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Radiances from microwave temperature sounders have been assimilated operationally at ECMWF for two decades, but observations significantly affected by clouds and precipitation have been screened out. Extending successful assimilation beyond clear-sky scenes is a challenge that has taken several years of development to achieve. In this paper we describe the all-sky treatment of AMSU-A, which enables greater numbers of temperature sounding radiances to be used in meteorologically active parts of the troposphere. Successful all-sky assimilation required combining lessons learned from the clear-sky assimilation of AMSU-A with the approach initially developed for humidity-sensitive microwave radiances. This concerned particularly observation thinning, error modeling, and variational quality control. As a result of the move to all-sky assimilation, the forecast impact of AMSU-A now replicates and exceeds that of the previous clear-sky usage. This is shown via trials in comparison to the current ECMWF assimilation system, judged with respect to forecast scores and background fits to independent observations. Persistently cloudy regions and phenomena such as tropical cyclones are better sampled when assimilating AMSU-A in all-sky conditions, causing an increase of about 13% in used channel-5 radiances globally. These impacts are explored, with an emphasis on tropical cyclones in the 2019 season. Independent observations provide consistent evidence that representation of humidity is improved, for example, while extratropical Z500 forecasts are improved by about 0.5% out to at least day 2. On the strength of these results, assimilation of AMSU-A moved to all-sky conditions with the upgrade to IFS cycle 47R3 in October 2021.

Satellite infrared (IR) sounder and imager measurements have become one of the main sources of data used by data assimilation systems to generate initial conditions for numerical weather prediction (NWP) models and atmospheric analysis/reanalysis. This paper reviews the development of satellite IR data assimilation in NWP in recent years, especially the assimilation of all-sky satellite IR observations. The major challenges and future directions are outlined and discussed.

Promising new opportunities to apply artificial intelligence (AI) to the Earth and environmental sciences are identified, informed by an overview of current efforts in the community. Community input was collected at the first National Oceanic and Atmospheric Administration (NOAA) workshop on “Leveraging AI in the Exploitation of Satellite Earth Observations and Numerical Weather Prediction” held in April 2019. This workshop brought together over 400 scientists, program managers, and leaders from the public, academic, and private sectors in order to enable experts involved in the development and adaptation of AI tools and applications to meet and exchange experiences with NOAA experts. Paths are described to actualize the potential of AI to better exploit the massive volumes of environmental data from satellite and in situ sources that are critical for numerical weather prediction (NWP) and other Earth and environmental science applications. The main lessons communicated from community input via active workshop discussions and polling are reported. Finally, recommendations are presented for both scientists and decision-makers to address some of the challenges facing the adoption of AI across all Earth science.

Predictions of the Earth system, such as weather forecasts and climate projections, require models informed by observations at many levels. Some methods for integrating models and observations are very systematic and comprehensive (e.g., data assimilation), and some are single purpose and customized (e.g., for model validation). We review current methods and best practices for integrating models and observations. We highlight how future developments can enable advanced heterogeneous observation networks and models to improve predictions of the Earth system (including atmosphere, land surface, oceans, cryosphere, and chemistry) across scales from weather to climate. As the community pushes to develop the next generation of models and data systems, there is a need to take a more holistic, integrated, and coordinated approach to models, observations, and their uncertainties to maximize the benefit for Earth system prediction and impacts on society.

The benefit of hyperspectral infrared sounders to weather forecasting has been improved with the representation of interchannel correlations in the observation error model. The aim is now to assimilate these observations in all-sky conditions. However, in cloudy skies, observation errors exhibit much stronger interchannel correlations, as well as much larger variances, compared to clear sky conditions. An observation error model is developed to represent these effects, building from the symmetric error models developed for all-sky microwave assimilation. The combination of variational quality control with correlated errors is also introduced. The new error model is tested in all-sky assimilation of 7 water vapour sounding channels from the Infrared Atmospheric Sounding Interferometer (IASI). However, its initial formulation degrades both tropospheric and stratospheric analyses. To explain this the eigendeparture and eigenjacobian are introduced as a way of understanding the effect of correlated observation errors in data assimilation. The trailing eigenvalues can be problematic because they strongly amplify high-order harmonic combinations of the water vapour channels, which could have at least three consequences: first, if there are small inter-channel biases, these can be greatly amplified; second, the trailing eigenjacobians map onto features resembling gravity waves that the data assimilation may not be able to handle; finally, these harmonic combinations can amplify trace sensitivities, for example revealing a strong upper stratospheric sensitivity over high cloud in what are usually mid- to upper-tropospheric water vapour channels. The most likely explanation is the sensitivity to gravity wave features that are present in the observations but hard for the data assimilation to handle. After reducing the sensitivity to the trailing eigenjacobians, the new error covariance matrix gives good results in all-sky infrared assimilation.

Satellite observations of radiation in the microwave and sub-mm spectral regions (broadly from 1 to 1000 GHz) can have strong sensitivity to cloud and precipitation particles in the atmosphere. These particles (known as hydrometeors) scatter, absorb and emit radiation according to their mass, composition, shape, internal structure, and orientation. Hence, microwave and sub-mm observations have applications including weather forecasting, geophysical retrievals and model validation. To simulate these observations requires a scattering-capable radiative transfer model and an estimate of the bulk optical properties of the hydrometeors. This article describes the module used to integrate single-particle optical properties over a particle size distribution (PSD) to provide bulk optical properties for the Radiative Transfer for TOVS microwave and sub-mm scattering code, RTTOV-SCATT, a widely-used fast model. Bulk optical properties can be derived from a range of particle models including Mie spheres (liquid and frozen) and non-spherical ice habits from the Liu and Atmospheric Radiative Transfer Simulator (ARTS) databases, which include pristine crystals, aggregates and hail. The effects of different PSD and particle options on simulated brightness temperatures are explored, based on an analytical two-stream solution for a homogeneous cloud slab. The hydrometeor scattering "spectrum" below 1000 GHz is described, along with its sensitivities to particle composition (liquid or ice), size and shape. The optical behaviour of frozen particles changes in the frequencies above 200 GHz, moving towards an optically thick and emission-dominated regime more familiar from the infrared. This region is previously little explored but will soon be covered by the Ice Cloud Imager (ICI).

