Daily averages of the Japanese 55-year Reanalysis (JRA-55) data (Kobayashi et al., 2015) are used as a representation of the real world when the S2S HC data are verified in this study. The JRA-55 data period for this study is from January 1979 to June 2018, extending for 40 northern winter seasons from 1978/79 to 2017/18.
Onset dates of MSSWs are identified in the JRA-55 data during DJF, and 22 cases for the 40 seasons are obtained (Table 1). The MSSW onset dates are basically identified as reversals of the zonal mean zonal wind [U] at (60°N, 10 hPa) (Charlton and Polvani, 2007). Here, the square brackets denote the zonal mean. All onset dates are identical to the results obtained by Butler et al. (2017) for the JRA-55 data, except for the MSSW #22 that occurred in February 2018. Another MSSW occurred in the 2018/19 winter season (Rao et al., 2019b), but is not included here as it is outside the 40-season period of interest. The onset dates are also referred to as lag = 0 d.
Number # Onset date Wave 2 amplitude Aspect ratio Karpechko 1 1979/02/22 S S S 2 1980/02/29 D D D 3 1981/02/06 S D D 4 1981/12/04 D D D 5 1984/02/24 D S D 6 1985/01/01 S S S 7 1987/01/23 S D D 8 1987/12/08 D D S 9 1989/02/21 S S S 10 1998/12/15 D D D 11 1999/02/26 S S S 12 2001/02/11 D S S 13 2001/12/31 D S D 14 2003/01/18 S S S 15 2004/01/05 D D D 16 2006/01/21 S D D 17 2007/02/24 D D D 18 2008/02/22 D D D 19 2009/01/24 S S S 20 2010/02/09 D S S 21 2013/01/07 S S S 22 2018/02/12 S D S
Table 1. MSSW onset dates (yyyy/mm/dd format) identified for DJF in the JRA-55 data. Each MSSW is classified into the VD (D) or VS (S) type using three methods.
Each MSSW is further classified as either VD or VS type using three methods (Table 1). The first method uses the amplitude of wave 2 in the JRA-55 10 hPa geopotential height (Z10) field at 60°N around each MSSW onset date (lag = −2 to +2 d). An MSSW is classified as a VS MSSW if the wave 2 amplitude is equal to or larger than the median of the 22 values (i.e., for the 22 MSSWs), and the rest are VD MSSWs (Fig. 1). The second method similarly uses the aspect ratio of the 5 d mean Z10 around each onset date (Seviour et al., 2013). The last method follows the result from Karpechko et al. (2017) after Lehtonen and Karpechko (2016), except for #3, #21, and #22. These studies look for two separate minima in Z10. The three MSSWs are not included in these studies, and are judged from the JRA-55 Z10 field subjectively. The method based on the wave 2 amplitude is used to demonstrate example results below.
Figure 1. (a) Scatterplot between the wave 1 and wave 2 amplitudes of the 10 hPa height Z10 at 60°N for all 22 MSSWs in the JRA-55 data. The Z10 field is averaged for 5 days (lag = −2 to +2 d) around each MSSW onset date. The best-fit line and correlation coefficient for the 22 MSSWs are indicated. The filled markers are for the MSSWs #10–#21 covered by the ECMWF HC data, and are colored according to the RMSE of the ECMWF LTG-15 forecasts (see the colorbar). Panel (b) is similar, but uses the centroid latitude and aspect ratio of the 5 d averaged Z10 field.
From the S2S data archive, this study employs HC data of the four systems of BoM, CMA, ECMWF, and NCEP (Table 2). The four systems are chosen because they provide relatively abundant data in terms of initialization frequency and ensemble size (Vitart et al., 2017). HC data are obtained that were initialized from November to February since northern winter is the focus in this study. The different systems cover different MSSWs. The present analysis uses 12 MSSWs (#10–#21) for a fair comparison that are commonly covered by three of the four systems, except for NCEP. For NCEP, the MSSWs #11–#20 are examined.
