Seasonal range test run with Global Eta Framework

Global Eta Framework (GEF) is a global atmospheric model developed in general curvilinear coordinates and capable of running on arbitrary rectangular quasi-uniform spherical grids, using stepwise (“Eta”) representation of the terrain. In this study, the model is run on a cubed-sphere grid topology, in a version with uniform Jacobians (UJ), which provides “equal-area” grid cells, and a smooth transition of coordinate lines across the edges of the cubed-sphere. Within a project at the Brazilian Center for Weather Forecasts and Climate Studies (CPTEC), a nonhydrostatic version of this model is under development and will be applied for seasonal prediction studies. This note describes preliminary tests with the GEF on the UJ cubed-sphere in which model performance is evaluated in seasonal simulations at a horizontal resolution of approximately 25 km, running in the hydrostatic mode. Comparison of these simulations with the ERA-Interim reanalyses shows that the 850 hPa temperature is underestimated, while precipitation pattern is mostly underestimated in tropical continental regions and overestimated in tropical oceanic regions. Nevertheless, the model is still able to well capture the main seasonal climate characteristics. These results will be used as a control run in further tests with the nonhydrostatic version of the model.


Introduction
Global Eta Framework (GEF) is a global atmospheric model, based on general curvilinear coordinates and thus capable of running on various rectangular spherical grids, developed by Zhang and Rančić (2007).This model is chosen for a study with the objective to estimate the effects of higher-resolution treatment of convection on seasonal prediction skills.To this end, the GEF, operating in the cubed-sphere version, will be supplied with a nonhydrostatic option and run at very high resolutions in seasonal simulations.Sadourny (1972) suggested application of cubed-sphere, whose grid topology was promising a major increase of computational efficiency in the general circulation models of the atmosphere.The interest in application of cubed-sphere was renewed during the 1990s, with the advent of parallel computing, because the grid uniformity and the geometrical symmetry made this grid very attractive for application of parallel computing paradigm.In comparison, the standard longitude-latitude grid requires application of Fourier filtering around poles, which, on the massively parallel computers, degrades com-putational efficiency.A series of papers appeared, suggesting application and various improvements of the cubed-sphere: Rančić et al. (1996) and McGregor (1996) designed a conformal cubed-sphere; Ronchi et al. (1996) found a new way to use the original Sadourny's gnomonic cubed-sphere; Purser and Rančić (1998) suggested an improvement of the conformal cubed-sphere which was used in the first version of GEF in 2007.The current version of the model uses a further improvement that provides an "equal-area" cubed-sphere, without angular discontinuities across the edges of the cube (Purser and Rančić, 2011;Purser et al., 2014;Rančić et al., 2017) (Fig. 1).
The Brazilian Center for Weather Forecasts and Climate Studies (CPTEC) has been using a spectral global model (Bonatti, 1996) to provide weather and seasonal climate forecasts since the beginning of the center operational activities.The seasonal forecasts at CPTEC are currently produced by an ensemble of global atmospheric model (Cavalcanti et al., 2002), an ensemble of coupled ocean-atmosphere model (Siqueira and Nobre, 2006), and an ensemble of the regional Eta model (Chou et al., 2005).The high computational de- mand of the spectral model for long-term simulations limits the CPTEC global models to the coarse resolution of about 200 km.The GEF development at CPTEC for seasonal forecasts is a future, less computationally demanding alternative for the operational seasonal forecasts at the center.
The objective of this work is to evaluate the GEF model on the UJ cubed-sphere in seasonal range simulations at a 25 km horizontal resolution.
2 Comparison of GEF with the regional Eta model GEF represents a globalization of the regional Eta model (Mesinger, 1974(Mesinger, , 2000;;Janjić, 1984Janjić, , 1990Janjić, , 1994;;Mesinger et al., 1988Mesinger et al., , 2012;;Mesinger and Lobocki, 1991;Black, 1994;Chen et al., 1997;Chou et al., 2000Chou et al., , 2002Chou et al., , 2005Chou et al., , 2012;;Ek et al., 2003;Bustamante and Chou, 2009;Gomes and Chou, 2010;Pesquero et al., 2010;Doyle et al., 2013;de Andrade Campos et al., 2017;Lyra et al., 2017;Mesinger and Veljovic, 2017;Pilotto et al., 2017).The unique feature of the Eta model is a stepwise formulation of terrain, which was introduced with the idea to reduce the error of pressure gradient force of the sigma system in the presence of steep mountains, but turned out to offer many other advantages.For example, in one of recent tests (Mesinger and Veljovic, 2017), it is shown that in a situation of a major topographic impact, upper level trough crossing Rocky Mountains, the Eta model in ensemble experiments outperformed its ECMWF driver members to the extent that a number of times all 21 Eta ensemble members placed strongest 250 hPa winds more accurately than their ECMWF driver members.A problem of flow separation in the lee of the bell-shaped topography, dis- covered by Gallus Jr. and Klemp (2000), has been removed by a refinement of the eta discretization, referred to as "sloping steps" but in fact a simple version of a cut-cell scheme (Mesinger and Jović, 2002;Mesinger et al., 2012;Mesinger and Veljovic, 2017).The step-terrain approach is especially important in the case of areas where weather conditions are strongly affected by high mountains, such as the Andes in South America.Therefore, this is one of the reasons for choosing the Eta approach in this study.Being an efficient, global version of the regional Eta model, GEF seems appropriate for seasonal climate studies over this area.Although it is built upon the Eta model, GEF at present still does not employ sloping steps (Mesinger et al., 2012).Other differences in comparison with the regional Eta model are that GEF is reformulated in terms of general curvilinear coordinates and uses the Arakawa B-grid for distribution of variables (Arakawa and Lamb, 1977, Fig. 2), while the regional Eta model is designed in longitude-latitude grid and uses the E-grid.

