Downward propagation and statistical forecast of the near-surface weather

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2004jd005431, 2005 Downward propagation and statistical forecast of the near-surface weather Bo Christiansen Danish Meteorological Institute, Copenhagen, Denmark Received 10 September 2004; revised 17 March 2005; accepted 14 April 2005; published 23 July [1] We investigate the potential for using the downward propagation of anomalies from the stratosphere to the troposphere in extended-range statistical forecasts. Considering the near-surface zonal mean zonal wind at 60 N and the near-surface temperature in northern Europe as predictands, we find that the inclusion of stratospheric information improves the daily forecast on lead times larger than 5 days. The best forecasts are obtained for predictors in the lower stratosphere. Similar predictions cannot be obtained if the statistical forecast only includes tropospheric information. The simple statistical forecast based on stratospheric winds compares favorably to the forecasts of a state-of-theart dynamical ensemble prediction system. The statistical forecast can be substantially improved by considering only strong stratospheric anomalies and by predicting averaged values. Citation: Christiansen, B. (2005), Downward propagation and statistical forecast of the near-surface weather, J. Geophys. Res., 110,, doi: /2004jd Introduction [2] Downward propagation of anomalies in middle and high latitudes was first observed in mechanistic models of the stratosphere in the 70ies [Holton and Mass, 1976]. In typical perpetual January experiments the variability has an oscillating form where the death of an anomaly at the lower boundary is followed by the birth of a new anomaly at the upper boundary. This phenomenon is known as stratospheric vacillations. The typical timescale of the downward propagation is days although it depends on the parameters of the mechanistic model, in particular on the strength of the wave forcing at the lower boundary. The stratospheric vacillations were recently [Christiansen et al., 1997; Christiansen, 2000] observed in general circulation model (GCM) experiments. It is important to note that in both the mechanistic models and the GCM [Christiansen, 1999] the stratospheric vacillations are a result of a stratospheric instability and the vacillations exist even if all boundary conditions, including the wave forcing at the tropopause, are constant in time. [3] In the last two decades several papers analyzing the observed poleward and downward propagation in the stratosphere have been published [Kodera et al., 1990; Kodera, 1995]. However, with the discovery of the Arctic Oscillation [Thompson and Wallace, 1998] and the connection between the downward propagation and this global circulation mode [Baldwin and Dunkerton, 1999] the interest in the field grew remarkably. A major driver of the interest is the possibility of using the downward propagation to improve extended-range forecasts. Several papers show significant connections between stratospheric anomalies and Copyright 2005 by the American Geophysical Union /05/2004JD anomalies near the surface when the surface lags the stratosphere by days [Christiansen, 2001; Baldwin and Dunkerton, 2001; Thompson et al., 2002; Kuroda, 2002; Black, 2002; Baldwin et al., 2003]. A natural next step in this direction would be to develop statistical forecast models which incorporate this connection. Charlton et al. [2003] reported such a model which, however, seems to underestimate the coupling between the stratosphere and the troposphere. We will comment on this study in more details in both section 2 and in the Conclusions. Dynamical forecasting with GCMs is also an attractive possibility as the downward propagation is very well represented at least in some GCMs [Christiansen, 2001]. However, it is not known how well the downward propagation is represented in current extended-range and seasonal forecast systems. [4] In this paper we present a systematic study of a simple statistical forecast model. A major focus will be on forecasting the surface zonal mean zonal wind at 60 N by the zonal mean zonal wind at other altitudes. This parameter was chosen because it is physically meaningful and because it shows strong downward propagation. We will study how the forecast depends on parameters such as the lead time, the number of predictors, the time over which the predictand is averaged, and the strength of the predictor. Also, the predictions of the statistical forecast will be compared to the predictions of a dynamical ensemble forecast system. 2. Data and Methodology [5] Most previous studies of the downward propagation have relied on the NCEP reanalysis. In this study we will use the ERA-40 reanalysis [Simmons, 2001] which has the advantage that it extends to 0.1 hpa where the NCEP [Kalnay et al., 1996] reanalysis stops at 10 hpa. We will see that concerning the zonal mean zonal wind at 60 N the 1of10

