## 1. Introduction

In atmospheric general circulation models, the representation of the radiation transfer within the atmosphere is usually the most expensive among the various parameterizations of the physical processes. If the impact of the radiation transfer were to be computed for every grid point and at all time steps, it would generally require as much central processing unit (CPU) time or more than the rest of the model dynamical and other physical parameterizations. Traditionally, to limit this radiation burden, radiation transfer is only computed every few model hours. For example, with full radiation computations performed every 2 h at all grid points, radiation transfer accounts for 27% of the run time of the “GME” forecast model (Majewski et al. 2002).

The recent introduction of the McRad package for radiation computations (Morcrette et al. 2008) in the Integrated Forecasting System (IFS) has increased the cost of the radiation computations and required revisiting the use of the interface between radiation and the rest of the model, for the various meteorological applications run at the European Centre for Medium-Range Weather Forecasts (ECMWF). A flexible interface introduced in 2003 allows for delocalized radiative computations with a potential increase in the computer efficiency of the model through a spatial representation of the radiation transfer differing from that of the other physical processes.

This paper first presents in section 2 how various approaches have been used over the years to manage the cost of the radiation computations, leading to the present interface. Section 3 describes the strategy used, and the resulting interface between the radiative parameterizations and the rest of the model is described in more detail in the appendix. Then the impact of this new interface is discussed for different configurations of the model, including medium-resolution forecasts as used in the Ensemble Prediction System in section 4, high-resolution 10-day forecasts in section 5, and annual simulations at low resolution without and with a coupled ocean model in sections 6 and 7. A summary and conclusions are given in section 8.

## 2. Controlling the cost of radiation calculations in the ECMWF model: Historical background

At ECMWF, the interface for radiation computations in the IFS has evolved over the years to accommodate changes in computer architecture. A description of this evolution including technical details is given in the appendix.

Prior to the mid-1990s, full radiation computations were done every 3 h for all latitude lines in a rectangular grid, with a horizontal sampling one point out of four in the longitudinal direction. On this sampled radiation grid, a shortwave (SW) transmissivity was computed at the layer interface by dividing the net SW flux by *μ _{m}*, the cosine of the solar zenith angle at the midpoint of the time interval between two full radiation calculations. These full radiation quantities were then interpolated back to the normal physical grid. The net longwave fluxes were kept fixed between two full radiation time steps whereas the net SW fluxes were evaluated at every time step. For every time step within the period between two full radiation computations, the net SW fluxes were obtained by multiplying the SW transmissivity by

*μ*relevant for the time step and grid point. This approximate treatment therefore was making the radiation fields interact with cloudiness only every 3 h, and further was introducing spatial smoothing of the cloud–radiation interactions.

_{t}From September 1991, the ECMWF model started to use a reduced horizontal grid for all its computations, keeping roughly the same grid size (in kilometers) when going from the equator to the Poles (Hortal and Simmons 1991). On input, model fields required by the radiation package were still sampled on each latitude with one point out of four being selected in subtropical and tropical areas. To accommodate this radiation grid the previous frequency of one in four reduced gradually to every point in polar areas. On output, Lagrangian cubic interpolation was used. From September 1991 to October 2003, full radiation computations were only performed every 3 h (every hour during the first 12 h after June 2001) and on that reduced spatial grid (Morcrette 2000). For a given model horizontal resolution, an increase in model vertical resolution leads to a reduced time step. As full radiation computations are called with a given frequency independent of the time step, the relative cost of the radiation transfer (if dealt with using two-stream radiation codes as at ECMWF) therefore decreases relative to the total cost of a model integration with an increase in the model vertical resolution. In September 2004, the frequency of full radiation computations was decreased to 1 h, and in the ECMWF *T _{L}*511

*L*60 model operational until January 2006, radiation transfer represented about 10% of the computer time.

A neural network approach to the longwave radiation transfer was also tested in the ECMWF model (Chevallier et al. 2000) and was found to give adequate results (sufficient accuracy together with a sixfold decrease in the computer time for the longwave radiative calculations) at low to medium vertical resolution (up to 50 layers). At 60 layers and above (the vertical resolution since December 2001), both accuracy and rapidity could not be kept at once given the increased nonlinearity in the lowest and uppermost atmospheric layers. Consequently the neural network approach is used only for the four-dimensional variational data assimilation (4DVAR) linearized physics (Janisková et al. 2002) when the accuracy requirements are weaker.