Preliminary results and discussion
A preliminary evaluation reported in Latinović et al. (2013) verified model capability to simulate extreme climate events and stability in long-term, low-resolution ( ∼ 230 km) climate type runs.With a new, "equal-area" grid and increased resolution (∼ 25 km), continuous seasonal (90-day) runs were performed (Fig. 3).
The initial condition used was 00:00 UTC 9 February 1996.Figure 3 shows globally averaged 850 hPa temperature, 850 hPa wind and 200 hPa wind from GEF simulation in comparison against ERA-Interim reanalyses (Dee et al., 2011).The time series of 850 hPa temperature show that the global mean values are slightly underestimated when compared with reanalysis, although they follow the trend of seasonal increase/decrease, exactly like in the reanalysis.In addition, the simulated time series of 850 hPa temperature shows a phase lag of a few days at the beginning of integration before it reaches the state of equilibrium and later it continues to vary around 1-2 • C lower than the reanalysis.The significant difference between GEF and ERA-Interim temperatures in at the beginning of the integration is probably a consequence of different discretization and vertical interpolations of temperature in GEF.The model uses geopotential  height to calculate temperature and vertically interpolates it to the levels of the model.In the post-processing phase, another vertical interpolation is applied to the temperature from model levels to the standard pressure levels.Wind magnitude compares reasonably with the reanalysis both in the lower and upper troposphere.The 850 hPa mean wind simulation follows approximately the reanalysis, but mostly underestimates and occasionally overestimates, especially at the beginning of integration, when the differences reach at most about 1.5 m s −1 .In contrast, the simulated 200 hPa mean wind shows underestimate by up to 4 m s −1 .Figure 4 shows that the global pattern of the seasonal mean precipitation agrees relatively well with the observed precipitation from GPCP (Global Precipitation Climatology Project).However, model produces a significant overestimate, mostly in the tropical oceanic regions, and produces some underestimate in tropical continental regions, especially in parts of Africa and South America, where it fails to represent typical pattern of precipitation on each continent.
These results show the model ability to perform simulations at an increased horizontal resolution using an upgrade of the cubed-sphere, and demonstrate the model stability in the long-term, seasonal run.It is important to mention that this is the first seasonal run made with the GEF.Further adjustments in convective parameterization schemes are planned in order to improve precipitation simulation, but the main focus will be on inclusion of nonhydrostatic effects and the further increase of horizontal resolution.

Conclusions and further plans
Preliminary results show that GEF is capable of producing reasonable results over seasonal range running at high resolution.It is important to point out that all simulations were performed with relatively modest use of computational resources, 600 processor cores.We see these results as encouraging and it is expected that with the inclusion of the nonhydrostatic mode, GEF will improve on the seasonal predictions at higher horizontal resolution.The method of Janjić et al. (2001) and Janjić (2003) provides a useful approach to analyze the influence of nonhydrostatic processes, since it offers an easy way to switch the model from the hydrostatic to the nonhydrostatic option.Comparing the outputs of both hydrostatic and nonhydrostatic versions of the model, running at a horizontal resolution higher than 10 km, it is expected to give insight in the contribution of the nonhydrostatic convective processes in the seasonal runs, especially in tropical regions.

Figure 3 .
Figure 3. February to April (FMA) 1996 time series of global mean variables from ERA-Interim reanalyses and simulated by GEF: (a) 850 hPa temperature ( • C) (the green curve is GEF and the red curve is the reanalysis) and (b) 850 hPa wind (m s −1 ), and (c) 200 hPa wind (m s −1 ) (the blue curves are GEF and the brown curves are the reanalyses).