This article reviews traditional practices in atmospheric data assimilation and explores scientific strategies to assimilate data at resolutions spanning from tens of kilometers to even hundreds of meters. Such advances leverage the latest technological developments in computing hardware and methods. Two focal points are specifically chosen to illustrate the opportunities and the associated challenges: ① How to fully exploit satellite-observed cloud and rainband structures in tropical cyclones for high-resolution data assimilation; and ② which traditional data assimilation core techniques need re-evaluation and improvement. Specific topics include making an innovative advancement in all-sky brightness temperature assimilation by seeking the connection between satellite observed brightness temperature and unobservable relative vorticity within tropical cyclones; constructing a global data assimilation framework suitable for satellite-orbit-data observation times; developing advanced data thinning and quality control methods to avoid losing the most needed atmospheric small-scale and large gradient structural information. Finally, how to effectively integrate meteorological data assimilation with deep learning is discussed, such as incorporating artificial intelligence (AI) physical parameterization models into 4D-Var system; combining image assimilation with AI to make prediction from image data; making data assimilation and meteorological deep learning mutually beneficial.
Xiaolei Zou.
Traditional Data Assimilation and Its Effective Integration with Meteorological Deep Learning.
Engineering, 2026, 64 (9) : 95-109 DOI:10.1016/j.eng.2025.11.023
The purpose of data assimilation is to provide the optimal estimate of atmospheric state variables on a regular grid given various types of observational data, which are often unevenly distributed in space and time. Some of these observational data are only functions of thermal variables rather than dynamic variables, while others depend only on dynamic variables rather than thermal variables. The optimal estimate is either the maximum likelihood or the minimum variance estimation, and is called the “analysis” or “reanalysis.” Timely analyses serve as initial conditions for numerical weather predictions—crucial in both meteorological services and research—while multidecadal reanalysis datasets form a backbone for weather and climate studies. An operational data assimilation system is continuously updated to assimilate new data or improve the system; research data assimilation systems, in contrast, often target specialized goals and may handle fewer data types than their operational counterparts. Reanalysis systems rely on a frozen state-of-the-art global data assimilation approach that assimilates all available data (real-time or otherwise), using consistent bias correction and rigorous quality controls to avoid introducing spurious climate trends [1,2]. With the rapid development of computer capabilities, observational instruments, numerical methods, and data assimilation methods have become increasingly complex.
Data is the reason for carrying out data assimilation. Without observations, there is no need to generate an analysis. More observations—combined with more advanced methods—naturally improve accuracy and precision. As remote-sensing technology has advanced rapidly over the past decades, satellite observations of the global atmosphere has expanded in both volume and variety. Examples include multiple global positioning system (GPS) radio occultation (RO) missions initiated by the first GPS/meteorology (GPS/MET) experiment [3], microwave temperature/humidity sounders and hyperspectral infrared sounders on polar-orbiting operational environmental satellites (POES) [[4], [5], [6], [7]], and imagers on geostationary operational environmental satellites (GOES) [[8], [9], [10]]. GPS RO adopts active limb-sounding technology, whereas POES and GOES adopt passive vertical-sounding and imaging, respectively. They each carry strengths and weaknesses in terms of accuracy, coverage, resolution, sampling frequency, and so forth. However, when assimilated collectively, they compensate for each other’s limitations, enhancing the overall reliability of the analysis and reanalysis datasets [11].
Early data assimilation used polynomial interpolation to project in situ observations onto regular grids [[12], [13], [14]]. Major progress followed the advent of modern electronic computers—starting with electronic numerical integrator and computer (ENIAC) in 1946. Ongoing improvements in computational capacity have fostered increasingly advanced numerical algorithms. Emergent multi-graphics processing unit (GPU) technology and quantum computing technologies are poised to future revolutionize meteorological data assimilation. They will undoubtedly open up a new era for further advancing meteorological data assimilation technology. Deep-learning models have achieved initial success in large-scale numerical weather prediction by using traditional analyses/reanalyses as training datasets [[15], [16], [17]]. Such deep-learning techniques could allow Earth-system data assimilation systems to run at extremely high spatiotemporal resolution, enabling analyses/reanalyses to capture not only synoptic-scale synoptic phenomena but also smaller-scale cloud, rain, gravity waves, and even tornados.
The challenge of meteorological data assimilation is not purely mathematical; it also demands appropriate dynamical and physical considerations. Small-scale noise in both observations and analyses must be minimized to prevent spurious gravity-wave oscillations in subsequent weather forecasts. For example, which specific dynamical constraints best incorporate hurricane cloud and rainband structures from satellite observations to improve forecasts of intensity, size, and structure? How can we differentiate genuine small-scale signals from observational noise to enhance convective triggering forecasts? How should vertical model levels be aligned with higher horizontal resolution to accurately depict the three-dimensional character of small-scale weather events?
This article presents a concise overview and outlook for meteorological data assimilation. Fundamentals of data assimilation are presented in Section 2. Section 3 uses tropical cyclones to illustrate core data assimilation concepts, including system characteristics, observational features, and key challenges: the evolution from tropical disturbances to hurricanes (Section 3.1); center positioning and warm-core structures derivable from satellites (Section 3.2), and innovative approaches for all-sky data assimilation of hurricane clouds and rainbands (Section 3.3). Section 4 addresses traditional data assimilation practices that may need rethinking. Topics include the limitations of synchronizing global data assimilation with fixed coordinated universal time (UTC) times (Section 4.1); mismatched grid configurations between data assimilation and forecasting models (Section 4.2); shortcomings in handling different data types independently (Section 4.3); the pitfalls of data thinning and overzealous quality control (Section 4.4); and the loss of valuable cloud-structure information (Section 4.5). Section 5 provides the vision of a 4D-Var deep-learning system with physically informed deep-learning parameterizations (Section 5.1), and ways that data assimilation and meteorological deep learning may mutually reinforce each other (Section 5.2). Section 6 concludes with final remarks.
2. Fundamental components of data assimilation
A general form of the data assimilation analysis (xa) can be written as
where x represents the vector of control variables at the targeted analysis time ta; xb represents the background state vector; B is the error covariance matrix of xb; yobs is the observational data vector at ta; O is the diagonal matrix consisting of observation error variances; H(·) is the observation operator; F is the error covariance matrix of observation operator, G(x) = 0 is a chosen dynamical and/or physical function constraint, and r is a penalty coefficient. The larger the specified value of r, the more the control variable x satisfies the constraint conditions. The minimizer of J(xa) is defined as the analysis. The first term in Eq. (1) is called background term (Jb) and ensures the analysis (xa) to stay close to the background field (xb); and the second term in Eq. (1) is called the observation term (Jo) and measures the fit to observations.
