a. Quality control

The so-called rogue check is the final test for AMSU-A quality control. If the difference between the observed brightness temperature and the corresponding value simulated using the background state (OMB) is larger than a constant factor (F) times the constant precomputed innovation stddev (σ), the observation is rejected from assimilation. Even though AMSU-A observations of channels 1–3 are not assimilated, the quality control procedure is still applied to them. Rejection of any observations of channels 1–3 will induce removal of the corresponding observations of channels 4 and 5 from assimilation. As an example, Table 1 indicates the values of F and σ used for the AMSU-A MetOp-1 clear-sky rogue check.

Table 1.

Constant factor (F) and constant innovation stddev (σ) used for AMSU-A MetOp-1 clear-sky rogue check.

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Spatial thinning is applied to the observations not flagged for rejection to reduce the effect of spatial error correlation. After spatial thinning, the minimum distance between all radiance observations is about 150 km in the current ECCC operational global deterministic prediction system.

b. Bias correction

At ECCC, satellite radiances are bias corrected using dynamically computed bias model coefficients. As described in Buehner et al. (2015), a 3DVar analysis in which only the nonradiance observations are assimilated, is used as an unbiased reference state. Linear regression is used to estimate the bias model coefficients by fitting the quality controlled and thinned radiance observations to the past seven days of these 3DVar analyses. The bias model predictors for satellite radiance observations are 1000–300-, 200–50-, and 50–5-hPa geopotential height thicknesses, and a scan-dependent bias. The biases are calculated and applied for each instrument and channel of a given satellite separately.

c. 4D-EnVar system

In the 4D-EnVar assimilation system (Buehner et al. 2015) at ECCC, the background error covariances include flow-dependent and climatological contributions. The flow-dependent component is estimated from ensembles of short-term forecasts which are produced by the 256-member operational ensemble Kalman filter (Houtekamer et al. 2019). The climatological estimate is from a static term produced using the so-called National Meteorological Center method (NMC; Parrish and Derber 1992) and estimates the forecast errors using the differences between 24- and 48-h forecasts valid at the same time.

The description of the currently assimilated observations in ECCC’s 4D-EnVar system parallels that of Shahabadi et al. (2019) as follows “The length of the assimilation window is 6 h, and it is discretized in 15-min time slots for calculating the innovations of the assimilated observations. About 13 million observations per day are currently assimilated in the operational global system and include those from radiosondes, aircrafts, land stations, ships and buoys, scatterometers, atmospheric motion vectors, satellite-based radio occultation, ground-based GPS instruments and microwave and infrared satellite sounders and imagers. The analyzed variables are the horizontal winds, temperature, humidity, surface pressure, and surface skin temperature.”

There is no outer-loop in ECCC’s 4D-EnVar assimilation system. The incremental approach is used to compute the analysis increments and the cost function gradient on a lower-resolution horizontal grid (39-km grid spacing) than the atmospheric model grid used to compute the innovations (15-km grid spacing).

To obtain the observation error stddev used at the analysis step, the constant innovation stddev used at the quality control stage (σ in Table 1 for AMSU-A channels 1–5 observations) are inflated by a multiplicative factor (IF) that accounts for the neglected spatial observation error correlations. The inflation factors for AMSU-A channels 4 and 5 are 1.6 and 1.4, respectively.

a. New innovation standard deviation for quality control and observation error definition

The use of a constant innovation stddev (σ in Table 1) is not suitable for use in the observation quality control of the all-sky approach as the accuracy of simulated radiances is closely related to the cloud amount and the accuracy of the background state. Over the ocean surface, CLW retrievals from both observed radiances (CLW_obs) and radiances simulated using the background state (CLW_FG) are computed using Eq. (1) and averaged to yield the symmetric cloud amount ($\overline{\text{CLW}}$). It is essential that the variables used to represent the observation and model cloudiness are consistent and comparable. This means we must work in radiance space, and use CLW retrievals to get comparable estimates of observation and model cloud amounts, as suggested by Geer and Bauer (2011). For AMSU-A channels 4 and 5 over the ocean surface, the new innovation stddev values are obtained based on the piecewise linear fit to the stddev of OMB binned by $\overline{\text{CLW}}$, as proposed by Geer and Bauer (2011) and Geer et al. (2012). This piecewise linear function describing the all-sky innovation stddev as a function of $\overline{\text{CLW}}$ is defined as

