Estimation of AMSU-A Radiance Observation Impacts in an LETKF-Based Atmospheric Global Data Assimilation System: Comparison with EFSO and Observing System Experiments

a. Development and performance of ALEDAS

We updated ALEDAS to resolve stratospheric circulation and enable assimilation of AMSU-A satellite radiances. ALEDAS is briefly described here. An atmospheric general circulation model called AFES is used for the model part. The horizontal resolution is T119 (∼1° × 1°), and there are 56 vertical levels with the model top of ∼0.1 hPa. The cumulus convection and radiation schemes follow those of Emanuel (1991) and Sekiguchi and Nakajima (2008), respectively. The nonorographic gravity wave drag scheme of Scinocca (2003) is newly implemented (Orr et al. 2010; Baba 2019; Yamazaki and Noguchi 2023, manuscript submitted to Mon. Wea. Rev., hereafter YN23). Detailed AFES information is given by Enomoto et al. (2008, 2013), and Kodama et al. (2019). The ocean boundary condition is given by the daily 1/4° Optimum Interpolation Sea Surface Temperature (Reynolds et al. 2007). Data assimilation applies to the LETKF with an ensemble size of 63. The localization functions are 400 km horizontally and 0.4lnp vertically. The spatially uniform 10% multiplicative inflation method is adopted. These settings follow those of Enomoto et al. (2013) and Yamazaki et al. (2021). Other observations derived from the PrepBUFR³ datasets include conventional types, aircraft observations, and satellite-derived winds in addition to AMSU-A satellite radiances. ALEDAS is used to generate an experimental atmospheric global ensemble reanalysis (ALERA).

As already noted, there are two main ALEDAS updates. One is in its model part: the vertical resolution has been increased from 48 vertical levels (up to ∼3 hPa) to 56 (up to ∼0.1 hPa). YN23 describe the benefits of this update. The other is in the data assimilation part, and is particularly significant for ALEDAS’s handling of AMSU-A assimilation: the scheme is similar to that of Terasaki and Miyoshi (2017), which implements the following:

• the satellite radiance assimilation scheme for the LETKF [initially developed by Miyoshi and Sato (2007) and Miyoshi et al. (2010)] and

• online (adaptive) airmass and scan bias corrections (section S1.4 in the online supplemental material).

Terasaki et al. (2019) used this scheme to create multiyear global analysis data. The supplemental material (section S1) summarizes the implementation of the scheme in ALEDAS.

Implementing Terasaki and Miyoshi (2017)’s scheme, ALEDAS assimilates AMSU-A channels 6, 7, and 8, which are sensitive to temperature in the midtroposphere to lower stratosphere (Fig. 4 in Terasaki and Miyoshi 2017); the sensors are onboard polar-orbiting satellites NOAA-15, NOAA-18, and NOAA-19, and MetOp-A (Table S1). We follow Terasaki and Miyoshi’s (2017) choice of assimilated channels and satellites for AMSU-A. Sections 3 and 4 show that AMSU-A is expected to have large areas of beneficial OI over the Southern Hemisphere (SH) oceans. This is due to the strict quality control of the AMSU-A observations, which results in channels 6 and 7 being disregarded over land (see section S1.3), and to there being few conventional observations over oceans. Using the same limited AMSU-A channels as Terasaki and Miyoshi (2017) is the first step to assimilating satellite radiance observations in ALEDAS. Improving the use of satellite radiance observations would require further steady developments of previous methods.