2 Figure 1. Schematic overview of the forecast model. The predictand P is separated from the n predictors p i, i =0,1,...n 1, by the lead time T. The predictand is averaged over a time interval t. The predictors are averaged over a time interval d and separated by a time interval D. two data sets agree exceptionally well below 10 hpa. We use daily averages of the zonal wind defined on 26 pressure levels for the ERA-40 data set (16 above 100 hpa, 5 above 10 hpa). The 44 years from 1958 to 2001 are used. [6] At the European Centre for Medium Weather Forecasts (ECMWF) a new dynamical ensemble seasonal forecast system (S2) based on a coupled ocean-atmosphere model was introduced in 2002 [Anderson et al., 2003]. The atmospheric component of the forecast system, which is initialized from the ECMWF operational system, is the version of IFS (Integrated Forecast System) used in the ERA-40 reanalysis, but with 40 vertical levels. The topmost level is at 10 hpa and the model has 5 levels above 100 hpa and 9 levels above 200 hpa. The seasonal forecast system shares the dynamical core (IFS) with the general circulation model ARPEGE, which has been shown to simulate the downward propagation and the stratosphere-troposphere coupling very well at least in a statistical sense [Christiansen, 2001]. However, ARPEGE extends deeper into the stratosphere than the seasonal forecast system. ARPEGE has 41 vertical levels with the top near 0.1 hpa, 5 levels above 10 hpa, 10 levels above 100 hpa, and 14 levels above 200 hpa. With the seasonal forecast system five-member ensembles starting at the first of each calendar month since 1987 have been performed. We use the forecasts starting the first of January, February, and December from 1987 to Thus we have a total of 51 dynamical forecasts. [7] The forecast study deals exclusively with anomalies, i.e., deviations from the annual cycle. For the reanalysis the anomalies were calculated by subtracting from each day the long-term mean over that day of the year. For the dynamical forecasts the anomalies were calculated by subtracting from each day the combined ensemble and long-term mean over that day. However, removing the annual cycle has only marginal effects on the results presented in this paper. We mainly focus on the three winter months December, January, and February, because the stratosphere-troposphere coupling is strongest then (see the discussion at the end of section 4). [8] Our statistical forecast model is based on simple multiple linear regression. Denoting the n predictors p i, Pi =0,1,...n 1, we determine the coefficient a i such that i a i p i (t) is the best fit to the predictand P(t + T), by minimizing the squares of the residuals (the summation is over i). Here, T is the lead time. As a measure of the goodness of the fit we use the correlation between the forecast P and the predictand, i.e., the correlation between i a i p i (t) and P(t + T) (the summation is over i). Often we want to predict the zonal mean zonal wind at the surface, u 0, from its own previous values or from previous values of the zonal mean zonal wind at another level, u l. We want to allow for time averaging of both the predictand and the predictors so we put P(t + T) =hu 0 (t)i t+t+t t+t and p i (t) =hu l (t)i t id t id d, t where hxi 2 t1 denotes the time average of x over the interval from t 1 to t 2. The situation is shown schematically in Figure 1. Note, that with these definitions data included in the predictand and the predictors are separated by the lead time T despite the time averaging. Any dependence of the predictand on the predictors is therefore a consequence of a dependence in the data being it physical or fortuitous. [9] Recently, Charlton et al. [2003] presented a statistical forecast model where the Arctic Oscillation at the surface is predicted from the Arctic Oscillation at different vertical levels. Their study is based on a conceptual model describing the stratosphere-troposphere connection for positive lags as an indirect relationship, and lagged correlations between the surface and the stratosphere are never presented directly but always multiplied by the correlation coefficient between the predictand and the predictor at lag zero. However, one could as well argue that the stratosphere-troposphere coupling is the direct relationship. The justification would include the clear downward propagation seen in Figure 2 and the underlying mechanism based on the interactions between zonal mean wind and planetary waves [Christiansen, 1999, 2001]. In the present paper the correlation coefficients between the stratosphere and the troposphere are presented directly and the description of the stratosphere-troposphere relationship as direct or indirect is therefore avoided. As the instantaneous correlation coefficient between the Arctic Oscillation at the surface and the Arctic Oscillation in the lower stratosphere is 0.5, the model chosen by Charlton et al. [2003] leads to a underestimation of the variance connected to the stratosphere-troposphere relationship with a factor of 4 compared to the results of the present paper. [10] To estimate the significance of the correlations we use the Monte Carlo approach described by Christiansen [2001]. This approach involves the construction of surrogate time series with the same length, the same autocorrelation spectrum, and the same seasonal asymmetry in the variability as the original predictand. The seasonal asymmetry in the anomalies is caused by the seasonality of the variance which is usually stronger in winter than in summer. These surrogate time series are then forecasted in the same way as the original predictand. The distribution of the correlations between the surrogate time series and their forecasts (these correlations are different from zero only because of the finite sampling) are then compared to the correlation calculated with the original predictand. If s% of the surrogate time series have correlation coefficients numerically larger than the correlation coefficient of the original predictand the latter is considered significantly different from zero at the (1 s)% level. 3. Downward Propagation in Reanalysis Data [11] As mentioned in the previous section most work on the downward propagation has been based on data from the 2of10

