Potential impact of all-sky assimilation of visible and infrared satellite observations compared with radar reflectivity for convective-scale numerical weather prediction

Although cloud-affected satellite observations are heavily used for nowcasting applications, their use in regional data assimilation is very limited despite possible benefits for convective-scale forecasts. In this article, we estimate the potential impact of assimilating cloud-affected satellite observations of visible (0.6 μ m) and near thermal infrared wavelengths (6.2 and 7.3 μ m) relative to the impact of assimilating radar reflectivity observations. We employed observing-system simulation experiments with a perfect-model forecast for two cases of strong convective summertime precipitation. Observations are simulated using the radiative transfer model RTTOV/MFASIS and assimilated by the ensemble adjustment Kalman filter in the Data Assimilation Research Testbed. The Weather Research and Forecasting model at 2-km grid resolution was used for forecasts. Results show that satellite observations can be nearly as beneficial as three-dimensional radar reflectivity observations. Under favorable conditions, where the prior contains no error in the stage of storm development but only in horizontal position and strength, the assimilation of visible observations leads to 88% of the radar impact. Under more difficult conditions, the impact of visible and infrared observations still reached 50 and 79%, respectively.


INTRODUCTION
Clouds are the first area-wide observable signal of convection and are heavily used in nowcasting applications.However, in contrast to nowcasting, the use of cloud-affected satellite observations in data assimilation is very limited (Gustafsson et al., 2018).Clouds are detected earlier by the visible satellite channel than by radars, which are more commonly used in regional data assimilation systems.In contrast to radar, satellite observations are available in most parts of the world, including mountainous or sparsely populated areas, and they provide homogeneous quality across borders (Maddox et al., 2002;Roebeling et al., 2012;Saltikoff et al., 2019;Martinaitis et al., 2020).Additionally, thermal infrared satellite channels observe tropospheric water-vapor content (6.2 and 7.3 μm) as well as cloud-top temperature (10.8 μm).Near-infrared channels can distinguish between ice and water clouds (1.6 μm) and detect nighttime low-level clouds and fog (3.9 μm).
Additionally, visible channels can observe low-level stratus clouds during daytime, which is a major issue for regional weather forecasts (Hu et al., 2022).Thus, there is a large potential for improving weather forecasts by assimilating cloud-affected satellite observations.Nevertheless, current operational regional data assimilation systems largely ignore satellite observations of clouds and thereby omit crucial information on clouds and developing storms.The assimilation of cloud-affected satellite observations in current assimilation systems is a challenging task.However, most related challenges also apply to the more commonly assimilated radar observations.First, the limited numerical representation of cloud processes and hydrometeors, as well as simplification of observation operators, leads to systematic errors between models and observations (Scheck et al., 2018;Geiss et al., 2021), which violates the basic assumption of an unbiased first-guess forecast of current data assimilation schemes (Gustafsson et al., 2018).These issues were avoided in this study by employing an observing-system simulation experiment (OSSE) with an identical model for the nature run and forecasts, as well as perfect observation operators in the forecast.Second, cloud-affected observations violate the assumption of linear observation operators and Gaussian error distributions, as the observations are nonlinear functions of model state variables and their error distributions are often non-Gaussian.In consequence, assimilating these observations violates assumptions of current data assimilation schemes and may lead to a suboptimal analysis in certain conditions.
Most studies on the assimilation of thermal infrared satellite observations focused on wavelengths in the water-vapor sensitive band (5-8.5 μm), since these wavelengths are less sensitive to surface emission, which is difficult to model accurately.Otkin (2012aOtkin ( , 2012b) ) pioneered direct assimilation using four channels between 6.2 and 8.5 μm, albeit at a resolution of 15 km that resolves deep convection only partly.In convection-permitting models, infrared observations had a positive analysis and forecast impact for the prediction of typhoons, mesoscale convective systems, and severe weather events under weak and strong large-scale forcing (Jones et al., 2015(Jones et al., , 2016(Jones et al., , 2020;;Honda et al., 2018;Sawada et al., 2019;Zhu et al., 2022;Eure et al., 2023).Comparing the assimilation of infrared and radar observations, Zhang et al. (2019) found that assimilating infrared observations before storm initiation can advance the warning time for mesocyclones by several tens of minutes compared with assimilating radar observations only.Similarly, assimilating visible observations is expected to advance warning times even further.A direct comparison between the impact of visible and infrared satellite channels with that of radar observations has, however, never been conducted so far.
While several studies investigated the assimilation of infrared channels in convective-scale numerical weather prediction (NWP) models, visible channels have received little attention by the research community so far.Since the fast visible forward operator method for fast satellite image simulation (MFASIS, Scheck et al., 2016) was published, only two studies have investigated the benefit of visible observations for convective-scale NWP.Both these studies used the regional NWP system of Deutscher Wetterdienst, which recently also included the assimilation of visible observations in its operational configuration in March 2023.The two studies investigated the impact of visible observations in an idealized and near-operational setup: Schröttle et al. (2020) conducted an idealized OSSE and found a positive impact by assimilating infrared and visible observations, with the infrared leading to higher impact.Scheck et al. (2020) evaluated the impact of only visible observations in a case study with a near-operational assimilation system and found beneficial impact not only on cloud cover but also on temperature, humidity, and precipitation.Given their experimental setup, however, they could not quantify the impact in comparison with other observation types.Additionally, both previous studies used the regional model ICON and a local ensemble transform Kalman filter (LETKF) data assimilation system, whereas the impact of visible observations has not been investigated in any other convection-permitting numerical weather prediction (NWP) system.This motivated the direct comparison of the impact of different observation types in the present study and the use of a different modelling and assimilation system.
Data-denial experiments with operational NWP systems can be misleading in the way they estimate the analysis impact of a new observation type, as the impact of additional observations may be hampered by systematic model deficiencies without extensive tuning of the assimilation and model physics settings.Additionally, increments from other observation types may conceal the impact of the newly added observations.To avoid this, we assess the forecast impact of each observation type in separate experiments.The separate assimilation of different observation types allows for a detailed analysis of the effects of each type and reveals the potential weaknesses of each one.To put the impact of satellite observations in this setup in the context of more commonly assimilated observations, we additionally conducted comparable experiments that assimilated 2D and 3D radar observations.Furthermore, current operational systems are suboptimal in many respects: for example, concerning the representation of hydrometeors and related biases as well as the representation of related model errors.The resulting systematic differences between the forecast model and the nature run affect the analysis quality and need to be taken into account when estimating the absolute impact of observations in an OSSE (Errico and Privé, 2018).In this study, we avoid systematic model error to focus on the efficacy of assimilating cloud-related observations in an ensemble Kalman filter and only estimate the impact of observations in relative terms.Thus, we assess the forecast impact in a perfect model OSSE using the identical model configuration for the nature run and forecasts.
Convective-scale data assimilation is a challenging task full of open research questions, as for example, outlined in Hu et al. (2022).To gain further insights on the assimilation of additional complex observation types, researchers have studied the assimilation in weather scenarios of increasing complexity for data assimilation: (1) isolated supercells triggered from a "warm bubble" (Snyder and Zhang, 2003;Tong and Xue, 2005), (2) supercells, convective lines, and multicells (Aksoy et al., 2009), and (3) chaotically triggered deep convection (Bachmann et al., 2019(Bachmann et al., , 2020)).The third scenario describes deep convection triggered at random locations and is termed the "random" case in this article.It can be considered one of the most difficult and least predictable scenarios, as this case exhibits a high sensitivity to initial conditions and low predictability due to fast error growth and interaction between different cells.
In this study, we evaluate two cases, the less predictable "random" case and the "warm-bubble" case, and estimate the potential impact of assimilating visible and infrared satellite observations, relative to the impact of assimilating radar reflectivity.We employ the ensemble adjustment Kalman filter (EAKF), as it is a commonly used algorithm, which allows for a detailed analysis of the impact of different observations.Specifically, we investigate the following: 1 whether the EAKF is able to extract useful information from visible observations into a convective-scale model; 2 the relative impact of visible and infrared observations on precipitation and cloud forecasts relative to the impact of radar observations (Section 3.1); 3 the effect of assimilating visible and infrared observations on unobserved state variables (section 3.2); 4 why the assimilation of satellite observations is surprisingly beneficial in one case but less beneficial in the other (Section 3.3).
By this investigation, we intend to contribute to a better understanding of the impact of satellite observations, which is crucial for the efficient use of computational, observational, and staff resources (Gustafsson et al., 2018).