The analysis vector x consists of the dynamic variables of wind in three-dimensional space and the thermodynamic variables of density, temperature or potential temperature (θ), and mixing ratios of water vapor, cloud liquid water, cloud ice, rain, snow, and graupel. The remote-sensing observations of POES and GOES brightness temperature and GPS RO bending angle mentioned earlier are only functions of thermodynamic variables and not related to dynamic variables. In the real atmosphere, the changes in dynamic and thermodynamic variables remain interdependent and jointly satisfy a set of nonlinear partial differential prediction equations representing conservation laws of momentum, mass, energy, water vapor, and hydrometeors. If the assimilation of brightness temperature or bending angle observations affects the analysis of thermodynamic variables but not the analysis of dynamic variables, the impact of data assimilation on numerical weather forecasting will be minimal. In addition, some regions may not have observational data at certain time periods. Through properly construction of the background error covariance matrix B and the observation operator H(x), and appropriate dynamical and/or physical constraint G(x) = 0, the assimilation of thermodynamic variable sensitive observations can affect the analysis of dynamic variables; and the assimilation of dynamically sensitive observations can affect the analysis of thermodynamically sensitive variables.
The background error covariance matrix is defined as $\boldsymbol{B}=\overline{\varepsilon_{\mathrm{b}} \varepsilon_{\mathrm{b}}^{\mathrm{T}}}$, where εb = xb −xtruth, xtruth is the true state, and εb is the error of xb. Not only xtruth and εb do not exist, but also the B matrix in atmospheric data assimilation is too large to be stored and its inverse matrix B−1 cannot be calculated. Therefore, developing feasible methods for constructing B−1 or calculating B−1(x − xb) is one of the major tasks in data assimilation. The earliest for constructing B was proposed by Parrish and Derber [18], which was implemented in the 3D-Var operational system with a global spectral model at National Centers for Environmental Prediction (NCEP). It is called the NMC method. There are other methods applicable to model B for non-spectral model grid settings. Recognizing that the minimization algorithm only requires the matrix and vector product for an arbitrary input vector, a B model can be developed that uses a few easily obtainable parameters of the background error statistics (e.g., error correlation lengths). One such method is the recursive filter [[19], [20], [21]]. The incorporation of case-dependent background error parameters in the recursive filter allows for building situation-dependent, anisotropic, and non-homogenous structures into a background error covariance matrix.
The 4D-Var can be viewed as an extension of 3D-Var into four dimensions by incorporating the numerical weather forecast model M(x) into the observation operator H(M(x)). Since changes in the dynamic and thermodynamic variables are interdependent through M(x), the 4D-Var assimilation of any observations affects the analysis of every variable in the analysis vector x.
3. Hurricane observations and all-sky simulations
3.1. An introduction to the evolution from tropical disturbances to hurricanes
Tropical cyclones originate from tropical disturbances common to the tropics. The easterly waves formed in the West African monsoon are the major source of tropical disturbances for North Atlantic tropical cyclones [22]. For tropical cyclogenesis in the Western Pacific and Indian Oceans, summer monsoons are the major source [23,24]. Other contributors include equatorial Rossby waves and mixed Rossby gravity waves [25,26], easterly waves from the North Atlantic, and strong disturbances formed by the merger of several weak disturbances in mesoscale convective systems [27].
The environmental conditions favorable for tropical cyclogenesis include the coexistence of tropical disturbances with maximum relative vorticity in the lower troposphere, sea surface temperature greater than 26 °C, high relative humidity at 700 hPa, conditionally unstable atmosphere, and weak vertical shear [28,29]. A tropical storm is capable of sustaining itself and continuing to intensify even without favorable environmental conditions if its horizontal length scale is larger than the Rossby radius of deformation [30]. A continuous intensification of tropical storms generates strong hurricanes, which are classified into five intensity categories H1, H2, H3, H4, and H5 based on whether the 1 min averaged maximum surface wind exceeds 33, 43, 50, 59, and 70 m·s−1, respectively.
A storm’s track is primarily determined by the large-scale circulation in which the storm is embedded, and secondarily by the beta drift [31]. In the Northern Hemisphere, the cyclonic circulation of the storm brings air of smaller (larger) absolute vorticity (i.e., the Coriolis parameter f) northward (southward) to form an anticyclonic (cyclonic) sub-circulation to the northeast (southwest) of the storm center, which is called the β-gyre. The pair of the β-gyre produces a systematic northwest wind vector that causes the storm to move northwestward. Other environmental factors, including sea-surface temperature, topography, diabatic latent heat release, and so on. As tropical cyclones move, they induce high winds, heavy precipitation, storm surges and floods along their paths, which can affect hundreds of millions of people and cause huge economic losses every year.
The tragedies caused by hurricanes in summer and autumn each year continue to draw people’s attention to tropical cyclone forecasting. Advances in numerical weather forecasting models, satellite observations and data assimilation have significantly improved forecasts for large-scale environments surrounding tropical cyclones in recent decades, which in turn has led to improved storm tracks. However, forecasts of hurricane intensity changes have not improved notably. Intensity changes of tropical cyclones are affected by the rapidly varying fine structural changes of clouds and precipitation within the hurricane. For example, cloud coalescence and rainbands evolving into axisymmetric structures may form a new eyewall at a greater radial distance than the old eyewall. A “moat” region that exists between the new and old eyewalls becomes dynamically similar to the eye for the new eyewall but is inimical to survival of the old eyewall. As the old eyewall dies and the new eyewall replaces it, large oscillatory changes occur in intensity. At present, neither data assimilation methods nor numerical weather forecasts have effectively captured the rapid changes of these small-scale, dynamically driven cloud/rainbands within and around tropical cyclones.
3.2. Deducing center position and warm core of tropical cyclones from satellite observations
For a typical hurricane, the radius of maximum wind is located in its eyewall. The eyewall is a narrow band of heavily precipitating cloud, often circular in shape, sometimes elliptical or even polygonal, and rotating cyclonically [32]. It encircles the relatively calm eye of the storm. Outside the eyewall are cloud/rainbands of convective cloud that spiral in toward the eyewall [33]. The hurricane eye, eyewall and cloud/rainbands are clearly revealed in satellite observations of brightness temperature by different remote-sensing instruments.
