Scale‐dependent impact of Aeolus winds on a global forecast system

The European Space Agency's Aeolus mission, launched in August 2018, provides the first global horizontal line‐of‐sight wind profile measurements. Previous studies have shown that Aeolus winds in global forecast systems improve the overall forecast skill, especially in the upper tropospheric tropics and in other data‐sparse regions. In this study, we use a series of observing system experiments with the latest version of the reprocessed Aeolus wind product (2B11) to better characterize the locations and drivers of improved skill from Aeolus with Environment and Climate Change Canada's Global Deterministic Prediction System. Observing system experiments that test the impact of Aeolus winds and the impact of all operational wind observations are carried out, covering the period summer 2019 and winter 2019–2020. Assimilation of operational winds improves the tropospheric wind forecast over the Tropics by a reduction of 8% in the forecast error, and adding the Aeolus winds to the assimilations results in an extra 0.7–0.9%. Aeolus wind impacts are improvements are 0.7–0.9% for the Arctic, and 0.4–0.6% over the Northern and Southern Hemisphere extratropics. The scale dependence of these impacts is investigated using spatial spectra (spherical harmonic decomposition). The improvement is quantified using the difference of the 250 hPa kinetic energy forecast error spectra between experiments. The operational winds largely improve the forecast of planetary scale to intermediate scale for spherical wave numbers between 1 and 20 in the short‐range forecasts. The operational wind impact decreases as the forecast lead time increases. On the other hand, the impact of Aeolus is mostly seen in the intermediate to large scale range with a peak around spherical wave number 8. The Aeolus‐related improvement around this wave number increases with forecast lead time. This analysis suggests that Aeolus winds provide estimates of the wind state that are valuable and complementary to that provided from current operational winds.


INTRODUCTION
Increasing the sampling of profiles of the wind field has been highlighted as essential to improving forecasts from numerical weather prediction (NWP) systems (Benjamin et al., 2010;Bouttier & Kelly, 2001;Horányi et al., 2014;James et al., 2020;Kelly & Thépaut, 2007).The European Space Agency's (ESA's) Aeolus satellite, launched in August 2018, is the first spaceborne Doppler wind lidar (DWL) designed to provide global wind-profile observations that partially address this observational need.
The main mission objective is to improve the estimation of winds in the Tropics, where the lack of direct wind observations and the failure of simple dynamical balance limits forecast skill (Horányi et al., 2014), with consequences for extratropical forecasts.Aeolus is in a near-polar orbit and has a line of sight pointing 35 • from the nadir that is perpendicular to the satellite's velocity (Reitebuch, 2012).This DWL measures global horizontal line-of-sight (HLOS) wind profiles that are predominantly zonal.Its Level-2 wind products have undergone extensive validation and processing (Baars et al., 2020;Guo et al., 2021), both globally (Martin et al., 2021) and for specific regions such as the Arctic (Belova et al., 2021;Chou et al., 2022).Aeolus HLOS winds have a proven beneficial impact on forecast systems, including those from European Centre for Medium-Range Weather Forecasts (ECMWF; Rennie et al., 2021), National Centre for Medium Range Weather Forecasting (George et al., 2021), Deutscher Wetterdienst (Martin et al., 2023), National Oceanic and Atmospheric Administration (NOAA; Garrett et al., 2022), and Météo-France (Pourret et al., 2022).As per its design, most of the impact was found in the tropical troposphere to lower stratosphere.But Aeolus winds also provide improved forecast skill in data-sparse regions, such as the Southern Hemisphere (SH) extratropics (George et al., 2021;Laroche & St-James, 2022;Pourret et al., 2022).
In this study, we assess the impact of wind observations from the Aeolus HLOS product on the Environment and Climate Change Canada's (ECCC's) global forecast system.Our assessment will be carried out in the context of evaluating the overall impact of operational wind observations in this forecast system.To do so, we use a set of observing system experiments (OSEs) in which wind observations are selectively retained or withheld.We investigate the impact of Aeolus winds on several predicted fields, using as primary verification dataset the fifth generation ECMWF atmospheric reanalysis of the global climate (ERA5; Hersbach et al., 2023) over a 7-month period for which up-to-date processed Aeolus data are available.This extends the work of Laroche and St-James (2022), who assess Aeolus's impact on ECCC's forecast system using the near-real time (2B06) and the first reprocessed (2B10) products over a 2-month period in summer 2019.They find that, especially in the stratosphere over the SH, forecast skill is sensitive to the quality of the Aeolus winds.Garrett et al. (2022) also demonstrate that an additional bias correction on a previous version of the Aeolus wind product enhances the positive impact on the forecasts.In this study, we will extend the OSEs from Laroche and St-James (2022) to July to September 2019 and December 2019 to March 2020, using the second reprocessed Aeolus HLOS product, 2B11.
