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In this paper, data from spaceborne radar, lidar and infrared radiometers on the “A‐Train” of satellites are combined in a variational algorithm to retrieve ice cloud properties. The method allows a seamless retrieval between regions where both radar and lidar are sensitive to the regions where one detects the cloud. We first implement a cloud phase identification method, including identification of supercooled water layers using the lidar signal and temperature to discriminate ice from liquid. We also include rigorous calculation of errors assigned in the variational scheme. We estimate the impact of the microphysical assumptions on the algorithm when radiances are not assimilated by evaluating the impact of the change in the area‐diameter and the density‐diameter relationships in the retrieval of cloud properties. We show that changes to these assumptions affect the radar‐only and lidar‐only retrieval more than the radar‐lidar retrieval, although the lidar‐only extinction retrieval is only weakly affected. We also show that making use of the molecular lidar signal beyond the cloud as a constraint on optical depth, when ice clouds are sufficiently thin to allow the lidar signal to penetrate them entirely, improves the retrieved extinction. When infrared radiances are available, they provide an extra constraint and allow the extinction‐to‐backscatter ratio to vary linearly with height instead of being constant, which improves the vertical distribution of retrieved cloud properties.

In human biometeorology, the estimation of mean radiant temperature (MRT) is generally considered challenging. This work presents a general framework to compute the MRT at the global scale for a human subject placed in an outdoor environment and irradiated by solar and thermal radiation both directly and diffusely. The proposed framework requires as input radiation fluxes computed by numerical weather prediction (NWP) models and generates as output gridded globe-wide maps of MRT. It also considers changes in the Sun’s position affecting radiation components when these are stored by NWP models as an accumulated-over-time quantity. The applicability of the framework was demonstrated using NWP reanalysis radiation data from the European Centre for Medium-Range Weather Forecasts. Mapped distributions of MRT were correspondingly computed at the global scale. Comparison against measurements from radiation monitoring stations showed a good agreement with NWP-based MRT (coefficient of determination greater than 0.88; average bias equal to 0.42 °C) suggesting its potential as a proxy for observations in application studies.

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Radiation schemes are critical components of Earth system models that need to be both efficient and accurate. Despite the use of approximations such as 1D radiative transfer, radiation can account for a large share of the runtime of expensive climate simulations. Here we seek a new state-of-the-art in speed and accuracy by combining code optimization with improved algorithms. To fully benefit from new spectrally reduced gas optics schemes, we restructure code to avoid short vectorized loops where possible by collapsing the spectral and vertical dimensions. Our main focus is the ecRad radiation scheme, where this requires batching of adjacent cloudy layers, trading some simplicity for improved vectorization and instruction-level parallelism. When combined with common optimization techniques for serial code and porting widely used two-stream kernels fully to single precision, we find that ecRad with the TripleClouds solver becomes 12 times faster than the operational radiation scheme in ECMWF's Integrated Forecast System (IFS) cycle 47r3, which uses a less accurate gas optics model (RRMTG) and a more noisy solver (McICA). After applying the spectral reduction and extensive optimizations to the more sophisticated SPARTACUS solver, we find that it’s 2.5 times faster than IFS cy47r3 radiation, making cloud 3D radiative effects affordable to compute in large-scale models. The code optimization itself gave a threefold speedup for both solvers. While SPARTACUS is still under development, preliminary experiments show slightly improved medium-range forecasts of 2-m temperature in the tropics, and in year-long coupled atmosphere-ocean simulations the 3D effects warm the surface substantially.