ALEDAS can perform adequately in global atmospheric data assimilation systems, and ALERA is somewhat comparable to recent global reanalysis families (Fujiwara et al. 2017, 2022). Figure 1 shows the root-mean-square difference in the 850- and 250-hPa temperature fields, respectively, of ALERA and JRA-55 (Kobayashi et al. 2015). For comparison, the differences of ERA5 (Hersbach et al. 2020) and NCEP-NCAR (Kalnay et al. 1996) reanalyses against JRA-55 are also shown. ALERA departs from JRA-55 by no more than 2 times the difference between ERA5 and JRA-55 in the upper troposphere and 1.5 times in the lower troposphere, and it has a comparable difference between the NCEP–NCAR reanalysis and JRA-55. ALEDAS and ALERA may also be used as a global reanalysis family, because the NCEP–NCAR reanalysis has been used in enormous studies. The 500-hPa geopotential height fields from ALERA and JRA-55 look almost identical over the extratropics (Figs. 1c,f). Moreover, ALERA reproduces two stratospheric sudden warming events in the Northern Hemisphere and the Southern Hemisphere (YN23). Note that similar results were obtained using ERA5 as the reference instead of JRA-55 (see Fig. S4). In light of this, ALERA can faithfully simulate true synoptic–large-scale atmospheric circulations in the troposphere and stratosphere.

View Full Size

(a),(b),(d),(e) Time series of the globally averaged root-mean-square difference of ALERA (thick black lines), NCEP–NCAR reanalysis (gray lines), and ERA5 (thin black lines) relative to JRA-55 for (top) 300-hPa zonal wind (m s⁻¹) and (middle) 850-hPa temperature (K) for the periods of December 2018–January 2019 in (a) and (b) and August–September 2019 in (d) and (e). (bottom) Snapshots of 500-hPa geopotential height fields in ALERA (red solid lines) and JRA-55 (black dashed lines) at (c) 0000 UTC 21 Dec 2018 and (f) 0000 UTC 23 Aug 2019.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

b. Definition of accumulated OI

As mentioned in section 1, (E)FSO estimates the OI obtained by noncycling data assimilation. Yamazaki et al. (2021) physically interpreted the OI and the OI_EFSO. Here, we define the accumulated OI obtained by cycling data assimilation, which can be compared with OI_EFSO.

Similar to Eq. (1), the OI of the OSE is evaluated by considering the difference between the two forecast errors from the analysis with AMSU-A observations (CTL) and from that without (OSE). Due to the accumulation of OI, cycling AMSU-A data denials separate ${\overline{x}}_{\text{OSE}}^a(t)$ from ${\overline{x}}_{\text{CTL}}^a(t)$. As ${\overline{x}}_{\text{OSE}}^a(t)$ relates to the initial values of ${\overline{x}}_{\text{OSE}}^g(t)$ and ${\overline{x}}_{\text{OSE}}^f(t)$, these OSE forecasts likely diverge from the corresponding CTL values [${\overline{x}}_{\text{CTL}}^g(t)$ and ${\overline{x}}_{\text{CTL}}^f(t)$]. The OI by the OSE thus depends on ${\overline{x}}_{\text{CTL}}^a(t),{\overline{x}}_{\text{OSE}}^a(t),{\overline{x}}_{\text{CTL}}^f(t),{\overline{x}}_{\text{OSE}}^f(t),{\overline{x}}_{\text{CTL}}^g(t)$, and ${\overline{x}}_{\text{OSE}}^g(t)$. In a noncycling OSE, on the other hand, the forecast from the background state [${\overline{x}}^f(t)$] and the analysis as the reference state [${\overline{x}}^a(t)$] are the same as those in the CTL, respectively: i.e., ${\overline{x}}_{\text{OSE}}^f(t)={\overline{x}}_{\text{CTL}}^f(t)$ and ${\overline{x}}_{\text{OSE}}^a(t)={\overline{x}}_{\text{CTL}}^a(t)$. The EFSO formulation starts from Eq. (1) of $\mathrm{\Delta }{E}_{\text{CTL}}^2$, and EFSO can separate the relative contribution of AMSU-A observations, which constitute the total observations in CTL and are excluded from the OSE. Here, the relative contribution of AMSU-A is a constituent part of $\mathrm{\Delta }{E}_{\text{CTL}}^2$. As shown in Eq. (5) of Yamazaki et al. (2021), OI_EFSO approximates OI by the noncycling OSE, which is described by ${\overline{x}}_{\text{CTL}}^a(t),{\overline{x}}_{\text{CTL}}^f(t),{\overline{x}}_{\text{CTL}}^g(t)$, and ${\overline{x}}_{\text{OSE}}^g(t)$.