${\sigma }^{\text{all}}=\{\begin{array}{c}{\sigma }^{\text{clr}}\left(\overline{\text{CLW}}\le C_{\text{clr}}\right)\\ {\sigma }^{\text{clr}}+\lambda \left(\overline{\text{CLW}}-C_{\text{clr}}\right)\left(C_{\text{clr}}<\overline{\text{CLW}}<C_{\text{cld}}\right)\\ {\sigma }^{\text{cld}}\left(\overline{\text{CLW}}\ge C_{\text{cld}}\right)\end{array},$(3)

where

$\lambda ={\displaystyle \frac{{\sigma }^{\text{cld}}-{\sigma }^{\text{clr}}}{C_{\text{cld}}-C_{\text{clr}}}};$(4)

C_clr and C_cld are the clear and cloudy threshold values for the linear fit, respectively; and σ^clr and σ^cld are the clear and cloudy innovation stddev, respectively. The channel-dependent C_clr, C_cld, σ^clr, and σ^cld parameters of the innovation stddev model are summarized in Table 2 for AMSU-A channels 1–5. Figure 1 shows the variation of stddev of OMB (blue) and the piecewise linear fit (red) as function of $\overline{\text{CLW}}$ for AMSU-A channels 4 and 5 for the period from 15 June to 11 July 2019. The data count in each bin is shown in green.

Table 2.

Piecewise linear fit parameters to define the AMSU-A channels 1–5 model for the innovation stddev in the all-sky assimilation.

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The OMB stddev (K, blue) for the period from 15 Jun to 1 Jul 2019 as function of $\overline{\text{CLW}}$ (kg m⁻²) for AMSU-A channels (left) 4 and (right) 5. The piecewise linear fit (red) and the data count (green) are also shown. Only the $\overline{\text{CLW}}$ bins with sample size greater than 30 are shown. The $\overline{\text{CLW}}$ bin width 0.025 kg m⁻² is used to generate this plot.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The OMB stddev (K, blue) for the period from 15 Jun to 1 Jul 2019 as function of $\overline{\text{CLW}}$ (kg m⁻²) for AMSU-A channels (left) 4 and (right) 5. The piecewise linear fit (red) and the data count (green) are also shown. Only the $\overline{\text{CLW}}$ bins with sample size greater than 30 are shown. The $\overline{\text{CLW}}$ bin width 0.025 kg m⁻² is used to generate this plot.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The OMB stddev (K, blue) for the period from 15 Jun to 1 Jul 2019 as function of $\overline{\text{CLW}}$ (kg m⁻²) for AMSU-A channels (left) 4 and (right) 5. The piecewise linear fit (red) and the data count (green) are also shown. Only the $\overline{\text{CLW}}$ bins with sample size greater than 30 are shown. The $\overline{\text{CLW}}$ bin width 0.025 kg m⁻² is used to generate this plot.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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To perform the rogue check quality control of AMSU-A channels 4 and 5 observations, the same F factor (Table 1) as used in the clear-sky system is also used in the all-sky system, but applied to the cloud-dependent all-sky innovation stddev [σ^all in Eq. (3)]. Similarly, the observation error stddev used for the all-sky assimilation is computed with the same error inflation factor (IF) as used for the clear-sky assimilation, but applied to the cloud-dependent all-sky innovation stddev (σ^all).

The ability of the new model for the innovation stddev to describe the OMB statistics is now examined. The histograms of OMB for all AMSU-A channels 4 and 5 radiances over the ocean surface for the period from 1 to 5 July 2019 are shown in Fig. 2. Similar to Geer et al. (2012) and Tong et al. (2020), if the OMB is normalized by the stddev of the complete data sample (blue) the distribution is non-Gaussian. However, normalization by the symmetric model for the innovation stddev brings the distribution closer to Gaussian by assigning larger error to cloudy scenes and smaller error to clear scenes (red curve) when OMB values are not too far away from zero. At large negative OMB values, where there is discrepancy between the Gaussian and normalization by the symmetric model for the innovation stddev distributions (green and red curves in Fig. 2), the observations are rejected at the quality control stage.