Description of the cases
We estimated the potential impact of cloud-affected satellite observations in two scenarios, one isolated supercell and scattered supercells.Both cases were simulated on the same idealized domain with a homogeneous flat surface and horizontally periodic boundary conditions (see Section 2.2).Both cases share the same base-state profiles of temperature, water vapor, moisture, and wind illustrated in Figure 1.It is a modified sounding from Payerne, Switzerland on July 30, 2008 and offers a highly unstable environment with 2670 J⋅kg −1 CAPE and 26 J⋅kg −1 CIN at 0700 UTC in the nature run.In this article, time UTC is equivalent to local solar time, since the solar radiation is that of 0 • longitude.We start with a description of the nature run.A more detailed description of initial conditions and ensemble perturbations follows in Section 2.3.

2.1.1
Nature run for case "random" In the "random" case, small random perturbations of temperature and vertical velocity (for details see Section 2.3) trigger storms at random locations scattered throughout the whole domain.The nature run is initialized at 0600 UTC (= local solar time) with the sounding profile depicted in Figure 1. Figure 2 shows the evolution of storms from the perspective of a 7.3-μm infrared satellite image and Figure 3 shows the same in 0.6-μm visible reflectance.At 1100 UTC, 5 hr into the simulation, convection reached altitudes of about 10 km.Shortly after, at 1200 UTC, about 10-15 cells are visible and continue to grow while others dissipate.The resulting storms are in different stages of their development and interact dynamically, which leads to fast-growing model error and a low predictability of the order of hours.After 1600 UTC, convection decays.
2.1.2Nature run for case "warm bubble" In the second case, a positive temperature increment ("warm bubble") is added to the initial temperature field (see Figure 4).It triggers an isolated and well-organized supercell with >200 m 2 ⋅s −2 updraft helicity (Kain et al., 2008) in a confined region of the domain and suppresses convection elsewhere.Similar warm-bubbles have been used by Snyder and Zhang (2003) and Tong and Xue (2005).This warm-bubble case was initialized at 1200 UTC with initial conditions as described in Section 2.3.

Prediction model
We used the Weather Research and Forecasting model (WRF) version 4.3 (Skamarock et al., 2021) in an idealized mode for both the forecast ensemble and the nature run in identical configurations (perfect model).As in preceding studies (Lange and Craig, 2014;Bachmann et al., 2019Bachmann et al., , 2020;;Schröttle et al., 2020), we neglected the Coriolis force, as it does not have a significant effect on the dynamics at this timescale.Also, it would lead to veering of the mean wind given the periodic domain.

Initial conditions of the nature run
The initial conditions of the nature run feature a highly unstable stratification with a CAPE of 2670 J⋅kg −1 and a CIN of 26 J⋅kg −1 at 0700 UTC, such that relatively small perturbations trigger deep convection (Figure 1).for humidity and wind.The humidity was clipped to 80% relative humidity, which reduced the humidity in the pressure intervals 900-750 hPa and 350-200 hPa, in order to avoid stratiform clouds in the whole domain.The wind shear was increased considerably to bulk shears of 14, 38, and 61 knots in the layers 0-1, 0-3, and 0-6 km, respectively, to support long-lived supercells.
In the "warm-bubble" case, an additional temperature increment ΔT(x, y, z) was added to the initial temperature field, defined as where r(x, y) = √ (x − x c ) 2 + (y − y c ) 2 is the distance from the bubble center; A is the maximum perturbation (3 K), the tuple (x c , y c ) is the center of the bubble, c r is the horizontal decay (15 km), and c z is the vertical decay (2 km).

