## 1. Introduction

The Institute of Atmospheric Sciences and Climate of the National Research Council of Italy (ISAC-CNR) has recently developed a new global numerical weather prediction model, named GLOBO, based on a uniform latitude–longitude grid. The model is an extension to the global atmosphere of the Bologna Limited Area Model (BOLAM), developed and employed at the same institute beginning in early 1990. BOLAM is a hydrostatic model used to simulate mesoscale phenomena; it was tested and found to favorably compare with other mesoscale limited-area models in the course of the Comparison of Mesoscale Prediction and Research Experiments (COMPARE) investigation, a multiannual project organized by the World Meteorological Organization (WMO; see, e.g., Nagata et al. 2001). BOLAM is currently employed in a number of international, national, and regional centers for weather forecasting purposes (see, e.g., Lagouvardos et al. 2003).

The new global model inherits from BOLAM all of its basic numerical schemes and physical parameterizations. In particular, it retains the latitude–longitude coordinates and the split-explicit time scheme. The use of explicit time schemes generally requires shorter time steps than semi-implicit and semi-Lagrangian methods but, at the same time, has the advantage of a much simpler implementation and a more accurate numerical description of the phase speed of gravity waves. Moreover, it is more prone of being efficiently implemented on high-performance parallel-computing architectures by domain decomposition. The polar singularities are dealt with by the application of a simple polar average, consisting in a smooth low-pass filter.

The aim of this work is to describe the main numerical features and physical parameterizations of the GLOBO model, and to give a first evaluation of how forecast errors grow with time. The verification period covers from August 2009 to January 2011, during which time the model has been running once a day starting from initial conditions (valid at 0000 UTC) defined from Global Forecast System (GFS) analyses. Since August 2010, the horizontal resolution employed has been 32 km × 32 km at midlatitudes and 60 vertical levels. The daily real-time forecasts up to 6 days ahead can be viewed online (http://www.isac.cnr.it/dinamica/projects/forecasts/globo.html).

The paper is organized as follows. Section 2a is devoted to the dynamical formulation of GLOBO. Section 2b presents some aspects of the numerical discretization, especially those concerning the numerical stability in the polar regions. Section 2c highlights the main features of the physical parameterizations. In section 3, we describe how the initial conditions for the validation experiment are constructed, starting from GFS daily global analyses. Section 4 reports the results concerning the evaluation of the GLOBO forecast error. Finally, the conclusions are presented in section 5.

## 2. Model description

### a. Dynamical formulation

*t*the hydrostatic, primitive equations on the spherical domain in latitude–longitude coordinates:

*λ*,

*θ*. The main prognostic variables are the horizontal component of velocity (

*u*,

*υ*), the surface pressure

*P*, and the virtual temperature

_{S}*T*. GLOBO uses a hybrid vertical coordinate system in which the terrain-following coordinate

_{V}*σ*(0 <

*σ*< 1) smoothly tends to a pressure coordinate

*P*with increasing height above the ground. This is accomplished by the following formula:

*P*

_{0}is a reference pressure and

*a*is a constant [

*α*= 1 reduces to the classical Phillips (Phillips 1957) sigma coordinate]. Clearly,

*P = P*(

_{S}*P =*0) when

*σ =*1 (

*σ =*0), so that the atmosphere’s top and bottom boundaries becomes

*σ*surfaces. The larger the α, the greater the rapidity with which

*σ*surfaces relax to

*P*surfaces as

*P*decreases. Provided

*σ*. The horizontal momentum equations in this

*σ*coordinate become

*R*is the perfect gas constant for dry air,

_{d}*a*is the earth’s radius, Ω is the earth’s angular velocity, and Φ is the geopotential height. The geopotential height Φ is computed by vertical integration of the hydrostatic equation:

*C*is the specific heat at constant pressure), can be written in terms of the above quantities as

_{p}*q*and the other water species (cloud water and ice, rain, snow, and graupel–hail) constitute the dynamical core of the model.