The histograms of OMB for all AMSU-A channels (left) 4 and (right) 5 radiances over the ocean surface for the period from 1 to 5 Jul 2019, normalized by the sample stddev (blue) or by the fit to the all-sky innovation stddev (red). Gaussian distribution is shown in green dots.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The histograms of OMB for all AMSU-A channels (left) 4 and (right) 5 radiances over the ocean surface for the period from 1 to 5 Jul 2019, normalized by the sample stddev (blue) or by the fit to the all-sky innovation stddev (red). Gaussian distribution is shown in green dots.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The histograms of OMB for all AMSU-A channels (left) 4 and (right) 5 radiances over the ocean surface for the period from 1 to 5 Jul 2019, normalized by the sample stddev (blue) or by the fit to the all-sky innovation stddev (red). Gaussian distribution is shown in green dots.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Finally, for this implementation the scan-dependent change in the model for the innovation stddev and its possible variation with latitudinal band (Geer et al. 2012) are not considered.

b. Model cloud scaling

Comparing the AMSU-A channels 4 and 5 OMB values, produced with and without using the background cloud in the observation operator, showed the OMB statistics change considerably due to the existence of model cloud. Comparison of the background and observation components of $\overline{\text{CLW}}$ (CLW_FG and CLW_obs) showed the background-state clouds are largely overestimated (CLW_FG > CLW_obs). As explained in Geer et al. (2012), the existence of cloud affects the AMSU-A channels 4 and 5 simulated brightness temperatures by two mechanisms: 1) cloud increases the simulated brightness temperature as it is a warm emitter over the cold ocean surface (positive feedback); 2) cloud reduces the simulated brightness temperature by moving the weighting function upward where it is colder and through scattering (negative feedback). The positive feedback is dominant for AMSU-A channels 4 and 5, which their weighting functions have low-peaking altitudes and when the scattering effect is small (for non-precipitating clouds). Increasing cloud amount increases the simulated brightness temperatures and consequently decreases the OMB values.

There are overestimates of latent heat flux, boundary layer humidity, and precipitation over the ocean surface in the ECCC global forecast model (P. Vaillancourt 2020, personal communication ). To diminish the negative impact of the model cloud overestimation on the OMB statistics, the background clouds are scaled globally by a multiplicative factor, which is applied to the vertical LCP profile, before using the cloud profile in the observation operator. Applying the global multiplicative factor to model clouds is a simple solution to reduce the overall model cloud overestimation, though the OMB may still be large due to errors in the horizontal location of clouds.

The proper cloud scale factor maintains the linear relation between stddev of OMB versus $\overline{\text{CLW}}$ and would suppress large negative mean of OMB values happening in cloudy bins ($\overline{\text{CLW}}>0.0{5\text{kg m}}^{-2}$). With this approach, the model cloud biases are not interpreted as observation bias and the all-sky bias correction system (section 3d) is able to remove the mean bias. We conducted multiple sensitivity experiments by running assimilation cycles with different cloud scaling factors and the factor of 0.5 yielded the best forecast results for low-tropospheric mean temperature and humidity biases. Hence, for AMSU-A channels 4 and 5 radiances over the ocean surface, the cloud scaling factor of 0.5 is used for the simulation of observations for the purposes of quality control and bias correction, and assimilation of observations in the 4D-EnVar system. It is important to mention the cloud scaling is not used in the innovation stddev model, even though this introduces inconsistency with the data assimilation system. Refinement to the model for innovation stddev is among the items that will be examined in our future all-sky developments.

c. Additional changes to quality control

In the current all-sky implementation, AMSU-A channels 4 and 5 are assimilated only if $\overline{\text{CLW}}<0.{6\text{kg m}}^{-2}$. Observations with larger $\overline{\text{CLW}}$ are generally associated with large OMB values and often exceed the threshold of the rogue check test in the quality control. However, this criteria is used to ensure these observations are not assimilated since the model for the innovation stddev is based on inadequate sampling of large $\overline{\text{CLW}}$ bins. The overestimation of model cloud at ECCC implies that the model is most probably cloudier than the observation at large $\overline{\text{CLW}}$ bins and rejecting these observations will protect the analysis. The clear-sky and all-sky $\overline{\text{CLW}}$ thresholds for assimilating AMSU-A channels 4 and 5 observations are marked as vertical dashed lines on Fig. 1.

Finally, a new quality control test based on cloud effect (Geer and Bauer, 2011; Geer et al. 2012; Zhu et al. 2016) of channel 5 AMSU-A is introduced to screen out observations affected by extreme scattering, mainly from frozen hydrometeors, in deep convective regions. The following description of the approach for measuring the cloud effect parallels that of Zhu et al. (2016), which is “the difference between brightness temperature calculated from cloudy profile and the clear-sky brightness temperatures.”

d. Bias correction

The same observation error bias model as used for the clear-sky assimilation is also used for the all-sky assimilation system with a small adjustment: the bias correction coefficients are derived using selected quality controlled radiances where model and observed cloud information sufficiently agree and indicate nearly clear sky. Contrary to Zhu et al. (2016), where the criteria was the matching of cloud presence (or absence) in the background state and observation, we exclude observations with $\overline{\text{CLW}}>0.0{5\text{kg m}}^{-2}$ from computing bias correction coefficients in the all-sky system. The clear and cloudy radiance data are then bias corrected using the latest available bias correction coefficients.