Initial perturbations in the forecast ensemble
While a real-data experiment comes with a prior forecast ensemble, we have to make a realistic guess about (1) Before initializing the ensemble forecast, we perturb the vertical profile of temperature, moisture, and wind.This inter alia leads to modified convective stability, which delays or accelerates the evolution of deep convection.The perturbations are created by choosing one random number for every 20th vertical level of the original 200-level profile and then interpolating between them, such that we end up with a vertically auto-correlated profile of random perturbations for every ensemble member.The random numbers are created using a standard deviation of 0.25 K for temperature and 2% for relative humidity and wind.The resulting profiles are used as input profiles for the WRF initialization program (ideal.exe), which modifies the profiles slightly for hydrostatic balancing.
(2) Small-scale random noise was added to the temperature and vertical velocity in the lowest levels to avoid unrealistic spatially homogeneous fields.The perturbations are relaxed toward zero with height: for temperature following x exp((p − p sfc )∕25) with p in hPa, for velocity following x exp((1 where k is the level number, where x was drawn from a Gaussian with  = 0.02 (K or m⋅s −1 ) for each column.Although the horizontal variation of temperature was this small at the initialization time, the perturbations grew considerably in the following 6 hr, reaching a spread of 1 K in temperature, 20% in relative humidity, and 2 m⋅s −1 in zonal wind (random case, Figure 7).In the warm-bubble case, the horizontal average spread was smaller due to the shorter spin-up time of 0.5 hr and the small fraction of the domain in which convection took place, reaching a spread of 0.5 K in temperature, 5% in relative humidity, and 1 m⋅s −1 in zonal wind at 1300 UTC (not shown).

Additional perturbations in the "warm-bubble" case
In the "warm-bubble" case, we imposed another uncertainty in two parameters (see Equation 1): • the horizontal location of the warm bubble by perturbing the center (x c , y c ) in the north/south and east/west direction by ± 60 km (uniformly random) and • the spatial extent and strength by perturbing the amplitude A by ± 1 K (uniformly random).

Simulated observations
Four types of observations have been used in this study, as listed below.
(1) Satellite observations of visible reflectance at a wavelength of 0.6 μm reveal how much sunlight is reflected by clouds or the surface.In contrast to radar reflectivity, the observations already provide information on clouds in their early stage, right after rising plumes reach the condensation level.Reflectance describes the ratio of reflected radiance to the total incoming irradiance and is therefore a dimensionless value in the range of 0-1.The lowest possible value in practice is, however, determined by the surface albedo, which is around 0.27 in our setup.The instrument error for the visible channel was chosen to be 3% following Schröttle et al. (2020).
(2) Satellite observations of infrared brightness temperature of the 6.2-μm channel (Meteosat Second Generation (MSG) 4 Spinning Enhanced Visible and Infrared Imager (SEVIRI) channel 5, Geostationary Operational Environmental Satellites (GOES) Advance ABI, and Advanced Himawari Imager (AHI) band 8) are specifically sensitive to upper tropospheric water vapor and clouds.For clouds, the observations mainly provide information on the cloud-top height, as can be seen by lower brightness temperatures for higher cloud tops.The instrument error was chosen to be 1 K.In contrast, Cintineo et al. (2016) did not simulate instrument errors for brightness temperature (BT) observations.(3) Satellite observations of infrared brightness temperature of the 7.3-μm channel (MSG-4 SEVIRI channel 6, GOES ABI, and Himawari AHI band 10) provide similar information to the 6.2-μm channel but are more sensitive to lower tropospheric water vapor.An instrument error of 1 K was selected.(4) Finally, three-dimensional radar reflectivity (10 cm) serves as a reference observation type to for evaluating the impact of satellite observations.An instrument error of 2.5 dBz was chosen, half the error of Wheatley et al. (2015) and Bachmann et al. (2020), who used 5 dBz.
Observations y o were generated using the Data Assimilation Research Testbed (DART) provided by UCAR/N-CAR/CISL/DAReS (2022).It interpolates the nature run's state x nat to each observation's location and applies an observation operator  to the state x nat before adding Gaussian instrument error: The resolution of satellite observations was effectively grid-scale (2 km).The model equivalents of observations, y b = (x b ), were generated using the same observation operators to avoid systematic errors between forecast and observations.Satellite observations were simulated using the default Chou scaling for the infrared channels (Chou et al., 1999) and MFASIS Scheck et al., 2016) for the visible channel, as provided in the RT model for the television and infrared observational satellite (TIROS) operational vertical sounder (RTTOV) v13.3 (Saunders et al., 2018).For radar reflectivity, the operator included in the WRF Thompson microphysics module was used.The surface albedo and emissivities are given by RTTOV default values.To simulate cloudy radiances, we assumed an effective particle diameter of 20 μm for water droplets and 60 μm for ice crystals.For the satellite geometry, we assumed a geostationary satellite at the Equator with an azimuth of 180 • and zenith of 45 • .The solar angles were computed using the pysolar module assuming a latitude of 45 • and longitude 0 • .

Assimilation system and settings
Our experiments applied the EAKF by Anderson (2001) included in DART Anderson et al. (2009) 1 to a 40-member forecast ensemble.The EAKF is a serial deterministic square-root filter, which assimilates one observation after another.The following variables were updated: temperature, water-vapor mixing ratio, dry air mass in column, geopotential, wind components U, V, W, cloud water, and ice mixing ratio.
Posterior covariance inflation was applied, since experiments without inflation indicated that analysis ensemble spread would have been underestimated.Specifically, relaxation to prior spread (RTPS) with factor  = 0.9 was used to inflate ensemble perturbations.Note that a value of  = 1 would prevent any variance reduction and restrict updates to updates of the mean, while  = 0 would mean no inflation.We localized covariances in the horizontal to 20 km half-width of the Gaspari-Cohn function.Radar observations were localized to 3 km in the vertical.Satellite radiances were not localized vertically.Lastly, a sampling error correction (Anderson, 2012) was applied.We assimilated all observations, including those that were far from the first guess, as we noticed a relatively strong error reduction by these observations in our experiments.It should be noted, however, that real NWP systems might require such a first-guess check to exclude erroneous observations.
The horizontal distribution of observations was chosen to be equal for all observation types.In the horizontal, we assimilated observations every 10 km.However, we did not assimilate observations within 50 km of the domain boundary, so that only observations of the inner 300 × 300 km were assimilated.This was necessary to avoid discontinuous increments at domain boundaries, since we assumed a periodic WRF domain but a limited area domain in DART.In the vertical, we assimilated radar reflectivity observations every 2 km from 2-14 km.
Superobbing can be a useful approach to assimilate high-resolution observations, as it averages observations towards the resolved scale of the model.However, an experiment that superobbed 5 × 5 grid-scale observations towards one observation every 10 km did not generally improve forecasts.Given the perfect-model assumption, this might not be too surprising.Furthermore, we only superobbed observations, but not the model prior following the standard implementation in DART, which is not fully consistent.As the difference in impact was negligible, we decided not to include those experiments in this article.
The assimilation of satellite observations in a Gaussian filter is suboptimal for reasons of non-Gaussianity, like heteroscedasticity (the increase of variance with cloudiness) or boundedness.Additionally, non-linear observations operators as well as sampling error and suboptimal ensemble perturbations lead to a suboptimal analysis and ensemble spread.These effects can be mitigated by assigning inflated observation errors (Geer and Bauer, 2011), but the optimal choice of assigned observation errors often needs to be tested by sensitivity studies (see Section 3.3).