Atmospheric radiation is the main driver of weather and climate, yet due to a complicated absorption spectrum, the precise treatment of radiative transfer in numerical weather and climate models is computationally unfeasible. Radiation parameterizations need to maximize computational efficiency as well as accuracy, and for predicting the future climate many greenhouse gases need to be included. In this work, neural networks (NNs) were developed to replace the gas optics computations in a modern radiation scheme (RTE+RRTMGP) by using carefully constructed models and training data. The NNs, implemented in Fortran and utilizing BLAS for batched inference, are faster by a factor of 1–6, depending on the software and hardware platforms. We combined the accelerated gas optics with a refactored radiative transfer solver, resulting in clear‐sky longwave (shortwave) fluxes being 3.5 (1.8) faster to compute on an Intel platform. The accuracy, evaluated with benchmark line‐by‐line computations across a large range of atmospheric conditions, is very similar to the original scheme with errors in heating rates and top‐of‐atmosphere radiative forcings typically below 0.1 K day−1 and 0.5 W m−2, respectively. These results show that targeted machine learning, code restructuring techniques, and the use of numerical libraries can yield material gains in efficiency while retaining accuracy. Plain Language Summary Solar and terrestrial radiation interact with Earth's atmosphere, surface, and clouds and provide the energy which drives climate and weather. Simulating these radiative flows in climate and weather models is crucial and can also be very time‐consuming. One possible way to model radiative effects more efficiently is to use neural networks or similar machine learning algorithms, but predictions are not guaranteed to be realistic because such models do not use physical equations. Here we investigate using neural networks to replace only one part of traditional radiation code, where the optical properties of the atmosphere are computed. We have found that this approach can be several times faster, while still being accurate in various situations, such as simulating future climate. Key Points Neural networks (NNs) were trained to predict the optical properties of the gaseous atmosphere Training data were generated with a recently developed radiation scheme for dynamical models (RRTMGP) RRTMGP‐NN is roughly 3 times faster than the reference code and has a similar accuracy, also in future climate scenarios

The treatment of cloud structure in numerical weather and climate models is often greatly simplified to make them computationally affordable. Here we propose to correct the European Centre for Medium‐Range Weather Forecasts 1D radiation scheme ecRad for 3D cloud effects using computationally cheap neural networks. 3D cloud effects are learned as the difference between ecRad's fast 1D Tripleclouds solver that neglects them and its 3D SPARTACUS (SPeedy Algorithm for Radiative TrAnsfer through CloUd Sides) solver that includes them but is about five times more computationally expensive. With typical errors between 20% and 30% of the 3D signal, neural networks improve Tripleclouds' accuracy for about 1% increase in runtime. Thus, rather than emulating the whole of SPARTACUS, we keep Tripleclouds unchanged for cloud‐free parts of the atmosphere and 3D‐correct it elsewhere. The focus on the comparably small 3D correction instead of the entire signal allows us to improve predictions significantly if we assume a similar signal‐to‐noise ratio for both. Plain Language Summary Solar and terrestrial radiation is the primary driver of the Earth's weather and their detailed representation is essential for improving weather predictions and climate projections. Several aspects, however, such as the flow of radiation through the side of clouds and other three‐dimensional effects are often too costly to compute routinely. In this paper we describe how machine learning can help account for these effects cheaply. Key Points Emulators are used to add 3D cloud effects to the fast 1D radiation solver Tripleclouds cheaply Emulators are trained on 3D cloud effects from SPARTACUS, which is five times slower than Tripleclouds For a 1% slowdown in Tripleclouds' runtime, 3D fluxes are emulated with an average error of about 20%–30%