The effects of wind measurements on forecast skill are expected to vary regionally and across different length scales.On scales of motion greater than the Rossby deformation radius, the initial state of atmospheric winds can be determined by the initial mass field; that is, the surface pressure and atmospheric temperature field (Horányi et al., 2014;Žagar et al., 2004).On smaller scales, direct wind observations are required.Thus, forecast skill and error characteristics reflect different dynamical characteristics at different scales (Boer, 1994;Boer, 2003;Judt, 2020;Jung & Leutbecher, 2008;Privé & Errico, 2015).For example, Boer (1994Boer ( , 2003) ) demonstrates how forecast errors in the troposphere quickly saturate at small scales and then penetrate through the spectra to larger scales, as expected classically in geostrophic turbulence.Since the deformation radius decreases poleward, we might expect regional dependence of the length scales that are impacted by a given set of wind observations.Indeed, Judt (2020) has shown that scale-dependent error growth and predictability over the Tropics and extratropics have different behavior.
These considerations motivate investigating the impacts of wind observations across different regions and across different length scales, separately and in combination.We first carry out an analysis of the impact of Aeolus and operational winds on forecast skill in different regions (the Northern Hemisphere (NH) and SH extratropics, the Tropics, and the Arctic), and at different vertical levels (the troposphere and stratosphere).The separate focus on the Arctic is motivated by our ongoing research on the impact of Aeolus winds on Arctic forecasting, which began with an assessment of Aeolus quality in the Arctic region (Chou et al., 2022) and previous literature examining impacts of different observing systems on the Arctic region (Naakka et al., 2019;Randriamampianina et al., 2021;Yamazaki et al., 2015).
We then use spectral analysis to examine the impact of Aeolus and operational winds across different length scales.To do so, we will decompose the 250 hPa kinetic energy forecast error using the spherical harmonic decomposition (Skamarock, 2004) and identify the scales on which operational winds and Aeolus winds have the greatest impact.We also introduce diagnostics on how wind observations affect the regional distribution of errors in different spectral bands.To our knowledge, a spectral analysis of how Aeolus winds affect error growth and predictability has not yet been carried out.
The OSE set-up will be presented in Section 2, forecast skill statistics and related spherical harmonic spectral methods will be presented in Section 3, and results will be presented in Section 4. Section 5 discusses the main conclusions of the study.

EXPERIMENTAL SET-UP
OSEs are used to test the impact of a given set of observations on forecast skill; they do so by selectively retaining or withholding these observations in the forecast model's data assimilation cycle (Bouttier & Kelly, 2001;Laroche & St-James, 2022).In this study, we use a series of OSEs to examine the impact of the operational wind observations and of Aeolus HLOS winds on the forecasts of the Canadian Global Deterministic Prediction System (GDPS).
The atmospheric component of the forecast system is the latest version of the operational Global Environmental Multiscale model implemented at the ECCC in 2019 (McTaggart-Cowan et al., 2019).The model uses ∼15 km horizontal grid spacing and 84 vertical levels, with over 13 million observations assimilated daily.The ocean component of the forecast system is the NEMO ocean model (Smith et al., 2018).The data assimilation scheme is the operational four-dimensional (4D) ensemble-variational (Buehner et al., 2015) system, which produces the analysis, using observations over a 6 hr assimilation window and the background state, which is the short-range forecast from the previous analysis.The 4D ensemble covariances in the 4D ensemble-variational are obtained from an ensemble of 256 members at ∼39 km horizontal resolution.To minimize the computational cost while retaining the impact of the Aeolus winds on forecasts on large scales, a simplified version of the GDPS with a coarser horizontal grid resolution of 39 km is used to carry out the OSEs.Furthermore, the ocean-ice coupling is turned off, since this is most beneficial for subseasonal and longer range forecasts.In addition, there are simplifications in the Global Environmental Multiscale physics that save additional computational time.Further details and justifications on this simplified GDPS version are provided in Laroche and St-James (2022).Forecasts were produced daily at 0000 and 1200 UTC.
