson et al., 00; Baldwin et al., 00; Charlton et al., 00; Christiansen, 00]; ) by comparing numerical forecasts initalized with varying stratospheric initial conditions [e.g., Charlton et al., 00, 00; Scaife and Knight, 00]; and ) by comparing numerical forecasts run on models with and without a model stratosphere [e.g., Kuroda, 00]. The results of previous forecast experiments suggest tropospheric skill is enhanced on extended-range timescales when the forecast is initialized with observed stratospheric initial conditions [Charlton et al., 00, 00; Scaife and Knight, 00] and when the forecast model top extends above 0 hpa [Kuroda, 00]. However, both of these conditions are already met in most numerical weather prediction schemes. Hence, the results of previous forecast experiments point to the importance of stratospheric processes in extended-range forecasts. But they do not suggest current numerical

0 weather prediction schemes need to be adjusted to better exploit the role of stratospheric processes in extended-range forecasts. In this study, we examine the impacts on tropospheric extended-range weather prediction not of stratospheric initial conditions but of vertical resolution of the stratosphere. The results reveal that raising the forecast model top and increasing the number of stratospheric levels yields a modest but significant increase in tropospheric forecast skill roughly ~- weeks into the future. In Section we outline the experiment set-up and tests used for assessing forecast skill. In Section we examine the effect of increasing model stratospheric resolution on forecast skill. In Section we discuss the implications of the results for current numerical weather prediction schemes. 0. Methodology Model setup The forecasts are run using the atmospheric component of the Australian Community Climate and Earth Systems Simulator (ACCESS) model [Puri, 00]. The atmospheric model is based on the U.K. Meteorological Office Unified Model version., and the model version used here is identical to the first generation Hadley Centre Global Environmental Model (HADGEM) [Martin et al., 00]. Forecasts are made with two configurations of the model that differ only in the number and placement of the vertical levels above 00 hpa. The stratospheric levels used in the two configurations are shown in Figure. The -level configuration (L) has levels below 00 hpa and 0 levels between 00 hpa and the model top at. hpa; the 0-level configuration (L0) has the same levels below 00 hpa, but levels between 00 hpa and the model top at ~0. hpa. Hence, relative to the

0 0 L configuration, the L0 configuration has both a higher top and increased resolution in the stratosphere. Both configurations are run with prescribed climatological sea surface temperatures, horizontal resolution of o. latitude and o. longitude, and the same physical parameter settings. A spectral gravity wave scheme is applied in both runs to help limit excessive westerlies in the polar vortex [Warner and McIntyre, 00, Scaife et al., 00], but simulations without this scheme yield similar results. Atmospheric initial conditions and verifying analyses for the forecasts are derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) re-analysis (ERA-0) [Uppsala et al., 00]. The forecasts are initialized using ERA- 0 Reanalysis data at six hour intervals over the three day period from 0000 UTC November to 00 UTC November, and for every year from to 00. Thus sets of initial conditions are drawn per year for ten years, resulting in 0 sets of initial conditions. The forecasts are run for 0 days and the model output is recorded at daily resolution. Note that the forecast initiation dates (mid-november) coincide with the time of year when both the month-to-month variance and the long- term trends in the Southern Hemisphere extratropical stratosphere are largest [Thompson and Solomon, 00; Thompson et al., 00]. The forecasts are run with three sets of initial conditions: the L initial conditions (L IC ); the L0 initial conditions (L0 IC ); and the L0 initial conditions degraded to L resolution. The L and L0 initial conditions are created by bilinearly interpolating the ERA-0 analyses onto the L and L0 model levels, respectively (the ERA-0 levels are indicated as diamonds in Figure ). The degraded L0 initial conditions (hereafter L0 IC ) are generated in order to assess the relative impacts on forecast skill of improved stratospheric resolution versus improved

stratospheric initial conditions. The L0 IC initial conditions are produced by interpolating the ERA-0 initial conditions first onto the L levels and then onto the L0 levels. From Figure it is clear that the primary effects of this degradation are above ~0 hpa. For example: the L0 initial conditions use all available information from ERA-0 up to hpa, and are fixed at the ERA-0 hpa values to the L0 model top; in contrast, the L0 IC initial conditions use all available information from ERA- 0 only up to the top of the L model (~ hpa), and are fixed at those values to the L0 model top. 0 0 Assessing forecast skill We focus on forecasts of geopotential height poleward of 0 o S. This is done since: a) we are interested in forecast skill in the Southern Hemisphere due to extratropical stratosphere/troposphere coupling; and b) geopotential height over the Southern Hemisphere polar cap is tightly linked to variability in the Southern Annular Mode [Kidson, ; Thompson and Wallace, 000]. Forecast skill is quantified by computing the mean-square-error ( MSE ) for - day running means of geopotential height, where the -day smoothing is done since we are interested in assessing skill on extended range timescales and not for individual days. MSE is first calculated for both the L and L0 forecasts as a function of ensemble member ( per year for 0 years) and at each model grid point and level in the vertical. The resulting values of MSE are then averaged over ensemble member and the polar cap to yield polar-mean MSE as a function of vertical level (z), and forecast time (t). The polar cap-mean values of MSE are thus found as:

MSE( z, t) = Z F ( φ, θ, z, t, en) Z N N N ( φ, θ, z, t, en) ) ( ) en φ θ en φ θ A 0 where φ is the longitude, θ is the latitude, z is the vertical level, t is the forecast day, en is the ensemble member, Z F and Z A are the forecast and analysed values of geopotential height, N φ is the number of longitudes around a latitude circle (), N θ is the number of latitudes over the polar cap (), and N en is the number of ensemble members (0). We also compute MSE for anomalies (rather than the full geopotential height field) in order to differentiate between a) forecast skill due to model representation of the climatological mean state versus b) forecast skill due to model prediction of the anomalies. The MSE of the anomalies ( MS E ) is computed using Eq. except that Z F is replaced by Z F, and Z A is replaced by Z. Here Z ' F denotes the forecast geopotential height minus the forecast model climatology and A Z A denotes the analysed geopotential height minus the ERA-0 forecast climatology, where both climatologies are functions of forecast day and computed from all 0 ensemble members. Skill scores are computed from the MSE as follows: MSE ) SS = ( ) * 00 MSE ref 0 where SS > 0 indicates a forecast improvement (i.e., a reduction in MSE ) relative to the reference forecast, and SS = 0 indicates a perfect forecast [e.g., Wilks, ]. In order to assess the improvement of the L0 forecasts relative to the L forecasts, we compute:

MSEL0 ) SS L0 / L = ( ) * 00 MSE L In order to assess the forecast skill of each version of the model relative to a climatological forecast, we use: MSEL0 MSEL ) SS L0 / c lim = ( ) * 00 and SS L / c lim = ( ) * 00. MSE MSE c lim c lim 0 For forecast anomalies, the MSE of a model forecast climatology (i.e., a forecast of zero anomaly) is simply MSE c lim = MSA, where MS A is the variance of the ERA-0 anomalies: = MSA ( z, t) N N N en ) φ θ en φ θ ( Z A ( φ, θ, z, t, en)) 0 When MS E / MSA < (or equivalently S S c lim > 0 ) for either model, the forecasts are deemed to be skilful because the magnitude of the forecast error is less than the magnitude of the variability that is being predicted. The significance of the improvement of L0 over L as expressed by SS L0 / L from Eq. is assessed using the t-statistic for the difference between two sample means (i.e., the difference between MSE L0 and MSE L ) evaluated for each ensemble member and each latitude over the polar cap, implying a sample size of N en. Nθ

0 0. Results The top panel in Figure shows SS L0 / L from Eq. (i.e., the relative skill score for the L0 version compared to the L version) averaged over the Southern Hemisphere polar cap as a function of forecast day and vertical level. The results are based on the full geopotential height field and thus reflect differences due to both the model climatologies and the model forecasts of the anomalies. Blue values indicate reduced forecast error for the high vertical resolution configuration (L0) relative to the low vertical resolution configuration (L). The most pronounced improvements in the L0 forecast are found in the stratosphere above ~0 hpa. The stratospheric differences are largely expected since the L0 configuration has considerably higher vertical resolution in the stratosphere and a higher model top than the L configuration. But surprisingly, the improvement in the L0 forecast extends from the stratosphere into the troposphere after about day 0. Relative to the L configuration, the L0 configuration yields ~-% reduced forecast error in the polar tropospheric geopotential height field at lead times of ~- weeks. Since geopotential height over the polar cap is an excellent proxy for the annular modes, the improved skill of predicting geopotential height at individual grid points over the polar cap suggests L0 provides improved prediction of the Southern Hemisphere annular mode at lead times of more than ~0 days. Do the differences in tropospheric skill in the top panel of Figure reflect better simulation of the climatological mean state or better forecasts of the anomalies by the L0 configuration? To test this, we show in the middle panel of Figure the skill score from Eq. calculated for geopotential height anomalies (i.e., we calculate MS E for both models using Eq., and then calculate S S L0/ L using Eq. ). Comparing the top and middle panels of Figure, it is clear that most of the improvements in tropospheric