Cloud information from the model background state and observations is grouped into four categories: the observation and background state cloud free (O:clear/F:clear), the observation cloudy and the background state clear (O:cloudy/F:clear), the observation clear and the background state cloudy (O:clear/F:cloudy), and the observation and background state both cloudy (O:cloudy/F:cloudy). With our proposed approach, it is assumed that most of the observation bias in all four categories can be captured by the O:clear/F:clear category. The choice is justified because the areas where either the observation or background state is cloudy often correspond with large OMB values. The OMB become increasingly large with more cloud in clear and moderately cloudy scenes (below CLW_avg = 0.6 kg m⁻² threshold), as shown by the state-dependent model for the innovation stddev, and the large OMB values can have large impact on the estimated bias correction values, even though the majority of the observations are clear-sky (Fig. 1). We do not take into account the cloud-dependent bias correction to ensure that the remaining model cloud bias does not impact the bias correction of the clear-sky observations.

e. 4D-EnVar system

In the initial set of all-sky assimilation experiments, the analysis increments are computed for the LCP variable in the 4D-EnVar assimilation system. Consequently, a new set of short-term ensemble forecasts was generated with LCP in the outputs to define the cross covariance between cloud and other state variables. The static NMC background covariance matrix does not include cloud, hence the cloud-related error covariances are solely defined with the ensembles. As LCP is a diagnostic variable in the atmospheric model, its increments are discarded and not used at the forecast step. Compared to the clear-sky assimilation framework, there are three major changes within the 4D-EnVar system for the all-sky assimilation: 1) adding background error cross covariance between noncloud analyzed variables with LCP field; 2) using LCP for computing the innovations in the nonlinear observation operator and; 3) using LCP in the linearized observation operator.

In our original tests, the observation error stddev for the all-sky assimilation was set to the observation error inflation factor (IF) times the cloud-dependent innovation stddev σ^all [Eq. (3)]. The all-sky assimilation experiments using this configuration did not produce satisfactory forecast scores. Large analysis increments were generated and large temperature and humidity biases were found in the extratropical regions where persistent cloud cover exists (plots not shown). In these experiments, we found assimilation of observations that have large disagreement with the background state in terms of cloud location and amount deteriorate the quality of temperature and humidity analysis. This is referred to as the “double-penalty” effect in Geer et al. (2012) and contributed to the forecast degradation in tropics in their original all-sky AMSU-A channels 4 and 5 assimilation tests.

As a workaround, similar to the Zhu et al. (2016), we introduced two new observation error inflation terms to lower the weight of observations during the analysis step when there is disagreement with the background-state cloud. The two inflation terms considered are based on the cloud placement and CLW differences between the observation and the background state. The difference in the cloud placement is based on (CLW_obs − C_clr) × (CLW_FG − C_clr) < 0 and |CLW_obs − CLW_FG| ≥ 0.005. If this condition is satisfied, the observation error inflation due to the difference in cloud placement between the observation and background state is ${\sigma }_{\inf 1}^O=\left|\text{OMB}\right|$, otherwise it is set to zero. The observation error inflation due to CLW difference is ${\sigma }_{\inf 2}^O=\min \left(\gamma \left|{\text{CLW}}_{\text{obs}}-{\text{CLW}}_{\text{FG}}\right|{\sigma }^{\text{all}},3.5{\sigma }^{\text{all}}\right)\times \text{IF}$, where γ = 13.0 m² kg⁻¹, similar to Zhu et al. (2016), and IF is the clear-sky inflation factor. The final observation error stddev used at the analysis step is the combined original observation error and the two additional inflation terms:

${\sigma }_{\text{analysis}}^O={\left[{\left(\text{IF}{\sigma }^{\text{all}}\right)}^2+{\left({\sigma }_{\inf 1}^O+{\sigma }_{\inf 2}^O\right)}^2\right]}^{0.5}.$(5)

Figure 3 compares the original symmetric observation error stddev (IFσ^all, top panel) and the ratio of the final and original symmetric observation error stddev at the analysis step [${\sigma }_{\text{analysis}}^O/\left(\text{IF}\hspace{0.17em}{\sigma }^{\text{all}}\right)$, bottom panel] for assimilated AMSU-A channel 4 observations at 0000 UTC 1 July 2019 analysis date.