This paper describes a new radiation scheme ecRad for use both in the model of the European Centre for Medium‐Range Weather Forecasts (ECMWF), and off‐line for noncommercial research. Its modular structure allows the spectral resolution, the description of cloud and aerosol optical properties, and the solver, to be changed independently. The available solvers include the Monte Carlo Independent Column Approximation (McICA), Tripleclouds, and the Speedy Algorithm for Radiative Transfer through Cloud Sides (SPARTACUS), the latter which makes ECMWF the first global model capable of representing the 3‐D radiative effects of clouds. The new implementation of the operational McICA solver produces less noise in atmospheric heating rates, and is 41% faster, which can yield indirect forecast skill improvements via calling the radiation scheme more frequently. We demonstrate how longwave scattering may be implemented for clouds but not aerosols, which is only 4% more computationally costly overall than neglecting longwave scattering and yields further modest forecast improvements. It is also shown how a sequence of radiation changes in the last few years has led to a substantial reduction in stratospheric temperature biases. Plain Language Summary Solar and thermal infrared radiation provide the energy that drives weather systems and ultimately controls the Earth's climate. Accurately simulating these energy flows is therefore a crucial part of the computer models used for weather and climate prediction. This paper describes a flexible and efficient new software package, ecRad, for computing radiation exchange. It became operational in the forecast model of the European Centre for Medium‐Range Weather Forecasts (ECMWF) in July 2017, and is 41% computationally faster than the previous package. This offers the possibility to update the radiation fields in the model simulations more frequently for the same overall computational cost, which we show in turn can improve the skill of weather forecasts. A unique feature for a radiation package of this kind is the ability to simulate radiation flows through the sides of clouds, not just through the base and top, making it well suited as a tool for research into atmospheric radiation exchange. Key Points A new radiation scheme for the ECMWF model is described that is 41% faster than the original scheme We describe how longwave scattering by clouds can be represented with only a 4% increase in computational cost, improving forecast skill A sequence of changes have reduced the long‐standing warm bias in the middle to upper stratosphere of the ECMWF model

A fast, approximate method is described for the calculation of the intensity of multiply scattered lidar returns from clouds. At each range gate it characterizes the outgoing photon distribution by its spatial variance, the variance of photon direction, and the covariance of photon direction and position. The result is that for an N-point profile the calculation is O(N) efficient yet it implicitly includes all orders of scattering, in contrast with the O(Nm/m!) efficiency of models that explicitly consider each scattering order separately for truncation at m-order scattering. It is also shown how the shape of the scattering phase function near 180° may be taken into account for both liquid water droplets and ice particles. The model considers only multiple scattering due to small-angle forward-scattering events, which is suitable for most ground-based and airborne lidars because of their small footprint on the cloud. For spaceborne lidar, it must be used in combination with the wide-angle multiple scattering model described in Part II of this two-part paper.

Spaceborne lidar returns from liquid water clouds contain significant contributions from photons that have experienced many wide-angle multiple-scattering events, resulting in returns appearing to originate from far beyond the end of the cloud. A similar effect occurs for spaceborne millimeter-wave radar observations of deep convective clouds. An efficient method is described for calculating the time-dependent returns from such a medium by splitting the photons into those that have taken a near-direct path out to and back from a single backscattering event (in the case of lidar, accounting for small-angle forward scatterings on the way, as described in Part I of this paper) and those that have experienced wide-angle multiple-scattering events. This paper describes the modeling of the latter using the time-dependent two-stream approximation, which reduces the problem to solving a pair of coupled partial differential equations for the energy of the photons traveling toward and away from the instrument. To determine what fraction of this energy is detected by the receiver, the lateral variance of photon position is modeled by the Ornstein–Fürth formula, in which both the ballistic and diffusive limits of photon behavior are treated; this is considerably more accurate than simple diffusion theory. By assuming that the lateral distribution can be described by a Gaussian, the fraction of photons within the receiver field of view may be calculated. The method performs well in comparison to Monte Carlo calculations (for both radar and lidar) but is much more efficient. This opens the way for multiple scattering to be accounted for in radar and lidar retrieval schemes.

A fast scheme is described to compute the 3-D interaction of solar radiation with vegetation canopies. The canopy is split in the horizontal plane into one clear region and one or more vegetated regions, and the two-stream equations are used for each, but with additional terms representing lateral exchange of radiation between regions that are proportional to the area of the interface between them. The resulting coupled set of ordinary differential equations is solved using the matrix-exponential method. The scheme is compared to solar Monte Carlo calculations for idealized scenes from the RAMI4PILPS intercomparison project, for open forest canopies and shrublands both with and without snow on the ground. Agreement is good in both the visible and infrared: for the cases compared, the root-mean-squared difference in reflectance, transmittance and canopy absorptance is 0.020, 0.038 and 0.033, respectively. The technique has potential application to weather and climate modelling.