To examine the impact of winds, three experiments are carried out: 1. CNTRL, an experiment with all operational observations.Henceforth, the expression "impact of operational winds" refers to the change in the forecast scores from the CNTRL compared with the CNTRL − winds (i.e., error of CNTRL − winds minus error of CNTRL, so positive for improvement), and the expression "impact of Aeolus winds" refers to the change from the CNTRL + Aeolus compared with the CNTRL (i.e., error of CNTRL minus error of CNTRL + Aeolus, so again, positive for improvement).The forecasts were conducted over July to September 2019 and over December 2019 to March 2020.

Regional forecast impact
We examine the impact of operational winds and Aeolus winds in the latitude bands of the NH extratropics (20 • N-90 • N), the Tropics (20 • S-20N), the SH extratropics (20 • S-90 • S), and the Arctic (70 • N-90 • N).We use the hourly winds and temperature from ERA5 (Hersbach et al., 2023) on 37 pressure levels from the ECMWF as verification fields to examine the forecast errors from the OSEs.The dataset is based on a 4D variational data assimilation scheme using Cycle 41r2 of the Integrated Forecast System.The data are gridded on a regular latitude-longitude grid of 0.25 • that are interpolated onto a grid of 0.5 • to match the resolution of the OSEs.The mean-square error (MSE) between the forecasts and the verification field over the area at each forecast hour and for each pressure level for a scalar field like temperature is given by where the index i indicates a horizontal location, the subscript f indicates the forecast, and the subscript v indicates the verification field.The weight w i = cos  i , where  i is the latitude at location i.For the vector wind field, the MSE statistic used is expressed as where ⃗ v is the vector wind field and ||⋅|| indicates the norm of the vector field.The MSE statistics are calculated across all 7 months of the two-times-daily forecasts unless noted otherwise, and the root-mean-square error (RMSE) is the square root of this.The impact of wind observations is defined as the percentage difference of RMSE between a pair of OSEs.The impact of operational winds is the percentage difference of CNTRL and CNTRL − winds; the impact of Aeolus is the percentage difference of CNTRL + Aeolus and CNTRL.Again, positive values of these impacts indicate improvement arising from including either operational winds or Aeolus data.We summarize the impact in the troposphere by taking the average of the impact from the four pressure levels 850, 500, 250, and 100 hPa.Similarly, we get an impact score in the stratosphere from the average over the four stratospheric pressure levels 70, 50, 30, and 10 hPa.
Aeolus has the potential to improve the vertical structure of the wind field since it provides the first global wind profile measurements.To examine this aspect, the impact on the vector wind shear has been analyzed similarly to Equation (2) and the calculation described, which is of interest for assessing impacts of wind observations such as Aeolus on temperature gradients and shear-related clear-air turbulence (Lee et al., 2019).The tropospheric wind shear is defined as the vector wind difference between 250 and 850 hPa, and the stratospheric wind shear is the vector wind difference between 10 and 70 hPa.

Spherical harmonic decomposition
An atmospheric field, as a function of longitude , latitude , pressure level p, and time t, may be decomposed into spherical harmonics (e.g., Boer, 1994;Boer, 2003): where n, the order of the Legendre polynomial, is the two-dimensional wave number on the sphere.In this study, we focus on the kinetic energy (KE) spectrum at 250 hPa (KE250), where KE in the spherical harmonic representation (Hamilton et al., 2008) is where a is the radius of the Earth and  m n and  m n are the spherical harmonic coefficients of the vorticity and divergence with zonal wave number m and Legendre polynomial of degree n.
The MSE of a forecast can be further decomposed into the mean or systematic error and the transient or random error.For example, for a scalar field x, for a forecast with a given lead , where the overbar represents the time-mean (i.e., the mean over multiple forecasts) over the period, the decomposition x f () = x f () + x ′ f () splits the forecast into its mean and transient components at forecast lead , and v is a similar decomposition for the verification (also called the analysis) field.
By combining Equations 4 and 5 we get the KE250 mean and transient error spectra as a function of degree n (corresponding to specific length scales) and forecast lead: where ⟨⋅⟩ denotes the global mean and represents the MSE as a function of two-dimensional wave number n.That is, KE250 is the KE associated with the vector differences between the forecast winds and the verification product winds.