### b. Considerations of the numerical discretization on the sphere

*T*points only (see stencil in Fig. 1);

*T*points are grid points where mass variables (temperature, pressure, water species) are defined, while the remaining points (red and green in Fig. 1) are named

*V*and

*U*points, respectively, because they carry wind components. The shaded region in Fig. 1 is treated as a single volume and tendencies are computed by averaging over that area. In particular, the divergences

*D*

_{1}and

*D*

_{2}[see Eq. (7)] at the poles are discretized by computing the net flux across the boundary of the polar grid box divided by the area, according to Gauss’s theorem. The same approximation is made for the horizontal advection of

*T*variables at the poles, which can be written in flux form as follows:

*D*

_{2}terms appearing in the advection expressions, like in (10), is extended here also to the computation of

*D*

_{2}(

*P*) [see Eq. (7)], in place of the usual centered approximation. This is a novel feature of GLOBO (and BOLAM), which allows a better estimate of the mass flux divergence.

_{S}*D*

_{1}and

*D*

_{2}appearing in Eq. (7). This is accomplished by iterating the simple three-point digital filter:

*j*denotes the grid point along the longitude, ν is a real positive number, and

*τ*represents the iteration. The asymptotic behavior of large

*τ*can be expressed as the convolution with the Green function of the heat diffusion problem:

*n*th component of the zonal Fourier transform of

*f*(

*λ*) averaged

*τ*times is the

*n*th component of

*f*itself multiplied by the Gaussian weight

*n*defined by (13). If 2

_{T}*N*denotes the number of grid points along longitude, in order to have the same effective zonal resolution at all latitudes above a given latitude

*θ*

_{0}, it must be set to

*n*=

_{T}*N*cos

*θ*/cos

*θ*

_{0}. Coding of (12) would be too expensive in terms of computer time. Hence, a hybrid filtering approach is adopted: the zonal average is performed by iterating (11) over those latitudes for which

*τ <*100 and by applying the low-pass spectral filter (13) at the remaining latitudes closer to the poles, with

*θ*

_{0}

*=*π/4.

*τ =*0 to the meridional direction. For similar reasons, polar averages must be performed on velocity and temperature tendencies generated by the physical parameterizations. In addition, a divergence damping term, defined by the following

*u*and

*υ*tendencies

### c. Physical parameterizations

The GLOBO physical scheme consists of the parameterizations of the surface layer (SL), of the planetary boundary layer (PBL), of the vertical diffusion in the “free” atmosphere, of the microphysical processes related to slantwise precipitation (both solid and liquid), of the convective precipitation, of the soil water and thermal balance (including vegetation), of the atmospheric radiation, and of the gravity wave drag related to excitation of orographic waves.

The SL is modeled accordingly to classical Monin–Obukhov similarity theory (Monin and Obukhov 1955). The Businger (see Fleagle and Businger 1980) stability functions are used in the unstable SL, while Holtslag (Beljaars and Holtslag 1991) functions apply to the stable case. The roughness length over land, initially defined depending on the vegetation and subgrid orographic variance, is also modified as a function of snow coverage conditions. Over the sea, a Charnock roughness representation is introduced for computing momentum fluxes. It takes into account the dependence of wave height on the surface wind speed, while roughness lengths for temperature and humidity in stable and unstable conditions are defined according to Large and Pond (1981).

The ML-based turbulence closure, widely used to compute the PBL fluxes for atmospheric modeling (see, e.g., Cuxart et al. 2006), is applied to model the turbulent vertical diffusion of momentum, potential temperature, and specific humidity in the free atmosphere. The turbulence closure is of order 1.5, in which the turbulent kinetic energy (TKE) equation is integrated in time (Zampieri et al. 2005). However, given the relatively low resolution employed in GLOBO, advection of TKE is not computed because it is usually negligible with respect to local sources and sinks. To take into account buoyancy effects in cases of a saturated atmosphere, the ML definition depends on the Richardson number based on the equivalent potential temperature. In the unstable case, a modified version of the nonlocal ML (Bougeault and Lacarrere 1989) is applied while, in the stable case, a modified Blackadar (Blackadar 1962) formulation is used. Finally, the TKE dissipated is fed back into resolved temperature in the form of “frictional heating.”