Numerical weather prediction systems still employ many simplifications when assimilating microwave radiances under all-sky conditions (clear sky, cloudy, and precipitation). For example, the orientation of ice hydrometeors is ignored, along with the polarization that this causes. We present a simple approach for approximating hydrometeor orientation, requiring minor adaption of software and no additional calculation burden. The approach is introduced in the RTTOV (Radiative Transfer for TOVS) forward operator and tested in the Integrated Forecast System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). For the first time within a data assimilation (DA) context, this represents the ice-induced brightness temperature differences between vertical (V) and horizontal (H) polarization – the polarization difference (PD). The discrepancies in PD between observations and simulations decrease by an order of magnitude at 166.5 GHz, with maximum reductions of 10–15 K. The error distributions, which were previously highly skewed and therefore problematic for DA, are now roughly symmetrical. The approach is based on rescaling the extinction in V and H channels, which is quantified by the polarization ratio ρ. Using dual-polarization observations from the Global Precipitation Mission microwave imager (GMI), suitable values for ρ were found to be 1.5 and 1.4 at 89.0 and 166.5 GHz, respectively. The scheme was used for all the conical scanners assimilated at ECMWF, with a broadly neutral impact on the forecast but with an increased physical consistency between instruments that employ different polarizations. This opens the way towards representing hydrometeor orientation for cross-track sounders and at frequencies above 183.0 GHz where the polarization can be even stronger.

Recent progress in machine learning (ML) inspires the idea of improving (or learning) earth system models directly from the observations. Earth sciences already use data assimilation (DA), which underpins decades of progress in weather forecasting. DA and ML have many similarities: they are both inverse methods that can be united under a Bayesian (probabilistic) framework. ML could benefit from approaches used in DA, which has evolved to deal with real observations—these are uncertain, sparsely sampled, and only indirectly sensitive to the processes of interest. DA could also become more like ML and start learning improved models of the earth system, using parameter estimation, or by directly incorporating machine-learnable models. DA follows the Bayesian approach more exactly in terms of representing uncertainty, and in retaining existing physical knowledge, which helps to better constrain the learnt aspects of models. This article makes equivalences between DA and ML in the unifying framework of Bayesian networks. These help illustrate the equivalences between four-dimensional variational (4D-Var) DA and a recurrent neural network (RNN), for example. More broadly, Bayesian networks are graphical representations of the knowledge and processes embodied in earth system models, giving a framework for organising modelling components and knowledge, whether coming from physical equations or learnt from observations. Their full Bayesian solution is not computationally feasible but these networks can be solved with approximate methods already used in DA and ML, so they could provide a practical framework for the unification of the two. Development of all these approaches could address the grand challenge of making better use of observations to improve physical models of earth system processes. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

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Permittivity models for microwave frequencies of liquid water below 0 ∘C (supercooled liquid water) are poorly constrained due to limited laboratory experiments and observations, especially for high microwave frequencies. This uncertainty translates directly into errors in retrieved liquid water paths of up to 80 %. This study investigates the effect of different liquid water permittivity models on simulated brightness temperatures by using the all-sky assimilation framework of the Integrated Forecast System. Here, a model configuration with an improved representation of supercooled liquid water has been used. The comparison of five different permittivity models with the current one shows a small mean reduction in simulated brightness temperatures of at most 0.15 K at 92 GHz on a global monthly scale. During austral winter, differences occur more prominently in the storm tracks of the Southern Hemisphere and in the intertropical convergence zone with values of around 0.5 to 1.5 K. Compared to the default Liebe (1989) approach, the permittivity models of Stogryn et al. (1995), Rosenkranz (2015) and Turner et al. (2016) all improve fits between observations and all-sky brightness temperatures simulated by the Integrated Forecast System. In cycling data assimilation these newer models also give small improvements in short-range humidity forecasts when measured against independent observations. Of the three best-performing models, the Stogryn et al. (1995) model is not quite as beneficial as the other two, except at 183 GHz. At this frequency, Rosenkranz (2015) and Turner et al. (2016) look worse because they expose a scattering-related forward model bias in frontal regions. Overall, Rosenkranz (2015) is favoured due to its validity up to 1 THz, which will support future submillimetre missions.

This paper presents an evaluation of the quality of data from the MicroWave Humidity Sounder-2, flown on the FY-3C polar orbiting satellite, and first results of trials assimilating the data in all-sky conditions in the European Centre for Medium Range Weather Forecasts’ assimilation system. This instrument combines traditional microwave humidity sounding capabilities at 183 GHz with new channels at 118 GHz, which have never before been available from space. The aim of this paper is twofold: to contribute to the calibration/validation of this satellite by evaluating the data and to test for the first time the impact of assimilating 118-GHz sounding channels in a global numerical weather prediction system. MWHS-2 was first evaluated by comparing observation minus short-range forecast statistics to similar instruments, which indicated that the quality was generally similar. Adding the 118- and 183-GHz channels to the full operational observing system led to small improvements in the short-range (~12 h) forecast accuracy for both sets of channels, and improvements in the 2–4-day wind forecast accuracy for the 183-GHz channels. Short-range forecasts were improved for global humidity in particular when assimilating the 183-GHz channels (0.5% improvement) and for cloud and low-level wind in the Southern Hemisphere extra-tropics when assimilating the 118-GHz channels (by, respectively, 0.5% and 0.2%). In the absence of other atmospheric observations, assimilating the 118-GHz channels improved the global forecast accuracy, but the overall impact was less than for the 183-GHz channels, or for equivalent Advanced Microwave Sounding Unit-A channels.

This article reviews developments towards assimilating cloud and precipitation-affected satellite radiances at operational forecasting centres. Satellite data assimilation is moving beyond the ‘clear-sky’ approach that discards any observations affected by cloud. Some centres already assimilate cloud and precipitation-affected radiances operationally and the most popular approach is known as ‘all-sky’, which assimilates all observations directly as radiances, whether they are clear, cloudy or precipitating, using models (both for radiative transfer and forecasting) that are capable of simulating cloud and precipitation with sufficient accuracy. Other frameworks are being tried including the assimilation of humidity retrieved from cloudy observations using Bayesian techniques. Although the all-sky technique is now proven for assimilation of microwave radiances, it has yet to be demonstrated operationally for infrared radiances, though several centres are getting close. Assimilating frequently-available all-sky infrared observations from geostationary satellites could give particular benefit for short-range forecasting. More generally, assimilating cloud and precipitation-affected satellite observations improves forecasts into the medium-range globally, and it can also improve the analysis and shorter-range forecast of otherwise poorly-observed weather phenomena as diverse as tropical cyclones and wintertime low cloud.