3 Figure 2. Zonal mean zonal wind at 60 N as function of time and pressure. The annual cycle and timescales faster than 30 days have been removed. The data are from the ERA-40 reanalysis. The contour levels are separated by 5 m s 1. Positive anomalies are yellow and red. Negative anomalies are green and blue. 3 of 10

4 Figure 3. Lagged correlations at 60 N (top) between the zonal mean zonal wind at the surface and the zonal mean zonal wind at other levels and (bottom) between the zonal mean zonal wind at 10 hpa and the zonal mean zonal wind at other levels. The annual cycle has been removed. Figure 3 (left) shows correlations for the unsmoothed daily data, and in Figure 3 (right), timescales faster than 30 days have been removed. The data are from the ERA-40 reanalysis. Light and dark shading indicate regions where the correlations are significantly different from zero on 95 and 99% levels according to a Monte Carlo test. NCEP reanalysis. Before we use the ERA-40 reanalysis we want to investigate if the two reanalyses differ with respect to the details of the downward propagation. The downward propagation at 60 N is clearly seen when the zonal mean anomalies are plotted as function of time and pressure as in Figure 2 for the ERA-40 data. Here the annual cycle has been removed and the data have been low-pass filtered to retain only timescales slower than 30 days. A figure similar to Figure 2 for 6 years of the NCEP reanalysis was shown by Christiansen [2001]. We note the exceptional similarity of the two reanalyses although they are based on different models with different horizontal and vertical resolutions. This comparison suggests that the large-scale features reflect the data and are only weakly affected by the model system. We also note that the downward propagation is present up to the highest levels of the ERA-40 reanalysis. [12] The downward propagation in the ERA-40 reanalysis is summarized in Figure 3. In Figure 3 (top) the correlations between the zonal mean zonal wind at 10 hpa (1000 hpa in Figure 3, bottom) and the zonal mean zonal wind at other levels are shown as function of time lags between 50 and 50 days. Data from the whole year have been included. Figure 3 (left) is calculated from low-passed filtered data, and Figure 3 (right) is calculated from unfiltered daily values. Downward propagation is clearly seen in Figure 3. The low-pass filtering has only little effect when the center of the analysis is at 10 hpa. A larger effect of the filtering, up to a factor of two, is found when the center is near the surface. An important feature of Figure 3 (top) is that the correlations are larger in the stratosphere than in the troposphere for sufficiently large negative lags. This holds for lags less than 7 days for the unfiltered data and for lags less than 15 for the smoothed data. This observation suggests that the stratosphere may provide information for the prediction of the near-surface wind that cannot be obtained from the troposphere. [13] From Figure 3 the predictive power of the stratosphere seems rather low with correlations between the stratosphere and surface less than 0.2 for the daily data and less than 0.3 for the smoothed data. However, these correlations are significantly different from zero on the 99% level and in the next section we will see that the predictive power can be increased by restricting the forecast to the winter season, forecasting averaged values, and including only strong stratospheric anomalies. 4. Statistical Forecast [14] In this section we present results from the statistical approach described in section 2. We will in particular be interested in how the forecast depends on the lead time T and the time interval t over which the predictand is averaged. Other parameters are the number of predictors n, the time interval between the predictors D, and the time interval d over which the predictors are averaged. The predictand will be the zonal mean zonal wind at the surface at 60 N and the near-surface temperature (1000 hpa) in northern Europe. The predictors will be the zonal mean zonal wind at 60 N in different vertical levels in the troposphere and the stratosphere. In the following we consider the winter season (December, January, and February) where the downward propagation is strongest. At the end of the section we will briefly touch upon the seasonal dependence of the forecasts. [15] Figure 4 shows the correlation between the forecast and the predictand as function of the lead time T for predictors chosen at the surface (green curve), at 70 hpa (red curve), and at 10 hpa (blue curve). In Figure 4 (top) t = 4of10