(a) Original symmetric observation error stddev for assimilated AMSU-A channel 4 observations at the 0000 UTC 1 Jul 2019 analysis date. (b) The ratio of final and symmetric observation error stddev for when the ratio > 1 for the same date.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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(a) Original symmetric observation error stddev for assimilated AMSU-A channel 4 observations at the 0000 UTC 1 Jul 2019 analysis date. (b) The ratio of final and symmetric observation error stddev for when the ratio > 1 for the same date.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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(a) Original symmetric observation error stddev for assimilated AMSU-A channel 4 observations at the 0000 UTC 1 Jul 2019 analysis date. (b) The ratio of final and symmetric observation error stddev for when the ratio > 1 for the same date.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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a. Experiments

The ECCC global deterministic weather prediction system (Buehner et al. 2015; McTaggart-Cowan et al. 2019) was used to run 4D-EnVar assimilation experiments, using a forecast model with 15 km grid spacing for the background state and 39-km grid spacing for the analysis increments, to examine the impact of all-sky assimilation of AMSU-A channels 4 and 5 over the ocean surface. Experiments were conducted for two periods of 2 months from 1 July to 31 August 2019 (summer 2019), and from 1 January to 28 February 2020 (winter 2020). For each period, the control experiment uses the clear-sky assimilation framework, similar to the current operational configuration at ECCC. In the modified experiment, the all-sky assimilation framework is activated. A brief list of modifications to change from the clear-sky to all-sky framework is mentioned in Table 3. The all-sky experiments were launched with the same initial conditions (including the dynamic bias correction coefficient for satellite radiances) as the clear-sky experiments.

Table 3.

List of modifications to change from the clear-sky to all-sky framework.

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b. Impact on fit to the observations and data count

It is difficult to do a clean comparison of the fit of the background state to the observations between the clear-sky and all-sky experiments, as pointed out in Geer et al. (2012) and Zhu et al. (2016). In addition to using model cloud in the observation operator, there are many other changes for transitioning from the clear-sky to all-sky framework (section 3) that contribute to the change to fit to observations.

The thinned bias-corrected AMSU-A and ATMS observations between 50°S and 50°N latitudes over the ocean surface (the latitudinal limits where AMSU-A channels 4 and 5 are assimilated in ECCC) were used to compute the OMB for the clear-sky and all-sky experiments. Data were collected from the first month of each evaluation period (from 1–31 July 2019 to 1–31 January 2020) and OMB statistics were computed for each period separately. Quality control was not applied when sampling the data. The results for the two evaluation periods are very similar. The stddev of OMB in the all-sky experiment, normalized by the stddev of OMB in the clear-sky experiment for the 1–31 January 2020 evaluation period for AMSU-A and ATMS observations are shown in Fig. 4. The statistical significance is computed from an F test with a 95% confidence level. For AMSU-A, there is a 2% increase in channel 4 stddev of OMB, whereas channel 5 stddev of OMB was reduced by 2% in the all-sky experiment. The observation error inflation at the analysis step seems to decrease the fit of the background state to the cloud-affected observations and therefore, the increase in AMSU-A channel 4 stddev of OMB was expected. The results for other AMSU-A channels were not statistically significant and the two experiments’ performances are comparable. For ATMS, there is a 1% decrease and a 0.7% increase in stddev of OMB for channels 8 and 10 in the all-sky experiment. The 0.6% degradation of the fit to ATMS channel 10 is not statistically significant. There are no statistically significant differences between the two experiments for other ATMS temperature channels. There is a 1% increase in stddev of OMB for channel 16 and a 1.5%–3% reduction of stddev of OMB for upper tropospheric humidity channels 21 and 22. Overall, the changes in fit of the background state to the AMSU-A and ATMS observations are mixed positive and negative.