System name Period Initialization frequency Ensemble
MSSWs covered BoM (Australian Bureau of Meteorology) 1981–2013 Six per month 11** #3–#21 CMA (China Meteorological Administration) 1994–2014 Daily 4 #10–#21 ECMWF* (European Centre for Medium-Range
Two per week 11 #10–#21 NCEP (National Centers for Environmental
1999–2010 Daily 4 #11–#20 *The ECMWF HC data in the S2S archive are performed for an “on-the-fly” mode, whereas the three others use a “fixed” mode. The ECMWF HC data used in this study are those associated with real-time forecasts for the 2017/18 northern winter season.
**This study uses 11 members of BoM for each initial date to facilitate the download and analysis, whereas 33 members are available. A preliminary analysis indicated that 11 members of BoM are sufficient for the present purpose.
Table 2. Four S2S systems employed in this study.
The HC data analyzed here can be simply expressed for any quantity of interest, A, for each HC set (ensemble forecasts initialized on a day) as AHC_set (forecast time, ensemble member). Each forecast set is determined by its initial date and forecast system. Spatial information is omitted here for simplicity.
For each MSSW and system, the HC data are further organized into four lead-time groups (LTGs) of LTG-20, LTG-15, LTG-10, and LTG-5 to facilitate a comparison among different MSSWs and systems, e.g., as in Taguchi (2018), Rao et al. (2018), and Domeisen et al. (2019). For example, the LTG-15 for each MSSW and system combines all available HC data of the system initialized from lag = −15 to −11 d of the target MSSW (Fig. 2). The HC data in each LTG are sorted in time lag with respect to the MSSW onset date as ALTG-i (time lag, ensemble member). Here, the ensemble size of ALTG-i may increase from that of AHC set when multiple initial dates are available for the LTG. Then, the JRA-55 and HC data around the observed MSSW onset dates are compared (Fig. 2). The possible effects of different initialization frequencies and ensemble sizes among different LTGs, MSSWs, and systems are not considered. The HC data are not bias-corrected in order to examine their intrinsic forecast skill, although bias corrections might lead to improved MSSW forecasts (Rao et al., 2019a). We use ensemble means for each ALTG-i for most verifications, unless stated otherwise.
Figure 2. Schematic showing the analysis procedure for the forecast verification using the MSSWs (lag = 0 d) as a key. This figure uses LTG-15 as an example.
The forecast verification employs the following measures:
(1) Zonal mean zonal wind [U] at (60°N, 10 hPa) around the MSSW onset dates (averaged from lag = −2 to +2 d). The HC zonal wind data around the onset dates are roughly equivalent to zonal wind errors (differences from the JRA-55 data), since the JRA-55 counterpart can be approximated as zero.
(2) Hit rate (HR). This is defined as a ratio (in percentage) of the number of successful ensemble members to the ensemble size for each LTG, MSSW, and system. The successful ensemble members are those that show a reversal of [U] at (60°N, 10 hPa) for the first time between lag = −3 to +3 d, i.e., a 3 d difference is allowed between the observed and HC onset dates. This measure was introduced in Taguchi (2016a) to verify MSSW forecasts and was used, for example, in Rao et al. (2018) and Domeisen et al. (2019).
(3) Root-mean-square error (RMSE). RMSE is calculated for errors of HC Z10 from JRA-55 Z10 poleward of 20°N. Both Z10 data are averaged for the 5 d around each MSSW onset date. The calculation of RMSE includes weighting of Z10 by cosine of latitude (Taguchi, 2016a).
(4) Anomaly correlation (AC). This is similar to RMSE, but for the spatial correlation between JRA-55 and HC anomalous Z10 fields. The anomalous fields are calculated from the JRA-55 climatology (i.e., long-term mean).
(5) Error of the poleward heat flux [V*T*] of planetary waves 1–3 in (40°–90°N, 100 hPa). Here, the asterisks denote deviations from the zonal means. The heat flux is proportional to the vertical component of the Eliassen–Palm flux with the quasi-geostrophic assumption (Andrews et al., 1987). The heat flux in the lower stratosphere well measures the planetary wave activity that enters the stratosphere and disturbs the polar vortex. The heat flux error is examined by taking the 11 d mean, e.g., from lag = −10 to 0 d, for each MSSW onset date (Fig. 2). The heat flux in the lower stratosphere preceding MSSWs was examined by Taguchi (2014, 2016a) when verifying MSSW forecasts.
|Number #||Onset date||Wave 2 amplitude||Aspect ratio||Karpechko|