0 0 0 skill by the L0 configuration derive from the model forecasts of the anomalous geopotential height field. The improvements in anomaly forecast skill are significant at the % level throughout the depth of the troposphere ~- weeks into the future (Figure c). Figure shows the skill associated with the model configurations relative not to each other, but to a climatological forecast. Hence we show S S L0 / c lim and S S L / c lim from Eq. evaluated over the polar cap and mass-weighted from 00-00 hpa. The skill scores from the two model configurations exhibit identical decreases prior to day and a levelling off of skill starting day. The skill scores diverge noticeably after day. The skill in the L configuration (dotted curve) begins to decline around day, and crosses the zero (no skill) threshold around day 0. In contrast, the skill in the L0 configuration (solid curve) does not decline until around day 0, and does not cross the zero (no skill) threshold until ~day. Hence, the tropospheric skill period (i.e., the period when MS E < MSA ) is extended by ~ days in the L0 version of the model relative to the L version. The dashed line in Figure shows the analogous forecast skill for the L0 configuration initialized with the L initial conditions (L0 IC ). The L0 runs initialized with the degraded L initial conditions have slightly weaker skill than the runs initialized with the L0 initial conditions. Hence the improvement in tropospheric skill attained from improved stratospheric resolution derives in roughly equal parts from ) the higher resolution of the initial conditions and ) the higher resolution used in the forward integration of the initial conditions.. Conclusions

0 0 The experiments shown here demonstrate that stratospheric resolution has a demonstrable effect on tropospheric forecast skill. Previous studies have examined the effects on numerical weather prediction of degraded stratospheric initial conditions [Charlton et al., 00, 00; Scaife and Knight, 00] and the effect of removing levels above 0 hpa [Kuroda, 00]. Previous work has also quantified the effect of stratospheric variability on statistical forecasts of tropospheric weather [Thompson et al., 00; Baldwin et al., 00; Charlton et al., 00; Christiansen, 00]. To our knowledge, this is the first study to explicitly quantify the improvements in tropospheric forecast skill derived from improved model stratospheric resolution. The experiments are run on two model configurations that differ only in the height and number of vertical levels in the model stratosphere. The high resolution model yields a ~-% increase in forecast skill integrated over the Southern Hemisphere polar troposphere at lead times between ~0-0 days. It is unclear why the increase in tropospheric skill is limited to the period after 0 days, though the lag in improved skill is consistent with results reported in previous studies that assess the impact of stratospheric initial conditions on tropospheric forecast skill [e.g., Charlton et al., 00]. The lagged improvement in skill suggests that increasing stratospheric resolution improves tropospheric forecasts on extended-range timescales but has a weak effect on tropospheric forecasts on shorter-term timescales. The improved skill reported here appears to stem in roughly equal parts from ) the increased vertical resolution of the stratospheric initial conditions, and ) the increased vertical resolution of the model used to integrate the initial conditions. We assessed forecast skill by first calculating the forecast error in geopotential height as a function of grid point and then averaging the resulting errors over the Southern Hemisphere polar cap. Virtually identical results are derived by first

averaging geopotential height over the polar cap and then calculating the forecast error of the resulting geopotential height averages (not shown). Geopotential height over the polar cap is highly correlated with variability in the Southern Hemisphere annular mode. Hence the results shown here have implications for extended-range forecasts of the SAM and its widespread climate impacts, including, for example, temperatures over Antarctica and southern South America [Thompson and Solomon, 00] and rainfall over Australia [Hendon et al., 00]. 0 Acknowledgements. Dave Thompson was funded by NSF Climate Dynamics program and by the CSU Monfort Professorship. This work was instigated by Dave Thompson s visit to CAWCR in February 00, which was partly supported by the South East Australian Climate Initiative. The authors would also like to thank the ACCESS group within CAWCR for all their modelling efforts which made this study possible.

0 0 References Baldwin, M. P., and T. J. Dunkerton (), Propagation of the Arctic Oscillation from the stratosphere to the troposphere, J. Geophys. Res., 0, 0-0. Baldwin, M. P., and T. J. Dunkerton (00), Stratospheric Harbingers of Anomalous Weather Regimes, Science,, -. Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. J. Charlton, and A. O'Neill (00), Stratospheric memory and extended-range weather forecasts, Science, 0(0), -0. Charlton A. J., A. O'Neill, D. B. Stephenson, W. A. Lahoz, and M. P. Baldwin (00), Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?, Q. J. R. Meteorol. Soc.,, 0-, doi:0./qj.0.. Charlton A. J., A. O'Neill, W. A. Lahoz, and A. C. Massacand (00), Sensitivity of Tropospheric forecasts to Stratospheric initial conditions, Q. J. R. Meteorol. Soc., 0, -, doi:0./qj.0.. Charlton A. J., A. O'Neill, W. A. Lahoz, A. Massacand, and P. B. Berrisford (00), The impact of the Stratosphere on the Troposphere during the southern hemisphere stratospheric sudden warming, September 00, Q. J. R. Meteorol. Soc.,, -, doi:0./qj.0.. Christiansen, B. (00), Downward propagation and statistical forecast of the near surface weather, J. Geophys. Res., 0, D0, doi:0.0/00jd00. Hendon, H. H., D. W. J. Thompson, and M. C. Wheeler (00), Australian rainfall and surface temperature variations associated with the Southern Hemisphere annular mode, J. Climate, 0(), -.