## 3. A reduced grid for radiation computations

A new interface for radiation computations was developed and implemented in October 2003. Radiation calculations are performed on a grid with a coarser resolution than the current model grid. Interpolation between model and radiation grids are performed using interfaces existing within the IFS libraries and as a result help reduce code maintenance.

This radiation grid has been used since October 2003, with a coarsening factor of 2 in both latitude and longitude w.r.t. the rest of the model. With the continuous increase in both horizontal and vertical resolutions, the time step is simultaneously reduced—to Δ*t* = 12 min for the *T _{L}*799

*L*91 model [spectral truncature of order 799, corresponding to a physical grid (0.225°)

^{2}, with 91 levels on the vertical] operational since February 2006—so the radiation parameterizations, now being called every hour, saw their fractional cost decreasing (7.3% of the total computer time for the above configuration), but this limited cost was obtained through the use of a radiation grid twice as coarse as the grid for the rest of the model. In consequence, the

*T*799

_{L}*L*91 model was run with a radiation grid at

*T*399, in the following referred to as

*R*399.

The operational implementation in June 2007 of a new more-computer-intensive radiation package (McRad; Morcrette et al. 2008) with an increased number of spectral intervals (16 in the longwave, 14 in the shortwave radiation parts of the spectrum) in all the ECMWF forecasts applications has led to the search for an optimal radiation grid for each of the different weather forecasting applications run at ECMWF.

Table 1 presents for the various model configurations used at ECMWF an overview of the timing with and without McRad. Depending on the model resolution, associated time step, and the frequency for calling the full radiation schemes, the cost of the model integration increased from 15% to 27% with the adoption of McRad. Comparisons of results with the different radiation grids were systematically carried out (from *R*399 to *R*95 for the *T _{L}*799

*L*91 high-resolution model, from

*R*255 to

*R*31 for the

*T*399

_{L}*L*62 model run in the Ensemble Prediction System, and from

*R*159 to

*R*31 for the

*T*159

_{L}*L*91 model used for annual simulations and seasonal forecasts).

For the choice of the radiation grid, a compromise has to be made between the computer time required to run a given configuration and how detailed one wants the representation of the spatial cloud structure and of its associated radiative fluxes to be. Different meteorological applications lead to different answers: for the high-resolution deterministic forecast where the position of clouds as affected by land–sea temperature and orographic effects is an important factor, the highest radiation resolution is to be kept as much as possible. However, it must be kept in mind that McRad as such allows subgrid-scale information on the horizontal distribution of cloud elements to be taken into account (via the standard deviations of the cloud fraction and associated condensed water divided by their respective mean), so what appears as a reduced radiation grid in fact includes more information than the original radiation grid used with the pre-McRad scheme (Morcrette et al. 2008). For EPS, the constraint to have the highest radiation resolution possible can certainly be relaxed. The impact of such a reduction appears in the next section. A best compromise was chosen (e.g., *R*319 for *T _{L}*799,

*R*95 for

*T*399, and

_{L}*R*63 for

*T*159), which allows the maximum benefit of McRad within the main time constraint in an operational environment: the on-time delivery of the various operational products.

_{L}The impact of coarsening the radiation grid on the objective scores provided by high-resolution models and on results relevant to the other meteorological applications [EPS; seasonal (up to 9 months) and annual simulations] is addressed in the following sections.

## 4. Impact on medium-resolution 10-day forecasts as used in the EPS

As discussed in Buizza et al. (1999), for each of the 50 forecast members of the EPS, the model uncertainties deriving from parameterized physical processes are simulated by applying a random number between 0.5 and 1.5 to the sum of the physical tendencies within a 10° × 10° box over 3 h. The scaled physical tendencies are then passed to the thermodynamic equation to be solved. Therefore, introducing a more approximate treatment of the radiation tendencies (as through the use of a more reduced radiation grid) is not likely to deteriorate the quality of the EPS forecasts. The central panel in Table 1 shows the various radiation resolutions from *R*255 down to *R*31 that could be used for the current *T _{L}*399

*L*62 EPS configuration.