GLOBO includes an original soil model that implements three prognostic and one “climatological” layers, with depths ranging from a few centimeters to more than 1 m, increasing downward. The soil model computes the heat and water vertical transfer and vegetation effects at the surface (transpiration and interception of precipitation) and in the soil (extraction of water by roots depending on wilting conditions), taking into account different soil types and physical parameters. The soil model includes a treatment of freezing and melting processes of the water content. At the surface, the evolution of the snow cover is computed, taking into account snow accumulation and melting, with a single-layer, snow mantle model. A surface skin temperature is defined by imposing no net flux divergence of heat at the soil–atmosphere interface. The water balance at the surface (including runoff and pond formation) is calculated. Albedo and emissivity variations are also computed as a function of the uppermost soil water content. The sea surface temperature is predicted using a slab-ocean model, where latent and sensible heat fluxes, and radiation contributions, are taken into account. The same kind of model is adopted over the sea ice fraction, which is assumed to remain constant during the forecast period.

The large-scale stratiform precipitation and microphysical processes are treated with a simplified approach, suitable for non-convection-resolving models, and similar to that proposed by Schultz (1995). Schultz compares the results of his scheme against both the results of a well-documented research microphysics algorithm and observations, finding generally skillful precipitation forecasts with the advantage of low computational costs. The scheme includes five water categories: cloud ice, cloud water, rain, snow, and graupel–hail. Horizontal and vertical advection is applied only to cloud water and ice-specific quantities; and is neglected for other hydrometeors. The fall of hydrometeors is computed by means of the conservative (and dispersive) backward-upstream integration scheme.

The subgrid-scale precipitation is treated in GLOBO following the Kain–Fritsch (KF) convective parameterization scheme (Kain and Fritsch 1990; Kain 2004). The KF scheme has shown considerable success in simulating the development and evolution of convection under a variety of convective and synoptic environments (Kuo et al. 1996; Wang and Seaman 1997; Ferretti et al. 2000). The KF scheme is based on the Fritsch–Chappel triggering algorithm, with improvements on the detrainment effect and the cloud model. It has been developed for mesoscale models with a grid size of a few tens of kilometers. In this scheme, convection is triggered by lifting a lower-level slab layer with an impetus heating as a function of the grid-scale vertical motion at the lifting condensation level. The convective adjustment is based on convective available potential energy (CAPE) and, once convection is triggered, CAPE is assumed to be removed in a grid column within a convective time scale. This time scale is in the range of 30–40 min, depending on the averaged wind speed between the lifting condensation level and 500 hPa. The triggering vertical velocity is automatically adjusted to the grid spacing. The KF parameterization used in GLOBO has been completely recoded, using liquid water static energy (instead of a Bolton approximation of the equivalent potential temperature) as the thermodynamic conserved quantity. Moreover, additional modifications have been introduced with respect to the Kain (2004) version regarding the dependency of the downdraft on ambient relative humidity (the downdraft mass flux has been increased at low humidity) and the precipitation rate (the fraction of total condensate converted into precipitation has been made to increase with height above the cloud base). The cloud-depth threshold establishing the onset of shallow convection has been increased. The above changes tend to diminish slightly, on average, the temperature at lower-tropospheric levels around and below cloud base, hence stabilizing a little more efficiently the lower troposphere. This also has the effect of reducing to some extent the intensity of small-scale cyclogenesis in the presence of convection.