Radiation from infrared window channels (such as 10.45 μm) cannot penetrate cloud layers except for thin cirrus clouds. When clouds exist, the radiation from GOES imager window channels comes from the top of the cloud layer. Often, researchers construct horizontal distribution maps of brightness temperature observations at the 10.45 μm channel to display cloud and rain distributions from space. On the other hand, the microwave radiation measured by POES imagers can penetrate through clouds in the atmosphere except for heavy precipitation. The scattering effects from ice particles and large raindrops in cloud layers will reduce the measured values of brightness temperatures at high microwave frequencies (∼183 GHz). Therefore, regardless of whether the brightness temperature observations come from GOES imagers or POES microwave imagers and microwave humidity sounders, the observed values of brightness temperature are low in hurricane eyewalls and cloud/rainbands with active convection and high in the hurricane eye, moat and areas with inactive convective activity. Hence, the cloud distribution maps observed via the GOES infrared window channel are different from those via the POES microwave window channel. The former cannot capture low-level clouds located beneath high-level clouds, but the latter can. As shown in Hu and Zou [34], using four POES microwave instruments, the formation of the secondary eyewall of Typhoon Lekima (2019) could be observed about 19 h earlier than the advanced Himawari-8 imager (AHI). Note that a POES instrument can provide up to two times per day observations of Lekima, while the AHI can continuously observe Lekima at 10 min intervals. The four microwave instruments are the special sensor microwave imager/sounder (SSMIS), the advanced microwave scanning radiometer-2 (AMSR2), the global precipitation measurement microwave imager (GMI), and the advanced technology microwave sounder (ATMS). The selected channel from SSMIS, AMSR2, GMI, ATMS, and AHI has its center frequency of 92 GHz, 89 GHz, 89 GHz, 165.5 GHz, and 10.4 μm, respectively. Specifically, based on the microwave observations, a concentric secondary eyewall appeared on August 8, 2019 at 1746 UTC and lasted for about 21 h. However, in AHI observations, the concentric secondary eyewall did not appear until 1210 UTC on August 9, 2019, and only lasted for about an hour. This also implies that the secondary eyewall initially formed in the lower troposphere and then extends upwards, increasing the height of the eyewall; but its dissipation starts from the upper levels, and the height of the eyewall decreases over time.
The actual center position of the tropical cyclone is a key parameter important for vortex initialization in regional and global numerical hurricane forecasting models. The National Hurricane Center (NHC) Tropical Prediction Center (TPC) provides the most complete and reliable best track dataset for tracking all tropical cyclones over the North Atlantic and Eastern North Pacific Oceans, including the center location (latitude and longitude), maximum sustained surface wind, minimum sea-level pressure, radii of maximum sustained surface wind, 34, 50, and 64 knots winds, as well as sea-level pressure along the outermost closed isobar, every 6 h. The best track is a post-analysis dataset based on all available data from various sources and obtained through an optimal reconstruction. The trajectory of each tropical cyclone throughout its entire lifecycle is subjectively smoothed to remove oscillations with a period less than the smallest time periods of 24 h that can be adequately represented by the 6 h interval best track dataset [30]. Therefore, the center positions at some particular times in the best track may differ from the ones seen in satellite observations. An erratic motion implied by connecting individual center positions may not be reflected in the best track.
Satellite remote-sensing observations are becoming accessible in real-time, making the determination of the actual center position of a tropical cyclone possible. In tropical and central oceanic regions far from land, satellite observation data are even more valuable since other types of observations are sparse or nonexistent. The vortex initialization in regional and global numerical hurricane forecasting models requires the center position and several other parameters describing the intensity and size of tropical cyclones. As described below, the center position, size and warm core structure of a tropical cyclone can be inferred from “raw” satellite brightness temperature.
A tropical cyclone rotates as a whole, reflecting the basic physics of vortex axisymmetrization [35]. Hurricane’s strong axisymmetric component has been observed by airborne radars [36,37] and POES microwave imagers and GOES imagers [[38], [39], [40], [41]]. An azimuthal spectral analysis can extract the symmetric (wavenumber-0) component and other wavenumbers’ components with respect to any assumed center position in a given field. The closer a candidate center is to the real center, the larger the corresponding wavenumber-0 amplitude. This recognition was used to determine tropical cyclone center positions directly from infrared and microwave brightness temperature observations [[38], [39], [40], [41]].
A tropical cyclone often has a warm core in the middle and upper troposphere and the low stratosphere. A warm core forms as a result of adiabatic warming of the descending air in the eye caused by the detrainment of convective bursts in the eyewall, and subsidence adiabatic warming associated with cyclonic radial inflows above the upper-level outflow layer. The latent heat release from cloud condensation also warms the atmosphere within the tropical cyclone. The warm core’s formation, intensification and structural change as the tropical cyclone evolves [42,43]. Fortunately, POES microwave temperature sounders can provide measurements of thermal radiation in the oxygen absorption band located at 50-60 GHz emitted from different vertical layers of the atmosphere from the Earth’s surface to the stratosphere. A measured brightness temperature at a specific microwave temperture sounding channel is linearly proportional to a weighted sum of the atmospheric temperature within a specific vertical layer. Based on this physical property, warm core structures of tropical cyclones can be retrieved through a traditional linear regression method [44,45] or a deep-learning method [46]. The temperature retrieval helps address the disadvantage of not directly presenting the warm core structure of tropical cyclones in brightness temperature observations. This is because the cross-track microwave temperature detector receives atmospheric emissions from longer/shorter optical paths at larger/smaller scanning angles, resulting in significant edge effects in the global distributions of brightness temperature observations.
Several other key features of tropical cyclones can be extracted from satellite observations besides center positioning and warm cores. The radii of eye, eyewall, inner and outer rainbands can also be determined from brightness temperature observations by GOES imagers [47] and POES microwave humidity sounders [15,34], global total ozone in a column of air (referred to as total ozone hereinafter) from various satellite remote-sensing instruments [[48], [49], [50], [51], [52]], liquid water path from POES microwave temperature sounders [53], and ice water path from POES microwave humidity sounders [54]. The vertical high-resolution composite structures of tropical depressions, tropical storms, and hurricanes over different ocean basins have been deduced from GPS RO measurements [55,56]. The traditional vortex initialization scheme remains too simplified to incorporate these key parameters of tropical cyclones from satellite observations. More advanced vortex initialization schemes must still be developed to improve hurricane intensity changes. In the future, such vortex initialization schemes are needed to improve forecasts of hurricane intensity, especially during the initial six to twelve hours of prediction.
Assimilation of non-dynamical variable observations can also improve analysis of dynamic variables by using an observation operator H(x). The approach is to construct an observation operator H(x) that creates a relationship between the observed values and dynamic variables. A simple such example is the assimilation of the satellite observed total ozone using a regression model that relates the vertical mean potential vorticity to the total ozone as the observation operator. The regression model between the vertical mean potential vorticity ($\overline{P}$) and the total column ozone (${O}_{3}^{\text{model}}$) is established based on satellite total ozone data (${O}_{3}^{\text{obs}}$):
where P is the Ertel’s potential vorticity in the isentropic coordinate (unit: K·m2·kg−1·s−1), α and β are regression coefficients, f is Coriolis parameter, θ is potential temperature, $\vec{k}$ is unit vertical vector, ∇ is vector differential operator, $\vec{v}$ is meridional wind, p is pressure, pt is the model top pressure, pl = 500 hPa, the overbar represents vertical mean from 500 hPa to model top, and g is gravity constant. Using the regression model as an observation operator, any difference between the assimilated observation (${O}_{3}^{\text{obs}}$) and the corresponding model value (${O}_{3}^{\text{model}}$) in total ozone data assimilation will directly introduce adjustments to the potential vorticity, even though ${O}_{3}^{\text{obs}}$ is not a direct dynamic variable. The reason is that the day-to-day fluctuations of total ozone are mainly caused by daily weather variations related with advection and/or convection processes. A location affected by an advection from the north or by a downward motion often has an increase in total ozone. A decrease in total ozone occurs if there is a southerly advection or an upward motion [[57], [58], [59]]. Regions of high total ozone content are often characterized by high mean integrated potential vorticity, low tropopause, low temperature in the upper troposphere, high temperature in the lower stratosphere, and low pressure in both the upper troposphere and lower stratosphere [[60], [61], [62], [63], [64]]. By using this regression Eq. (2), the assimilation of total ozone mapping spectrometer (TOMS) total ozone data improved the forecast skill of the moving track, intensity and rainfall of the famous east coast winter storm on January 24-25, 2000 [65] and track prediction of Hurricane Erin of 2001 [51].