Assimilation experiments
The experiments of this study are listed in Table 1.To investigate optimal assigned observation-error settings, we conducted sensitivity experiments with different assigned observation errors in Section 3.3.The resulting optimal observation errors used for the standard experiments are listed in Table 1.The timeline of the experiments is illustrated in Figure 8.In the random case, the forecast ensemble was initialized at 0700 UTC and ran freely without assimilation for 6 hr.By 1300 UTC, the model had generated a sufficient amount of spread (Figure 7).From 1300-1400 UTC we assimilated five times (every 15 min), followed by free forecasts until 1800 UTC.
In the warm-bubble case, we started to assimilate at 1230 UTC after a free forecast of 30 min.Despite this short spin-up time, the deep convection had already developed.From 1230-1330 UTC we assimilated five times, followed by free forecasts until 1800 UTC.Although the assimilation window is 1 hr in both cases, it covers different phases of convection in each case.
Figure 9 shows the time series of the strongest cloud signal in each observation type, that is, the lowest value TA B L E 1 Experiments and their assimilated variable together with standard errors for generating observations (instrument error) and assimilating observations (assigned error).for infrared BT and the highest value for visible and radar observations.The earliest stages of convection were only detected by visible observations.For radar, it took up to 60 min for convection to become apparent in the observations.In the "random" case, all observation types detected convection at the start of the assimilation window.In the warm-bubble case, however, infrared channels did not detect convection at the beginning of the assimilation, but later in the assimilation window.Overall, the warm-bubble case was more predictable.A measure of uncertainty is the time duration between earliest and latest convective initiation in the ensemble.While the time difference of convective initiation was 1.5 hr in the "random" case, the initiation happened within 20 min in the "warm-bubble" case (not shown).This demonstrates that adding a warm bubble can act to synchronize the triggering time of convection across the ensemble, since it forces convection regardless of the stratification.

RESULTS
The first goal in this section is to estimate how forecasts of precipitation and cloudiness benefit from assimilating cloud-affected satellite observations (Section 3.1).Subsequently, we analyze the impact on vertical profiles of state variables in Section 3.2.Lastly, we try to explain the larger impact of 3D radar observations compared with 2D satellite observations in the case of random convection in Section 3.3.

Relative potential impact
We evaluate forecasts using the Fractions Skill Score (FSS) for three quantities: • precipitation rate > 1 mm⋅hr −1 • radar reflectivity > 50 dBz, • visible reflectance > 0.6, The 24-km window FSS of these quantities describes how well a forecast was able to pinpoint the location of precipitation and optically thick clouds.We calculated the FSS using neighborhood ensemble probabilities after Schwartz et al. (2021), in contrast to, for example, Scheck et al. (2020), who calculated the FSS from the ensemble mean.

3.1.1
Case "random" Figure 10a shows the impact of assimilating four different observation types in the case with deep convection scattered randomly throughout the whole domain.
Compared with the REFL experiment and averaged over 1400-1700 UTC, the VIS experiment revealed an FSS improvement of 50% compared with the FSS of noDA, the WV73 experiment 79%, and the WV62 experiment 20% for the prediction of radar reflectivity >50 dBz.Within the first forecast hour, the VIS experiment performed nearly as well as the REFL experiment but lost impact thereafter.The WV73 experiment showed similar skill to the VIS experiment in the first 1.5 hr lead time, but provided  better forecasts afterwards.The WV62 experiment's forecast skill was the lowest of all observation types.It seems that channels that see deeper into the atmosphere (visible and 7.3 μm) have a higher impact than the 6.2-μm channel, which does not sense lower tropospheric vapor and clouds.Overall, forecasts in the REFL experiment were best, with 2.5 hr of skillful forecasts for light precipitation and 1.5 hr for strong precipitation, except for the prediction of visible reflectance >0.6, where forecasts of the VIS experiment were slightly better.
In Figure 11a, we show the root-mean-square error (RMSE) of visible reflectance and 7.3-μm brightness temperature forecasts, relative to the RMSE of the noDA experiment.Specifically, we computed the RMSE of the ensemble mean forecast over all 200 × 200 grid points, while only 31 × 31 satellite observations were assimilated.At analysis time, the experiment that assimilated visible reflectance had the lowest errors in visible reflectance, as expected.The same applies to the WV73 experiment and the verification of 7.3-μm BT.After the analysis, however, the RMSE of the WV73 experiment was similar to the error of the REFL experiment.The experiments REFL, VIS, and WV73 overall showed similar skill in predicting the visible channel, while the WV62 experiment had lower skill in the first 1.5 hr.The VIS experiment had relatively good forecasts of 7.3-μm BT and the WV73 experiment had good forecasts of visible reflectance.The WV62 experiment had less accurate forecasts of both 7.3-μm BT and visible reflectance, which is presumably related to the higher peak of its weighting function leading to smaller sensitivity to low and mid-level clouds.

