The atmosphere component of FORTE 2.0 is IGCM4 , run with a T42 spectral resolution. A longitudinally regular and Gaussian in latitude grid with a grid spacing of 2.8∘ is used for advection and diabatic processes. The resolution is sufficient to enable stable climate integrations without the need for flux adjustments. There are two pre-configured choices for the number of vertical levels: a troposphere-only atmosphere represented by 20σ levels (L20) which extends to around 25 km altitude or a 35σ level configuration (L35) which includes the stratosphere and extends to around 65 km altitude. To avoid issues with 2Δz oscillations under certain conditions, the NIKOSRAD radiation scheme in IGCM3 (used previously in FORTE) was replaced with a modified version of the Morcrette radiation scheme . For further details of the IGCM4 and its performance, we refer the reader to and references therein. The model is run with 96 (L35) or 72 (L20) time steps per day. Orography is derived from the US Naval 1/6th degree resolution dataset. IGCM4 is Message Passing Interface (MPI) parallelised, and at this resolution integration on 16–32 cores achieves the best performance.

Atmospheric convection is dealt with via a Betts–Miller scheme . Low, medium and high layer clouds and convective cloud amounts are represented based on a critical relative humidity criterion (see the Appendix of ). The formula which determines low-level cloud amount has an additional factor of 50 % compared to that used by to correct a cold bias within the tropical ocean which led to unrealistic circulation in the Pacific. In addition to variation with solar zenith angle (and hence latitude), sea surface albedo is increased away from polar regions to compensate for the absence of aerosols which would otherwise scatter incoming solar radiation. Land grid boxes are assigned a vegetation index, one of 24 pre-defined vegetation types, which determine the albedo and roughness length.

Coupling to the dynamic ocean model requires some changes to the surface boundary layer. In order to conserve water, it is necessary to account for soil moisture and implement river runoff. Soil moisture for each land grid box is represented as a bucket, or reservoir, 0.5 m in depth. Excess water, i.e. when the volume of water is greater than the volume of the bucket, is accumulated and added to the ocean as runoff at each coupling time step. The land surface is divided into catchment basins, and the accumulated runoff is distributed on a list of predetermined atmospheric grid cells that lie over the ocean and represent river mouths. The catchment areas and river discharge points are derived from , as explained in . Runoff accumulated over Antarctica is distributed uniformly over the ocean south of 55∘ S, as a simplistic representation of iceberg calving and melting. Additionally, land snow cover is capped at a maximum thickness of 4 m. Excess snow over Antarctica and the Arctic region is treated separately as an additional runoff term that represents iceberg melting and calving. As with the soil moisture, runoff from excess snow over Antarctica is distributed uniformly over the ocean south of 55∘ S. Excess snowmelt over the Arctic is handled similarly, with a uniform distribution over the ocean north of 66∘ N.

A coastal tiling routine is implemented in order to handle the differences between the atmosphere and ocean grids. Grid cells in the ocean are either ocean or land, whilst atmospheric grid cells can be ocean, land or partial (i.e. they extend over both ocean and land cells on the ocean grid). Atmospheric grid cells that wholly overlie ocean are updated using the normal IGCM4 boundary layer scheme and the SST from the ocean model that is exchanged through the coupler. Similarly, cells that wholly overlie land are updated using the IGCM4 land surface scheme. For partial atmosphere grid cells, two sets of boundary layer variables (e.g. latent heat flux) exist. One set is updated like any other land point using the IGCM4 boundary layer scheme, and the other set is updated like any other ocean point. The atmosphere then sees the weighted average of the heat fluxes over the land and sea. Care is taken to ensure that atmospheric moisture is conserved and that precipitation is also apportioned correctly between the land surface scheme and the ocean fraction of the atmosphere cell.

To improve the representation of the effects of sea surface roughness on momentum exchange, a wind-dependent drag coefficient, Cd, is implemented, such that Cd=Cd0+5.6e-5⋅min⁡(U10,40), where U10 is the 10 m wind speed . This gives a maximum Cd=0.003 at a wind speed of 40 m s-1 without ice cover. Cd0 is the drag coefficient over ocean cells, calculated using a globally uniform value for surface roughness over the open ocean.