Impact of winds and Aeolus at different latitudes
Figures 1 and 2 respectively show the impact of operational winds on tropospheric and stratospheric forecast RMSE in the Arctic, NH extratropics, Tropics, and SH extratropics.As described in Section 3.1, this impact is expressed as a percentage change in RMSE with positive values indicating improvement.The impact on the wind vector (red), temperature (blue), and wind shear (black) are presented, and the significant impacts are marked with asterisks (double asterisks for 95% confidence level and F I G U R E 1 Impact of operational winds-that is, the percentage change in root-mean-square (RMS) forecast error between CNTRL minus winds and CNTRL compared with fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis in the troposphere for wind vector (red), temperature (blue), and wind shear (black) in the troposphere (850-100 hPa layer) for 5-day forecasts over the Northern Hemisphere (NH) extratropics, Tropics, Southern Hemisphere (SH) extratropics, and Arctic.Positive values mean a reduction in the forecast error.The impacts that are significant at the 95% confidence level are marked with double asterisks, and impacts that are significant at the 90% confidence level are marked with single asterisks.
F I G U R E 2 Similar to Figure 1, but for the stratosphere (70-10 hPa layer).
single asterisks for 90% confidence level).The significance is tested using a t-test for the null hypothesis that two experiments have identical average RMSE.We consider a sample as the RMSE from all four layers when calculating the impact in the troposphere or stratosphere (Figures 1-4) and as the RMSE from a single pressure level when calculating the impact as a function of level (Figure 5).As expected, the operational winds improve significantly at the 95% confidence level the forecasts of the wind and mass fields in both atmospheric layers around the globe with an exception for the temperature and wind shear fields in the stratosphere over the Arctic.The averaged improvement over five forecast days is between 4% and 8% in the troposphere and between 2% and 6% in the stratosphere.The stratospheric impact is less pronounced, possibly due to there being fewer wind observations in the stratosphere.Horányi et al. (2014) have shown that the forecasts are greatly improved when adding the wind and mass observations into the ECMWF forecast system, especially in the Tropics.However, the impact of the conventional wind observations in the ECCC global forecast system has not yet been discussed.We can compare the results with Laroche and St-James (2022, fig.11), where they examined the impact of atmospheric motion vectors on the forecasts.The greatest tropospheric impact was seen in the wind field over the Tropics on day 1 and over the SH from day 1 to day 5 with impact scores between 1.8% and 2.7%.This comparison indirectly shows that other operational winds (i.e., measurements from radiosondes, aircraft, etc.) further reduce the forecast error by up to 10%.
The operational winds, as expected, have a direct influence on the predicted wind fields (i.e., the wind vector and wind shear) and so have a relatively large impact on forecast.For example, in the tropospheric Tropics, the impact scores averaged over 5 days for the wind fields are 6.6% and 7.9%, whereas they are only 4.3% for the temperature field.We also notice that, in the troposphere, the impact on the wind shear is 0.1-4% greater than the impact on the wind vector in the first three regions defined.For example, on day 1 of the forecast the impact in the Tropics on the wind shear in around 17%, but the impact on the wind vector is a little less than 13%.
The predicted wind and mass fields are potentially further enhanced when including the Aeolus HLOS winds in the forecast system, as shown in Figure 3. Previously published work has demonstrated that the previous versions of Aeolus wind products have the greatest impact on global forecast system (e.g., from ECMWF, Météo-France, and NOAA) in the upper tropospheric to lower stratospheric tropical regions and tropospheric polar regions in the short-to medium-range forecasts (days 1-3) by 2-4% in the forecast error (Garrett et al., 2022;Pourret et al., 2022;Rennie et al., 2021).A consistent result is seen here.The tropospheric improvement in the RMS forecast error during the first five forecast days is around 0.7-0.9% in the Tropics and the Arctic, 0.5-0.6% in the SH extratropics, and 0.4% in the NH extratropics.Although the impact score is less than the results from other forecast centers (e.g., Garrett et al., 2022;Rennie et al., 2021) and there is a lack of statistical significance, these results are nevertheless consistent with Laroche and St-James (2022), who use the same ECCC global forecast system.For example, the impact score over the Tropics and the Arctic is about 1% in the short-to medium-range forecasts, which is about the same magnitude as Laroche and St-James (2022).Note the significant positive impact on the tropospheric wind shear field in the short-range forecasts over the Tropics and SH extratropics, which reflects the ability of Aeolus to measure wind profiles.