Stddev of OMB of thinned bias-corrected (left) AMSU-A and (right) ATMS global observations for the all-sky experiment, normalized by the stddev of OMB of the clear-sky experiment. Error bars indicate significance interval from an F test at the 95% confidence level. The statistics are calculated for the 1–31 Jan 2020 period.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Stddev of OMB of thinned bias-corrected (left) AMSU-A and (right) ATMS global observations for the all-sky experiment, normalized by the stddev of OMB of the clear-sky experiment. Error bars indicate significance interval from an F test at the 95% confidence level. The statistics are calculated for the 1–31 Jan 2020 period.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Stddev of OMB of thinned bias-corrected (left) AMSU-A and (right) ATMS global observations for the all-sky experiment, normalized by the stddev of OMB of the clear-sky experiment. Error bars indicate significance interval from an F test at the 95% confidence level. The statistics are calculated for the 1–31 Jan 2020 period.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The fit of the background state to GPSRO refractivity observations is also compared between the clear-sky and all-sky experiments during the first month of the two evaluation periods. The statistics are calculated with the global observations grouped in 2-km-thick layers between 0- and 60-km altitude above mean sea level. Similar to before, the comparisons are very similar between the two evaluation periods. Stddev of OMB in the all-sky experiment, normalized by the stddev of OMB in the clear-sky experiment, shows small statistically significant improvement (~0.5%) at 4- and 13-km altitudes during the summer period and 7 and 16 km during the winter period (not shown).

The fit of the background state to radiosonde observations is similar between the clear-sky and all-sky experiments (not shown). Overall, similar to Zhu et al. (2016) the results of our all-sky AMSU-A channels 4 and 5 assimilation experiments indicate mostly neutral impacts related to OMB statistics.

The number of AMSU-A channels 4 and 5 assimilated observations is increased by 5%–12% at each 6-h assimilation window in the all-sky experiment. The increase in assimilated observation count is mostly in the Southern Hemisphere where there is more ocean coverage since these channels are only assimilated over the ocean surface. This number can be further augmented in future upgrades by relaxing the threshold $\overline{\text{CLW}}<0.{6\hspace{0.17em}\text{kg m}}^{-2}$ criteria used for quality control of the observations to a higher value.

c. Impact on analysis

The impacts of the all-sky approach on the analysis are expected for the regions where the background state or the observations are cloudy. The clear-sky and all-sky 850-hPa temperature analyses of the summer experiments are compared against the ECMWF analyses for the first analysis of the summer period at 0000 UTC 1 July 2019 in Figs. 5a, 5b, respectively. For the same date and level, the temperature analysis increments are shown in Figs. 5c, 5d and the difference between the temperature analysis in the two experiments is shown in Fig. 5e. Three regions (1: 60°–30°S, 80°–120°E; 2: 30°S–0°, 85°–105°W; and 3: 35°–65°N, 160°E–180°) are marked on the plots to highlight the differences between the clear-sky and all-sky experiments. Compared to the clear-sky, the all-sky experiment analysis is more consistent with the ECMWF temperature analysis (Figs. 5b vs 5a) by generating smaller temperature analysis increments (Figs. 5d vs 5c) which reduces the temperature analysis by 0.5–1 K (Fig. 5e) in regions 1 and 2. There are approximately 4000 extra AMSU-A channel 4 and 5 observations assimilated in the all-sky but not in the clear-sky experiment at this analysis date. These are the cloud-affected observations, with many located in regions 1–3, that contribute to the differences seen between the clear-sky and the all-sky experiments and are shown in Fig. 6 for the extra AMSU-A channel 4 observations. Using scaled cloud in the model for innovation stddev will induce small changes in the 850-hPa temperature analysis on the order of 10⁻² K (not shown). As will be discussed later, the cloud biases will be addressed in our future all-sky assimilation development with the goal of removing the need to use cloud scaling in DA system. Comparison of the clear-sky and all-sky 850-hPa specific humidity analysis at 0000 UTC 1 July 2019 shows small differences, mostly in the tropical regions, between the two experiments (not shown). The relation between additional assimilated AMSU-A observations and more consistency with ECMWF analyzed temperature in the all-sky experiment exists at the other analysis times.