3.3. Seeking innovative ideas for all-sky data assimilation of hurricane cloud/rainbands
Observations of brightness temperature at 10 min intervals from the GOES-16 advanced baseline imager (ABI) showed that during the rapid intensification period of Hurricane Irma (2017), the eye was elliptical, rotating counterclockwise over time, and the spiral cloud and rainbands exhibited the phase velocity of vortex Rossby waves. These features were consistent with those observed by airborne dual-Doppler radar [37].
Spiral cloud/rainbands in tropical cyclones resemble the spiral perturbation distributions of relative vorticity described by the barotropic vorticity equation in cylindrical coordinate system whose center is placed at the center of the storm [35]. The barotropic vorticity equation linearized around the azimuth averaged radial wind ($\bar{v}(r)$), r is radial distance) in the cylindrical coordinate system has the same form as a barotropic vorticity equation linearized around a zonal wind ($\bar{u}$) in the Northern Hemisphere except that the azimuth average relative vorticity ($\bar{\xi}=\bar{v} / r+\mathrm{d} \bar{v} / \mathrm{d} r$) takes the role of the f. The vortex Rossby waves outside the eyewall of tropical cyclones function similarly to Rossby waves in mid-latitude regions of the Northern Hemisphere. The numerical solution of relative vorticity perturbation ϛ′ of the linearized barotropic vorticity equation exhibits spiral cloud/rain band like distributions in hurricanes. The exact shapes of the predicted relative vorticity perturbation depend on the basic state $\bar{v}(r)$ and the initial condition $\left.\xi^{\prime}\right|_{t=0}$. In addition, with a hurricane-like vortex as initial conditions, a shallow-water asymmetric-balance model in cylindrical coordinate system can simulate the basic mechanisms of secondary eyewall formation and its structural changes. Therefore, the evolution and structure of spiral cloud/rainbands in tropical cyclones are related to hurricane dynamics, just as the thermal and dynamic changes in the atmosphere are mutually constrained.
Due to the lack of high-resolution vorticity observations (like the GOES imager brightness temperature), we are unable to compare the two in the observation space. However, we can compare the band-like vorticity distribution predicted by high-resolution models with the all-sky simulation of brightness temperature with the model forecasts serving as input to radiative transfer operator observation operator. Fig. 1 shows the spatial distributions of absolute vorticity at 500 and 300 hPa of Typhoon Hinnamnor at 0500 UTC on September 1, 2022 (Figs. 1(a)-(d)) and the simulated distribution of brightness temperature at AHI channel 13 (∼10.3 µm; Figs. 1(e) and (f)). The results come from 6 h forecasts at 3 km horizontal resolution with two microphysical parameterization schemes of the weather and research forecast (WRF) single-moment 6-class scheme (WSM6) and the double-moment Thompson microphysics scheme (THOM). Additional details on the model setup are in Niu and Zou [66]. The model predicted Typhoon Hinnamnor shows a small area of maximum positive vorticity exceeding 10−5 m·s−1 at its center, small-scale positive and negative vorticity perturbations in the eyewall, several outward propagating spiral vorticity bands originating from the eyewall, and several spiral vorticity bands far to the east of the center (Figs. 1(a)-(d)). The absolute vorticity at the 500 hPa level is slightly stronger than that at the 300 hPa pressure level. Generally speaking, the distribution of cloud/rainbands characterized by low brightness temperature (Figs. 1(e) and (f)) is quite consistent with absolute vorticity (Figs. 1(a)-(d)). The reason is the turbulent motion in the cloud. Although the absolute vorticity difference between the two predictions is small, the brightness temperature difference is noticeable. The THOM microphysical parameterization scheme generates more clouds than the WSM6 scheme. The vorticity disturbance is related to the interaction between gravity waves and turbulence that arise within convective clouds.
The currently available global atmospheric analysis fields, such as the ERA5 reanalysis and the NCEP Global Forecast System (GFS) analysis at a horizontal resolution of about 30 km, cannot adequately describe the vorticity and cloud and rainband characteristics of tropical cyclones [15]. High-resolution data assimilation (3 km or higher) may achieve this. To succeed, some old practices must be abandoned and innovative ideas must be developed. Only when high-resolution observational data are assimilated more effectively can high-resolution atmospheric analysis fields accurately describe rapidly changing weather in four-dimensional space.
4. Which traditional practices in data assimilation need to be improved for future?
Having discussed some examples of satellite data applications and assimilation for hurricane cases in Section 3, we switch to a broader discussion on some traditional practices in data assimilation that may be further improved with an effective integration with meteorological deep learning.
Rapid development of advanced technologies in artificial intelligence (AI) computing, remote-sensing instrumentation, and computer hardware has made it possible to perform ultra-high resolution numerical weather forecasting and data assimilation. Numerical weather prediction models and data assimilation analysis at ultra-high resolutions of several kilometers or even hundreds of meters can resolve individual clouds, internal gravity waves, and so forth. These small-scale phenomena play an important role in the initiation and development of severe weathers. In order to fully leverage the opportunities brought by advanced technologies, some old practices in data assimilation warrant reconsideration. This section provides a brief review of traditional data assimilation methods to discuss their appropriateness for ultra-high resolution data assimilation.
4.1. The drawbacks of global data assimilation at UTC
The numerical weather forecast model describes a set of governing equations that global atmospheric variables must satisfy at UTC. The same is true of the global data assimilation in which the control variables x consist of all variables at the same UTC.
The essential components of any global data assimilation system are illustrated in Fig. 2. Here, we focus on Jo, especially POES observational data, which typically account for over 90% of all assimilated data.
The observation times for global radiosonde profiles are 0000 UTC and 1200 UTC. The assimilation of global atmospheric data at UTC best accommodates global radiosonde data. Another important data source for sampling atmospheric vertical profiles is the global navigation satellite systems (GNSS) RO mission. Through a limb sounding technique, the GNSS RO missions provide observations of atmospheric refractivity profiles with vertical resolution (about 100-200 m) and relatively coarse horizontal footprint of several tens of kilometers [67]. Various GNSS RO missions together provide unprecedentedly dense RO observations globally. Fig. 3 shows the global distributions of the RO data during 1500-1800 UTC on July 18, 2023 from COSMIC-2, MetOp-B, MetOp-C, KOMPSAT, PAZ, TanDEM-X, TerraSAR-X, Spire, PlanetiQ, and Tian Mu (Figs. 3(a) and (c)). Within a 3 h window, there are 815, 51, 49, 15, 25, 26, 30, 393, 308, and 733 RO profiles from COSMIC-2, MetOp-B, MetOp-C, KOMPSAT, PAZ, TanDEM-X, TerraSAR-X, Spire, PlanetiQ, and Tian Mu, respectively, totaling 2445. More than half of the RO profiles can reach below 200 m above the Earth surface (Figs. 3(b) and (c)). The availability of RO data over other three-hour windows in a day is similar (figures not shown). Therefore, it is appropriate to assimilate global GNSS RO data within a certain UTC time window.