The tropospheric impact on the temperature field has similar improvement to the impact on the wind fields in the NH and SH extratropics.In the Tropics, the impact on the winds is 0.03-0.04%greater than the impact on the temperature field.Over the Arctic, the impact on the wind fields is 0.05-0.22%greater than the impact on the temperature field.In general, the tropospheric forecast over the Arctic, where wind observations are rare, has the most positive impact from assimilating the Aeolus HLOS winds.The forecasts over the Tropics have comparable improvement, which reflects how Aeolus has achieved its main mission objective.The NH extratropics, where most of the radiosonde stations and aircraft measurements are found, see a 0.4% improvement in the forecasts in the troposphere.The SH extratropics benefit more from Aeolus winds than the NH extratropics do, presumably reflecting the availability of fewer meteorological observations there.
We have also assessed the impact of Aeolus on stratospheric forecasts (Figure 4).Laroche and St-James (2022) (using versions 2B06 and 2B10 of the Aeolus wind product) find an apparent negative impact of Aeolus observations on the stratosphere in the ECCC forecast system.More precisely, they find that disagreement with ERA5 analysis is generally greater when Aeolus information is assimilated than when it is not.They suggest that this issue is due to the quality of the Aeolus wind retrieval in the stratosphere and can be improved by not assimilating the Aeolus winds above 15 km.In Figure 4, we see that this issue persists with the new 2B11 Aeolus product; that is, that disagreement in the stratosphere with ERA5 increases with Aeolus winds in the short-range forecasts.Other than the potential issue in assimilation of stratospheric data, including Aeolus, in the ECCC and ECMWF systems, the verification with model fields is always uncertain in the short-range (Ebert et al., 2013), especially in data-sparse regions such as the stratosphere.
Even though some studies have shown that Aeolus has a positive impact in the tropical stratosphere (e.g., Rennie et al., 2021), Laroche and St-James (2022) also find a negative impact in the tropical stratosphere (Figure 6) when assimilating Aeolus winds, with or without Aeolus winds above 15 km, in the ECCC global forecast system, which is consistent with our finding.This issue might arise from the simplification of the ECCC model version used in this work to reduce computational cost, systematic model issues beyond this simplification, or assimilation system deficiencies.Nevertheless, although not significant, Aeolus still provides a positive impact in all the regions for forecast lead time beyond day 3.
Figure 5 compares the impact of operational winds and Aeolus winds on the vector wind error as a function of pressure level and forecast lead.Note that the color bar for the impact of operational winds (Figure 5a,c,e,g) extends from −8% to +8% and from −2% to +2% for the impact of Aeolus winds (Figure 5b,d,f,h).We notice that Aeolus could significantly improve the predicted wind field in some layers where the operational winds alone have weaker impact on the short-range forecasts.For example, between 100 and 200 hPa and between 400 and 600 hPa in the Tropics, Aeolus further enhances the forecast by 1-2% to complement operational winds in the short-to medium-range forecasts.Another example can be seen in the lower troposphere in the Arctic.Although not F I G U R E 5 Normalized change in root-mean-square forecast error as a function of pressure level between CNTRL minus winds and CNTRL (a, c, e g) and between CNTRL and CNTRL + Aeolus (b, d, f, h) for wind vector for 10-day forecasts over the (a, b) Northern Hemisphere (NH) extratropics, (c, d) Tropics, and (e, f) Arctic.Positive impact means a reduction in the forecast error.The impacts that are significant at the 95% confidence level are marked with black plus signs and impacts, that are significant at the 90% confident level are marked with red plus signs.
significant at the 90% confidence level, Figure 5 shows that Aeolus also has the ability to improve long-range forecasts.The positive impact in the troposphere over the Tropics and NH is consistent and extends to day 10 of the forecast.As discussed earlier, the impact score shows a consistent sign but a smaller signal compared with other studies, possibly due to the simplified model used.We suspect that this consistent positive impact would extend its significance to a longer forecast lead time if a non-simplified ECCC forecast model was used.There is also a noticeable positive impact of 2% or greater seen in the stratosphere in the NH extratropics and the Arctic from day 4 onward.The positive impact in the stratosphere mostly comes from the improvement in the boreal winter season (Supporting Information Figure S3 shows the impact during the summer and winter periods separately).During the boreal winter period of the study, there was an anomalously strong Arctic stratospheric polar vortex (Lawrence et al., 2020).This suggests that Aeolus was able to detect the strong stratospheric winds occurring at this time and thus improve stratospheric forecasts.