In a series of 92 10-day single forecasts with McRad running the *T _{L}*399

*L*62 model (i.e., the horizontal and vertical resolution of the IFS in the EPS) with various resolutions for the radiation grid, the impact on the objective scores was small. For example, Fig. 1 presents the rmse of the temperature at 850 and 200 hPa (the most sensitive parameter) in the tropics for sets of 92 forecasts starting every fourth day spanning a year from 2 February 2006. For these sets of forecasts with the resolution of the radiation grid being reduced from

*R*255 to

*R*31, the impact on the geopotential is small and does not appear before day 6 of the forecasts (not shown). Similarly small is the impact on the rmse of temperature at 850 and 200 hPa. Only the mean error in temperature at 850 hPa for all areas (Northern and Southern Hemispheres, tropical area) and the mean error in temperature at 200 hPa in the tropics show a distinct signal. However, the difference between

*R*255 and

*R*31 [i.e., a radiation grid coarsening from (0.70°)

^{2}to (5.625°)

^{2}] is at most 0.06 K, with the resolutions between

*R*255 and

*R*63 very close to each other, and

*R*47 and

*R*31 showing a more undesirable impact. In the tropics, where these differences in temperature between the various radiation grids are the most marked, the impact on the wind is very small (not shown). So it appears that reducing the resolution of the radiation grid could allow for a decreased cost of the EPS with a rather small effect on its overall quality. Given the impact of the radiation grid in the above series of single forecasts, it should translate into an impact on the EPS forecasts at similar resolutions, albeit dampened by the sample size of forecasts run from perturbed initial conditions.

Further tests were conducted within the variable-resolution EPS (VarEPS) system (Buizza et al. 2007) running for 10 days at *T _{L}*399, then at

*T*255 for the last 5 days using three sets of radiation grids:

_{L}*R*159/

*R*95,

*R*95/

*R*63, and

*R*47/

*R*31, respectively. Ensemble forecasts including 51 members (the unperturbed forecast plus the 50 ones with perturbed initial conditions) were started every other day between 3 December 2006 and 2 January 2007 (16 cases). As shown in Fig. 2, the low-resolution radiation configuration

*R*47/

*R*31 indeed produces an obvious deterioration of the ranked probability skill score of the temperature at 850 hPa in the Southern Hemisphere, whereas the other two configurations are very similar. Individual forecasts were checked with only very small differences between

*R*159/

*R*95 and

*R*95/

*R*63. The EPS, operational since 5 June 2007, is therefore run at

*T*399

_{L}*L*62

*R*95 then at

*T*255

_{L}*L*62

*R*63.

## 5. Impact on high-resolution T_{L}799L91 10-day forecasts

_{L}

Results in terms of objective scores (i.e., anomaly correlation at different geopotential heights, rmse and mean errors in temperature and winds) when the radiation resolution is reduced, are not shown for the *T _{L}*799

*L*91 forecasts as they are as or more consistent than for the model at

*T*399

_{L}*L*62 discussed in the previous section. Here the emphasis is put on the impact on the so-called surface parameters, the model parameters that can be verified against measurements at synoptic stations. Table 2 presents the statistics [i.e., bias, standard deviation (SD), and mean absolute error (MAE)] computed for sets of 31 forecasts for January 2007 for a model with a radiation grid varying between

*R*511 and

*R*95. Table 2 shows that for these parameters, the impact of a reduction of the radiation grid is very small at the beginning of the forecasts, when the model behavior is largely led by the initial conditions and gets slightly larger during the forecasts. However, even at day 5 (FC + 108 h and FC + 120 h), the variations in the statistics introduced by the reduction in the radiation grid are small showing that the overall circulation patterns and the three-dimensional distribution of the radiative heating have not had sufficient time to diverge much.

## 6. Impact on annual simulations at T_{L}159L91 with specified SSTs

_{L}

Sets of 13-month simulations at *T _{L}*159

*L*91 starting 30 h apart from 0000 UTC 1 August 2000 to 1800 UTC 4 August 2000 were run with the sea surface temperature updated every day, and with the radiation grid varying from

*R*159 to

*R*31 (see bottom panel of Table 1). The difference in the 40-yr ECMWF reanalysis (ERA-40; Uppala et al. 2005) of the zonally averaged temperature (Fig. 3), zonal wind (Fig. 4), and vertical velocity (Fig. 5) shows that a large reduction in the radiation grid resolution does not markedly affect the annual mean climate. This is confirmed by the differences in various globally averaged parameters presented as annual means in Table 3. Results for seasonal means [December–February (DJF) and June–August (JJA)] are very similar and are not shown.