5 Figure 4. Correlations between forecast and predictand as function of lead time T: (top) t = 1 day and (bottom) t = 14 days. The other parameters are n = 1 and d = 1 day. The vertical level of the predictors are 1000 hpa (green curve), 70 hpa (red curve), and 10 hpa (blue curve). The purple curve shows the correlations when the zonal winds at 1000 hpa and 70 hpa are simultaneously used as predictors. 1 day, and in Figure 4 (bottom) t = 14 days. The other parameters are n = 1 and d = 1 day. With the zonal wind at the surface as the predictor and t = 1 day the correlation is larger than 0.6 for a lead time of 1 day but the correlation decreases fast as function of the lead time. With the zonal wind at 70 hpa as predictor the correlation is 0.4 for a lead time of 1 day. However, now the correlation decreases more slowly with the lead time and for lead times larger than 5 days it is larger than for the predictor at the surface. The largest difference in the correlation is found for lead times of days where the difference is more than a factor of two. The correlation for the predictor at 10 hpa is lower than for the predictor at 70 hpa for lead times less than 30 days while the two correlations are almost identical for lead times larger than 30 days. For t = 14 days a similar picture is found but now a larger correlation is obtained with the predictor in the lower stratosphere. This correlation is now much larger than the correlation for the predictor at the surface for all lead times. [16] Calculating the distribution of correlations from surrogate time series resembling the predictand as discussed in section 2 allows us to estimate whether the correlations are significantly different from zero. For t = 1 day (Figure 4, top) significant correlations at the 95% level are obtained for T < 25 days for the predictor at 1000 hpa and for T < 50 days for predictor in the stratosphere. For t = 14 days (Figure 4, bottom) the equivalent limits are 20 days and 40 days, respectively. [17] Figure 5 offers a closer look at the dependence of the statistical forecast on the vertical level of the predictor. While the correlations are almost constant with height when the predictor is located in the troposphere a large jump is seen around the tropopause. In the stratosphere below 3 hpa the correlations decrease slowly with height for lead times less than 25 days while the correlations are almost constant for lead times larger than 25 days. For lead times less than 25 days a maximum is found near 70 hpa in agreement with the results of Charlton et al. [2003]. The correlations are significantly different from zero at the 99% level except for large lead times and when the predictor is located in the uppermost layers of the stratosphere. [18] Details of the dependence of the forecast on the time interval t over which the predictand is averaged and the lead time T are given in Figure 6. Here the predictor is at 70 hpa. The correlations between the forecast and the predictand increase with small values of t, reach a maximum, and then start to decrease. The maximum is reached around t = 25 days for small lead times. As the lead time increases the maximum correlation is found for decreasing values of t. The correlation increases strongest with t for small lead times. For T = 10 days the correlation increases from 0.35 for t = 1 day to 0.48 for t = 20 days. For a lead time of 10 days and a t of 30 days we still have a correlation of This is in good agreement with the result of Baldwin et al. [2003] who considered a forecast of the Arctic Oscillation at the surface using the Arctic Oscillation at 150 hpa as predictor for these specific values of the lead time and t. In Figure 6 the correlation is significantly different from zero everywhere except for the largest lead times and the largest t. [19] The forecast improves only very weakly when more predictors describing the previous state of the stratosphere Figure 5. Correlations between forecast and predictand as function of lead time T and the vertical level of the predictor. The other parameters are n =1,d = 1 day, and t = 1 day. Light and dark shading indicate regions where the correlations are significantly different from zero on 95 and 99% levels according to a Monte Carlo test. 5of10

6 Figure 6. Correlations between forecast and predictand as function of the lead time T and the time t over which the predictand is averaged. The other parameters are n = 1 and d = 1 day. The level of the predictor is 70 hpa. Shading is as in Figure 5. are included. This can be seen from Figure 7 where the predictors are daily values of the zonal mean wind at 70 hpa separated by 5 days. Also, the forecast improves only marginally when predictors at different stratospheric levels are included simultaneously (not shown). This suggests that only little is gained by including more information about the previous state of the stratosphere. Using both stratospheric and tropospheric predictors simultaneously only improves the forecast marginally for lead times larger than 10 days as seen from the purple curves in Figure 4. This suggests that the forecast with only one predictor at a vertical level of 70 hpa will be hard to improve upon regarding lead times larger than 10 days as has been confirmed by additional calculations. We have investigated if the inclusion of information from other latitudes in the stratosphere would improve the forecasts. As predictors we used the leading principal components obtained from an Empirical Orthogonal Function analysis of the stratospheric zonal mean zonal wind north of 20 N. We did not find correlations that are larger than the correlations obtained when the zonal mean zonal wind at 60 N, 70 hpa is used as predictor. [20] Up to now we have considered all winter days regardless of the strength of the predictor. We expect that the forecast can be improved if it is restricted to days where the predictor has strong anomalies. With the zonal mean wind at 70 hpa as predictor we have selected the days where the numerical value of the predictor exceeds a given threshold. Figure 8 shows the resulting correlations between forecast and predictand as function of lead time and the threshold. The threshold is measured in units of the standard deviation of the predictor over the winter season. The correlations increase drastically by 30 50% for all