Impact of operational and Aeolus winds on the KE250 error spectra
Figure 6 shows the KE250 spectra from ERA5 (black) and days 1-10 of the forecast spectra from CNTRL (red).The spectra are decomposed into the mean component (dotted) and transient component (dashed) using the method described in Section 3.2.In the low wave numbers, the spectrum is dominated by the mean component (i.e., the persistent structure).The transient component (i.e., the weather structure) starts to take over around wave number 10 (around 4,000 km).For wave numbers greater than 10, the transient components exhibit the n −3 power F I G U R E 7 The evolution of the (a) total, (b) transient, and (c) mean error spectra for CNTRL forecasts of the 250 hPa kinetic energy per unit mass (KE250, m 2 ⋅s −2 ) for days 1-5 and the kinetic energy spectrum of the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (black).law for two-dimensional homogeneous and isotropic turbulence (Boer & Shepherd, 1983), whereas the mean spectrum is steeper than expected for wave numbers between 10 and 60.A line with slope of −3 is shown in Figure 6 for reference.Boer (2003, fig. 4) was similar, but for 500 hPa geopotential height.In Boer (2003), the forecasts started to deviate away from the analysis (ERA5 verification) around wave number 40 (spatial scales around 1,000 km).In the subsequent decades, the forecast system has improved, and the spectra of the forecasts closely resemble those from the analysis for wave numbers smaller than 100 (spatial scales greater than 400 km).
The KE250 error spectra of days 1-5 from CNTRL for the total, transient, and mean components are displayed in Figure 7, as well as the KE250 spectrum from ERA5 for reference.As expected, the forecast error saturates at around twice the energy spectrum and the error saturates immediately for small scales for both components and penetrates to larger scales with time (Boer, 2003).At low wave numbers, the error grows relatively slower.The transient growth rate decreases as forecast lead increases, but the mean error does not show an indication of decrease in the error growth rate by day 5 of the forecast.
To examine the impact of operational and Aeolus winds as a function of length scale, we calculate the difference of the error spectra from CNTRL − winds and CNTRL and from CNTRL and CNTRL + Aeolus, as shown in Figures 8  and 9. To ease the visualization, a running average over every five wave numbers has been applied.For comparison, the differences in Figure 8a without smoothing are shown in Supporting Information Figure S4.The KE250 error decreases by 0.02-0.06m 2 ⋅s −2 when adding the operational winds in the forecast model for wave number smaller than 9, with a peak around wave number 8 (scale about 5,000 km).Most of the improvement comes from the transient error, for which the difference is four times larger than the improvement of the mean error.(This is expected from the greater power in the transient error at these wave numbers.)The improvement of the transient error is greater in the first 2 days of the forecasts.On the other hand, the impact on the mean error is the largest on days 4 and 5.
Figure 9 shows that Aeolus further improves the KE250 error from days 1 to 4 between wave numbers 2 and 10.Unlike the impact of operational winds, Aeolus winds provide weaker impact on short-lead forecasts and the impact increases as forecast lead increases.The largest scales (wave numbers 1 and 2) show little to no effect from adding the Aeolus winds to the forecast system.Most of the impact is instead seen in the large to intermediate scales (wave numbers 3-10).The peak of the difference in the error spectra is also found at around wave number 8, with a magnitude of around 0.025 m 2 ⋅s −2 for the transient error.The impact is negligible for wave numbers above 60 in both the operational-and Aeolus-wind, presumably because the error saturates almost immediately for small scales.In addition, we note that in both cases the transient errors get larger around wave numbers 10-30 after adding these wind observations in the forecast system in the medium-range forecasts.The reason for this behavior remains unclear.
Figures 10 and 11 provide regionally specific information about the spatial distribution of these errors and the impacts over different length scales for the upper troposphere (250 hPa) and the lower troposphere (850 hPa) respectively.The left column of each figure shows the spatial distributions of the CNTRL KE250 and KE850 of wind difference (i.e., [ ∕2) for a forecast lead of 5 days, averaged over the period.The middle column of each figure shows the impact of Aeolus winds on this field, and the right column shows the zonal average of these differences (the zonal average of the middle column).
F I G U R E 8 Impact of operational winds on kinetic energy (KE) error spectra: The evolution of the differences of the (a) total, (b) transient, and (c) mean error spectra for forecasts of the 250 hPa KE per unit mass (KE250, m 2 ⋅s −2 ) for days 1-5 between CNTRL minus winds and CNTRL, which measures the impact of operational winds.Running average over five wave numbers was used to reduce noise on the differences.

F I G U R E 9 Impact of Aeolus
winds on kinetic energy error spectra; similar to Figure 8, but for differences between CNTRL and CNTRL + Aeolus.