At present, FORTE 2.0 does not include dynamic sea-ice representation. Instead, sea ice is represented by a barrier to heat fluxes between the ocean and atmosphere components, which is imposed when the sea surface temperature reaches 271 K, and surface albedo is increased to 0.6 to represent ice cover. The albedo continues to linearly increase, reaching 0.8 at 261 K as a means to represent the albedo effects of snow on ice. Once the albedo reaches 0.8, it will not reduce until the temperature rises above freezing point and the flux barrier deactivates. There is no advection of sea ice, and salinity and runoff fluxes remain unaffected. SST under ice is relaxed toward the freezing point of seawater (-1.8 ∘C) on a 10 d timescale.

The ocean component of FORTE 2.0 is MOMA , a version of the Geophysical Fluid Dynamics Laboratory (GFDL) MOM (Modular Ocean Model) coded to work more efficiently on array processors, which solves the primitive equations discretised using finite differences on an Arakawa B grid . It has a linear free surface and uses “full cell” ocean bathymetry. In the configuration used for this integration, the ocean horizontal resolution is 2∘ × 2∘, with 15 z-layer levels, increasing in thickness with depth from 30 m at the surface to 800 m at the bottom. A polar island, comprising the top row of grid cells (88–90∘ N), is required in the Arctic to prevent numerical instability due to convergence of lines of longitude. There are 64 baroclinic time steps per day (22.5 min time steps) implemented using the modified split QUICK (MSQ) advection scheme . The version of MOMA used in FORTE 2.0 uses OpenMP shared-memory parallelisation, and running it on four to six cores is typically sufficient to match the IGCM4 performance.

Bathymetry is derived from the 1/12∘ resolution dataset, and interpolated onto the model resolution. Due to the horizontal resolution, in order to encourage dense water formation and flow between the Nordic Seas and North Atlantic, bathymetry is manually excavated in a manner similar to HadCM3 . The Bering, Gibraltar and Kattegat/Skagerrak straits are represented by a single grid box which, due to the Arakawa B grid, means that there is no advection through them, but diffusion of potential temperature (T) and salinity (S) does occur.

Ocean isopycnal mixing is represented in MOMA through the isoneutral mixing scheme of . The eddy-stirring process of is introduced as a skew flux . Where isopycnal slopes become large, exponential tapering scales isoneutral diffusivities to zero as the slope increases . The isopycnal mixing parameters used for the control simulation described in Sect.  are shown in Table .

To ameliorate some of the shortcomings identified in earlier FORTE simulations, some additional changes have been made to MOMA. Firstly, the background vertical diffusion, κ, is set to be stability dependent , albeit with the surface to sea floor potential temperature gradient as a simple proxy for stability, such that κs=(0.3+1.7e-(0.15[max⁡(Ts,Tb)-Tb])2)×10-4m2s-1,κ=κs+(2×10-4-κs)z/Hm2s-1, where Ts is the surface potential temperature, Tb is the bottom potential temperature, z is depth, and H is the local total depth of the ocean. Thus, the vertical diffusivity takes a maximum value of 2×10-4 m2 s-1 at the sea floor and at high latitudes, with lower values, approaching 3×10-5 m2 s-1 in the upper ocean at low latitudes.

Secondly, starting from 5∘ N/S the horizontal diffusion in the surface layer increases towards the Equator from its default value to 20 times this value at the Equator to counteract equatorial upwelling and, in a simple way, parameterise the eddy heat convergence associated with tropical instability waves which was highlighted by .

