## 3 Results
As expected, in most areas the ES increased (red) while the EME decreased (blue). It is noteworthy that, for all variables, the EME significantly decreased (i.e., the accuracy increased) over the tropics, especially below 700 hPa (Figure 4b,d,f). For temperature, the accuracy increased over higher latitudes as well in the lower atmosphere while it prominently decreased in the stratosphere over the SH (Figure 4b); for zonal wind, the accuracy also increased in the middle to upper troposphere but decreased in the stratosphere over the tropics while it generally decreased at high latitudes, especially over the SH (60\({}^{\circ}\) S) (Figure 4f). The ES generally enlarged in all variables: for temperature, the ES substantially increased in most latitudes and atmospheric layers except in the mid- to upper-troposphere and over the low-level tropics (10\({}^{\circ}\) S-10\({}^{\circ}\) N) below 700 hPa (Figure 4a); for specific humidity, the ES was mostly enhanced within the mid-latitudes below 700 hPa (Figure 4c); for zonal wind, the ES was significantly augmented in most of the global atmosphere, especially in the subtropical troposphere below 700 hPa and in most of the stratosphere except over 40\({}^{\circ}\) S-10\({}^{\circ}\) N (Figure 4e). For the mass variable variation, the SPDT acts indirectly through the mass-wind balance  
Figure 3: Differences in the ES between stochastic perturbation run (STO) and CTL (i.e., ES\({}_{\text{STO}}\)-ES\({}_{\text{CTL}}\)) in the globally averaged vertical profiles of (**a**) temperature (in K), (**b**) specific humidity (in g kg\({}^{-1}\)), and (**c**) zonal wind (in m s\({}^{-1}\)) for forecast times of +3 h (blue), +6 h (green), and +9 h (red) from the initial time (+0 h; black dots) at 12:00 UTC on 22 June 2018. Variations in the ES reflect the effect of the new SPHT scheme. Figure 2: The zonal mean ES for temperature from (**a**) the SPDT, (**b**) the SPPT, and (**c**) the stochastic perturbation hybrid tendencies (SPHT) scheme (i.e., SPDT\(+\)SPPT). Results are shown for the first cycle background fields at 12:00 UTC on 22 June 2018.  
and the cycling, thus having a weaker impact on the temperature and specific humidity than the SPPT, while the wind field variation is induced comparably by both SPDT and SPPT. Regarding the reliability, Figure 5 shows a time series of the reliability index (\(\gamma\); see Equation (3)) for the 6 h forecasts. When the ES is properly described, \(\gamma\approx 1\). Compared to CTL, the reliability has widely improved (i.e., \(\gamma\) increased) in STO: for temperature, in the layer below 150 hPa; for specific humidity, in the layer below 850 hPa; for zonal wind, in the mid-troposp  
Figure 4: The zonal mean differences between STO and CTL for the 6 h forecasts of the ES (ES\({}_{\text{STO}}\)-ES\({}_{\text{CTL}}\); left panels) and the EME (EME\({}_{\text{STO}}\)-EME\({}_{\text{CTL}}\); right panels) against the IFS analysis: (**a**,**c**) temperature (in K), (**b**,**d**) specific humidity (in g kg\({}^{-1}\)), and (**e**,**f**) zonal wind (in m s\({}^{-1}\)). Results are represented with a composite of the 49 cycles’ background fields from 18:00 UTC on 25 June to 18:00 UTC on 7 July 2018. Dots indicate the composite differences with the 99% statistical significance based on the two-tail \(t\)-test. (700-30 hPa). The globally averaged value of \(\gamma\) has increased by about 4% in temperature and specific humidity--from 0.706 to 0.734 for temperature, and from 0.386 to 0.401 for specific humidity; for zonal wind, it has increased by about 3% from 0.757 to 0.779. We also note that, for all the variables, the \(\gamma\) values nearest to unity appear in the middle atmosphere in both CTL and STO--around 100-700 hPa for temperature and zonal wind and around 900-300 hPa in specific humidity. Overall, by considering the model error representation, it is evident that the SPHT scheme improves both the reliability and the accuracy of the EDA system in KIAPS.