Radiation fluxes are computed with a combined application of the Geleyn scheme (Ritter and Geleyn 1992) and the European Centre for Medium-Range Weather Forecasts (ECMWF) scheme [cycle 26; Morcrette (1991); Mlawer et al. (1997)], with the Tegen et al. (1997) aerosol climatology. The Geleyn scheme, with the option of maximum cloud coverage, is called approximately every 0.5 h, and has been modified to take into account explicit cloud concentration. The ECMWF scheme is used to correct the surface and internal radiative fluxes of the Geleyn scheme. It is computed every 1.5 h at alternate horizontal grid points to reduce the computational time. Surface fluxes of visible and infrared radiation are then converted into one-time-step increments to obtain a smooth time evolution of surface temperature and turbulent fluxes of heat and moisture. Local cloud fraction is parameterized by a linear function of explicit cloud water/ice content, corrected with a linear function of relative humidity to account for subgrid fluctuations leading to cloud formation close to saturation.

Finally, a simple gravity orographic wave drag parameterization has been introduced, which basically follows the formulation used by Baines (1995), with some modifications. The drag vector is computed starting from the wave momentum flux near the surface, assumed proportional to the near-surface wind speed perpendicular to the local orographic relief, to the moist Brunt–Väisälä frequency, and to a function of the orographic profile along the direction of the wind vector that identifies topographic crests. The gravity wave momentum fluxes (upward and downward) are computed in a layer from the surface up to a critical level, defined as the first level, starting from below, where the scalar product between the local wind vector and the orographic drag vector becomes null or positive. In the case where a critical level is not encountered, the wave momentum flux is assumed to remain constant up to the first layer where the Richardson number becomes lower than a critical value (set to 0.25). Momentum flux divergence is modeled as a function of the local Richardson number, while partial reflection is assumed to occur at critical levels. The result is that wave drag can act in deep or shallow atmospheric layers above topography crests (no attempt has been made to spread it horizontally), depending on the stratification and shear. Application of the orographic drag reduces the error in the climatological westerly flow at midlatitudes, especially in the Northern Hemisphere. A positive impact has been also observed on the planetary wave dynamics at short time scales.

## 3. GLOBO initial conditions

Daily analyses valid at 0000 UTC for the GLOBO model are derived from GFS global analyses of the National Oceanic and Atmospheric Administration/National Centers for Environmental Prediction (NOAA/NCEP; information online at ftp://ftpprd.ncep.noaa.gov/pub/data/nccf/com/gfs/prod/). Atmospheric quantities (geopotential height, temperature, zonal and meridional wind components, relative humidity, and specific cloud concentrations) are downloaded onto a regular latitude–longitude grid of 0.5° resolution in the version 2 of the gridded binary (GRIB2) data format. These quantities are available at 47 isobaric levels ranging from 1 to 1000 hPa, though relative humidity and clouds are present only from 70 to 150 hPa, respectively. At the earth’s surface, orographic and geopotential height, land–sea and ice fraction, skin temperature, sea surface temperature, and snow height are downloaded onto the same grid. In addition, ground temperature and volumetric water content for the first four soil layers are obtained in order to initialize the GLOBO soil scheme. The downloaded atmospheric fields are then horizontally and vertically interpolated onto the GLOBO grid. To the ground temperature a correction is applied that is a function of season, latitude, and layer depth. In fact, GFS ground temperatures were found to be inconsistent with measurements (not shown) over a large portion of Europe, especially at the beginning of the summer season where observed temperatures in recent years are about 4°–5° warmer at about 1-m depth. However, in autumn and winter such a bias appears to be much reduced. The calibration of ground temperature is maintained over all continental areas, depending on the seasons and latitude [this somewhat arbitrary choice is also suggested by the comparison between GFS and ECMWF’s Integrated Forecast System (IFS) ground temperature climatology].

The orographic height is obtained from the NOAA dataset at 1/120° resolution (information online at www.ngdc.noaa.gov/mgg/topo/globe.html). Orography on the model grid points is obtained by averaging the data with a weighting function of distance (a Gaussian with half-width corresponding to 0.5°). Orography variance is then computed for each grid box and it is used to define an “envelope orography” and momentum roughness length. Once the orography and orography variance are interpolated onto the model grid, the polar average used by the model is passed on both fields to remove small zonal scales close to the poles.