c. Experimental design

We conducted two OSEs in which the entire AMSU-A observations were excluded from ALEDAS; i.e., ALEDAS generates ALERA or CTL. The OSEs were separated into two streams: one with a data assimilation cycle from 0000 UTC 21 December 2018 to the end of January 2019 (NH-winter experiment) and the other from 0000 UTC 23 August 2019 to 1800 UTC 3 October 2019 (SH-winter experiment), both initialized with ALERA. To verify our results, the CTL and the OSEs were compared using different data periods. Spinup periods of about 10 days after starting each OSE were discarded; the adjusted periods were from 0000 UTC 1 January to 1800 UTC 31 January 2019 for the NH-winter and from 0000 UTC 3 September to 1800 UTC 3 October 2019 for the SH-winter experiments. As a result, the same conclusions were obtained for the adjusted periods. The supplemental material gives further details (Figs. S6–S13 and Tables S3 and S4).

During the two OSEs, the AMSU-A observations were excluded for each data assimilation cycle; thus, these are the cycling OSEs. We try to evaluate accumulated OI by cycling data denials. Any OI localized in limited areas or altitudes can propagate and accumulate during the cycling data assimilation, affecting the general circulation.

a. Comparison of AMSU-A accumulated OI and OI_EFSO

We assess the effects of the accumulation of AMSU-A OI. Table 1 lists the OI of the OSEs and EFSO averaged over the NH-winter and the SH-winter experiments. In both OSEs, AMSU-A OI_EFSO become positive (i.e., beneficial), indicating the successful implementation of Terasaki and Miyoshi (2017)’s AMSU-A assimilation scheme in ALEDAS. Furthermore, I_AMSU-A is negative in both experiments, or $\mathrm{\Delta }{E}_{\text{CTL}}^2$ becomes smaller than $\mathrm{\Delta }{E}_{\text{OSE}}^2$. This demonstrates that the addition of AMSU-A observations reduces total OI, which is opposite to the expectation from AMSU-A OI_EFSO. Note that EFSO estimates OI well in both the CTL and the OSEs, because total OI_EFSO performs well in quantifying the total OI in both cases, and their correlation coefficients are very high (>0.9). Therefore, the negative I_AMSU-A results from the accumulation of AMSU-A OI.

Table 1

Total OI, total OI_EFSO of the CTL and the OSEs, AMSU-A OI_EFSO, and I_AMSU-A for the NH-winter and SH-winter experiments. All values are averaged for each experimental period. The rightmost column shows the correlation between total OI and total OI_EFSO. Units are J kg⁻¹ except for correlation coefficients.

View Table

The magnitudes (absolute values) of I_AMSU-A are greater than those of AMSU-A OI_EFSO by factors of 1.2–1.6, possibly due to the effect of the accumulation of AMSU-A OI.

The I_AMSU-A and AMSU-A OI_EFSO show larger values in the SH-winter experiments than in the NH-winter experiments, suggesting that AMSU-A OI is more significant and/or widespread in Southern Hemisphere winters than summers because of dynamical propagation in the extratropics (as discussed in section 4).

b. Physical interpretation of negative AMSU-A accumulated OI against the positive AMSU-A OI_EFSO