3.1.2
Case "warm bubble" Figure 10b shows the forecast impact in terms of FSS, but now for the warm-bubble case.In general, all observation types lead to a significant FSS improvement compared with the noDA experiment, but some aspects should be noted.First, the assimilation of visible reflectance in the VIS experiment improved the FSS faster than the assimilation of infrared BT in the experiments WV62 and WV73.As visible reflectance detected convection at an early stage (Figure 9), the VIS experiment was at a clear advantage.
The initially high impact in the VIS experiment deteriorated in the first forecast hour, handing over the lead to the REFL experiment.However, the VIS experiment overtook the REFL experiment again at around 3 hr lead time in precipitation scores.Second, the experiments WV62 and WV73 produced similar results, except for the FSS of cloudiness (visible reflectance > 0.6), where most of the impact vanished within 30 min of free forecast in the WV62 experiment.Note that the 6.2-μm channel is more  sensitive to higher tropospheric water vapor, while the 7.3-μm channel is more sensitive to lower tropospheric water vapor.Third, the experiments REFL and VIS show a similar performance except for the first hour, where the skill was slightly lower for precipitation.Interestingly, the VIS experiment only shows an advantage over the REFL experiment in the FSS for cloudiness during the first 2.5 hr.For cloudiness, both the REFL and the VIS experiment gave similar performance.Compared with the REFL experiment, the experiments WV62 and WV73 showed less impact.Lastly, the REFL experiment outperformed all other observation types in the first forecast hour for light and strong precipitation but only slightly for cloudiness, where the VIS experiment was best most of the time.
Figure 11b shows the RMSE of forecasts of visible reflectance and 7.3-μm BT for the warm-bubble case.Visible reflectance was best forecast by the REFL experiment, followed by the VIS experiment with similar forecast score, except for the first forecast hour.The experiments WV62 and WV73 performed worse, as they removed less error until the last assimilation time.While the experiments REFL and VIS removed up to 30% of error, the experiments WV62 and WV73 removed only 15-20% of visible reflectance error.Also 7.3-μm BT was best forecast by the REFL experiment, removing 40% of RMSE until the last assimilation time.Other experiments removed similar amounts of error, but lost impact faster.On average, the VIS experiment had the second best RMSE in 7.3-μm BT, followed by WV62 and WV73.

Comparison of cases
A major difference between the two cases is that the warm-bubble case is more predictable than the "random" case.While the REFL experiment skillfully predicted strong precipitation for nearly 4 hr (FSS > 0.5) in the warm-bubble case, the random case was skillfully predicted for only 1.5 hr.The difficult forecasting conditions probably result from faster growth of errors in the "random" case, as storms interact with each other and continuously trigger new cells, leading to a chaotic environment which is very sensitive to the initial conditions.
To compare the relative impact of the observation types, Table 2 shows the relative FSS improvement over noDA of each experiment compared with the REFL experiment.Overall, satellite observations lead to a remarkable impact given that the satellite experiments assimilated only 1/7th of the number of observations compared with the REFL experiment.Visible observations detect convection earliest and allow the filter to narrow down the location of convection much earlier than other observations can.To date, only Schröttle et al. (2020) compared the assimilation of visible (0.6 μm) and infrared observations (6.2 μm) in a convective-scale NWP model.Despite the similar setup, we clearly see more impact from assimilating visible observations than from 6.2-μm BT observations.This contrasts with Schröttle et al. (2020) who found stronger impact from the 6.2-μm channel and less impact from visible observations.However, this difference might be related to overly inflated observation errors for visible observations in that study, as they inflated the observation error for visible much more than for infrared observations, which presumably led to a lower weight for visible observations.
Although the WV62 experiment showed competitive forecasts of precipitation in the warm-bubble case, it performed poorly in forecasting cloudiness in both cases and precipitation in the "random" case (Figure 10).This might be due to the higher peak of the function of the 6.2-μm channel compared with the 7.3-μm channel.
In the warm-bubble case, the uncertainty lies mostly in the warm-bubble location and strength.As the evaluation showed, these can be easily derived from satellite observations.In the "random" case, however, visible and 6.2-μm BT observations lead to substantially less impact.We hypothesize that a possible explanation might be missing the vertically resolved information from radar observations.This hypothesis is investigated further in Section 3.3.1 by assimilating two-dimensional instead of three-dimensional radar reflectivity.Except for the higher impact of radar in the warm-bubble case, however, the experiments overall reveal the value of satellite and particularly visible observations, especially in scenarios with an uncertain location of convection.Figure 12 illustrates how assimilating visible reflectance improved the forecast of the location of clouds in the ensemble.