The soil-type, land-use, and vegetation dataset is obtained from the Global Land Cover Facility of the University of Maryland at 1/120° resolution. For a given grid point of GLOBO, the fractions of each land type–use (of the 14 types available in the dataset) and of each vegetation type present in the grid box are defined. These fractions are then used to define the land–sea mask and other physical parameters related to vegetation, such as leaf area index and vegetation fraction. The parameters that define the soil physical properties (dry soil density and heat capacity, saturated hydraulic conductivity and water potential, minimum and maximum soil water content, wilting point, dry soil albedo and emissivity, and so on) are defined in a similar way from the soil unit classification of Food and Agriculture Organization (FAO), available at 1/12° resolution.

## 4. GLOBO verification

Our comparison of the performance of different models is based on the regular exchange of scores between centers of the WMO Global Data Processing and Forecasting System (GDPFS), under the WMO Commission for Basic Systems (CBS) requirements (standard procedures for the verification of numerical weather prediction forecasts are given in the WMO Manual on the Global Data-Processing and Forecasting System, WMO-No. 485). In particular, since root-mean-square (RMS) error depends on resolution, it is agreed that comparisons should be performed by upscaling both model forecasts and verifying analyses on a 2.5° × 2.5° latitude–longitude grid, using standard domain definitions.

Figures 2–5 show time series of monthly averaged RMS of the forecast error over the northern (20°–90°N) and southern (20°–90°S) extratropics, for 500-hPa height and mean sea level pressure (MSLP). The error is defined here as the difference between the forecast and the verifying GLOBO analysis that, as explained in section 3, is derived from the GFS analysis. For the purpose of comparison, the left panel of each figure (taken from Richardson et al. 2009) reports the RMS error for 2- and 6-day forecasts for the models of several GDPFS centers over the last 10 yr, from January 1999 to July 2009. The right panels of the same figures report the corresponding quantity computed from the GLOBO model (curves marked with dots), starting in August 2009 and ending January 2011. The set of curves marked with triangles is relative to the GLOBO RMS errors with the monthly bias removed (calibration). The bias considered here is computed by averaging over the month the daily forecast errors; therefore, it is not a priori known and cannot be used to correct forecasts in real time.

(right) Monthly mean RMS error (m) of 500-hPa geopotential height of the northern extratropics for 2- and 6-day forecast. Dots show the total error, triangles are calibrated. (left) For comparison, the same quantity for the global forecast models of the main meteorological centers.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

(right) Monthly mean RMS error (m) of 500-hPa geopotential height of the northern extratropics for 2- and 6-day forecast. Dots show the total error, triangles are calibrated. (left) For comparison, the same quantity for the global forecast models of the main meteorological centers.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

(right) Monthly mean RMS error (m) of 500-hPa geopotential height of the northern extratropics for 2- and 6-day forecast. Dots show the total error, triangles are calibrated. (left) For comparison, the same quantity for the global forecast models of the main meteorological centers.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2 but for the MSLP (hPa).

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2 but for the MSLP (hPa).

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 2 but for the MSLP (hPa).

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 4, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 4, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

As in Fig. 4, but for the southern extratropics.

Citation: Weather and Forecasting 26, 6; 10.1175/WAF-D-11-00027.1

There is no overlapping period between the left and right panels of Figs. 2–5, so no direct comparison can be made between the RMS of GLOBO and that of the other GDPFS models. As a check, the upscaling procedure used to remap the GLOBO analyses and forecasts on the 2.5° × 2.5° latitude–longitude grid was also applied to GFS products for the month of August 2009. The GLOBO RMS turned out to be slightly higher than GFS’s, especially for 2-day forecasts. Nonetheless, the comparison with the historical record of the forecast error of the GDPFS models indicates that the GLOBO general performance is on the average, particularly for the 6-day forecasts in both extratropics. It can be also seen that the bias does not contribute significantly to the medium-range forecast error. The 2-day forecast error is larger than average only in the summer season of the Northern Hemisphere where, moreover, it is appreciably reduced by the calibration. Inspection of the monthly bias maps (not shown) indicates that the largest contribution comes from those regions characterized by high orography, especially the Himalayas and the Tibetan Plateau. Likely, the lack of an analysis procedure based on model forecasts and data assimilation penalizes the GLOBO scores for short-term forecasts.