lead times when the threshold increases from zero to one. For a lead time of 20 days the correlations increase from 0.38, when all days are included to 0.50, when only days with stratospheric winds exceeding one standard deviation are included. The correlations are significantly different from zero nearly everywhere, but one could worry that the observed increase of the correlations with the strength of the anomalies is a fortuitous effect of the associated reduced number of degrees of freedom, which will increase the statistical scatter of the correlations. To test if the increase in the correlations is only due to chance we have repeated the calculation for 6 subsets of the data. Two of the subsets were 22 winters long and four subsets were 11 winters long. For all these subsets we observed the same increase in correlations as in Figure 8 and we therefore conclude that the improvement of the forecast is a real physical effect. [21] The zonal mean zonal wind at 60 is closely related to the North Atlantic Oscillation and the Arctic Oscillation as will be quantified in the Conclusions. With regards to surface temperature we expect the largest influence of the stratospheric state to be in the regions most controlled by the Arctic Oscillation. In accordance we find the largest correlations with the stratospheric wind to be over Siberia, North Europe, Greenland, and North Africa. Figure 9 shows Figure 7. Correlations between forecast and predictand as function of lead time T and the number of predictors n. The other parameters are d = 1 day, D = 5 days, and t = 1 days. The level of the predictor is 70 hpa. Shading is as in Figure 5. Figure 8. Correlations between forecast and predictand as function of lead time T and the strength of the predictor. Only days where the absolute value of the predictor is larger than the threshold (measured as a fraction of the predictor s standard deviation) are included. The other parameters are t = 14 days, n = 1, and d = 1 day. The level of the predictor is 70 hpa. Shading is as in Figure 5. 6of10

7 Figure 9. Correlations between forecast and predictand function of the lead time T when predicting temperature in northern Europe. The predictor is the zonal mean zonal wind at the surface (green curve), the zonal mean zonal wind at 70 hpa (red curve), and the temperature in northern Europe itself (blue curve). The purple curve shows the forecast when the zonal wind at 70 hpa and the surface temperature are simultaneously used as predictors. The other parameters are t = 14 days, n = 1, and d = 1 day. the prediction of the temperatures in northern Europe (averaged over longitudes between 0 and 60 and latitudes between 50 and 75 ). For small lead times the prediction based on the temperature itself (persistence) performs better than the forecast based on stratospheric winds. However, for lead times larger than 20 days the stratospheric wind give larger correlations than both surface winds and surface temperatures. Using both the surface temperature and the stratospheric wind as simultaneous predictors improves the forecasts moderately. [22] Previously we have described forecasts based on all three winter months December, January, and February together. This period was chosen as where the downward propagation is strongest according to visual inspection of Figure 1. To assess the seasonality of the forecasts we have repeated the analysis leading to Figure 4 (top) now based on each of the 6 months from November to April. With the predictor at 70 hpa we find that in general the forecast model performs best in December, January and February, somewhat worse in March, and much worse in November and April. As an example the correlations for a lead time of 30 days are 0.05, 0.23, 0.26, 0.21, 0.15, and 0.06 for the months November, December, January, February, March, and April, respectively. Our results correspond to those of Baldwin et al. [2003] but do not support the conclusion of Charlton et al. [2003] based on their indirect model that the stratosphere-troposphere relationship is strongest in February and March. 5. Comparison With Dynamical Forecasts [23] In this section we compare our statistical forecast with a comprehensive dynamical forecast system. The ultimate question is if dynamical forecast systems can be improved by improving the stratosphere-troposphere coupling in the models. The ECMWF seasonal forecast system is based on a coupled ocean-atmosphere model and the atmospheric part does include the stratosphere although with the topmost layer as low as 10 hpa. Unfortunately no stratospheric fields have been stored from the forecast. We can therefore not address the stratosphere-troposphere coupling in the model directly, but must here be satisfied with a comparison of the statistical and dynamical forecasts. [24] As mentioned in section 2 we have 51 forecasts, where each forecast consists of a five-member ensemble. We will consider the ensemble mean over the five members as the forecast which will be compared with the corresponding analysis. Figure 10 shows the correlations between the forecasts and the analysis of the zonal mean zonal wind at 60 Nas function of lead time (blue curve) for t = 1 day. The green and red curves are the results from the statistical forecast with the predictor at 1000 hpa and 70 hpa. These two curves are identical to those in Figure 4 (top). Also shown (orange curve) is the correlations obtained from the statistical forecast with the predictor at 70 hpa but restricted to the same 51 events as the dynamical forecast. The curves in