The total error field is represented in the top row of these figures, while we calculate the errors associated with low wave numbers n = 5 to n = 10 in the middle row and intermediate wave numbers n = 11 to n = 30 in the bottom row.Patterns for these selected wave-number ranges are obtained by setting the coefficient of other wave numbers to zero in the unaveraged data in spectral space, then applying an inverse transformation back to grid space, and then applying averaging across forecasts.A similar figure to Figure 10, but for a forecast lead of 2 days, which highlights some of the early-forecast impact of Aeolus on the assimilation, is shown in Figure 12.
The 5-day KE250 errors are mostly seen over the extratropical storm track regions (Figure 10a), and the intermediate wave-number range is responsible for this pattern in the NH (Figure 10g).(In the SH storm track, a similar geographic pattern occurs in the low wave-number range.)The KE850 storm track errors in CNTRL (Figure 11a) are poleward of the errors found in KE250.The CNTRL KE of wind difference and the differences compared with CNTRL + Aeolus are both around half of the magnitude found in the upper troposphere.The errors for small wave numbers initiate over the Tropics, especially over the eastern Pacific (Figure 12d), then shift into to the midlatitudes (Figure 10d).The differences on day 5 (Figures 10b,e,h and  11b,e,h) show that the impact of Aeolus also occurs around the storm track regions.The zonal average of the impact shows that the improvement seen in the Tropics and latitudes poleward of 50 • at 2-day leads (Figure 12c,f,i) evolves at 5-day leads to an improvement in the midlatitudes, with little to no improvement in the Tropics.The negative impact for wave numbers around 10-30 at these longer lead times mostly comes from the high latitudes.There is good correspondence between regions of improvement in the upper tropospheric (Figure 10) and lower tropospheric (Figure 11) storm-track winds, showing the potential value of Aeolus wind profiles in characterizing the full vertical structure of baroclinic eddies.

DISCUSSION AND CONCLUSIONS
This study has explored the impact of the Aeolus' second reprocessed HLOS wind product (2B11) on the ECCC global forecast system, examining summer 2019 (July to September) and winter 2019 to spring 2020 (December to March).This extends Laroche and St-James (2022), who investigated aspects of Aeolus and wind impacts for Aeolus' near-real time (2B06) and the first reprocessed (2B10) products on the ECCC global forecast system during August to September 2019.To place the Aeolus impacts in context, an experiment without the operational winds (CNTRL − winds) has also been investigated.The operational winds have largely improved the tropical forecasts, especially the tropospheric forecasts of the wind fields with a normalized forecast error difference of 7-8%.The mass field (i.e., temperature) also benefits from the operational winds.It has been improved by 4-5% in the troposphere and 3-4% in the stratosphere.
Even though the Aeolus winds account for less than 1% of the observations used in the forecast system, they further improve the forecast by 0.7% in the Tropics (which represents a 10% improvement over the benefits of the operational winds).This is the region where Aeolus was anticipated to benefit forecasts the most (Horányi et al., 2014).Aeolus 2B11 winds also enhance the tropospheric forecast skill over the Arctic and SH extratropics by 0.5-0.9%,where the operational winds are sparse and rare.Over the NH extratropics, where we can find most of the operational winds, Aeolus winds have the least impact, but they still improve the tropospheric forecast error by 0.4%.
Statistical significance testing suggests that it is challenging to extract a strong signal of Aeolus in isolation from the much more significant impact of operational winds on forecast quality.For example, testing on individual regions and lead times suggests that only the impact on the tropospheric wind shear field is significant at the 95% confidence level for short-range forecasts over the Tropics and SH extratopics.Though signal to noise is weak here, we see broad consistency of the Aeolus impact in the troposphere in Figure 3 across fields, regions, and lead times.This signal is consistent with the impact studies from other forecast centers-for example, ECMWF (Rennie et al., 2021) and NOAA (Garrett et al., 2022)-with percentage differences generally greater than the ones we found.The weaker signal possibly arises from the simplification of the ECCC forecast model to reduce the computational cost, because a similar magnitude of impact was found in Laroche and St-James (2022), where they used the same simplified ECCC model.Thus, with a more extended observational period we might expect a robust and long-term benefit on forecast skill from spaceborne DWL instruments like Aeolus.