Impact on model state variables
In the OSSE framework, we can compare how different observation types impact the prior model state as the true state is perfectly known.To do that, we analyzed the vertical structure of the increments (Figure 13) and error/error reduction (Figure 14).
Figure 13 shows the vertical profiles of the absolute ensemble-mean increments, averaged spatially and over the five assimilation times.Panels 13a and 13b show the increments of the warm-bubble case and the random case, respectively.In the warm-bubble case, the temperature increments of experiments VIS and REFL are substantially lower than those of WV62 and WV73.Interestingly, WV73 shows larger increments than WV62 below 7 km, while above this the relation is reversed.In the random case, WV62 and WV73 produced very similar temperature increments.Concerning water vapor, the experiments WV62 and WV73 lead to higher increments than VIS and REFL in the warm-bubble case, but not in the random case, where most profiles are similar.The largest increments in vapor can be seen in the WV73 experiment and the lowest increments in the VIS experiment.Regarding the increments of cloud water, the VIS experiment again revealed the smallest increments in both cases, while the other experiments do not differ substantially in increment magnitude.Cloud ice increments are also similar among the experiments except for the VIS experiment.Wind increments are strongest for WV62 and WV73 and smallest  for VIS.Generally, the increment profiles are more similar in the "random" case, while in the "warm-bubble" case, the increments of the experiments VIS and REFL differ from WV62 and WV73, especially for temperature, vapor, and wind.Furthermore, we see that the visible reflectance observations, while less sensitive to ice clouds, still lead to increments in cloud ice.Lastly, note that the magnitude of increments in the "warm-bubble" case is lower due to the large clear-sky area, where hydrometeor-related observations contain little information.
Figure 14 shows vertical profiles for temperature (top left), vapor mixing ratio (top right), cloud water, and ice mixing ratio (bottom left and right).Each panel shows the mean absolute error (MAE) of the noDA experiment (left), the MAE reduction in the experiment (center), and the relative MAE reduction in % of the noDA MAE (right).The error was evaluated at 1405, five minutes after the last assimilation in the "random" case, as mean (over 961 observed atmospheric columns) absolute error of the ensemble mean forecast.The corresponding increments can be seen in Figure 13a.
The temperature error profile (Figure 14a) shows four peaks: at the surface, 5, 8, and 13 km.The error reduction was largest in these layers in absolute and relative terms.The experiments WV62 and WV73 removed nearly as much temperature error as the REFL experiment, reaching up to 0.5 K and 40% of error.The VIS experiment also reduced the errors, but reaches only 0.2 K and 25%.
Regarding water vapor (Figure 14b), the relative error reduction was largest at altitudes with low vapor concentration, reaching 40% at 7 km but still removing 20% in the boundary layer.The experiments VIS and WV73 reduced the errors by a similar amount, except above 6 km, where the WV73 experiment shows a larger error reduction.The WV62 experiment, however, was worse than WV73 and increased the error at altitudes between 1 and 3 km.
Somewhat surprisingly, the vertical distribution of cloud water (WRF's QCLOUD variable) was not generally improved (Figure 14c).Most layers show increased errors compared with the noDA experiment.Only the layer with the highest errors shows slightly reduced errors in the REFL experiment, which assimilated radar observations.Note that radar is mostly blind to cloud droplets.The largest error increase occurred for WV62, the least for REFL.Although the vertically resolved MAE of cloud water did not improve, the FSS and RMSE evaluation (Figures 11 and 10) showed that forecasts of cloudiness were improved overall when the vertical distribution of hydrometeors was not considered.
The vertical distribution of cloud ice (QICE) improved between 10 and 12 km.Reductions reached 0.01 g⋅kg −1 (40%) in the experiments assimilating 6.2 or 7.3 μm, but were less in the VIS experiment.Below 10 km the errors were increased.
In summary, there are overall improvements in temperature and water vapor, except for low-level water vapour in the experiment assimilating 6.2-μm BT.The vertical distribution of clouds was not improved despite the sensitivity of the observations to clouds and despite the improvements in terms of cloudiness revealed in the last section.Our explanation is that the assimilation improves the model equivalents but does not necessarily improve the vertical distribution of model hydrometeors, as the observations only see the uppermost part of clouds.Additionally, visible observations do not provide any information on the height of the observed cloud.Infrared observations provide information on cloud-top height, but a semi-transparent high cloud can lead to the same observed value as an optically thick cloud at a lower altitude.This means it is not necessary for the cloud to have the correct vertical structure and be at the correct height in order to reproduce observations.Instead, existing ensemble perturbations will be scaled up or down depending on the ensemble correlation between the state variable and the observation.This deficiency, however, may be overcome to some extent when multiple satellite channels with different sensitivities are assimilated together.

3.3
Sensitivity tests

Why radar outperforms satellite observations
A prominent detail in the results is that radar observations have an advantage over satellite observations in the random case, but not so much in the warm-bubble case.Given the differences between the cases, we hypothesized that the advantage of radar observations comes from their vertical resolution.To test this hypothesis, we computed a two-dimensional grid of radar observations similar to the two-dimensional satellite observations by projecting the three-dimensional radar observations onto a two-dimensional grid.The projection used the maximum reflectivity of each grid column, as maximum column reflectivity is a common tool for operational forecasters and sometimes also used for data assimilation.The result of assimilating this two-dimensional radar (Figure 15) shows a forecast that is relatively similar to experiments that assimilated satellite observations, indicating that vertically resolved observations are indeed crucial in the "random" case in order to reach a high forecast skill.

Additional update variables
Radar reflectivity is mostly sensitive to large precipitating hydrometeors, which can be found in the model variables QRAIN, QGRAUP, and QSNOW.Therefore, it may be necessary to update these variables in order to improve the analysis towards the observations.After the analysis, however, hydrometeors will naturally adjust given unstable and moist conditions.To reduce complexity, we chose not to update the large hydrometeor variables in the main experiments listed in Table 1, but to investigate the impact in a sensitivity experiment.As shown in Figure 16, additionally updating these variables does not generally improve forecasts for more than 20 min after the Furthermore, there is an indication that the vertical distribution of water vapor between 1 and 4 km is negatively affected by updates of large hydrometeors (not shown).

Assigned observation-error variance
We tested a range of constant values (Table 1) for the assigned observation error in order to find the observation errors that performed best in terms of the FSS. Figure 17 shows the sensitivity of the FSS (of light precipitation) for the increased assigned observation errors.Increasing the observation error never improved the results.Assigning the instrument error as observation error gave best results for all observation types.As there were seven times more radar observations than satellite observations due to its vertical resolution, radar had a higher combined weight in the assimilation.Nevertheless, assigning less weight (increased error) did not lead to improved forecasts.Doubling the assigned error removed its advantage compared with other experiments and led to a forecast impact that was mostly between the experiments WV73 and VIS, yet still higher than the WV62 experiment after 1630 UTC.Cloud-affected BTs of 7.3 μm show much larger first-guess deviations than in the 6.2-μm channel, a possible reason why assigning 2 K led to better forecasts after 3-hr lead time.

Dynamic observation errors
For infrared satellite observations, the first-guess departures increase with the occurrence of clouds, mainly due  to misplacement of clouds (Harnisch et al., 2016).Following Geer and Bauer (2011), this error can be considered to be part of the observation error.Thus, assigning constant observation errors can be suboptimal, especially for 7.3-μm BT, which shows the largest first-guess departures.
We tested the dynamic observation-error model of Harnisch et al. (2016) but found the results to be substantially worse than using constant observation errors.This is in contrast to Schröttle et al. (2020), who successfully applied the dynamic model for the 6.2-μm channel, but used the ICON model and an LETKF assimilation system instead of the WRF model with the EAKF in our study.A possible explanation could be underestimated ensemble spread together with the inflated observation error, which would lead to negligible weights for observations.However, it seems that the prior error variance was well estimated in the warm-bubble and "random" cases (Figure 18), although a small deviation from the ideal relationship can be seen.Nevertheless it should be noted that a dynamic observation-error model refined for the scenarios investigated in our study and the WRF EAKF system may still lead to higher impact of infrared observations than in our comparison.is the prior ensemble variance, averaged over observations.RMSE is √ ⟨(H(x b ) − H(x nat )) 2 ⟩, where x b is the prior, x nat nature, and ⟨⋅⟩ the average over observations.Numbers in the dots refer to the number of the cycle.In order to use one axis for different observation types, we rescaled by dividing by the maximum RMSE for each observation type.[Colour figure can be viewed at wileyonlinelibrary.com]