Difference in 850-hPa temperature analysis (K) at 0000 UTC 1 Jul 2019 between ECMWF and the (a) clear-sky and (b) all-sky experiments. Temperature analysis increments (K) at 850 hPa for the (c) clear-sky and (d) all-sky experiments for the same date. (e) Difference in 850-hPa temperature analysis (K) between the clear-sky and all-sky experiments. Plots in each row have common color scales. Three regions (1: 60°–30°S, 80°–120°E; 2: 30°S–0°, 85°–105°W, and 3: 35°–65°N, 160°E–180°) are marked on the plots to highlight the differences between the clear-sky and all-sky experiments.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Difference in 850-hPa temperature analysis (K) at 0000 UTC 1 Jul 2019 between ECMWF and the (a) clear-sky and (b) all-sky experiments. Temperature analysis increments (K) at 850 hPa for the (c) clear-sky and (d) all-sky experiments for the same date. (e) Difference in 850-hPa temperature analysis (K) between the clear-sky and all-sky experiments. Plots in each row have common color scales. Three regions (1: 60°–30°S, 80°–120°E; 2: 30°S–0°, 85°–105°W, and 3: 35°–65°N, 160°E–180°) are marked on the plots to highlight the differences between the clear-sky and all-sky experiments.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Difference in 850-hPa temperature analysis (K) at 0000 UTC 1 Jul 2019 between ECMWF and the (a) clear-sky and (b) all-sky experiments. Temperature analysis increments (K) at 850 hPa for the (c) clear-sky and (d) all-sky experiments for the same date. (e) Difference in 850-hPa temperature analysis (K) between the clear-sky and all-sky experiments. Plots in each row have common color scales. Three regions (1: 60°–30°S, 80°–120°E; 2: 30°S–0°, 85°–105°W, and 3: 35°–65°N, 160°E–180°) are marked on the plots to highlight the differences between the clear-sky and all-sky experiments.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Averaged cloud liquid water (CLW_avg kg m⁻²) at locations where AMSU-A channel 4 observations are assimilated in the all-sky but not the clear-sky experiment at 0000 UTC 1 Jul 2019. The three highlighted regions correspond to the same regions marked in Fig. 5.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Averaged cloud liquid water (CLW_avg kg m⁻²) at locations where AMSU-A channel 4 observations are assimilated in the all-sky but not the clear-sky experiment at 0000 UTC 1 Jul 2019. The three highlighted regions correspond to the same regions marked in Fig. 5.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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Averaged cloud liquid water (CLW_avg kg m⁻²) at locations where AMSU-A channel 4 observations are assimilated in the all-sky but not the clear-sky experiment at 0000 UTC 1 Jul 2019. The three highlighted regions correspond to the same regions marked in Fig. 5.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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d. Impact on upper-air forecasts

The medium-range forecasts launched at 0000 and 1200 UTC were evaluated against radiosondes and ECMWF operational analyses. The verification against radiosondes did not show statistically significant differences between the clear-sky and all-sky experiments. This is expected as the geographical coverage of the radiosonde observations is limited to areas over land, away from regions where the cloudy observations are assimilated in the all-sky system.

For the forecast verification against analyses, only the statistically significant differences between the two experiments are highlighted. The normalized difference in the stddev of the error of the temperature between the clear-sky and all-sky experiments [(σ_clearSky − σ_allSky)/σ_clearSky] over the northern extratropics (NE), tropics (TR), and southern extratropics (SE) domains as a function of forecast lead time are shown for the summer 2019 and winter 2020 assimilation periods in Fig. 7. For the summer extratropics (NE for the summer 2019 and SE for the winter 2020 periods, Figs. 7a,f), there is a 2%–4% reduction in the stddev of the error of the temperature forecasts in the all-sky experiment in the lower-to-midtroposphere, up to a maximum of 4 days. Over the tropics in the all-sky experiment, the stddev of the error in the temperature forecasts is reduced by 2%–3% in the midtroposphere from day 2 to 4 for the summer 2019 (Fig. 7b), and at 850 hPa up to 2 days for the winter 2020 period (Fig. 7e). Forecast scores from the clear-sky and all-sky experiments are comparable in the winter extratropics (SE for the summer 2019 and NE for the winter 2020 periods, Figs. 7c,d). This might be due to the assimilation of more non-precipitating cloudy observations in the summer extratropics, where persistent clouds exist over the ocean surface, whereas the winter extratropics are usually associated with more severe weather and the cloudy observations are most probably precipitating and rejected.