Figure 10 showing the correlations based on the 51 events have been smoothed with a 5-day running mean filter before plotting to suppress noise. The difference between the orange and red curves gives an impression of the effect of sampling only 51 events. Monte Carlo simulations confirm that the correlations based on 51 events have a 95% confidence interval of around ±0.09. The main conclusion to be drawn from Figure 10 is that for lead times larger than 10 days the simple statistical forecast based on stratospheric winds performs as well as the dynamical forecast model. Similar results have been found when forecasting the temperature in northern Europe. [25] It would be interesting to know how much of the forecast in the dynamical model that is related to the Figure 10. Dynamical ensemble forecast (blue curve) compared to the the statistical forecast. The predictand is the surface zonal mean wind at 60 N. The red and green curves (also shown in Figure 4, top) are statistical forecasts with the predictor at 1000 and 70 hpa, respectively. The orange curve is a statistical forecast with the predictor at 70 hpa including only the same 51 events as the dynamical ensemble forecast. The solid black curve is the combined statistical forecast using both the zonal mean wind at 70 hpa and the dynamical ensemble forecast as predictors. The dashed black curve is the theoretical correlations of the combined forecast if the two predictors were uncorrelated. 7of10

8 Figure 11. Growth of errors in the dynamical ensemble forecast as function of lead time and vertical level. (top) Bias, B, and (bottom) divergence, D, of the zonal mean wind (m/s). downward propagation from the stratosphere and if a better representation of the stratosphere would improve the forecast. Because of the limited numbers of dynamical forecasts available this question is hard to answer firmly at present. However, if a bad stratospheric representation in the dynamical model inhibits or deteriorates the propagation of stratospheric information to the troposphere we would expect that the dynamical forecasts could be improved by including the stratospheric information more directly. Therefore, as a first step we have made a statistical forecast using both the stratospheric winds and the ensemble mean forecast simultaneously as predictors. The dynamical forecast and the stratospheric winds at 70 hpa are included with the same lead time T, i.e., the forecast for the time t is based on the dynamical forecast initialized at time t T and the observed stratospheric winds at t T. [26] It can be seen that the correlations of the combined model (Figure 10, solid black curve) are well above the correlations of the two individual models (blue and orange curves) for all lead times. As the introduction of an additional predictor will automatically improve the forecast when based on a finite number of events, we have tested if the observed improvement could be solely due to this effect. We applied a Monte Carlo test where the forecasts for each value of the lead time were made with the dynamical model (stratospheric wind) as one predictor and a the other predictor were constructed by randomly scrambling the 51 values of the stratospheric wind (dynamical forecast). We find that the observed increase with high confidence (more than 95%) cannot be explained only by the fortuitous effect of including a second predictor. In fact, the correlations of the combined model are very close to its theoretical maximum (black dashed curve), i.e., the correlations one would get if the two predictors were uncorrelated (calculated as the square root of the sum of the squares of the blue and orange curves). This result is in agreement with the rather weak correlations between the dynamical forecast and the statistical forecast based on stratospheric winds. These correlations are around 0.25 except for lead times near 20 days where they peak at 0.5. [27] In this study we have only used correlations between the forecast and the predictand to measure the quality of the forecast. However, also if we consider bias or bias corrected variance, does the statistical forecast based on stratospheric winds perform as well as or better than the dynamical forecast model. [28] The above results indicate that the stratosphere hosts information that is not treated properly in the ensemble forecast, and that the ensemble forecast therefore could be improved if the model included a better representation of the stratosphere-troposphere coupling. One of the main differences between the stratospheric representations in the dynamical forecast model and in the GCM ARPEGE is the height of the topmost layer (10 hpa versus 0.1 hpa). However, the models differ also in some of the parameterizations relevant for the stratosphere such as the gravity wave drag. As ARPEGE simulates the statistics of the stratosphere-troposphere coupling very well [Christiansen, 2001] one might be tempted to attribute the deficiency of the dynamical forecast model to one or more of these differences. [29] In this context it is interesting that the main source of errors in the dynamical model is related to bias and not to chaotic divergence of the ensemble members. This can be seen by dividing the mean error, E, into the bias, B, and divergence, D. We have E 2 (T) = ðp i ðtþ OÞ 2, B 2 (T) = (P(T) O) 2, and D 2 2, (T) = P i ðtþ PT ð Þ where Pi, i = 1,... 5 are the five ensemble members, O the analysis, and an overline denotes the ensemble average. Note that E 2 = B 2 + D 2. The average of the two terms B and D over the 51 forecasts are shown in Figure 11 as function of lead time and height. The bias grows much faster than the divergence for all levels. This indicates that it is not the chaotic nature of the atmosphere (and the model of it) that limits the extended-range forecasts. 6. Conclusions [30] We have investigated the potential for using the downward propagation of anomalies from the stratosphere to the troposphere in statistical forecasts for lead times up to 60 days. We have focused on forecasting the zonal mean zonal wind at the surface at 60 N. A simple forecast model based on linear regression was used (Figure 1). [31] We have used data from the ERA-40 reanalysis which extends to 0.1 hpa. Most other studies of the downward propagation have been based on the NCEP reanalysis which has the upper boundary at 10 hpa. We 8of10