(Beginning of WHAT, WHEN, WHERE Summary Box:) What: The work-shop gathered almost 50 scientists from Europe and the United States to discuss the progress towards developing electromagnetic scattering databases for ice and snow particles in the microwave region, their applications, the physical approximations used to compute these scattering properties, and how remote sensing and in situ observations can be used to validate scattering datasets. One of the main priorities of the workshop was to foster communication between users and developers of scattering databases, and to define standards and conventions for scattering data structures and variables. When: 28-30 June 2017. Where: Cologne, Germany (END of what, when, where summary box).

Ten years ago, humidity observations were thought to give little benefit to global weather forecasts. Nowadays, at the European Centre for Medium-range Weather Forecasts, satellite microwave radiances sensitive to humidity, cloud and precipitation provide 20% of short-range forecast impact, as measured by adjoint-based forecast sensitivity diagnostics. This makes them one of the most important sources of data and equivalent in impact to microwave temperature sounding observations. Forecasts of dynamical quantities, and precipitation, are improved out to at least day 6. This article reviews the impact of and the science behind these data. It is not straightforward to assimilate cloud and precipitation-affected observations when the intrinsic predictability of cloud and precipitation features is limited. Assimilation systems must be able to operate in the presence of all-pervasive cloud and precipitation ‘mislocation’ errors. However, by assimilating these observations using the ‘all-sky’ approach, and supported by advances in data assimilation and forecast modelling, modern data assimilation systems can infer the dynamical state of the atmosphere, not just from traditional temperature-related observations, but from observations of humidity, cloud and precipitation.

Recent success in assimilating cloud- and precipitation-affected satellite observations using the “all-sky” approach is thought to have benefitted from variational data assimilation, particularly its ability to handle moderate nonlinearity and non-Gaussianity and to extract wind information through the generalized tracer effect. Ensemble assimilation relies on assumptions including linearity and Gaussianity that might cause difficulties when using all-sky observations. Here, all-sky assimilation is evaluated in a global ensemble Kalman filter (EnKF) system of near-operational quality, derived from an operational four-dimensional variational (4D-Var) system. To get EnKF working successfully required a new all-sky observation error model (the most successful approach was to inflate error as a multiple of the ensemble spread) and adjustments to localization. With these improvements, assimilation of eight microwave humidity instruments gave 2%–4% improvement in forecast scores whether using EnKF or 4D-Var. Correlations from the ensemble showed that all-sky observations generated sensitivity to wind, temperature, and humidity. EnKF increments shared many similarities with those in 4D-Var. Hence both 4D-Var and ensemble data assimilation were able to make good use of all-sky observations, including the extraction of wind information. In absolute terms the EnKF forecast performance in the troposphere was still worse than that that with 4D-Var, although the gap could be reduced by going from 50 to 100 ensemble members. EnKF errors were larger in the stratosphere, where there are excessive gravity wave increments that are not connected with all-sky assimilation.

This chapter focuses on one of the major applications of space observations impacted by precipitation: the use of these data in Numerical Weather Prediction (NWP) data assimilation (DA) systems. Applications in global systems will be the focus of this study. The assimilation of observations impacted by precipitation is done either directly or after geophysical data (generally precipitation amount) is inverted. Assimilating and inverting data using physical retrieval approaches are inherently intertwined and share the same objectives. After all, the purpose of retrieving precipitation from satellite data aims at extracting the precipitation signal from the measurements while accounting for non-precipitation signals in the same measurements. This is essentially the same objective as assimilating the precipitation-impacted data into NWP: the purpose being to extract the geophysical information from the measurements and use it to help generate a geophysical analysis. Different numerical weather prediction centers are adopting different approaches on how to handle the assimilation of precipitation data. Some are directly assimilating radiances and some are using pre-processed retrievals. The goal of this chapter is not to assess the pros and cons of the different methods, but instead to give the reader an overview of the approaches adopted or being explored. Assimilating precipitation-impacted measurements is an ongoing active effort in the research community, as well as in major operational NWP centers around the world. To remain concise, we will provide broad overviews of the current trends from multiple institutions, and do not pretend to be exhaustive in describing all approaches dealing with this issue. Instead, multiple and diverse references will be included to allow readers to obtain further details on a diverse set of methodologies being pursued. For completeness, the chapter will be outlined in a way that allows the reader a gradual understanding of (1) the main motivations behind the significant effort being undertaken by the international community to tackle this problem, (2) the challenges facing us when handling cloud and rain-impacted space observations, (3) the methodologies adopted by different teams and their potential shortfalls when addressing some of those challenges, and (4) some of the major results when using these approaches in an NWP context.

5 pags., 1 fig., descripción no proporcionada por scopus, The workshop was hosted by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT), Darmstadt, Germany. Maria Cadeddu is supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Atmospheric Radiation Measurement Infrastructure Basic Energy Sciences, under contract DE-AC02-06CH11357. Patrick Ericksson is was supported by the Swedish National Space Agency. Ralf Bennartz was supported by NASA USPI Grant NNX17AJ09G.

The extension of all-sky assimilation of SSMIS humidity sounding channels to land surfaces is investigated in this paper. The scattering index, which is able to discriminate cloudy and precipitating regions over land, is used as a predictor to develop a ‘symmetric’ model for observation error. This formulation is able to increase the observation error in those scenes which are more difficult to model because of radiative transfer and ‘mislocation’ errors. The implementation of an instantaneous emissivity retrieval from SSMIS observations is also presented. In clear-sky scenes, emissivity retrievals appear better at capturing daily differences in surface conditions, compared to emissivity atlas values. In the presence of clouds, retrievals have different behaviour. In the lower microwave frequencies (less than 50 GHz), emissivity estimates appear nearly as reliable as those in clear-skies, but at higher frequencies, as the magnitude of scattering increases, so does the error in the retrieval and the resultant emissivity estimate can be unphysically low or high. However, the retrieval still appears feasible at high frequencies in light cloud situations; the number of retrievals discarded due to these kinds of problems is around 10%. In these cases, an estimate from an emissivity atlas can be substituted instead. Together the new observation error model and the instantaneous emissivity retrievals were adopted for the assimilation of SSMIS 183 GHz channels over land in all-sky conditions. Assimilation experiments showed that the assimilation system is not degraded and the improvements on analysis and forecast scores are about the same as those which are obtained by the equivalent clear-sky approach. The developments described in this study were an essential first step to create framework to allow the all-sky assimilation over land of other microwave humidity sounders: this started operationally at ECMWF in 2015, covering both SSMIS and four MHS (Microwave Humidity Sounder) instruments.