CONCLUSIONS
This study presents the first direct comparison of the assimilation of visible and infrared satellite observations with that of radar reflectivity observations and the first study assimilating visible observations using the ensemble adjustment Kalman filter (EAKF) on the convective scale.We assimilated synthetic observations of 0.6-μm visible reflectance as well as 6.2-and 7.3-μm infrared brightness temperature and radar reflectivity in an idealized perfect-model OSSE.The forecast impact was evaluated in two weather situations: first a "supercell" case in which a

Main findings
(1) The EAKF is able to draw crucial information from satellite observations despite the nonlinear observation operators, and their assimilation substantially improves the subsequent forecasts of precipitation and cloudiness.Furthermore, we demonstrate that visible satellite observations can be considerably more beneficial than previously reported by Schröttle et al. (2020), reaching an impact of 88% of the impact of three-dimensional radar observations and also outperforming the assimilation of thermal infrared satellite observations.(2) Visible and infrared satellite observations can have an impact on forecasts of convective precipitation that is comparable to the impact of radar reflectivity observations.Given favorable conditions, that is, when the stage of convection is correct in the prior and only the location is uncertain ("warm-bubble" case), the assimilation of satellite observations strongly improved the precipitation forecasts: visible observations lead to 88% of the radar impact, while the vapor-sensitive channels at 6.2 and 7.3 μm lead to 74-76% of the radar impact.In more difficult conditions, that is, randomly located storms at different stages ("random" case), the relative impact was lower but still reached 50% for visible observations, 20% for 6.2-μm BT, and 79% for 7.3-μm BT.Assimilating two-dimensional (max-column) radar reflectivity yielded 64% of the impact of three-dimensional radar reflectivity assimilation.
(3) The differences between the simulated cases suggest that the impact of visible reflectance and 6.2-μm BT observations is highest when the uncertainty about the vertical structure of clouds is lowest.The vertical structure of clouds cannot be retrieved from a single channel and thus is a weak spot for satellite observations.Comparing the "warm-bubble" and "random" cases, we noticed that, in one case, the missing vertical resolution of the assimilated satellite observations did not seem to have a detrimental effect on subsequent forecasts.We hypothesized that the uncertainty in the vertical distribution of clouds is responsible for the reduced impact of satellite observations in the "random" case.Experiments that only assimilated 2D radar observations and withheld the vertical resolution of the radar data (Section 3.3) supported that hypothesis.This result is in agreement with Sawada et al. (2019), who found improved forecasts of isolated cells in case of weak large-scale forcing by assimilating observations of 7.3-μm infrared BT.

Additional remarks
In order to generalize our results for operational numerical weather prediction, additional error sources need to be considered, which have not been included in this study: systematic model and operator errors (biases), representativeness errors, and correlated observation errors.While Errico and Privé (2018) argued for the simulation of as many error sources as possible, we refrained from that to isolate particular aspects of assimilating cloud-affected satellite observations (e.g., nonlinearity) and understand better their potential impact on convective-scale forecasts in the absence of all complexities of a real system.Zhang et al. (2016) suggest that the impact derived from a perfect-model OSSE may deviate from that in real systems, but the results are still very informative in a qualitative sense.The impact of the observations in operational systems is likely lower in absolute terms due to additional error sources that, for example, require an inflation of observation errors.For this reason, our study focuses on the impact of the observations relative to more commonly assimilated radar observations, which can be assumed to be less affected by the simplifications of the setup mentioned above.The observation impact diagnosed from an OSSE depends on the choice of observation error and ensemble spread.In addition to a reasonable choice of observation error (Section 2.4) and spread (Section 2.3.2), the statistics of first-guess departures support our OSSE setup.The standard deviation of first-guess departures (for single members and not the ensemble mean) was 4.5 K for the 6.2-μm channel, 9.1 K for the 7.3-μm channel, and 0.22 for the visible channel at 1330.Compared with Harnisch et al. (2016), these values indicate that our setup features realistic departures and a case that is an even more difficult situation for numerical weather prediction.

Outlook
Our results reveal that the prediction of deep convection could strongly benefit from the assimilation of visible and infrared satellite observations.While the assimilation of infrared observations has been investigated previously, very few studies have investigated the assimilation of visible observations up to now.Furthermore, radar observations are not available in many parts of the world or they are of limited quality, for example, due to orography that can obscure parts of the precipitation.Despite recent progress in the effective assimilation of satellite observations, numerous open challenges still need to be addressed.The nonlinearity and non-Gaussianity of the observations and the model call for improved algorithms that allow non-Gaussian distributions, for example, as proposed by Anderson (2010Anderson ( , 2020Anderson ( , 2022)), and take observation operator nonlinearity into account.Furthermore, the vertical resolution is a weak spot of visible and infrared satellite observations.Different channels provide information about different atmospheric levels as shown by their correlation structures (Zhang et al., 2022).For example, while the 6.2-μm channel is mostly sensitive to upper tropospheric water vapor, the 7.3-μm channel sees further down into the lower troposphere.Both channels are sensitive to thin ice clouds, which makes them blind to clouds below.The 0.6-μm visible channel can be crucial here, as thin ice clouds are mostly transparent at this wavelength (Scheck et al., 2020).Lastly, cloud height information from window channels could be used to avoid assigning clouds to the wrong levels in the model.The combined assimilation of these different channels therefore has the potential to lead to a better vertical distribution of the increments and subsequently a better forecast.First experiments on this combined approach indeed revealed promising results, and a follow-on publication that investigates how the combined assimilation of visible, infrared, and radar observations affects the analysis increments and forecast is currently in preparation.