9 therefore opened the paper with a comparison of the downward propagation in the two data sets. We found an excellent agreement of the zonal mean zonal wind anomalies at 60 N at all levels. [32] For lead times larger than 5 days we found that predictors in the stratosphere give better forecasts than predictors in the troposphere. The best forecasts are obtained for predictors in the lower stratosphere in agreement with Charlton et al. [2003]. In particular for small lead times the correlations between forecast and predictand have a distinct maximum for predictors near the tropopause. The largest improvement by using stratospheric predictors, more than 100%, is obtained for lead times between 10 and 40 days. For example, when forecasting daily averages with a lead time of 20 days the correlation is 0.15 with the predictor at the surface and 0.30 with the predictor in the lower stratosphere. Next to the lead time the forecast is most dependent on the time over which the predictand was averaged. For lead times less than 25 days averaging the predictand over 10 or more days improves the forecast substantially. For larger lead times predicting daily values gives almost as good a forecast as predicting averaged values. We found that including more than one stratospheric predictor only improves the forecast marginally. Restricting the statistical forecast to periods with strong values of the stratospheric predictor improves the forecast drastically (Figure 8). [33] The results summarized above are based on the three winter months December, January, and February. Restricting the analysis to single months shows that large, comparable forecasts are obtained for these three months while the forecasts for March are somewhat worse. This is in contrast to Charlton et al. [2003], who found that the stratosphere-troposphere relationship is strongest in February and March, but in agreement with Baldwin et al. [2003]. [34] To test if the correlations are different from zero with statistical significance we have used a Monte Carlo approach. Surrogate data series were constructed with the same autocorrelation spectrum as the original time series. This method is very conservative and circumvent the problem of estimating the number of degrees of freedom in the time series. To further test the statistical robustness of our results we have used a cross-validation procedure, where the model is trained on one half of the data (e.g., the first half or every second year) and tested on the remaining half of the data. With this procedure we have reproduced the results of section 4 with only small differences. [35] We have seen that our simple statistical forecast based on stratospheric information performs as well as a state-of-the-art dynamical seasonal forecast model when forecasting the surface zonal mean zonal wind at 60 N and the temperature in northern Europe. It has not been possible directly to study the downward propagation from the stratosphere to the troposphere in the dynamical model, but in some other GCMs the statistical properties of the downward propagation are very well represented. The stratosphere-troposphere coupling might therefore offer an important contribution for improving the dynamical forecast systems. Some optimism may be found in the result that the statistical forecast and the dynamical forecast are only weakly correlated, and in our demonstration that the forecasts of the dynamical model are limited by the bias and not by chaotic divergence. [36] Correlations between the stratospheric predictor and the tropospheric predictand reach values larger than 0.5 for lead times around 20 days. This corresponds to an explained variance of 25%. Even without averaging of the predictand and without restricting the analysis to strong events correlations reach values larger than 0.3 for lead times around 20 days. This is a considerable fraction and much larger than the values reported by Charlton et al. [2003]. As explained in section 2 this is mainly because Charlton et al. [2003] only present correlations between the surface and the stratosphere multiplied by the instantaneous correlation coefficient between the Arctic Oscillation at the surface and the Arctic Oscillation in the stratosphere. Another difference is that Charlton et al. [2003] use the Arctic Oscillation instead of the zonal mean zonal wind. We will see below that the effect of this difference is smaller and of opposite sign. As the Arctic Oscillation at the surface and in the atmosphere is closely connected to the leading empirical orthogonal function of the Northern Hemisphere surface pressure and geopotential height [Baldwin and Dunkerton, 1999], respectively, we expect a considerable correlation between the zonal mean