This paper discusses the role of the observation operator in data assimilation and how the evolving strategy of Numerical Weather Prediction is creating new challenges for Radiative Transfer Model developments, placing an increasing demand on these models and their consistency, bias characterisation and range of capabilities. The paper concludes that to meet future challenges models will need to be developed in a modular style taking elements from many research groups, giving attention to consistency of physical assumptions, interfaces and coding standards.

Our understanding of the distribution of heat and water in the atmosphere still shows critical gaps on all temporal and spatial scales. This is mainly due to a lack of accurate measurements of water vapor and temperature profiles -hereafter called thermodynamic (TD) profiles -withhigh vertical and temporal resolution, especially in the lower troposphere. Accurate, high temporal-spatial resolution observations of TD profiles are essential for improving weather forecasting and re-analyses, for studying land-atmosphere feedback processes and for improving model parameterizations of land-surface and turbulent transport processes in the Atmospheric Boundary Layer. These observational gaps can be addressed with a new active remote sensing system in space based on the Raman lidar technique. Combining vibrational and rotational Raman backscatter signals, simultaneous measurements of water vapour and temperature profiles and a variety of derived variables are possible with unprecedented vertical and horizontal resolution, especially in the lower troposphere. This is the key concept of ATLAS, which was submitted in March 2018to the European Space Agency in response to the Call for Earth Explorer-10 Mission Ideas in the frame of ESAEOEP. An assessment of the expected performance of the systemand the specifications of the different lidar sub-systems has been performed based on the application ofan analytical simulation model for space-borne Raman lidar systems. Results from the simulations and technical aspects of the proposed mission will beillustrated at the conference.

This paper gives an update of the RTTOV (Radiative Transfer for TOVS) fast radiative transfer model, which is widely used in the satellite retrieval and data assimilation communities. RTTOV is a fast radiative transfer model for simulating top-of-atmosphere radiances from passive visible, infrared and microwave downward-viewing satellite radiometers. In addition to the forward model, it also optionally computes the tangent linear, adjoint and Jacobian matrix providing changes in radiances for profile variable perturbations assuming a linear relationship about a given atmospheric state. This makes it a useful tool for developing physical retrievals from satellite radiances, for direct radiance assimilation in NWP models, for simulating future instruments, and for training or teaching with a graphical user interface. An overview of the RTTOV model is given, highlighting the updates and increased capability of the latest versions, and it gives some examples of its current performance when compared with more accurate line-by-line radiative transfer models and a few selected observations. The improvement over the original version of the model released in 1999 is demonstrated.

Data from hyperspectral infrared sounders are routinely ingested worldwide by National Weather Centers (NWCs). The cloud-free fraction of this data is used for initializing forecasts which include profiles of temperature, water vapor, water cloud and ice cloud profiles on a global grid. Although the data from these sounders are sensitive to the vertical distribution of ice and liquid water in clouds, this information is not fully utilized. In the future, this information could be used for validating clouds in NWC models and for initializing forecasts. We evaluate how well the calculated radiances from hyperspectral Radiative Transfer Models (RTMs) compare to cloudy radiances observed by AIRS and to one another. Vertical profiles of the clouds, temperature and water vapor from ECMWF (European Center for Medium-range Weather Forecasting) were used as input for the RTMs. For non-frozen ocean day and night data, the histograms derived from the calculations by several RTMs at 900 cm(exp -1)have a better than 0.95 correlation with the histogram derived from the AIRS observations, with a bias relative to AIRS of typically less than 2 K. Differences in the cloud physics and cloud overlap assumptions result in little bias between the RTMs, but the standard deviation of the differences ranges from 6 to 12 K. Results at 2616 cm(exp -1) at night are reasonably consistent with results at 900 cm(exp -1). Except for RTMs which use full scattering calculations, the bias and histogram correlations at 2616 cm(exp -1) are inferior to those at 900 cm(exp -1) for daytime calculations.

This paper assesses the impact of Advanced Microwave Scanning Radiometer-2 (AMSR2) radiances in the all-sky assimilation of the European Centre for Medium-Range Weather Forecasts (ECMWF). Individual impacts of three microwave imagers including AMSR2 were examined by using a baseline experiment that had no microwave imager data. The three microwave imagers brought similar improvements in humidity, temperature, and wind first guess (FG) fields in the troposphere. Improvements were found both in fits to analyses and to other observations. Moreover, significant improvements of wind and geopotential height fields in the troposphere were found in day 3 to day 6 forecasts. AMSR2 made larger improvements than other microwave imagers to geopotential height forecasts in the northern hemisphere. The use of AMSR2 radiance data in addition to the other existing microwave imagers gave mixed results. Consistent improvements in the FG fit to humidity observations were confirmed. However, the FG fit for several channels of the microwave temperature sounding instruments was degraded. The mean FG departure of AMSR2 showed biases that varied according to time of day and meteorological conditions. The causes of the biases were identified as insufficient representation of cloud liquid water path (LWP) in the forecast model under unstable conditions and insufficient amplitude of LWP diurnal variation in stratocumulus areas in the tropics. The assimilation of too much biased data might start to bring negative effects for the analyses and forecasts, which for some parameters could outweigh the improvements in the assimilation. However despite this AMSR2 brought significant improvements of the geopotential height field in the southern hemisphere lower troposphere for day 5 to day 7 forecasts.