For the radiative fluxes at the top of the atmosphere, the differences to the corresponding Clouds and the Earth’s Radiant Energy System (CERES) observations are less than 0.4 W m^{−2} for the outgoing longwave radiation, less than 0.8 W m^{−}^{2} for the absorbed shortwave radiation, and less than 0.3 and 0.8 W m^{−}^{2} for the longwave and shortwave cloud forcing. The differences in the Special Sensor Microwave Imager (SSM/I) observations for the total column water vapor and total cloud liquid water and those in the International Satellite Cloud Climatology Project (ISCCP) C2 observations for the total cloud cover remain very similar when going from *R*159 to *R*31. Differences to observations for total precipitation [Global Precipitation Climatology Project (GPCP)], 2-meter temperature (T2m), and dewpoint temperature (DT2m; the last two from ERA-40) also show little dependence on the radiation grid. Finally, the components of the surface energy budget over the ocean show a small dependence on the resolution of the radiation grid, also seen on the maps of the difference of the surface net heat flux with the Da Silva and Levitus’s (1994) climatology (Fig. 6). For all parameters, the geographical location of the differences with observations is a steady feature when changing the resolution of the radiation grid (not shown).

## 7. Impact on multiannual and 9-month simulations at *T*_{L}159*L*62 with an ocean model

_{L}

Sets of 2-yr simulations were also run with the T* _{L}*159L62 atmospheric model coupled to an ocean model (Vialard et al. 2005). The ocean model has a horizontal resolution of 2° × 2° and 20 levels in the vertical. The coupled model was run with the

*R*159,

*R*63, and

*R*31 radiation grids. Figure 7 presents the differences with ERA-40 of the sea surface temperature (SST) averaged over the first and second year. For the radiation resolution varying from (1.125°)

^{2}to (2.8125°)

^{2}to (5.625°)

^{2}, the impact on the SST is small, as the error patterns are very similar from one radiation resolution to the other. From the first year, the Southern Ocean is too warm by up to 2 K, with too high SSTs also appearing in the tropics, whereas the midlatitudes of the Northern Hemisphere display SSTs that are too cold between 0.3 and 1.5 K. In the second year, the areas with too warm SSTs shrink and concern only the Southern Ocean south of 60°S and limited areas along the equator. However, these signals are consistent whatever the radiation resolution, corroborating the results found for the model with specified SSTs in section 5. A radiation grid of

*R*63 appears adequate for the operational application, given that, in that case, the coupled model is used within an ensemble prediction system to provide seasonal (up to 9 months) forecasts. It is worth emphasizing that the above results concern only seasonal- and annual-range simulations. The impact of a reduced radiation grid on long-term (10 yr and more) climate simulations involving an ocean model is out of the scope of this study.

## 8. Summary and conclusions

Radiation transfer is usually one of the most expensive parameterizations in the numerical atmospheric model. At ECMWF, over the years with changing computer environments, various strategies have been used to keep the fraction of the computation time devoted to radiation transfer under control. The cost of the radiation computations depends on the horizontal and vertical resolutions of the model. It also depends on the frequency at which full radiation computations are carried out, with intermediate time steps receiving radiation tendencies derived from temporally interpolated fluxes.

This paper has looked at an approach in which radiation transfer, thanks to a very flexible interface, can be computed at a lower spatial resolution than the rest of the physical tendencies.

Results of seasonal and annual simulations have been shown to be free of systematic differences linked to the spatial interpolation and to the coarser resolution of both the inputs to and the outputs from the radiation transfer schemes. When the radiation fluxes and tendencies are considered, averaged over a season, there are differences, but usually much smaller than can be found for a change in cloud optical properties and/or the radiation scheme (Morcrette et al. 2001, 2008). Furthermore, the new interpolation strategy, by using spatially averaged quantities as inputs, is a better framework to tackle the spurious behavior sometimes generated by the previously operational sampling scheme, when heavy precipitation could appear over islands due to a mismatch between the atmospheric profiles feeling the orography and surface forcing representative of ocean conditions.