zonal wind at 60 N and the Arctic Oscillation. We find a correlation coefficient of 0.72 between the Arctic Oscillation and the zonal mean wind at the surface while the correlation between the Arctic Oscillation and the zonal mean wind at 70 hpa is as large as The correlation between the Arctic Oscillation at the surface and the near-surface temperature in northern Europe is In agreement with these values we find that using the Arctic Oscillation at 70 hpa as predictor gives the same result as using the zonal mean zonal wind at 70 hpa. The situation is more complicated regarding the predictands at the surface. For t = 14 (1) days and for a lead time of 20 days the autocorrelation of the Arctic Oscillation is 0.21 (0.24) and the correlation between the Arctic Oscillation at the surface and at 70 hpa is 0.38 (0.37). The similar numbers for the zonal mean wind at the surface is 0.13 (0.14) and 0.38 (0.31). We first note that the Arctic Oscillation at the surface has a larger persistence than the surface zonal mean wind as can also be seen in more detail by comparing Figure 4 with, for example, Figure 5 of Charlton et al. [2003]. We see that predicting the Arctic Oscillation gives the same correlation for t = 14 days and moderately larger correlation for t = 1 day compared to predicting the zonal mean wind. However, including the stratosphere improves the forecast more when predicting the zonal wind than when predicting the AO. Altogether, the main difference between the present study and the study by Charlton et al. [2003] is that the latter is based on a model describing the stratospheretroposphere connection for positive lags as an indirect relationship. [37] Our results show that the stratosphere holds information important for the future development of the troposphere and suggests that this information is not present in the troposphere itself. The last point should be taken with some caution as we have only reported work where the zonal mean zonal wind was used as tropospheric predictors. Other tropospheric fields, perhaps related to the large-scale waves, may hold the same information as the stratosphere and if identified may be used as predictors instead of the 9of10

10 stratospheric zonal mean wind. However, initial work in this direction has not revealed any possible tropospheric predictor as good as the stratospheric zonal mean wind. [38] Acknowledgments. This work was supported by the Danish Climate Centre at the Danish Meteorological Institute. The ERA-40 reanalysis data and the dynamical ensemble seasonal forecast were provided by European Centre for Medium-Range Weather Forecasts. References Anderson, D. T. L. et al. (2003), Comparison of the ECMWF seasonal forecast systems 1 and 2, including the relative performance for the 1997/8 El Niño, Tech. Memo. 404, Eur. Cent. for Medium-Range Weather Forecasts, Reading, U. K. Baldwin, M. P., and T. J. Dunkerton (1999), Propagation of the Arctic Oscillation from the stratosphere to the troposphere, J. Geophys. Res., 104, 30,937 30,946. Baldwin, M. P., and T. J. Dunkerton (2001), Stratospheric harbingers of anomalous weather regimes, Science, 294, Baldwin, M. P., D. B. Stephenson, D. W. J. Thompson, T. J. Dunkerton, A. Charlton, and A. O Neill (2003), Stratospheric memory and skill of extended-range weather forecasts, Science, 301, Black, R. X. (2002), Stratospheric forcing of surface climate in the Arctic Oscillation, J. Clim., 15, Charlton, A. J., A. O Neill, D. B. Stephenson, W. A. Lahoz, and M. P. Baldwin (2003), Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?, Q. J. R. Meteorol. Soc., 129, Christiansen, B. (1999), Stratospheric vacillations in a general circulation model, J. Atmos. Sci., 56, Christiansen, B. (2000), A model study of the dynamical connection between the Arctic Oscillation and stratospheric vacillations, J. Geophys. Res., 105, 29,461 29,474. Christiansen, B. (2001), Downward propagation of zonal mean zonal wind anomalies from the stratosphere to the troposphere: Model and reanalysis, J. Geophys. Res., 106, 27,307 27,322. Christiansen,B.,A.Guldberg,A.W.Hansen,andL.P.Riishøjgaard (1997), On the response of a three-dimensional general circulation model to imposed changes in the ozone distribution, J. Geophys. Res., 102, 13,051 13,077. Holton, J. R., and C. Mass (1976), Stratospheric vacillation cycles, J. Atmos. Sci., 33, Kalnay, E., et al. (1996), The NCEP/NCAR 40-year reanalysis project, Bull. Am. Meteorol. Soc., 77, Kodera, K. (1995), On the origin and nature of the interannual variability of the winter stratospheric circulation in the Northern Hemisphere, J. Geophys. Res., 100, 14,077 14,087. Kodera, K., K. Yamazaki, M. Chiba, and K. Shibata (1990), Downward propagation of the upper stratospheric mean zonal wind perturbation to the troposphere, Geophys. Res. Lett., 17, Kuroda, Y. (2002), Relationship between the polar-night jet oscillation and the annular mode, Geophys. Res. Lett., 29(8), 1240, doi: / 2001GL Simmons, A. J. (2001), Development of the ERA-40 data assimilation system, ERA-40 Proj. Rep. Ser. 3, pp , Eur. Cent. for Medium- Range Weather Forecasts, Reading, U. K. Thompson, D. W. J., and J. M. Wallace (1998), The Arctic Oscillation signature in the wintertime geopotential height and temperature fields, Geophys. Res. Lett., 25, Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace (2002), Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction, J. Clim., 15, B. Christiansen, Danish Meteorological Institute, Climate Research Division, Lyngbyvej 100, DK-2100 Copenhagen Ø, Denmark. (boc@ dmi.dk) 10 of 10