We interpret here the reason for I_AMSU-A being negative in contrast to the positive beneficial AMSU-A OI_EFSO. First considered are the time series of $\mathrm{\Delta }{E}_{\text{CTL}}^2$ and $\mathrm{\Delta }{E}_{\text{OSE}}^2$ in the NH-winter and SH-winter experiments (Figs. 2a,d): the latter is almost always larger than the former except very near the start of each experiment (21 December 2018 for the NH-winter experiment and 23 August 2019 for the SH-winter experiment). Second, we separate ΔE² into two parts: ${({\mathbf{e}}^f)}^{\mathrm{T}}\mathsf{C}{\mathbf{e}}^f$ and ${({\mathbf{e}}^g)}^{\mathrm{T}}\mathsf{C}{\mathbf{e}}^g$ [Eq. (1)]. The former is equivalent to the 12-h forecast error (forecast from the background) and the latter corresponds to the 6-h error (forecast from the analysis). As total OI is defined as the difference between these errors, we examine each error’s time series individually and the reason for $\mathrm{\Delta }{E}_{\text{CTL}}^2$ becoming smaller than $\mathrm{\Delta }{E}_{\text{OSE}}^2$. From Figs. 2b and 2e, the errors in the CTL generally decrease relative to those in the OSEs. The above findings imply that in the CTL, or by accumulating AMSU-A OI, the short-range forecasts become closer to the analysis than those in the OSEs.

View Full Size

Time series of (a),(d) total OI in the CTL (black lines) and OSE (blue dashed lines); (b),(e) differences between 6-h (thin lines) and 12-h (thick lines) forecasts and their analyses (J kg⁻¹) in the CTL (black lines) and OSE (blue dashed lines); and (c),(f) differences between the CTL and OSE analyses (J kg⁻¹; black lines) and the analysis ensemble spreads (J kg⁻¹) in the CTL (red upward-pointing triangles) and the OSEs (blue downward-pointing triangles). (left) NH-winter experiment: 21 Dec 2018–31 Jan 2019 and (right) SH-winter experiment: 23 Aug–3 Oct 2019.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

Last, we consider the effects of the accumulation of AMSU-A OI. Figures 2c and 2f shows time series of the moist-total-energy differences of the analyses between the CTL and the OSEs. The accumulation of OI causes the analyses of the OSEs to depart substantially from the analysis of the CTL. The analyses of these experiments converge on different states after 10–14-day data assimilation cycles of the OSE periods. The differences converged to 7–9 (J kg⁻¹), about 100 times the values of AMSU-A OI_EFSO and 2–3 larger than the total OI values (Table 1). As the CTL and OSE forecasts start from different analysis states, the total OIs in the OSEs are larger than that in the CTL, and thus I_AMSU-A can be negative against a positive AMSU-A OI_EFSO. Interestingly, the disparities between the CTL and OSE analyses have similar values to the OSE analysis ensemble spreads. The analysis ensemble spreads become smaller in the CTL than those in the OSEs.

We consider the reason for the incorporation of AMSU-A observations resulting in a reduction in the total OI or I_AMSU-A becoming negative. From Table 1 and Fig. 2, we sketch the effect of the accumulation of AMSU-A OI on a data assimilation system (Fig. 3). The figure shows time sequences of the analysis and background (first guess) fields in the CTL (lines C and C′, respectively) and the OSE (lines O and O′, respectively). Suppose we start cycling data denials at t = t₀. Line O will depart from line C, and will reach a different equilibrium state (Figs. 2c,f): the analysis difference between lines O and C overall corresponds to the ensemble spread of the OSE analysis. Comparison of the CTL and the OSE indicates that the total OI in the CTL becomes smaller than that in the OSE (Figs. 2a,d), despite the CTL having more total observations than the OSE. The reason for this result is that the difference between the analysis and the short-range (6–12 h) forecast (i.e., the error) in CTL is smaller than the difference in the OSE (Figs. 2b,e). This further shows that the CTL increment (the difference between lines C′ and C) becomes smaller than the OSE increment (the difference between lines O′ and O). Decreasing the increment in a forecast–analysis cycle brings the short-range forecast closer to its analysis. Therefore, there is less shock in the data assimilation (forecast–analysis) cycle in the CTL, and the addition of AMSU-A observations stabilizes the data assimilation system. We can thus interpret the negative I_AMSU-A as being beneficial in a cycling data assimilation system, if we define positive OI_EFSO as beneficial [Eq. (1)].