0 0 Kidson, J. W. (), Interannual variations in the Southern Hemisphere circulation, J. Climate,, -. Kuroda, Y. (00), Role of the stratosphere on the predictability of medium-range weather forecast: A case study of winter 00 00, Geophys. Res. Lett.,, L0,doi:0.0/00GL00. Martin, G. M., M. A. Ringer, V. D. Pope, A. Jones, C. Dearden, and T. J. Hinton, (00), The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM). Part I: Model description and global climatology, J. Climate.,, -0. Puri, K. (00), Project Plan for ACCESS, http://www.accessimulator.org.au/report/index.html Scaife A. A., N. Butchart, C. D. Warner and R. Swinbank (00), Impact of a spectral gravity wave parameterization on the stratosphere in the Met Office Unified Model, J. Atmos. Sci.,, -. Scaife A. A., and J. R. Knight, (00), Ensemble simulations of the cold European winter of 00-00, Q. J. R. Meteorol. Soc.,, -. Thompson D. W. J., and J. M. Wallace (000), Annular modes in the extratropical circulation. Part I: Month-to-month variability, J. Climate,, 000-0. Thompson D. W. J., and S. Solomon (00), Interpretation of recent southern hemisphere climate change, Science,, -. Thompson D. W. J., M. P. Baldwin, and J. M. Wallace (00), Stratospheric connection to Northern Hemisphere wintertime weather: implications for prediction, J. Climate,, -. Thompson D. W. J., M. P. Baldwin, and S. Solomon (00), Stratosphere-troposphere coupling in the Southern Hemisphere, J. Atmos. Sci.,, 0-.

Uppala S. M., and Co-authors (00), The ERA-0 re-analysis, Q. J. R. Meteorol. Soc.,, -0. Warner C. D., and M. E. McIntyre (00), An ultrasimple spectral parameterization for nonorographic gravity waves, J. Atmos. Sci.,,, -. Wilks D. S. (), Statistical methods in the atmospheric sciences: an introduction, San Diego Academic Press, International Geophysics Series,, pp.

0 Figure captions Figure The vertical levels above 00 hpa used in the L (left) and L0 (right) model configurations. The vertical levels of the ERA-0 stratospheric data are indicated by diamonds. Figure a) Skill score of total geopotential height (anomaly plus climatology) for L0 relative to L ( SS L0 / L from Equation ) shown as a function of log pressure and forecast time. The skill score is derived from the mean square error ( MSE ) integrated over all grid points polewards of 0 degrees South. The skill score is expressed as the percentage change in the error in the L0 forecast relative to the L forecast, with blue shading indicating increased forecast skill for the L0 configuration. The heavy line is the zero contour. b) As in the top panel, but for the skill score based on the forecast anomalies ( S S L0 / L ). c) The statistical significance of the results in the middle panel. Please see text for details of the calculations. Figure Skill score of the L0 (solid) and L (dotted) forecast anomalies relative to a climatological forecast ( S S L0 / c lim and S S L / c lim, respectively, from Equation ). Results are computed from MS E and integrated over all grid points poleward of 0 degrees South and at all levels between 00 and 00 hpa. The dashed line shows the corresponding skill score computed for the L0 model initialized with degraded L initial conditions (L0 IC ). Please see text for details of the calculatio

Figures Figure The vertical levels above 00 hpa used in the L (left) and L0 (right) model configurations. The vertical levels of the ERA-0 stratospheric data are indicated by diamonds.

Figure a) Skill score of total geopotential height (anomaly plus climatology) for L0 relative to L ( SS L0 / L from Equation ) shown as a function of log pressure and forecast time. The skill score is derived from the mean square error ( MSE ) integrated over all grid points poleward of 0 degrees South. The skill score is expressed as the percentage change in the error in the L0 forecast relative to the L forecast, with blue shading indicating increased forecast skill for the L0 configuration. The heavy line is the zero contour. b) As in the top panel, but for the skill score based on the forecast anomalies ( S S L0 / L ). c) The statistical significance of the results in the middle panel. Please see text for details of the calculations.

Figure Skill score of the L0 (solid) and L (dotted) forecast anomalies relative to a climatological forecast ( S S L0 / c lim and S S L / c lim, respectively, from Equation ). Results are computed from MS E and integrated over all grid points poleward of 0 degrees South and at all levels between 00 and 00 hpa. The dashed line shows the corresponding skill score computed for the L0 model initialized with degraded L initial conditions (L0 IC ). Please see text for details of the calculations.