The assimilation of global atmospheric data within an UTC interval is not entirely suitable for satellite observations. A single POES carries several remote-sensing instruments and follows a sun-synchronous orbit. For any given POES, its inclination angle, which is defined as the angle between the equatorial plane and the counterclockwise direction of the orbital plane, is kept constant; all its orbital planes have the same geometric relationship with respect to the sun. All orbits pass the equator at the same local standard time (LST). The observation swaths of a POES remote-sensing instrument with an inclination angle greater than 90° cover the whole globe. All POESs have an inclination angle greater than 90°, providing global observations at all latitudes. For example, MetOp-B was launched on September 17, 2013 as a mid-morning POES with its equator crossing time at 9:30 LST. It has an inclination angle of 98.6°. MetOp-B orbits the entire globe once in about 101.3 min and completes 14 orbits in 12 h. Therefore, the AMSU-A and Microwave Humidity Sounder (MHS) instruments onboard MetOp-B observe the global atmosphere two times daily at 12 h interval. Similarly, the Suomi National Polar-orbiting Partnership (S-NPP) satellite, which was launched into an afternoon-configured orbit with an inclination angle of (98.7° ± 0.05°) on October 28, 2011, was later referred to as NOAA-20 because S-NPP was launched after NOAA-19. The FY-3E was launched into an early-morning orbit on July 5, 2021. Clearly, a three-orbit constellation provides much better global data coverage than a single POES or a dual orbit constellation. As shown by Niu and Zou [68], the six global observations per day provided by FY-3E, MWTS-3, MetOp-B, AMSU-A, NOAA-20, and ATMS can clearly reveal the diurnal changes of the warm-core intensity of Typhoon Malakas in 2022. Fig. 4 shows the orbital tracks from the early morning FY-3E, the mid-morning MetOp-B and the afternoon NOAA-20. If the time window is as short as 3 h, there are fewer than two orbits of a single satellite to observe the earth’s atmosphere. The ascending and descending parts of the two orbits are distributed in two longitudinal intervals, separated by 180° longitudes. The observed longitudinal areas shift westward in the next three hours. Within 3 h, each FY-3E, MetOp-B, or NOAA-20 misses about 70% of the globe.
Conventional data are scarce over oceans, the Xizang Plateau and the Rocky Mountains. The spatial and temporal variations in soil moisture, soil temperature, vegetation, ice, and snow cover, and ground roughness in the Xizang Plateau are complex, which increases the difficulty of assimilating satellite data. Assimilating observations within a certain UTC time interval faces the problem of some areas lacking POES observations. The shorter the interval, the larger the data-void area. A 12 h assimilation window can ensure global coverage of satellite data, but this is only feasible through a 4D-Var method, not 3D-Var. If there are no POES observational data in a large area, the assimilation problem becomes underdetermined. It also greatly wastes computing resources and introduces large uncertainties in the analysis. Such an issue becomes even more serious for data assimilation at higher resolutions with shorter time windows. Developing a multi-framework data assimilation system following satellite orbits and variable-resolution meshes is expected to alleviate this problem. Regions with abundant, high-resolution data would use finer grid resolutions, with a smooth transition to coarser grids in the remaining areas.
4.2. Inconsistent grid setting between data assimilation and forecast model
Several novel global model dynamical frameworks have been developed to replace older global spectral model framework. One is the finite-volume spherical centroidal Voronoi tessellation (SCVT) grid scheme of the compressible, non-hydrostatic global Model for Prediction Across Scales—Atmosphere (MPAS-A) developed by the National Center for Atmospheric Research (NCAR) [[69], [70], [71]]. Fig. 5 shows the global distribution of the MPAS-A quasi-uniform SCVT grid cells at 480 km resolution. Compared to latitude-longitude grids in global spectral models, tracking unstructured SCVT grids is more challenging. There are a total of 2561 grid cells in Fig. 5. Each grid cell is given a sorting number. The cell numbers are given increasing numbers according how the global sphere is quasi uniformly divided. The global sphere is firstly divided into the 20 equilateral triangles, which have 12 vertices and 30 sides. The 12 vertices have pentagon-shaped cells and are numbered 0-11 (red); and the 30 sides have 90 hexagon-shaped cells and are numbered 12-101 (orange). Then, three grid cells are added to each of the 20 equilateral triangles, which are numbered 102-161. The grids numbered 162-641 (green) are located between any two cells of 1-161. Finally, the cells surrounding the first 161 cells are numbered from 642 to 1601 (cyan), and the remaining cells are numbered from 1602 to 2561 (gray). It is noted that cells 0-161 are uniformly distributed globally, so does cells 0-641 and cells 0-2561. As the number of grid cells increases, the grid resolution also increases. The MPAS-A has an option for variable-resolution. Under this framework, regions of interest can have high resolutions, smoothly transitioning to other areas of the globe with coarse resolutions. Rauscher and Ringler [72] showed that the regionally refined meshes of MPAS-A helped resolve mid-latitude eddy activities that are often induced by orography, land-sea contrasts and sea surface temperature anomalies.
The inconsistent grid setting between a data assimilation system and the forecasting model is not desirable. Fig. 6 gives a schematic illustration of a typical data assimilation cycling process. Using the analysis field at the previous time ti−1, ${x}_{\text{a}}\left({t}_{i-1}\right)$, as the initial condition for a short-term (e.g., 6-12 h) forecast that is used as the background vector ${x}_{\text{b}}\left({t}_{i}\right)$ for the current data assimilation at time ti. The new analysis field generated by data assimilation at the current time ${x}_{\text{a}}\left({t}_{i}\right)$ serves as the initial condition for generating the ${x}_{\text{b}}\left({t}_{i+1}\right)$ for the next data assimilation, and so on. In other words, the numerical weather forecast model is an integrated component of data assimilation. If the data assimilation system and the forecasting model have different grid settings, xa must be interpolated onto the model grid to make short-term forecasts; and interpolation of xb onto the data assimilation grid to also necessary for data assimilation. Medium-range weather forecasts also use the analyses generated by data assimilation as initial conditions. The back-and-forth interpolation between the two grid settings not only introduces interpolation errors but also wastes computation time.