Some improvements in forecast error, particularly in the northern extratropics, have been achieved since August 2010 due to increases in the horizontal and vertical resolutions. This has been demonstrated, in particular, by a reforecast experiment of the month of February 2010 (not shown), which showed a reduction of a few percent of the forecast error in the northern extratropics (until July 2010, the model resolution was 35 km × 35 km, 50 vertical levels). From August 2010 to the end of the validation period, the GLOBO model has been running with 896 × 626 grid points and 60 vertical levels, corresponding to a 32 km × 32 km grid box at midlatitudes. This resolution is comparable to NCEP’, and roughly half of the latest IFS operational model. The time required to perform a 6-day integration (time step of 160 s) amounts to 2 h on a three-node cluster based on an Intel Xeon X5550 with 2.67-GHz processors (for a total of six CPUs, 24 “cores,” and 48 processes). A further increase in resolution to 28 km is planned shortly.

## 5. Conclusions

Starting from the BOLAM limited-area model, a new general circulation gridpoint model, termed GLOBO, has been devised. Some original numerical features (like the use of a modified *σ* coordinate and the computation of mass flux divergence with the flux-limiter technique) have been introduced and described. The new model has been implemented on the GFS analysis to provide daily real-time forecasts for up to 6 days. Starting in August 2009, the verification of GLOBO forecasts has been performed by computing the RMS of the difference field between the forecasts and their verifying analyses. The results have been compared with similar scores available for the principal global forecast models. Apart from the 2-day forecasts in the summer season of the northern extratropics (where bias gives a significant contribution), the GLOBO scores are in line with those of the other models, being only slightly worse than the GFS model, whose analyses are used here as the basis for comparison. This result is of significance, especially when considering the increasing importance that multimodel ensemble techniques assume in weather forecast.

Model skill is found to increase with increasing horizontal and vertical resolutions. The present resolution (32 km at midlatitudes) is coarser than the one at which the BOLAM model is usually employed (10–15 km), and where it is expected to perform at its best. For instance, the horizontal resolution is still too coarse for the advection of hydrometeors to become effective. It remains, however, to be verified if model computational efficiency is maintained at higher resolution.

Some systematic errors of the GLOBO model have been identified and are currently a subject of research. For instance, the soil water initialization in subtropical regions is likely to be incorrect (too large), giving an excess of simulated precipitation there. Studies related to the African monsoon have revealed soil moisture values that are much smaller than those present in the GFS analyses and, to an even larger extent, in ECMWF analyses. In fact, even the most up-to-date general circulation models fail in reproducing the correct seasonal water budget over West Africa (Meynadier et al. 2010). In general, there is still a large degree of uncertainty in the initialization of ground quantities and in the modeling of the vegetation seasonal cycle.

One of the recent applications of the GLOBO model at the ISAC is the monthly probabilistic forecasting of temperature and precipitation anomalies over Italy, promoted by the Italian Civil Protection Agency (Dipartimento della Protezione Civile Nazionale, DPCN). It is beyond the scope of the present paper to report in detail about the methodology and results of this activity, which will be the subject of a future presentation. In synthesis, it is based on calibrated ensemble forecasts with initial conditions derived from unperturbed and perturbed analyses from NCEP, with prescribed sea surface temperature (SST) anomaly (corresponding to the observed anomaly at the initial time), superimposed on the seasonal SST cycle. The GLOBO model has been employed in this ensemble mode with a resolution of 1.0° × 0.75°, and with 50 levels. Monthly forecasts have been produced once a month for a period of less than 2 yr, which is too short a time to allow for significant verification. However, preliminary evaluation and intercomparison with other centers’ monthly forecasting products suggests encouraging results, comparable with those obtained with independent models.

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