To simulate passive microwave radiances in all-sky conditions requires better knowledge of the scattering properties of frozen hydrometeors. Typically, snow particles are represented as spheres and their scattering properties are calculated using Mie theory, but this is unrealistic and particularly in deep-convective areas, it produces too much scattering in mid frequencies (e.g. 30–50 GHz) and too little scattering at high frequencies (e.g. 150–183 GHz). These problems make it hard to assimilate microwave observations in numerical weather prediction (NWP) models, particularly in situations where scattering effects are most important such as over land surfaces or in moisture sounding channels. Using the discrete dipole approximation to compute scattering properties, more accurate results can be generated by modelling frozen particles as ice rosettes or simplified snowflakes, though hexagonal plates and columns often give worse results than Mie spheres. To objectively decide on the best particle shape (and size distribution) this study uses global forecast departures from an NWP system (e.g. observation minus forecast differences) to indicate the quality of agreement between model and observations. It is easy to improve results in one situation but worsen them in others, so a rigorous method is needed: four different statistics are checked; these statistics are required to stay the same or improve in all channels between 10 GHz and 183 GHz and in all weather situations globally. The optimal choice of snow particle shape and size distribution is better across all frequencies and all weather conditions, giving confidence in its physical realism. Compared to the Mie sphere, most of the systematic error is removed and departure statistics are improved by 10 to 60%. However, this improvement is achieved with a simple “one-size-fits-all” shape for snow; there is little additional benefit in choosing the particle shape according to the precipitation type. These developments have improved the accuracy of scattering radiative transfer sufficiently that microwave all-sky assimilation is being extended to land surfaces, to higher frequencies and to sounding channels.

Both the Goddard Profiling Algorithm (GPROF) and European Centre for Medium-Range Weather Forecasts (ECMWF) one-dimensional + four-dimensional variational analysis (1D+4D-Var) rainfall retrievals are inversion algorithms based on Bayes' theorem. Differences stem primarily from the a priori information. The GPROF uses an observationally generated a priori database whereas ECMWF 1D-Var uses the model forecast first guess (FG) fields. The relative similarity in the two approaches means that comparisons can shed light on the differences that are produced by the a priori information. Case studies have found that differences can be classified into four categories based upon the agreement in the brightness temperatures (Tbs) and in the microphysical properties of cloud water path (CWP) and rainwater path (RWP) space. A category of special interest is when both retrievals converge to similar Tb through minimization procedures but produce different CWP and RWP. The similarity in Tb can be attributed to comparable total water path (TWP) between the two retrievals while the disagreement in the microphysics is caused by their different degrees of constraint of the cloud/rain ratio by the observations. This situation occurs frequently and takes up 46.9% in the 1 month 1D-Var retrievals examined. The two retrievals produce similar spatial patterns but with different magnitude. The allocation of a large amount of CWP in the 1D-Var retrieval seems to be related to the stratiform portion of rain, which is produced by the large-scale condensation scheme. To attain better-constrained cloud/rain ratios and improved retrieval quality, this study suggests the implementation of higher microwave frequency channels in the 1D-Var algorithm. Copyright © 2012 Royal Meteorological Society

The status of current efforts to assimilate cloud- and precipitation-affected satellite data is summarised with special focus on infrared and microwave radiance data obtained from operational Earth observation satellites. All global centres pursue efforts to enhance infrared radiance data usage due to the limited availability of temperature observations in cloudy regions where forecast skill is estimated to strongly depend on the initial conditions. Most systems focus on the sharpening of weighting functions at cloud top providing high vertical resolution temperature increments to the analysis, mainly in areas of persistent high and low cloud cover. Microwave radiance assimilation produces impact on the deeper atmospheric moisture structures as well as cloud microphysics and, through control variable and background-error formulation, also on temperature but to lesser extent than infrared data. Examples of how the impacts of these two observation types are combined are shown for subtropical low-level cloud regimes. The overall impact of assimilating such data on forecast skill is measurably positive despite the fact that the employed assimilation systems have been constructed and optimized for clear-sky data. This leads to the conclusion that a better understanding and modelling of model processes in cloud-affected areas and data assimilation system enhancements through inclusion of moist processes and their error characterization will contribute substantially to future forecast improvement. Copyright © 2011 Royal Meteorological Society, Crown in the right of Canada, and British Crown copyright, the Met Office

This article provides estimates of effective observation errors and their inter-channel and spatial correlations for microwave imager radiances currently used in the European Centre for Medium-Range Weather Forecasts (ECMWF) system. The estimates include the error contributions from the observation operator used in the assimilation system. We investigate how the estimates differ in clear and cloudy/rainy regions. The estimates are obtained using the Desroziers diagnostic. The results suggest considerable inter-channel and spatial error correlations for current microwave imager radiances, with observation errors that are significantly higher than the measured instrument noise. Inter-channel error correlations are even stronger for cloudy/rainy situations, where channels with the same frequency but different polarizations show error correlations larger than 0.9. The findings suggest that a large proportion of the observation error originates from errors of representativeness and errors in the observation operator. The latter includes the errors from the forecast model, which can be significant in the case of humidity or cloud and rain. Assimilation experiments with single SSM/I fields of view highlight how the filtering properties of a four-dimensional variational assimilation system are changed when inter-channel error correlations are taken into account in the assimilation. Depending on the first-guess (FG) departures in the channels used, increments can be larger as well as smaller in comparison with the use of diagonal observation errors. Copyright © 2011 Royal Meteorological Society

The FY-3A microwave temperature sounder (MWTS) suffers from nonlinearities in the calibration of the radiometer and uncertainties in the radiometer passbands. Corrections have been developed and are assessed here by comparing recalibrated MWTS data with equivalent advanced microwave sounding unit-A (AMSU-A) observations. The corrections are effective in improving the first guess departure statistics for MWTS, relative to the original uncorrected data, to values close to those for AMSU-A equivalent channels. In observing system experiments, MWTS observations improve the first guess fits for AMSU-A observations. Forecast verification shows a systematic improvement by using the recalibrated data, e.g. forecasts of 200 hPa geopotential are improved to Day 3 in the SH by approximately 1%. Copyright © 2011 Royal Meteorological Society

This article examines the first-guess (FG) departures of microwave imager radiances assimilated in all-sky conditions (i.e. clear, cloudy and precipitating). Agreement between FG and observations is good in clear skies, with error standard deviations around 2 K, but in heavy cloud or precipitation errors increase to 20 K. The forecast model is not good at predicting cloud and precipitation with exactly the right intensity or location. This leads to apparently non-Gaussian behaviour, both heteroscedasticity, i.e. an increase in error with cloud amount, and boundedness, i.e. the size of errors is close to the geophysical range of the observations, which runs from clear to fully cloudy. However, the dependence of FG departure standard deviations on the mean cloud amount is predictable. Using this dependence to normalise the FG departures gives an error distribution that is close to Gaussian. Thus if errors are treated correctly, all-sky observations can be assimilated successfully under the assumption of Gaussianity on which assimilation systems are based. This ‘symmetric’ error model can be used to provide a robust threshold quality-control check and to determine the size of observation errors for all-sky assimilation. In practice, however, this ‘observation’ error is being used to account for the model's difficulty in forecasting cloud, which really comes from errors in the background and in the forecast model. Hence in future it will be necessary to improve the representation of background and model error. Separately, symmetric cloud amount is recommended as a predictor for bias correction schemes, avoiding the sampling problems associated with ‘asymmetric’ predictors like the FG cloud amount. Copyright © 2011 Royal Meteorological Society