The finite-volume cubed-sphere dynamical core (FV3) is another novel global model dynamic framework. It was developed at the NOAA/Geophysical Fluid Dynamics Laboratory (GFDL) and coupled with the NCEP GFS physical parameterizations (fvGFS). Using variable-resolution, the fvGFS model improved predictions for convective scale weather while maintaining skillful global medium-term weather forecasts [73]. However, the initial conditions used for these forecasts were reanalysis and analysis fields generated by other global spectral data assimilation system, purely aiming to test the fvGFS model performance. The fvGFS was implemented into the NCEP operational GFS as version 15 in 2019.
As the first step toward developing a prototype 4D-Var data assimilation system with the same grid setting as the MPAS-A model, Tian and Zou [74,75] constructed the tangent linear model and the adjoint model of the MPAS-A dynamic core, and demonstrated the feasibilities of the MPAS-A 4D-Var system on quasi-uniform and variable-resolution grids. Clearly, much work remains to establish a global 4D-Var data assimilation system consistent with the MPAS-A framework.
4.3. Shortcomings of independent handling issues related to each type of data
The effectiveness of satellite data assimilation largely depends on the quality of the data assimilated. The minimum solution of J in Eq. (1) is equivalent to the maximum likelihood estimate only if observational data have uncorrelated errors and no biases, the observation operator is precise, and data errors satisfy a normal distribution [76]. To ensure these requirements, data are often thinned in three-dimensional (3D) space or spectral space; biases are corrected for normal distribution; cloudy data are detected to ensure the accuracy of brightness-temperature simulations; and outliers are removed to ensure Gaussian distribution. Only by effectively carrying out these data-related tasks can satellite data assimilation optimally benefit numerical weather prediction. The most widely used community regional data assimilation system is a joint system of the Gridpoint Statistical Interpolation (GSI) system and the Weather Research Forecasting (WRF) model [77,78]. The resolution of regional data assimilation is usually higher than the global data assimilation system. It aims to improve short-term numerical forecasting skills for important and rapidly changing local weather processes. Fig. 7 gives a flow chart of how these issues are handled in this community system. Note that the data thinning, bias correction, cloud detection and quality control are performed independently and sequentially for each type of data. The minimization of J starts afterward.
There are certain limitations to conducting cloud detection independently for each data type. An example is the cloud detection scheme for assimilating MHS data in the GSI/WRF system. MHS data have been available since the launch of NOAA-15 in 1998, and they contain valuable moisture information in the troposphere. Although MHS data assimilation began very early, few studies have discussed the impact of MHS data on assimilation results and numerical forecasting. In fact, Qin et al. [79] found, surprisingly, that adding MHS data from NOAA-18 and MetOp-A and AMSU-B data from NOAA-17 reduced the skill of short-term quantitative precipitation forecasts compared to assimilating only GOES-11/12 imager data. The all-satellite data assimilation that includes MHS data significantly reduced short-term quantitative precipitation forecast skills versus the no-MHS-data case. The problem in assimilating MHS data stemmed from deficiencies in cloud detection schemes. If AMSU-B and MHS data over areas where GOES detects clouds were removed from assimilation, AMSU-B/MHS data assimilation contributed positively to precipitation forecast scores as well as other data. The cloud detection scheme in the GSI system is based on the differences of brightness temperature between observations (yobs) and H(xb) at two MHS window channels. Due to mismatch between observed and simulated cloud locations, the scheme is usually unable to detect cloudy MHS data when there are no clouds in the background simulation. Two new MHS cloud detection algorithms were developed to improve MHS data assimilation results. The first algorithm establishes two regression functions, one applicable to land and the other applicable to ocean. It expresses the observation minus simulation differences of the GOES imager channel at 10.7 mm (${y}_{10.7\text{ }\text{μm}}^{\text{obs}}-{H}_{10.7\text{ }\text{μm}}\left({x}_{\text{b}}\right)$) as a function of brightness temperature observations at three MHS channels (two window channels and a sounding channel around 800 hPa) [80]. The second algorithm combines the AMSU-A and MHS observational data into a single data stream so that MHS data affected by liquid clouds can also be successfully detected by AMSU-A window channels [81]. By using these two improved cloud detection schemes, MHS data assimilation no longer degraded forecasts, but rather improved precipitation forecasting skills.
Satellite observed brightness temperatures are not absolutely calibrated and thus contain biases. Bias correction is a necessary step for satellite data assimilation. It has been shown that biases vary with latitude and scan angle. The traditional method for bias correction is the so-called variational air-mass bias correction. It works by replacing the observation operator for the ith channel simulation (Hi(x)) by a bias subtracted operator (${\tilde{H}}_{i}\left(x,\beta \right)={H}_{i}\left(x\right)-{\mu }_{i}\left(\beta,x\right)$), where ${\mu }_{i}\left(\beta,x\right)={\displaystyle \sum }_{j=1}^{5}{\beta }_{i,j}{P}_{i,j}$,${\beta }_{i,j}$ is the jth regression coefficients of the jth predictor Pi,j of the ith channel (j = 1, 2, …, 5), Pi,j (i = 1, 3) account for global bias, scan bias, and liquid water path (LWP) dependent bias, respectively, and Pi,j (i = 4,5) are the quadratic and linear functions of the vertical correlation between transmittance and temperature, respectively [82]. The variational air-mass bias correction introduces more variables (${\beta }_{i,j}$; i = 1, 2,…, Iall-channel; j = 1, 2, …, 5) to the cost function J, where Iall-channel represents the total number of channels assimilated. It also requires the radiative transfer model to be called a second time for the calculation of transmittance.
Other methods exist for air-mass bias correction. One example is the role of the 5th predictor. The 5th predictor deals with a channel’s frequency being slightly shifted after launch, which would move the transmittance profile up or down. The basic principle of the 5th predictor is that, assuming a slight increase in transmittance, if the temperature increases with height, the brightness temperature increases; if the temperature decreases with height, the brightness temperature decreases. After FY-3A entered orbit, its microwave temperature sounder (MWTS) did indeed experience frequency shift. The MWTS has four channels, and its designed center frequency is the same as AMSU-A channels 3, 5, 7, and 9 [83]. The center frequency shift occurs in channels 2, 3, and 4, resulting in significant temperature-dependent biases in these channels [84]. Wang et al. [85] showed that the MWTS bias caused by frequency offset can be estimated and corrected by the mean difference between brightness temperature simulations with and without frequency offset. If a frequency shift after launch is known, a more direct way to remove the frequency-shift-induced bias is to use the new center frequency in the radiative transfer model. This happened with AHI channel 16 whose center frequency had a smaller shift [86].
If the bias between observation and background (O-B bias) is reasonably estimated using training data about 2-4 weeks before the assimilation time, a simple static bias correction is sufficient for CrIS data assimilation, without having to incorporate variational air mass bias correction [87]. The simple bias correction scheme directly calculates the scan and latitudinal dependent bias (μ (𝜙,), φ is latitude, 𝛼 is scan angle) based on O-B samples in the training period, and subtract it from the term $H\left(x\right)-{y}^{\text{obs}}$. In a one-month CrIS data assimilation and forecasting cycling experiments, the use of the simple bias correction scheme was superior to the variational air-mass bias correction scheme, yielding smaller root-mean-square prediction errors of temperature and specific humidity, higher equivalent threat scores for precipitation forecasting, and more realistic structures of temperature and geopotential height troughs and ridges.