On the other hand, the Aeolus winds have apparently degraded the forecast skill in the stratosphere in the short-range forecast (e.g., the significant degradation of the wind fields for forecast lead time of 24 hr over the Tropics and SH extratropics in Figure 4).Laroche and St-James ( 2022) have pointed out that the reduction in the stratospheric forecast skill is sensitive to the quality of the Aeolus winds assimilated in the ECCC forecast system and could be improved by not assimilating the Aeolus winds above 15 km.The 2B11 product, which is the second reprocessed product, has reduced the degradation compared with the results from 2B10, the first reprocessed product.This suggests that the Aeolus wind product might need further quality control or bias correction to provide an improvement in the stratospheric forecast.However, the simplified model used, systematic model errors beyond these simplifications, or assimilation system deficiencies could also be possible causes of this apparent degradation, since some other centers have found a positive stratospheric impact by assimilating Aeolus winds, especially in the Tropics (Rennie et al., 2021).
The analysis where the impact is separated into layers (Figure 5) shows that the positive impact is mostly found in those layers where the impact of operational winds is less pronounced; for example, the significant impact in the troposphere in the short-range forecast over all four regions.The positive impact of around 2% over the NH extratropics in the stratosphere is also seen for forecast lead time beyond day 4, where the impact from operational winds is also less pronounced.
We have also studied the length-scale-dependence of the impact of operational and Aeolus winds on the forecasts using the spherical-harmonic decomposed 250 hPa KE field.The energy spectrum and forecast error spectrum could be further decomposed into the transient component, which is related to the weather component of the forecast, and the mean component, which is related to the climate component.Although the energy spectrum is dominated by the mean component for the largest scales, it starts to be taken over by the transient component around spherical wave number 10.The forecast error spectra from the CNTRL experiment show that both the transient and mean errors saturate almost immediately for small scales.For large to global scales, the transient error growth rate decreases as forecast lead time increases, and the mean error still grows at an exponential rate at a forecast lead time of 5 days.We then investigate the impact of operational and Aeolus winds as a function of length scale (Figures 8 and 9): operational winds reduce the forecast error up to 0.060 m 2 ⋅s −2 on spatial scales greater than 4,500 km (wave numbers smaller than 9), and an additional reduction of 0.025 m 2 ⋅s −2 is obtained by adding Aeolus winds mostly on spatial scales between wave numbers 2 and 10.Most of the improvement is seen from the transient component of the KE field, which is around four times greater than the improvement from the mean component.Interestingly, the relative improvement of the Aeolus winds (over the operational winds) is found to be increasing as forecast lead time increases for these spatial scales.One reason for this might be that the positive impact for this wave-number range starts in the Tropics and high latitudes for intermediate wave-number range propagates to the energetic baroclinic eddies in the midlatitudes, improving medium-range skill (Figures 10 and  12).The result is an encouragement to pursue the potential Aeolus follow-on mission, Aeolus-2 (Hélière et al., 2023), since having this additional global wind measurement partially addresses observation needs, can improve the forecasts in some layers and regions where the operational winds alone have weaker impact, and can improve the medium-range forecasts for certain length scales where the operational winds show decreasing improvement as forecast lead time increases.We also note the negative impact on the KE250 field from both the operational winds and Aeolus between wave numbers 10 and 30, especially during medium-range forecast (days 4 and 5).This negative impact mostly comes from the errors at high latitudes.The reason remains unclear and will be the focus of future work focused on the impact of Aeolus on forecasts over the Arctic.

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I G U R E 3 Impact of Aeolus winds; similar to Figure 1, but for the impact of Aeolus, measured as the percentage change in the root-mean-square (RMS) forecast error between CNTRL and CNTRL + Aeolus.F I G U R E 4 Similar to Figure 3, but for the stratosphere (70-10 hPa layer).

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Spectra of the total (solid line), mean (dotted line), and transient (dashed line) components of the 250 hPa kinetic energy per unit mass (KE250, m 2 ⋅s −2 ) field for the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis (black) and for the days 1-10 forecasts (red) from CNTRL.The solid line indicates the −3-power spectral slope.

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I G U R E 10 Distribution of the 250 hPa kinetic energy (m 2 ⋅s −2 ) of wind difference day 5 for (a) all wave numbers, (d) wave numbers between 5 and 10, and (g) wave numbers between 10 and 30, and the difference of the distribution between CNTRL and CNTRL + Aeolus for (b) all wave numbers, (e) wave numbers between 5 and 10, and (h) wave numbers between 10 and 30, and (c, f, i) the zonal average of the differences.Positive difference means the latter experiment has smaller error.F I G U R E 11Similar to Figure10, but for the 850 hPa kinetic energy.

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I G U R E 12 Similar to Figure10, but for a forecast lead of 2 days.