View Full Size

Schematic representation of the accumulation of OI in a cycling OSE (data-denial experiment) and OI in the CTL. The cycling OSE starts from t₀. Lines O and C show the analysis states of the OSE and of CTL, respectively; O′ and C′ are the corresponding backgrounds, or first guesses. Time is plotted on the horizontal axis and the error on the vertical axis. Thin black lines show t_e-h forecasts from the background state x^b(t) and from the analysis x^a(t) in the CTL and the OSE, where the data assimilation window is Δt. The difference between the thin lines at t + t_e is the total OI of the CTL and the OSE: i.e., $\mathrm{\Delta }{E}_{\text{CTL}}^2$ for line C and $\mathrm{\Delta }{E}_{\text{OSE}}^2$ for line O. The accumulated OI is the difference between $\mathrm{\Delta }{E}_{\text{CTL}}^2$ and $\mathrm{\Delta }{E}_{\text{OSE}}^2$.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

c. Changes of OI_EFSO in the AMSU-A OSEs

Figures 4a and 4d show the global averaged values and distributions of AMSU-A OI_EFSO and those by the other observation types during the NH-winter and SH-winter experiments. Relative rankings of OI_EFSO by observation type show the AMSU-A observations are estimated to have the seventh most beneficial impact among the nine types in both experiments. The AMSU-A OI_EFSO distributions in Fig. 5 indicate that the AMSU-A observations have large beneficial impacts in the middle and upper troposphere in the Southern Hemisphere midlatitudes. As only channels 6–8 are assimilated, the AMSU-A OI_EFSO distributions are confined to the upper troposphere. However, the distributions show that the Southern Hemisphere storm track areas benefit from the AMSU-A observations. Therefore, as storm tracks are important driving forces of the general circulation (Edmon et al. 1980; Thorncroft et al. 1993), the observations may have a generally positive influence. Regarding the other observation types, those with the three largest OI_EFSO are satellite winds (SATWND), ocean scatterometer (ASCATW), and in situ land (ADPSFC) in order. OI_EFSO overlapping with the large AMSU-A OI_EFSO distributions are radiosondes (APDUPA), aircraft (AIRCFT), and satellite winds (SATWND).

View Full Size

Global averages of OI_EFSO for each observation type per data assimilation cycle averaged for the periods of (left) the NH-winter experiment and (right) the SH-winter experiment. (a),(d) OI_EFSO (J kg⁻¹); (b),(e) differences between ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ and (minus) ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$ (J kg⁻¹); and (c),(f) ratios of ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$ to ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ (%) for each observation type.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

View Full Size

AMSU-A OI_EFSO distributions for each observation type per data assimilation cycle averaged for the periods of (a) the NH-winter experiment and (b) the SH-winter experiment. Latitude–height cross sections of the AMSU-A OI_EFSO distributions (J kg⁻¹) (large plots on the left) and the OI_EFSO distributions (J kg⁻¹) of the other observation types (small plots).

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

We anticipate that the addition of AMSU-A observations will alter the relative contributions of each observation type’s OI to the total OI. Comparison of OI_EFSO in the CTL and in the OSEs shows which observation types have their OI reduced by the addition of AMSU-A observations. Here, we distinguish the OI_EFSO derived from the CTL as ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ and that from the OSEs as ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$. Gelaro and Zhu (2009) previously used the same approach with FSO for different observation types.

Figures 4b and 4e show the differences of ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ and ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$. The AMSU-A observations contribute to the total ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ by reducing the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ of SATWND, ASCATW, ADPSFC, ADPUPA, AIRCAR (aircraft observations other than AIRCFT), and AIRCFT. These six observation types have the six greatest ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ (Figs. 4a,d). Moreover, in the OSEs, SATWND and ASCATW observations show the greatest reductions of their ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$. These two observation types have the two largest ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ (Figs. 4a,d). Figures 4c and 4f shows the ratios of ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$ to ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ for each observation type. Similar to the finding for the differences, the same six observation types show the greatest reductions of ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ relative to ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$. Nonetheless, the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ of ADPUPA, AIRCAR, AIRCFT, and SATWND decrease compared with the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ of ASCATW and ADPSFC; the former types are observed above the upper troposphere, whereas the latter are measured near the surface (Fig. 5). Among the observation types of ADPUPA, AIRCAR, AIRCFT, and SATWND, the ratios of AIRCAR are relatively small (Figs. 4c,f).