Data and Software
Experiments were conducted using the Python package available at https://github.com/lkugler/DART-WRF.This allows us to define experiment workflows using DART and WRF and contains routines to generate DART observation sequence files and a python-pandas interface to analyze observation sequence files.DART was used in version 10.5.3 with a slightly modified RTTOV interface with constant radii for water droplets and ice crystals, as mentioned in Section 2.
of the nature-run initial condition, from domain average fields.Shown are domain-average profiles of temperature, dewpoint, and a parcel-lifting curve.The temperature perturbation in the warm-bubble case modifies this profile.[Colour figure can be viewed at wileyonlinelibrary.com] Figures 5 and 6 display the evolution in simulated satellite images of the 7.3-and 0.6-μm channels.Within a few minutes of model integration, deep convection developed in the nature run.At approximately 1235 UTC, the first precipitation developed.After 1730 UTC, the storms reached the domain boundary.F I G U R E 2 Infrared 7.3-μm satellite images of the "random" case nature run.[Colour figure can be viewed at wileyonlinelibrary.com]

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Visible 0.6-μm satellite images of the "random" case nature run. [Colour figure can be viewed at wileyonlinelibrary.com]F I G U R E 4 Cross-sections through the warm-bubble (temperature perturbation): Vertical-horizontal slice (top) at north_south=0 and horizontal-horizontal slice (bottom) at Height=0, both marked by a dashed line.[Colour figure can be viewed at wileyonlinelibrary.com] 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License F I G U R E 6 Visible 0.6-μm satellite images of the warm-bubble case nature run. [Colour figure can be viewed at wileyonlinelibrary.com] the prior uncertainty for this OSSE.To be consistent with prior publications, we use the approach from Schröttle et al. (2020) that facilitates two kinds of perturbations: (1) Vertically auto-correlated profile perturbations representing large-scale errors and (2) small-scale boundary layer noise.

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I G U R E 8 Timeline of forecasts and assimilation in the "random" and "warm-bubble" cases.F I G U R E 9 Time series of the strongest cloud signal in each observation type, defined as the average of the 40 (0.1%) largest values of reflectance and lowest values of BT.Values are scaled to the range 0-1 from their respective ranges: 0.27-1 for visible reflectance; 235-205 K for 6.2-μm BT; 255-205 K for 7.3-μm BT; 15-70 dBz for radar reflectivity.The assimilation time frame is shown as a grey background.[Colour figure can be viewed at wileyonlinelibrary.com] warm-bubble case F I G U R E 10 Fraction skill score for precipitation > 1 mm⋅hr −1 ; radar reflectivity > 50 dBz and visible reflectance > 0.6 in (a) the "random" case and (b) the warm-bubble case.The assimilation time frame is marked by grey shading.[Colour figure can be viewed at wileyonlinelibrary.com] U R E 11 RMSE of ensemble mean forecasts of the visible (upper panel) and 7.3-μm channel (lower panel), normalized by the RMSE of the noDA control run for (a) the "random" case and (b) the warm-bubble case; the average is taken horizontally over 200 × 200 grid points.The assimilation time frame is marked by grey shading.[Colour figure can be viewed at wileyonlinelibrary.com] The for visible reflectance > 0.5, (a,c) in the noDA run and (b,d) after the assimilation in the VIS experiment.The ensemble-derived probability ranges from black (0) to white (1) and the nature ((x nat ) > 0.5) is shown in red contours.The warm-bubble case at 1335 is shown in (a,b).The "random" case at 1405 is shown in (c,d).[Colour figure can be viewed at wileyonlinelibrary.com] 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License (a) Case "random" (b) Case "warm-bubble" F I G U R E 13 Vertical profiles of the absolute ensemble-mean increments for model variables temperature (T), vapor mixing ratio (QVAPOR), cloud water and ice mixing ratio (QCLOUD and QICE), and wind speed (V); averaged horizontally and over five assimilation times.[Colour figure can be viewed at wileyonlinelibrary.com]1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License (a) Model variable potenঞal temperature (b) Model variable vapor mixing raঞo (c) Model variable cloud water mixing raঞo (d) Model variable cloud ice mixing raঞo F I G U R E 14 Vertical profiles for model variables temperature (top left), vapor mixing ratio (top right), cloud water, and ice mixing ratio (bottom left and right).Each panel shows the MAE of the noDA experiment (left), the MAE reduction in the experiment (center), and the relative MAE reduction in % of the noDA MAE (right).Negative values stand for lower errors in the assimilation experiments compared with noDA.The right panel shows the change in MAE, relative to the prior MAE.The error was evaluated at 1405 in the "random" case, as mean (over 961 observed atmospheric columns) absolute error of the ensemble mean forecast.Dots indicate the horizontal average, shading indicates the 95% confidence interval over 961 atmospheric columns in which observations were taken.The increments of neighboring observations were overlapping and thus not independent.[Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 15 Fraction skill score of forecasts assimilating two-dimensional radar reflectivity instead of three-dimensional radar reflectivity in the random case.The assimilation time frame is marked by grey shading.[Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 16 Fraction skill score of forecasts assimilating three-dimensional radar reflectivity, with (REFL+mpvars) and without updating large hydrometeors (REFL) in the random case.The assimilation time frame is marked by grey shading.[Colour figure can be viewed at wileyonlinelibrary.com] Fraction skill scores for light precipitation (>1 mm⋅hr −1 ) in the warm-bubble case using assigned observation errors of 1-3 times the instrument error for observations of (a) visible reflectance, (b) 6.2-μm infrared BT, (c) 7.3-μm infrared BT, and (d) radar reflectivity.The assimilation time frame is marked by grey shading.[Colour figure can be viewed at wileyonlinelibrary.com] Spread error relationship for both cases.Spread 2 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Infrared 7.3-μm satellite images of the warm-bubble case nature run.[Colour figure can be viewed at F I G U R E 5

Assimilated observation type 𝝈 generate 𝝈 assimilate (range of tested values)
, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Note: The range of tested values for the assigned error is indicated in parentheses.1477870x 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Table 2 also demonstrates that satellite and especially visible observations can be effectively used by the ensemble adjustment Kalman filter and lead to long-lasting forecast impact.1477870x,2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,WileyOnline Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)onWiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseFraction of each experiment's FSS improvement over noDA, relative to the REFL experiment in the respective case, that is, (FSS exp -FSS noDA )/(FSS REFL -FSS noDA ) for the event of reflectivity > 50 dBz, where FSS is averaged over the first three forecast hours.
TA B L E 2 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 1477870x, 2023, 757, Downloaded from https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4577,Wiley Online Library on [08/01/2024].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License warm bubble of 30-km diameter initiated a single supercell storm and second a case where multiple deep convective cells at different stages are scattered throughout the domain.The periodic boundary domain of 400 × 400 km 2 size was simulated using a 2-km resolution WRF model, which was used in identical configuration for the forecast as well as the nature run.The observations were assimilated five times (every 15 min) within 1 hr, during the growth and consecutive mature stage of convection.