With the new and more computer intensive McRad package, the versatile interface between radiation and the rest of the model is now used with various radiation resolutions depending on the application. For the high-resolution deterministic model run at *T _{L}*799

*L*91, the radiation grid has been reduced to

*R*319 without any detrimental impact on the quality of the forecasts as judged from the objective scores and comparisons of surface parameters with observations.

In high-resolution *T _{L}*799

*L*91 10-day forecasts, the differences in the objective scores for a change of radiation grid down to

*R*319 are very small and only appear in the last 2 days of the 10-day forecasts. Impact on analyses and on 2-m temperature around coastline or orographic features is small and only reaches 1 K for the coarsest spatial interpolation used. For the EPS run at

*T*399

_{L}*L*62, given the approach used to deal with the physical tendencies, a more drastic reduction on the resolution of the radiation grid (down to

*R*95) has been shown to have very limited impact of the quality of the forecasts. At the low resolution used for testing the impact of model developments on the model climate, it was shown that running the model at

*T*159 with an

_{L}*R*159 radiation grid does not bring obvious improvements when the sea surface temperature is specified, and that an

*R*63 radiation grid is adequate for such sensitivity studies.

At the same low resolution, in seasonal forecasts with a coupled ocean, the signal brought by the different radiation grids is far from systematic, and it would be necessary to run a much more extended set of simulations to get statistical significance. However, given that the seasonal forecasts are also run as an ensemble from perturbed initial conditions, the *R*63 radiation grid for the *T _{L}*159 model is a good trade-off between accuracy and efficiency.

## Acknowledgments

At ECMWF, A. Ghelli produced some of the statistics presented in section 4; A. Weisheimer and F. Doblas-Reyes helped with running the integrations with the coupled ocean model; P. Bougeault, M. Miller, and A. Beljaars are thanked for their comments on the manuscript, and R. Hine is thanked for his help on the figures.

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## APPENDIX

### Details of the Radiation Interface

At ECMWF, the interface for radiation computations in the Integrated Forecasting System has evolved over the years to accommodate changes in computer architecture.

- Prior to the mid-1990s, ECMWF’s computer systems were CRAY vector systems having up to 16 processors accessing a single shared memory. The parallelization strategy for gridpoint computations (i.e., physics including radiation and dynamics) on these systems was implemented by assigning full latitudes dynamically to processors via a macrotasking interface. For the radiation calculations, inputs were interpolated from the regular model grid to the radiation grid by a fast Fourier transform (FFT) and likewise outputs from the radiation grid to the model grid. In this configuration, the full radiation computations, done every 3 h, were carried out for all latitude lines with a horizontal resolution 4 times as low in the longitudinal direction. On this reduced radiation grid, a shortwave transmissivity was computed at the layer interface by dividing the net SW flux by
*μ*, the cosine of the solar zenith angle at the midpoint of the time interval between two full radiation calculations. These full radiation quantities were then interpolated back using an inverse FFT to the normal physical grid. The net longwave fluxes were kept fixed between two full radiation time steps whereas the net SW fluxes were evaluated at every time step. For every time step within the period between two full radiation computations, the net SW fluxes were obtained by multiplying the SW transmissivity by*μ*relevant for the time step and grid point. This approximate treatment therefore made the radiation fields interact with cloudiness only every 3 h, and further introduced spatial smoothing of the cloud–radiation interactions. - From September 1991, the ECMWF model started to use a reduced horizontal grid for all its computations, keeping roughly the same grid size (in kilometers) when going from the equator to the Poles (Hortal and Simmons 1991). The change in distributed memory vector systems (Fujitsu VPP700/VPP5000) presented a problem for the above scheme on the reduced horizontal grid as a two-dimensional partitioning of gridpoint space required on these systems meant that only a subset of points on each latitude was directly accessible. Furthermore, the message passing to gather full latitudes for the above FFTs was considered an unacceptable overhead. The solution to these problems was found by a combination of separating the radiation calculations from the physics call tree and providing new interpolation options for radiation input and output. On input, model fields required by the radiation package were sampled at each latitude with one point out of four being selected in subtropical and tropical areas. To accommodate the reduced model grid this frequency of one in four reduced gradually to every point in polar areas. This latter requirement resulted in a substantial load imbalance for radiation calculations, which was resolved by message passing to distribute radiation points evenly (Dent and Mozdzynski 1996). On output, Lagrangian cubic interpolation was used, which required some further message passing (albeit the nearest neighbor). On the whole this scheme has worked efficiently on both vector systems with less than 100 processors and scalar systems with about 1000 processors. The only real drawback was the complexity of the message passing, which was a direct result of the use of a nonstandard grid for radiation calculations (i.e., the sampled grid). Some concern was also raised with regard to the sampling approach, in particular the issue that sampling was only implemented east–west and not north–south.
- The new (October 2003) interface for radiation computations was developed to address some deficiencies of the scheme described above, by use of a standard IFS model grid for radiation calculations. With this interface, radiation calculations are performed on a grid with a coarser resolution than the current model grid. Interpolation between model and radiation grids are performed using interfaces existing within the IFS libraries and as a result this reduces future code maintenance.