Figure 6 shows the distributions of the differences between ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ and ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$ for six observation types: ADPUPA, AIRCAR, AIRCFT, SATWND, ADPSFC, and ASCATW. As anticipated from Fig. 5, the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ values (except for AIRCAR) generally decrease over the Southern Hemisphere midlatitudes (30°–60°S), which is the latitudinal band of peak beneficial AMSU-A OI_EFSO. The AMSU-A observations reduce the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ of these observation types. Regions of distinctly reduced ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ occur where both AMSU-A OI_EFSO and those ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ have substantial beneficial values; i.e., from the lower troposphere to the upper stratosphere. AIRCAR ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ has beneficial peaks in the upper troposphere, similar to AMSU-A OI_EFSO, although AIRCAR primarily observes the Northern Hemisphere midlatitudes. Overall, the OIs of various observation types that directly measure the Southern Hemisphere midlatitudes and/or the upper troposphere are largely substituted by AMSU-A OI.

View Full Size

As in Fig. 5, but with shading showing the difference between ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ and ${\text{OI}}_{\text{EFSO}}^{\text{OSE}}$ (J kg⁻¹) for the (a) NH-winter and (b) SH-winter experiments. Only results for observation types ADPUPA, AIRCAR, AIRCFT, SATWND, ADPSFC, and ASCATW are shown. Contours indicate the ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ (J kg⁻¹) of each observation type.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

It is difficult to explain the tendency of AIRCAR observations to reduce ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$, as the beneficial OI peaks of AIRCAR and AMSU-A observations show little overlap with each other. This may be related to the AIRCAR observed variables including temperature. Further research should assess which variables’ observations tend to be largely substituted by AMSU-A observations of brightness temperature.

d. Distributions of AMSU-A accumulated OI and OI_EFSO

We now assess the spatial correspondence between beneficial I_AMSU-A and AMSU-A OI_EFSO. Figure 7 shows latitude–height sections of zonal mean I_AMSU-A. We find distinct beneficial I_AMSU-A signals in the upper troposphere at Southern Hemisphere midlatitudes in the NH-winter and SH-winter experiments. These beneficial signals largely overlap with those of beneficial AMSU-A OI_EFSO in Fig. 5: the amplitudes (absolute values) of the I_AMSU-A and AMSU-A OI_EFSO signals are overall of the same order. The results indicate that EFSO is helpful in estimating beneficial I_AMSU-A distributions. However, the I_AMSU-A signals are distributed more broadly than the AMSU-A OI_EFSO signals, likely because of the propagation of accumulated AMSU-A OI. Beneficial I_AMSU-A is widely distributed in the troposphere and the Southern Hemisphere stratosphere: the accumulation of AMSU-A OI brings beneficial impacts globally. These findings are consistent with Table 1.

View Full Size

I_AMSU-A (J kg⁻¹; shading) averaged during the (a) NH-winter (21 Dec 2018–31 Jan 2019) and (b) SH-winter (23 Aug–3 Oct 2019) experiments. Latitude–height cross sections of zonal mean values are shown. Contours indicate the zonal mean wind fields (m s⁻¹) of the CTL analysis averaged over each experimental period.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

Similar to Fig. 7, Fig. 8 compares horizontal distributions of AMSU-A OI_EFSO and I_AMSU-A. Beneficial AMSU-A OI_EFSO is distributed mainly over the southeastern Pacific and the Southern Ocean, and is weakly apparent in the northeastern Pacific (Figs. 8a,c). These areas seem particularly beneficial because conventional observations are sparse, but AMSU-A measurements from polar-orbit satellites are distributed uniformly worldwide. In particular, we find distinct beneficial AMSU-A OI_EFSO signals over the southeastern Pacific off the coast of Peru, and Figs. 8b and 8d show the I_AMSU-A signals located just downstream of the midlatitude area of peak AMSU-A OI_EFSO in both experiments. These horizontal maps again suggest the propagation of accumulated AMSU-A OI in the Southern Hemisphere midlatitudes.