ERA-Interim is the latest global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF). The ERA-Interim project was conducted in part to prepare for a new atmospheric reanalysis to replace ERA-40, which will extend back to the early part of the twentieth century. This article describes the forecast model, data assimilation method, and input datasets used to produce ERA-Interim, and discusses the performance of the system. Special emphasis is placed on various difficulties encountered in the production of ERA-40, including the representation of the hydrological cycle, the quality of the stratospheric circulation, and the consistency in time of the reanalysed fields. We provide evidence for substantial improvements in each of these aspects. We also identify areas where further work is needed and describe opportunities and objectives for future reanalysis projects at ECMWF. Copyright © 2011 Royal Meteorological Society

This article describes a new radiance-assimilation scheme for microwave-imager observations, which unifies the treatment of clear-sky, cloudy and precipitation-affected situations, giving an all-sky approach. This became operational in the four-dimensional variational assimilation (4D-Var) system of the European Centre for Medium-Range Weather Forecasts in March 2009, replacing a previous approach that assimilated radiances in clear skies and 1D-Var retrievals of total column water vapour in clouds and precipitation. The new approach employs moist-physics parametrizations and a multiple-scattering radiative-transfer model in the observation operator for all microwave-imager observations. Observation-operator accuracy, observation-error definition and bias correction, basic observational impact, 4D-Var linearity and stability as well as computational cost are described. Because of careful quality control and relatively large observation errors, the all-sky system produces a weaker observational constraint on moisture analysis than the previous system. However, in single-observation experiments in precipitating areas, using the same observation errors as in the previous 1D-Var retrieval approach, the all-sky system is able to produce 4D-Var analyses that are slightly closer to the observations than before. Despite the nonlinearity of rain and cloud processes, 4D-Var minimizes successfully through the use of an incremental technique. Overall, the quality of the 4D-Var minimization, in terms of number of iterations and conditioning, is unaffected by the new approach. Copyright © 2010 Royal Meteorological Society

This paper assesses the performance of an all-sky (i.e. clear, cloudy and precipitating) direct assimilation of microwave imagers that was introduced operationally in the four-dimensional variational (4D-Var) assimilation system of the European Centre for Medium-Range Weather Forecasts (ECMWF) in March 2009. Results are based on data-denial experiments and are quantified using forecast verification scores and comparisons to observations. The reliability of forecast verification scores is examined. Humidity-based scores can be misleading in the initial three days of forecasts, but scores based on pressure and wind fields are more reliable, because they are less sensitive to the choice of verifying analysis. The new approach is compared with the previous rain and cloud-affected assimilation, which used a 1D+4D-Var technique. One downside of the old technique is that it ‘recycles’ the first guess as new information, which causes misleading ‘improvements’ in forecast scores. The new approach avoids this problem. It also does not require any cloud detection, so unlike the old approach used in clear skies, it is not susceptible to biases caused by undetected cloud. However the new system is implemented with a cautious quality control and large observation errors. Hence, the analysed and forecast tropical humidity fields are constrained only about half as much in the new system as in the old. However, the new approach is comparable in terms of its positive impact on dynamical fields (pressure and vector wind) in the tropical lower troposphere. Copyright © 2010 Royal Meteorological Society

The European Centre for Medium-Range Weather Forecasts (ECMWF) assimilates microwave imager observations for their information on humidity, cloud, and precipitation. However, Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) first-guess (FG) departure biases exhibit a 46-day oscillation with a peak-to-peak amplitude of up to 3 K in brightness temperature, which is linked to the precession of the equator crossing time of the TRMM orbit. The TMI bias has a diurnal cycle, but neither the Special Sensor Microwave Imager nor the Advanced Microwave Scanning Radiometer for the Earth Observing System shows a similar variation, so the bias must be in the TMI instrument itself. Its cause is probably solar heating of the main reflector, which is not perfectly reflective. This means that the instrument measures a combination of Earth emission and the physical temperature of the reflector. This effect has been partly corrected by the data providers, but their correction assumes a constant reflector temperature. In contrast, the ECMWF FG departures suggest that the reflector temperature varies by up to 70 K through the orbit. A method is presented for correcting the bias in the ECMWF assimilation system. It is also noted that when building future conical-scanning microwave imagers, it is important to provide reflectors that are as nonemissive as possible and to also carefully record the reflector's actual (possibly frequency-dependent) emissivity. The in-space temperature of the reflector surface should also be recorded so that it can be used in bias correction.

The assimilation of cloud- and precipitation-affected observations into weather forecasting systems requires very fast calculations of radiative transfer in the presence of multiple scattering. At the European Centre for Medium-Range Weather Forecasts (ECMWF), performance limitations mean that only a single cloudy calculation (including any precipitation) can be made, and the simulated radiance is a weighted combination of cloudy- and clear-sky radiances. Originally, the weight given to the cloudy part was the maximum cloud fraction in the atmospheric profile. However, this weighting was excessive, and because of nonlinear radiative transfer (the “beamfilling effect”) there were biases in areas of cloud and precipitation. A new approach instead uses the profile average cloud fraction, and decreases RMS errors by 40% in areas of rain or heavy clouds when “truth” comes from multiple independent column simulations. There is improvement all the way from low (e.g., 19 GHz) to high (e.g., 183 GHz) microwave frequencies. There is also improvement when truth comes from microwave imager observations. One minor problem is that biases increase slightly in mid- and upper-tropospheric sounding channels in light-cloud situations, which shows that future improvements will require the cloud fraction to vary according to the optical properties at different frequencies.