4.4. Data thinning and quality control that remove too much satellite data
A large amount of satellite data is discarded by data thinning and quality control procedures before J is minimized. The exact scheme varies with the assimilation system and also individual who may make modifications to the existing scheme for specific weather cases. Here is a brief discussion on assessing the impacts of ATMS data assimilation on hurricane track and intensity forecasts [88]. ATMS is a successor of AMSU-A/B onboard NOAA-15/16/17 and AMSU-A/MHS onboard NOAA-18/19 and MetOp-A/B/C. It combines most of the channels of AMSU-A and MHS. It is a total power radiometer and scans in a cross-track manner within 52.7° with respect to the nadir direction. It has a total of 22 channels with the first 16 channels primarily for temperature soundings from the surface to about 1 hPa (∼45 km) and the remaining channels for humidity soundings in the troposphere from the surface to about 200 hPa (∼10 km altitude). A single scan line of ATMS consists of 96 fields of views (FOVs). Any single FOV of channels 1-2 overlaps with four neighboring four FOVs and four scanlines [7]. As a result, data correlations exist among neighboring FOVs and scan lines. The data thinning strategy and quality control procedures for ATMS data assimilation in the GSI system are summarized as follows. The ATMS data thinning rejects FOVs 1-7 and 89-96 located at large scan angles, as well as four out of every five neighboring FOVs. In other words, 16 out of 96 FOVs on one of the five scan lines are assimilated, accounting for only about 3.3% of the ATMS data. Such a data thinning strategy aims to avoid the correlation of observation errors in the assimilated data. The quality control procedure to identify and remove outliers consists of a series of tests in the GSI system. If the sum of liquid water content (ql,b) and ice content (qi,b) is greater than zero: ql,b + qi,b > 0, the following data are rejected from assimilation: Outside the latitudinal range (60°S, 60°N) for channels 1-7 and 16-22, the model and observation difference is three times greater than the modified observation error, and the observed or simulated liquid water path is larger than 0.5 kg·m−2 over oceans. If ${q}_{\text{l},\text{b}}+{q}_{\text{i},\text{b}}$= 0, outliers are identified if model simulations greatly deviate from observations, are sensitive to LWP, have uncertainty in surface emissivity, or if a single type of surface covers less than 99% of the FOV area.
The second example on data thinning and quality control strategies involves the assimilation of GOES-11 and GOES-12 data at 10 km horizontal resolution using the GSI/WRF system [89]. GOES-11 and GOES-12 provide imager data for the west coast and the East Coast of the United States, respectively, with an imaging refresh rate of 15 min. GOES-11 imager had five channels 1-5 at 0.65, 3.9, 6.8, 10.7, and 12.0 μm, whose resolutions are 1, 4, 8, 4, and 4 km, respectively. GOES-12 imager is similar to GOES-11 except for channel 3 whose frequency and resolution are changed to 6.48 μm and 4 km, respectively. The GOES-11 and GOES-12 data assimilated in the GSI/WRF system are thinned to 40 and 60 km, respectively, and converted to a new data format called the binary universal form for the representation of meteorological data (BUFR). The BUFR data contains the brightness temperature, clear-sky fraction, and standard deviation of the brightness temperature of the raw data within the thinned 40 or 60 km box. The data thinning is performed not only because the model resolution is coarser than the data, but also to ensure that the observation errors are not correlated. After data thinning, less than about 6%-10% of the GOES data remains to undergo quality control to remove outliers with negative brightness temperatures, standard deviations greater than a prescribed value, and data different from the background value by more than three times the observation error standard deviations, as well as channels 2, 4, and 5 over land and all channels over ice and snow surfaces.
4.5. Loss of observation information on spatial distribution of cloud structures
The POES and GOES series of satellites continuously provide huge volumes of high-resolution observational data. The spatial resolution is 15 km for the MHS channels, 9 km for the FY-3D Microwave Radiation Imager (MWRI) channel at 89.0 GHz, 5 km for the AMSR-2 channels at 89.0 GHz, and 2 km for the ABI and AHI channels. However, as stated above, a significant amount of data is not used in numerical weather data assimilation and forecasting systems. Valuable observational information regarding the spatial distribution of cloud structures, such as Figs. 1(e) and (f), is lost. These satellite cloud images contain huge amounts of dynamic information. However, the dynamic constrains related to the evolution of some meteorological features (such as clouds, eddies, fronts, etc.) that are easily detected in satellite observations are not fully leveraged in all-sky data assimilation. In addition to pursuing an observation operator that links absolute vorticity to brightness temperatures discussed in the Subsection 3.3, another approach is “image assimilation,” directly incorporating image sequences into the data assimilation and forecasting systems. Although imager-assimilation ideas were proposed [90,91], they were mainly performed with synthetic data in simple models [[92], [93], [94]].
An image is a set of pixels containing visible structures such as clouds, fronts, tropical cyclones, and other singularities. From a mathematical perspective, any of these shapes can be considered a two-dimensional (2D) shape. One may first define a given cloud shape 𝛺c using some cloud mask tests in Ref. [95]:
where ∂𝛺c is the boundary of the targeted cloud shape 𝛺c. This enables conversion from observations (Tb) to a structure operator Hc(Tb). Finally, we have the following term added to the cost function in Eq. (1):
Image data assimilation is a generic problem with applications not only in atmospheric data assimilation, but also other fields (e.g., medical imaging and oil spread in oceans).
AI is a powerful tool for using image data to make predictions. If image assimilation could be combined with AI, it will be possible to expand the utilization of satellite and radar data and solve the problem of loss of observation information of spatial distribution of cloud and rain structures.
5. Integration with meteorological deep learning
5.1. The 4D-Var AI system with AI physical parameterization models
AI has brought about revolutionary changes in many fields. Preliminary results show exciting promises of AI in numerical weather prediction.
The 4D-Var data assimilation represents an optimal control method using adjoint techniques, which was introduced to meteorology by Le Dimet and Talagrand [97]. They used a 1D shallow-water model to illustrate the derivation of tangent linear and adjoint differential equations. This article by Le Dimet and Talagrand sparked a worldwide interest in adjoint techniques and 4D-Var meteorological data assimilation. Two global 4D-Var system using the adjoint model of the adiabatic version of the spectral multilevel primitive equation model were developed by late 1980s, one at the European Centre for Medium-Range Weather Forecasts (ECMWF) [98] and the other at NCEP [99]. Subsequently, the adiabatic version of the spectral multilevel primitive equation model was extended to include physical parameterization schemes by building their adjoints [100,101].