View Full Size

Horizontal distributions of vertically integrated (a),(c) AMSU-A OI_EFSO and (b),(d) I_AMSU-A (J kg⁻¹) averaged for the periods of the (left) NH-winter and (right) SH-winter experiments.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

In the Southern Hemisphere stratosphere, beneficial I_AMSU-A appears in both OSEs despite the estimation that AMSU-A observations do not directly affect these regions (Fig. 5). The stratospheric I_AMSU-A is attributed to the effects of the accumulation of AMSU-A OI. Small and broad beneficial I_AMSU-A in the NH-winter and SH-winter experiments would stem from the propagation of accumulated OI via radiation processes, as the distribution of beneficial I_AMSU-A is independent of the zonal wind fields (Fig. 7). A distinct beneficial I_AMSU-A signal appears in the polar Southern Hemisphere stratosphere below 10 hPa in the SH-winter experiment, because this experiment’s AMSU-A OI accumulation is greater than that in the NH-winter experiment (Table 1 and Fig. 2). The stratospheric signal is attributed to the propagation of accumulated AMSU-A OI through dynamical processes. This is explained in section 4.

Finally, we check whether the beneficial I_AMSU-A signals actually involve regions where the CTL analysis fields are improved relative those in the OSEs. Figure 9 shows the analysis fields’ root-mean-square difference distributions against JRA-55. This figure shows the difference of root-mean-square difference of the CTL minus the OSE analysis fields in moist total energy (J kg⁻¹): more negative values indicate the CTL analysis fields to be superior to the OSE analysis fields. In both the NH-winter and SH-winter experiments, the improved (negative root-mean-square difference) regions show a good correspondence to the beneficial I_AMSU-A signals in Fig. 7. Here, similar results were obtained using ERA5 as for the reference fields (Fig. S5). Therefore, regions of beneficial I_AMSU-A involve improving the analysis fields. Regions of beneficial I_AMSU-A signals also emerge where AMSU-A observations stabilize the forecast–analysis (i.e., data assimilation) cycles. EFSO can estimate such regions overall if we consider the OI distributions.

View Full Size

As in Fig. 7, but for the difference of the root-mean-square differences between the CTL analysis and the OSE analysis against JRA-55 (J kg⁻¹); i.e., the error of CTL referenced against JRA-55 minus that of OSE. Negative values indicate that the CTL analysis is closer to JRA-55 than the OSE.

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

e. Relative contributions of AMSU-A OI to kinetic, potential, and moist energy

As OI has been normalized by the moist total energy, we can decompose the OI of AMSU-A OI_EFSO or I_AMSU-A to the kinetic (e_KE), potential (e_PE), and moist (e_ME) energy components [Eqs. (7)–(9)]. To decompose and evaluate the relative contributions of those energy components, we can discuss which variables AMSU-A observations will contribute in ALEDAS.

