## 3 Results  
We first diagnosed the status of ensemble quality in CTL in terms of the zonally-averaged EME and ES (Figure 1). For temperature, large EMEs are found in the lower atmosphere over the Arctic and Antarctica regions and in the overall stratosphere (Figure 1a); for specific humidity, the tropics and mid-latitudes have larger EMEs than the other regions, especially below 700 hPa (Figure 1c); for zonal wind, large EMEs are found in the tropics from the middle troposphere to the lower stratosphere, Antarctica, and most of the stratosphere except the Northern Hemisphere (NH) (Figure 1e). These model errors should be correspondingly represented in the ESs (Figure 1b,d,f); however, the ESs were relatively underestimated compared to the EMEs. In summary, all the variables have insufficient ESs in the troposphere below 700 hPa in both hemispheres and above 10 hPa in the Southern Hemisphere (SH). Although the current inflation methods are quite effective in increasing the ES, this result evidently shows that we can further augment the ES. Note that the ES of zonal wind is quite similar to the EME in terms of patterns and magnitudes (cf. Figure 1e,f). Therefore, the zonal wind is considered to have sufficient ES already, especially in the jet regions, and additional inflation may have a negative impact on the mean error. For this reason, we perturbed only temperature and humidity mixing ratios that were the prognostic variables. Prior to the EDA runs, we compared the background ESs of SPDT, SPPT, and SPHT for temperature at the first cycle (see Figure 2). The ES was mainly affected by the SPPT below 700 hPa, with prominent increases over the subtropics and extratropics in the NH and over the subtropics and polar region in the SH; the ES was also increased by the SPDT below 700 hPa over the extratropics in the SH and in the polar stratosphere but with much smaller magnitudes. This can be expected because the RF amplitude is relatively small in the SPDT, along with vertical relaxation (see Table 1). The SPHT scheme increases the ES considerably in the overall troposphere and weakly in the stratosphere--these regions are where we desire to enlarge the ES. This supports our idea to run the SPDT and the SPPT simultaneously as a new stochastic perturbation approach. In Figure 3, we examine the effect of the SPHT scheme on the ES by comparing differences between STO and CTL for the globally averaged vertical profiles of temperature, specific humidity, and zonal wind. Starting with zeroes at the initial time, the differences gradually increased with time for all the variables. For temperature, the ES mainly increased in the troposphere below 500 hPa while it weakly increased in the stratosphere above 10 hPa (Figure 3a). For specific humidity, primarily distributed at the middle and lower troposphere, the ES also increased below 500 hPa (Figure 3b). However, the ES for zonal wind slightly increased as the others increased (Figure 3c), though the zonal wind was not perturbed. The increasing pattern of the zonal wind profile was quite similar to that of the temperature profile. Therefore, we confirm that the SPHT scheme leads to an increase in the ensemble BECs of the 6 h forecasts, serving as an inflation method. Figure 1: The zonal mean ensemble mean error (EME) (left panels) and ensemble spread (ES) (right panels) against the Integrated Forecast System (IFS) analysis for (**a,b**) temperature (in K), (**c,d**) specific humidity (in g kg\({}^{-1}\)), and (**e,f**) zonal wind (m s\({}^{-1}\)) as for the 6 h forecasts of the control run (CTL). Results are averaged from 18:00 UTC on 25 June 2018 to 18:00 UTC on 7 July 2018, excluding the spin-up period (first 78 h of the experiment time), with a composite of the 49 cycles’ background fields (i.e., one cycle per 6 h). In Figure 4, we show the effect of our proposed scheme on the accuracy of EDA, by showing the zonal mean differences of ES and EME between STO and CTL for the 6 h forecasts during the experimental periods.