The application of data assimilation in operational forecasting faces strict time constraints, that is, analysis and forecasts must be ready quickly enough for forecasting products to be disseminated in time. In order to meet these time constraints, an approximation to the 4D-Var called the incremental 4D-Var was developed. The numerical weather prediction model is used to produce a basic state of the atmosphere (xbasic), the tangent linear model with lower resolutions and simpler physics is used to generate perturbation forecasts with respect to the basic state (δ𝒙), and minimization is carried out in this simpler system and its adjoint model yielding the minimizer (δ𝒙)*, and the analysis of incremental 4D-Var is ${x}_{\text{a}}={x}_{\text{basic}}+{\left(\text{δ}x\right)}^{\ast }$. This process can be repeated twice or more. By using lower resolutions and simpler physics in the tangent linear model and its adjoint model than those in the original numerical weather prediction model, the incremental 4D-Var provides a way to reduce the computational cost of 4D-Var. The ECMWF implemented the incremental global 4D-Var operational system in 1997 [102,103], the Japan Meteorological Agency implemented the regional incremental 4D-Var operational system in 2002 [104], the Meteorological Service of Canada implemented the global incremental 4D-Var operational system in 2005 [105], and the China Meteorological Administration implemented the global incremental 4D-Var operational system in 2018 [106].
The 4D-Var approach assimilates observational data over a period of time. Using 4D-Var analyses to initialize numerical weather forecasts will not lead to internal dynamic imbalances that can be detrimental to forecasts [107]. For ultra-high-resolution data assimilation that aims to predict rapidly evolving small-scale extreme weather systems, 4D-Var is an optimal choice.
By utilizing high-resolution numerical weather forecasting models, a comprehensive dataset containing all scenarios of the targeted physical process can first be generated and used to develop an AI model to replace the original physical parameterization scheme. The tangent-linear and adjoint operators of physical parametrization schemes are complex to build manually or even with automatic differentiation, whereas the AI model can be easily differentiated. The AI model demands much less computational cost than the original physical parameterization schemes, so does its tangent-linear and adjoint operators [16]. Replacing physical parametrization schemes with AI models could open up new possibilities for 4D-Var method. It is anticipated that the 4D-Var AI system with AI physical parameterization models will unlock the full potential of 4D-Var data assimilation while meeting the operational constraints.
Preliminary successes in large-scale medium-range weather forecasts have been demonstrated by deep-learning techniques [[15], [16], [17]]. The ERA5 reanalysis dataset, which has 0.25° × 0.25° horizontal resolutions and 137 vertical levels from the surface to 0.01 hPa, was used as the training datasets for these AI models. This limits the current deep-learning (DL) models to properly forecasting extreme weather events or small-scale phenomena. In addition to improving the skill of high-resolution numerical weather forecasting, the future 4D-Var AI or pure AI data assimilation systems can also be used to generate high-resolution high-quality reanalysis datasets. This reanalysis dataset could accurately describe important features such as clouds, rain, gravity waves, planetary boundary layers, and inversion layers. Therefore, it can serve as a good training dataset to enable AI deep-learning models that successfully predict the triggering, development, and decay processes of small-scale weather systems.
5.2. Mutual reinforcement between data assimilation and meteorological deep learning
There are multiple time-scale variations in the atmosphere, ranging from convective, synoptic weather, low-frequency intra-seasonal, and interannual variations. The atmospheric variability on large time scales requires long data records. However, the lifespan of all satellite instruments is limited, ranging from a few years to over a decade. By keeping the channel frequency of similar instruments constant across missions, the continuity of the satellite data over a long period of time can be ensured. An example is satellite microwave temperature observations, which have the longest data record with global coverage. The AMSU-A channel 3, 5, 7, and 9 have the same center frequency as microwave sounding unit (MSU) channels 1, 2, 3, and 4; meanwhile the ATMS channels 1-3 are the same as AMSU-A channels 1-3, channels 5-15 match AMSU-A channels 4-14. The MSU data between 1978-1998 and AMSU-A data since 1998 were successfully merged [108,109], and showed global warming trends in the mid- and upper-troposphere and cooling trends in the low stratosphere over the past several decades [[110], [111], [112]]. In addition to decadal trends, satellite microwave temperature observations can also fully capture low frequency variability in the atmosphere, including teleconnection, blocking, and El Niño [113,114]. For example, AMSU-A channel 5 measures radiation from the middle troposphere. The explained variances of channel-5 brightness temperature observations from NOAA-15/18/19 and the EUMESAT MetOp-A/B during the 22-years period (December 1998 to November 2020) revealed several features in the tropics (15°S-15°N): the synoptic variability of weather systems centered at 3-5 and 10 days; the intra-seasonal variability on timescales of 30-60 and 90 days; the annual variations; as well as interannual variability at 1.5-2 and 3-5 years [113]. Not only that, the same AMSU-A dataset captures five main teleconnections during Northern Hemisphere winters, such as the eastern Atlantic pattern, the Pacific/North American pattern, the western Atlantic pattern, the western Pacific pattern, and the Eurasian pattern. The explained variances of the ERA5 500 hPa temperature over the same 22 years period showed a similar frequency spectrum in the tropics, except for lacking synoptic variability at 3-5 and 10 days. The ERA5 500 hPa geopotential height-derived teleconnections over the same 22 years period resembled those from the AMSU-A channel-5 brightness temperature observations.
Atmospheric phenomena of different scales interact and influence each other. Future data assimilation should be carried out at ultra-high, high, intermediate, and low resolutions, respectively, to assimilate grid-resolvable observational data and allowing their analyses to interact and influence each other. Here, the ultra-high, high, intermediate, and low resolutions are several hundred meters, several kilometers, tens of kilometers, and several hundred kilometers, respectively. In data assimilation, linear regression algorithms are used in many areas, such as the fast radiative transfer models [115], the total ozone observation operator [47,65], microwave retrievals of liquid water path [116] and ice water path [117], infrared cloud detection for the NOAA-20 CrIS [118] and the FY-3D hyperspectral infrared atmospheric sounder (HIRAS) [119], and bias correction that combines all‐sky simulations of brightness temperatures from short-term forecasts with three different microphysics schemes [66]. Anything performed by traditional linear regression algorithms in data assimilation can be replaced by DL models for more accurate results. The future data assimilation and meteorological deep learning will inevitably intertwine and reinforce each other. Specifically, higher resolution data assimilation will abandon more legacy methods; and data assimilation frameworks of dynamic cores of numerical weather prediction models will share the same grid settings at all resolutions; all reslution will employ deterministic dynamic cores with DL physical parameterization models; and the analysis fields generated by data assimilation over a sufficiently long period will accurately describe all relevant weather and serve as training datasets for various DL models. Only in this way will real-time forecasts of various weather systems reach users within a specific time limit, better meeting societal needs.
6. Concluding remarks
Data assimilation has always been limited by computing power, and will continue to be so in the future. Although powerful, AI’s creation involves the rapid reorganization of available information. Unconventional or even contradictory thinking, assisted with the AI technology, is more likely to give birth to truly original high-resolution data assimilation systems. Only with a thoughtful strategy and a series of incremental steps will AI data assimilation systems surpass and replace current data assimilation systems.
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