Table 2 lists the relative contributions of e_KE, e_PE, and e_ME to the total OI of CTL ($\mathrm{\Delta }{E}_{\text{CTL}}^2$) and total ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$, AMSU-A OI_EFSO, and I_AMSU-A. Initially, total observations at each cycle (for $\mathrm{\Delta }{E}_{\text{CTL}}^2$) show contributions to the moist total energy from e_KE of more than 60%, from e_ME of ∼23%, and from e_PE of ∼13%. EFSO (for total ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$) performs well in estimating the energy components of $\mathrm{\Delta }{E}_{\text{CTL}}^2$. Compared with $\mathrm{\Delta }{E}_{\text{CTL}}^2$ or total ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$, the AMSU-A observations estimated by AMSU-A OI_EFSO have contributions from e_PE of 20%–30%, which are about double those of e_PE for the total observations; in contrast, the contributions from e_ME are at most ∼5%, much smaller than those in $\mathrm{\Delta }{E}_{\text{CTL}}^2$. The relative contributions of AMSU-A accumulated OI (I_AMSU-A) show similar ratios to those in AMSU-A OI_EFSO, except that the contributions to I_AMSU-A from e_KE and e_PE become larger and smaller than those in AMSU-A OI_EFSO, respectively, in the SH-winter experiment.

Table 2

Contributions (%) of kinetic (e_KE), potential (e_PE), and moist (e_ME) energy to the moist total energy (=e_KE + e_PE + e_ME) in the global averages of total OI of CTL $\mathrm{\Delta }{E}_{\text{CTL}}^2$, total ${\text{OI}}_{\text{EFSO}}^{\text{CTL}}$ (in parentheses), AMSU-A OI_EFSO, and I_AMSU-A for the NH-winter and SH-winter experiments. All values are averaged for the period of each experiment.

View Table

Therefore, AMSU-A observations tend to improve the variables related to potential energy (i.e., temperature and surface pressure) among the global (total) observations. However, as the AMSU-A observations have a greater impact on the Southern Hemisphere midlatitudes than anywhere else (section 3d), kinetic (i.e., wind) and potential energy of I_AMSU-A are transferred interchangeably owing to extratropical geostrophic adjustment through the accumulation (cycling data assimilation) periods, which would be more active during Southern Hemisphere winters.

Figure 10 shows AMSU-A OI_EFSO and I_AMSU-A distributions decomposed into their e_KE, e_PE, and e_ME components. The AMSU-A OI_EFSO distributions (Figs. 10a,b) show large e_KE and e_PE contributions in the middle and upper troposphere in the Southern Hemisphere midlatitudes during both experiments. Their e_KE and e_PE distributions show similar patterns to each other, although the e_KE distributions are rather broad toward the tropics. In contrast, the e_ME distributions of AMSU-A OI_EFSO are small and mostly confined to the tropical middle troposphere, far from the major beneficial AMSU-A OI_EFSO region in the Southern Hemisphere midlatitudes (Figs. 5 and 8a,c).

View Full Size

Latitude–height cross sections of (top) e_KE, (middle) e_PE, and (bottom) e_ME of (a),(b) AMSU-A OI_EFSO and (c),(d) I_AMSU-A distributions (J kg⁻¹) averaged for the periods of the NH-winter experiment in (a) and (c) and the SH-winter experiment in (b) and (d).

Citation: Weather and Forecasting 38, 6; 10.1175/WAF-D-22-0159.1

• Download Figure
• Download figure as PowerPoint slide

For the I_AMSU-A distributions (Figs. 10c,d), the e_KE, e_PE, and e_ME contributions show similar but broader patterns to those of the AMSU-A OI_EFSO. As the e_KE and e_PE of the AMSU-A OI_EFSO are largely distributed in the Southern Hemisphere midlatitudes, those energy components of beneficial I_AMSU-A are distributed in the Southern Hemisphere extratropical stratosphere, possibly because of the propagation of accumulated OI (section 4).

In summary, AMSU-A observations have a relatively large impact on the potential energy of OI, which includes temperature improvements, compared with all the observation types (total observations). This is consistent with the AMSU-A channels used here being sensitive to atmospheric temperature. For accumulated AMSU-A OI, the potential energy and kinetic energy are exchanged with each other in the Southern Hemisphere midlatitudes through the cycling OSEs; much potential energy was transferred to kinetic energy during the SH-winter experiment. In contrast, AMSU-A observations contribute less to the moist energy of OI, because this energy is mainly distributed in the tropics, far from the Southern Hemisphere midlatitudes.