Mesosphere - stratosphere transport during Southern Hemisphere autumn (March-June 2003) is studied using a pole-centred approach of along-orbit sequences of vertical profiles of methane observations from the Envisat MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument supplemented by meteorological analyses from ECMWF and the Met Office. We hypothesize that the methane distribution can be explained as a combination of two transport processes: (1) isentropic transport in the lower mesosphere and upper stratosphere of methane-rich air from low/mid latitudes to high latitudes during early autumn, and (2) diabatic descent at high latitudes of methane-poor air from the lower mesosphere during autumn. Calculations of stratospheric effective diffusivity provide broad support for this hypothesis. The along-orbit data are shown to provide more information than studies using spatial and temporal averages of the same MIPAS methane data, and to explain anomalous features in the methane distribution, where the vertical gradient is reversed, reported by studies using MIPAS and ILAS-II data. Copyright c � 2009 Royal Meteorological Society

Rain- and cloud-affected Special Sensor Microwave/Imager (SSM/I) observations are assimilated operationally at the European Centre for Medium-Range Weather Forecasts (ECMWF). The four-dimensional variational analysis (4D-Var) assimilates total column water vapour (TCWV) derived from one-dimensional variational retrievals (1D-Var). From the SSM/I radiances, 1D-Var retrieves surface wind and the vertical profiles of temperature, humidity, cloud and precipitation. The main shortcoming of the ‘1D + 4D-Var’ technique is that, of all this information, only TCWV gets into the 4D-Var analysis. More information could be used: the rainwater path agrees well, in an instantaneous comparison, with observations from the precipitation radar on the Tropical Rainfall Measuring Mission. There are other issues, however: the simplified moist physics operators used in 1D-Var produce roughly twice the observed amount of rain, but the problem is masked by a sampling bias, which comes from applying 1D + 4D-Var when the observations are cloudy or rainy, but not when the first guess is rainy or cloudy and the observations are clear. The shortcomings of 1D + 4D-Var will be addressed by moving to a direct 4D-Var assimilation which includes all SSM/I observations, whether clear, cloudy or rainy, in the same stream. Copyright © 2008 Royal Meteorological Society

This paper evaluates the performance of various linear ozone photochemistry parametrizations using the stratosphere-troposphere data assimilation system of the Met Office. A set of experiments were run for the period 23 September 2003 to 5 November 2003 using the Cariolle (v1.0 and v2.1), LINOZ and Chem2D-OPP (v0.1 and v2.1) parametrizations. All operational meteorological observations were assimilated, together with ozone retrievals from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). Experiments were validated against independent data from the Halogen Occultation Experiment (HALOE) and ozonesondes. Additionally, a simple offline method for comparing the parametrizations is introduced. It is shown that in the upper stratosphere and mesosphere, outside the polar night, ozone analyses are controlled by the photochemistry parametrizations and not by the assimilated observations. The most important factor in getting good results at these levels is to pay attention to the ozone and temperature climatologies in the parametrizations. There should be no discrepancies between the climatologies and the assimilated observations or the model, but there is also a competing demand that the climatologies be objectively accurate in themselves. Conversely, in the lower stratosphere outside regions of heterogeneous ozone depletion, the ozone analyses are dominated by observational increments and the photochemistry parametrizations have little influence. We investigate a number of known problems in LINOZ and Cariolle v1.0 in more detail than previously, and we find discrepancies in Cariolle v2.1 and Chem2D-OPP v2.1, which are demonstrated to have been removed in the latest available versions (v2.8 and v2.6 respectively). In general, however, all the parametrizations work well through much of the stratosphere, helped by the presence of good quality assimilated MIPAS observations.

‘Fingerprint’ correlation studies of air temperatures have recently suggested the emergence of climate change patterns that are consistent with those simulated by Global Climate Models. Here we investigate the possibility of searching for climate change patterns within directly observed satellite radiance fields in order to utilise the vast amount of data available. As a first example of a technique which could be employed we extend the commonly used pattern matching statistics to develop a ‘spectral-spatial fingerprint’ method for the detection of climate change. To illustrate the technique, we apply it to two satellite channels: HIRS ch.12, sensitive to upper tropospheric water vapour, and SSU ch.1, sensitive to mid-stratospheric temperatures centred at 15 hPa.

This paper presents results from the first detailed intercomparison of stratosphere-lower mesosphere water vapour analyses; it builds on earlier results from the EU funded framework V "Assimilation of ENVISAT Data" (ASSET) project. Stratospheric water vapour plays an important role in many key atmospheric processes and therefore an improved understanding of its daily variability is desirable. With the availability of high resolution, good quality Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) water vapour profiles, the ability of four different atmospheric models to assimilate these data is tested. MIPAS data have been assimilated over September 2003 into the models of the European Centre for Medium Range Weather Forecasts (ECMWF), the Belgian Institute for Space and Aeronomy (BIRA-IASB), the French Service d'Aéronomie (SA-IPSL) and the UK Met Office. The resultant middle atmosphere humidity analyses are compared against independent satellite data from the Halogen Occultation Experiment (HALOE), the Polar Ozone and Aerosol Measurement (POAM III) and the Stratospheric Aerosol and Gas Experiment (SAGE II). The MIPAS water vapour profiles are generally well assimilated in the ECMWF, BIRA-IASB and SA systems, producing stratosphere-mesosphere water vapour fields where the main features compare favourably with the independent observations. However, the models are less capable of assimilating the MIPAS data where water vapour values are locally extreme or in regions of strong humidity gradients, such as the southern hemisphere lower stratosphere polar vortex. Differences in the analyses can be attributed to the choice of humidity control variable, how the background error covariance matrix is generated, the model resolution and its complexity, the degree of quality control of the observations and the use of observations near the model boundaries. Due to the poor performance of the Met Office analyses the results are not included in the intercomparison, but are discussed separately. The Met Office results highlight the pitfalls in humidity assimilation, and provide lessons that should be learnt by developers of stratospheric humidity assimilation systems. In particular, they underline the importance of the background error covariances in generating a realistic troposphere to mesosphere water vapour analysis.