By using such a standard grid for radiation calculations, there is no longer a load balance issue as each processor is given an equal number of grid points for both model and radiation grids. Interpolation options provided include spectral transform, 4-point bilinear, and 12-point bidimensional interpolation. It is to be noted that the spectral transform option is provided for debugging purposes only—in the ECMWF spectral model it was the most straightforward option to implement and it simplified the development and testing of the other options. It is also the most expensive in respect of CPU time and memory use. The technical aspects of the transformation package including these last two interpolations are described in Hamrud (2001). The 12-point bidimensional interpolation is used operationally.

Impact of the McRad radiation package on the timing of the ECMWF model forecasts for different configurations and different horizontal resolutions. Dyn is the resolution for the dynamics, Rad is that for the radiation. Freq is the frequency (hour) for calling the full radiation scheme, and %Rad is the fraction of computer time taken by the radiative transfer calculations. Ratio is the factor by which McRad increases the computer cost relative to the previous operational configuration (CY31R2). Boldface refers to the operational configuration implemented on 5 Jun 2007. For a given spectral truncature *T,* the corresponding linear physical (or radiation) grid is given by [180/(*T* + 1)]^{2}.

Comparison of surface parameters with values at the synoptic stations over Europe. Results are for sets of *T _{L}*799 L91 10-day forecasts for January 2007, with a radiation grid varying from

*R*511 to

*R*95.

*TCC*is the total cloud cover (in oktas), T2m is the 2-m temperature (K), Q2m is the 2-m specific humidity (g kg

^{−1}), and W10m is the 10-m wind (m s

^{−1}). The bias, SD, and MAE are given for every variable, every radiation grid resolution, and all forecast times.

Annual mean results (Sep 2000–Aug 2001) from sets of four 13-month simulations at *T _{L}*159

*L*91 with different radiation grids from

*R*159 to

*R*31. On the top line, Obs is the observational value given for each parameter and Clim is the climatological value for ocean surface parameters. Below are the bias and in parentheses, the standard deviation of the model value w.r.t. the Obs or Clim value. The radiative fluxes at the top-of-the-atmosphere (TOA) [i.e., outgoing longwave radiation (OLR), absorbed shortwave radiation (ASW), longwave cloud forcing (LWCF), and shortwave cloud forcing (SWCF); W m

^{−2}] are compared with equivalent CERES measurements. The total cloud cover (TCC) is compared with ISCCP D2 data, and the total column water vapor (TCWV; kg m

^{−2}) and total column liquid water (TCLW; g m

^{−2}) are compared with SSM/I data. The total precipitation TP (mm day

^{−l}) is compared with GPCP data and the temperature and dewpoint temperature at 2 m, T2m and DT2m (K) are compared with ERA-40 values. The ocean surface fluxes [i.e., surface net shortwave radiation (SSR), surface net longwave radiation (STR), surface sensible heat flux (SSH), surface latent heat flux (SLH), and net heat flux SNET (W m

^{−2})] are compared with the Da Silva–Levitus climatology. All means, biases (and rms when available) refer to averages over the 50°N–50°S latitude band.