The difference in the stddev of the error of the temperature between the clear-sky and all-sky experiments normalized by the stddev of the error of the temperature of the clear-sky experiment in percent [100 × (σ_clearSky − σ_allSky)/σ_clearSky] over (a),(d) northern extratropics (NE); (b),(e) tropics (TR); and (c),(f) southern extratropics (SE) domains as a function of forecast lead time for the (a)–(c) summer 2019 and (d)–(f) winter 2020 assimilation periods, with ECMWF analyses used as reference. Red contours show better all-sky and blue contours show better clear-sky, when verified against the reference analyses. The black dots on the plot show the statistically significant results above the 90% confidence level from the F test.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The difference in the stddev of the error of the temperature between the clear-sky and all-sky experiments normalized by the stddev of the error of the temperature of the clear-sky experiment in percent [100 × (σ_clearSky − σ_allSky)/σ_clearSky] over (a),(d) northern extratropics (NE); (b),(e) tropics (TR); and (c),(f) southern extratropics (SE) domains as a function of forecast lead time for the (a)–(c) summer 2019 and (d)–(f) winter 2020 assimilation periods, with ECMWF analyses used as reference. Red contours show better all-sky and blue contours show better clear-sky, when verified against the reference analyses. The black dots on the plot show the statistically significant results above the 90% confidence level from the F test.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The difference in the stddev of the error of the temperature between the clear-sky and all-sky experiments normalized by the stddev of the error of the temperature of the clear-sky experiment in percent [100 × (σ_clearSky − σ_allSky)/σ_clearSky] over (a),(d) northern extratropics (NE); (b),(e) tropics (TR); and (c),(f) southern extratropics (SE) domains as a function of forecast lead time for the (a)–(c) summer 2019 and (d)–(f) winter 2020 assimilation periods, with ECMWF analyses used as reference. Red contours show better all-sky and blue contours show better clear-sky, when verified against the reference analyses. The black dots on the plot show the statistically significant results above the 90% confidence level from the F test.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The normalized difference in the stddev of the error of the specific humidity and horizontal wind speed between the two experiments over the NE, TR, and SE domains as a function of forecast lead time are also displayed for the two seasons in Figs. 8 and 9, respectively. In the summer extratropics with the all-sky experiment, there is a reduction of the stddev of the error of the specific humidity at levels 1000 hPa by 2%–4% for 1–2 days, and at 850 hPa by 1%–2% that extends beyond day 2 during the winter 2020 period (Figs. 8a,f). The two experiments produce comparable results in the winter extratropics (Figs. 8c,d) while the tropical stddev of the error of the specific humidity is improved by 1%–4% at 1000 hPa and in the mid- to upper-troposphere by 2%–3% up to day 2 (Figs. 8b,e). The two experiments perform similarly for the horizontal wind forecast during the summer 2019 period (Figs. 9a–c) while there is a 1%–2% reduction in the stddev of the error of low- and midtropospheric horizontal wind speed in the all-sky experiment up to 1 day in the TR and SE domains during the winter 2020 period (Figs. 9e,f). Overall, the positive impact of the all-sky assimilation of AMSU-A channels 4 and 5 is up to a maximum 4% reduction in the stddev of the error for the temperature, specific humidity, and horizontal wind speed in the lower- and midtroposphere with the largest improvements up to 2 days in forecasts in several regions/seasons.

As in Fig. 7, but for specific humidity.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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As in Fig. 7, but for specific humidity.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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As in Fig. 7, but for specific humidity.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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As in Fig. 7, but for horizontal wind speed.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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As in Fig. 7, but for horizontal wind speed.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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As in Fig. 7, but for horizontal wind speed.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0044.1

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The all-sky assimilation of AMSU-A channels 4 and 5 resulted in degradation of 850 hPa temperature forecasts in the tropics at ECMWF (Geer et al. 2012), contrary to the results obtained here. The different results between ECMWF and ECCC could have multiple origins: 1) different assimilation systems, i.e., 4D-EnVar at ECCC and 4DVar at ECMWF; 2) different model cloud biases in the two systems and the cloud scaling method used at ECCC to mitigate the model cloud overestimation; 3) the all-sky assimilation of microwave imaging channels already constrained the low-tropospheric analysis at ECMWF and the subsequent all-sky assimilation of AMSU-A temperature channels did not add new observational information; 4) at ECCC, the “double-penalty” effect (Geer et al. 2012) was reduced by the additional observation error inflation during the analysis step, similar to the Zhu et al. (2016).

e. Impact of not computing analysis increments for cloud

We want to evaluate how much of the all-sky assimilation positive forecast impacts seen in the previous section are due to using the background error cross-covariance between noncloud analyzed variables with the LCP field and computing the LCP analysis increment. For this test, the analysis increments for LCP are not computed and there is no cross-covariance between LCP and other noncloud analyzed variables in the all-sky experiment. Compared to the clear-sky assimilation framework, in this configuration the background-state LCP is still used for 1) computing the innovations in the nonlinear observation operator and 2) linearizing the observation operator.

A modified all-sky experiment was conducted for the period of 1 January–1 February 2020 with the same setup as the original all-sky experiment for the winter 2020 period. The forecasts’ verification against radiosondes and ECMWF operational analyses showed the two flavors of all-sky experiments perform very similarly and the differences were not statistically significant. This implies that the all-sky assimilation forecast improvements result mainly from the use of cloud information for computing the innovations. To save time in the analysis step, it was decided to remove LCP as an analyzed variable in the global deterministic prediction system for the operational implementation planned for the fall of 2021.