International audience This paper discusses the highlights of the EU-funded "Assimilation of Envisat data" (ASSET) project, which has involved assimilation of Envisat atmospheric constituent and temperature data into systems based on Numerical Weather Prediction (NWP) models and chemical transport models (CTMs). Envisat was launched in 2002 and is one of the largest Earth Observation (EO) satellites ever built. It carries several sophisticated EO instruments providing insights into chemistry and dynamics of the atmosphere. In this paper we focus on the assimilation of temperature and constituents from Envisat. The overarching theme of the ASSET project has been to bring together experts from all aspects of the data assimilation problem. This has allowed ASSET to address several themes comprehensively: enhancement of NWP analyses by assimilation of research satellite data; studies of the distribution of stratospheric chemical species by assimilation of research satellite data into CTM systems; objective assessment of the quality of ozone analyses; studies of the spatial and temporal evolution of tropospheric pollutants; enhanced retrievals of Envisat data; and data archival and dissemination. Among the results from the ASSET project, many of which are firsts in their field, we can mention: a positive impact on NWP analyses from assimilation of height-resolved stratospheric humidity and temperature data, and assimilation of limb radiances; the extraction of temperature information from the assimilation of chemical species into CTMs; a first intercomparison between ozone assimilation systems; the extraction of information on tropospheric pollution from assimilation of Envisat data; and the large potential of the Envisat MIPAS dataset. This paper discusses these, often novel, developments and results. Finally, achievements of, and recommendations from, the ASSET project are presented.

This paper presents the results from the Observing System Experiments (OSEs) with the current ECMWF data assimilation and modeling system for quantifying the impact on both analysis and forecast quality of Special Sensor Microwave Imager (SSM/I) observations sensitive to moisture and clouds as well as precipitation. SSM/I radiances have been assimilated operationally in clear-sky areas for 8 yr and in cloud- and rain-affected areas since June 2005. This paper examines experiments set up such that clear-sky and rain-affected observations were either added to a baseline with a restricted observing system configuration or withdrawn from the full system. The experiment duration was 10 weeks of which the first 14 days were excluded from the evaluation to allow the system to lose the memory of the initial conditions at day −1. It is shown that both clear-sky and rain-affected observations account for the bulk correction of moisture in the ECMWF analysis. SSM/I data adds 1 day of forecast skill over the first 48 h when evaluated in addition to a baseline-observing system. In the tropics, the rain-affected data contributes more skill to the moisture forecast than the clear-sky data at 700 hPa and above. In the Northern and Southern Hemispheres, the effect is generally weaker and slightly in favor of clear-sky observations. A similar performance can be seen with respect to the wind vector forecast skill, which reflects the connection between the analysis of moisture and dynamics.

The European Centre for Medium-Range Weather Forecasts (ECMWF) provides global analyses of atmospheric humidity from the ground to the lower mesosphere. Unlike in the troposphere, in the stratopshere no humidity observations are assimilated. Humidity analyses here are essentially the results of a free-running model constrained by the ECMWF's well-analysed wind fields. So far only the broad-scale features of the resulting stratospheric water vapour distribution have been validated. This study provides the first in-depth comparison of stratospheric humidity from ECMWF with observations from an airborne microwave radiometer that has measured the distribution of stratospheric water vapour over an altitude range of roughly 15–60 km on several flight campaigns since 1998. The aircraft measurements provide a horizontal resolution that cannot be achieved by current satellite instruments. This study examines dynamical features in the moisture fields such as filamentation and the vortex edge, finding that features in the ERA-40 humidity analyses often do correspond to real atmospheric events that are seen in the aircraft measurements. However, the comparisons also show that in general the ECMWF model produces an unrealistically moist mesosphere. As a result it cannot replicate the descent of relatively dry mesospheric air into the polar vortex in winter and spring.

This paper aims to summarise the current performance of ozone data assimilation (DA) systems, to show where they can be improved, and to quantify their errors. It examines 11 sets of ozone analyses from 7 different DA systems. Two are numerical weather prediction (NWP) systems based on general circulation models (GCMs); the other five use chemistry transport models (CTMs). The systems examined contain either linearised or detailed ozone chemistry, or no chemistry at all. In most analyses, MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) ozone data are assimilated; two assimilate SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) observations instead. Analyses are compared to independent ozone observations covering the troposphere, stratosphere and lower mesosphere during the period July to November 2003. Biases and standard deviations are largest, and show the largest divergence between systems, in the troposphere, in the upper-troposphere/lower-stratosphere, in the upper-stratosphere and mesosphere, and the Antarctic ozone hole region. However, in any particular area, apart from the troposphere, at least one system can be found that agrees well with independent data. In general, none of the differences can be linked to the assimilation technique (Kalman filter, three or four dimensional variational methods, direct inversion) or the system (CTM or NWP system). Where results diverge, a main explanation is the way ozone is modelled. It is important to correctly model transport at the tropical tropopause, to avoid positive biases and excessive structure in the ozone field. In the southern hemisphere ozone hole, only the analyses which correctly model heterogeneous ozone depletion are able to reproduce the near-complete ozone destruction over the pole. In the upper-stratosphere and mesosphere (above 5 hPa), some ozone photochemistry schemes caused large but easily remedied biases. The diurnal cycle of ozone in the mesosphere is not captured, except by the one system that includes a detailed treatment of mesospheric chemistry. These results indicate that when good observations are available for assimilation, the first priority for improving ozone DA systems is to improve the models. The analyses benefit strongly from the good quality of the MIPAS ozone observations. Using the analyses as a transfer standard, it is seen that MIPAS is ~5% higher than HALOE (Halogen Occultation Experiment) in the mid and upper stratosphere and mesosphere (above 30 hPa), and of order 10% higher than ozonesonde and HALOE in the lower stratosphere (100 hPa to 30 hPa). Analyses based on SCIAMACHY total column are almost as good as the MIPAS analyses; analyses based on SCIAMACHY limb profiles are worse in some areas, due to problems in the SCIAMACHY retrievals.

We assess the ability of neural network emulators of physical parametrization schemes in numerical weather prediction models to aid in the construction of linearized models required by four‐dimensional variational (4D‐Var) data assimilation. Neural networks can be differentiated trivially, and so if a physical parametrization scheme can be accurately emulated by a neural network then its tangent‐linear and adjoint versions can be obtained with minimal effort, compared with the standard paradigms of manual or automatic differentiation of the model code. Here we apply this idea by emulating the non‐orographic gravity wave drag parametrization scheme in an atmospheric model with a neural network, and deriving its tangent‐linear and adjoint models. We demonstrate that these neural network‐derived tangent‐linear and adjoint models not only pass the standard consistency tests but also can be used successfully to do 4D‐Var data assimilation. This technique holds the promise of significantly easing maintenance of tangent‐linear and adjoint codes in weather forecasting centers, if accurate neural network emulators can be constructed.