Annual time mean surface air temperatures (SATs) in the tropics are 25 ∘C, with some regions over land reaching 30–35 ∘C. The Arctic reaches -20 ∘C, with temperatures over Greenland reaching as low as -40 ∘C and the interior of Antarctica reaches as low as -60 ∘C (Fig. a). Anomalies of annual mean SAT from the early years (1871–1896) of the 20th Century Reanalysis 20CR; are presented in Fig. b. FORTE 2.0 performs well at low latitudes, especially over the ocean. There is a pronounced warm anomaly of around 5 ∘C over most of the Southern Ocean, consistent with the positive SST bias shown in Sect. . A cold SAT anomaly with respect to 20CR also manifests over the Nordic Seas, extending into the Barents Sea. The L20 simulation exhibits very similar annual mean SATs (not shown). Values for L20 are within 1 ∘C of those shown for the L35, except for two regions over the northern Labrador Sea and the Weddell Sea which are cooler in L20 by several degrees. These differences are likely due to the difference in the response of the flux barrier which represents sea ice. The SAT seasonal ranges for FORTE 2.0 and 20CR (1871–1896) are presented in Fig. c and d. Seasonal SAT variability over the tropical ocean is low, whilst variations in SAT over land are much higher, reaching 40 ∘C over the Eurasian continent. The seasonal range of FORTE 2.0 compares reasonably well with 20CR throughout most of the low and midlatitudes. However, the seasonal ranges in SAT at high latitudes (both Arctic and Antarctic) are much larger than those in 20CR. Arctic and Antarctic seasonal SAT variability is 40–45 ∘C, with the coldest regions of Antarctica reaching as low as -85 ∘C during July.

Figure  shows winter (DJF) and summer (JJA) mean precipitation and anomalies with respect to the 20CR 1871–1896 climatological mean. During DJF (Fig. a), regions of high precipitation over the Northern Hemisphere oceanic western boundary currents (up to 6 mmd-1 and extending to northwestern Canada and along the Gulf Stream and western boundary current track in the northwest Atlantic) are evident, as well as high values (10–12 mmd-1) over tropical Africa and South America, Indonesia and over the Intertropical Convergence Zone (ITCZ) in the Atlantic and Pacific oceans. Very low values (0–1 mmd-1) are seen over the polar regions, the subtropical desert regions (terrestrial and oceanic) and (unrealistically) over the equatorial Pacific. During summer (JJA), the ITCZ and the corresponding high levels of rainfall shift northward (Fig. c). There is enhanced rainfall due to the Asian summer monsoon, though in FORTE 2.0 it does not extend sufficiently far east. The anomalies with respect to the 20CR 1871–1896 climatological DJF mean (Fig. b) show that, particularly over the tropical Pacific, FORTE 2.0 simulates too little rainfall. This is most pronounced over the western tropical Pacific during DJF and also over the northern extent of the ITCZ in the eastern Pacific during JJA (Fig. d). A major difference with the observed distribution is the South Pacific ITCZ, which is narrow and predominantly zonal in the model solution, whereas observations show a broader northwest- to southeast-oriented region.

Contours of annual average mean sea level pressure, displayed in Fig. a, show the expected bands of high pressure over the subtropical oceans (e.g. the Azores and North Pacific highs) and over the polar regions and low pressure cells at midlatitudes (e.g. Icelandic and Aleutian lows) and over the equatorial regions. The seasonal range is largest over land (Fig. b), particularly highlighting the seasonal variability over Siberia. Differences in the annual mean sea level pressure anomalies and seasonal range (L20–L35) are predominantly poleward of 60∘ N and S (Fig. c and d). The seasonal range is smaller in L20 over the Labrador and GIN seas and over the high-latitude Southern Ocean. Contours of sea level pressure show the intensification of the surface winds over the midlatitudes in both the Southern Hemisphere and Northern Hemisphere during the winter season (Fig. e and f). We note that the Siberian High is not very intense for mean January conditions, and this appears to have the effect of allowing the Icelandic Low to expand and displace eastwards over Scandinavia, resulting in a displacement of the winter North Atlantic Oscillation (NAO) pattern compared with observations (see Sect. 5).

Time mean zonal wind for both summer and winter is shown in Fig.  as a function of latitude and pressure. The model exhibits Northern and Southern Hemisphere jet streams at around 40∘ S and 40∘ N at 200 hPa. The southern jet stream exhibits a lower seasonal range (28–36 m s-1) than the northern jet stream (12–36 m s-1). Surface westerlies and easterlies are of the order of ±0–4 m s-1 in the annual mean. The most notable differences between the L20 and L35 configurations occur during JJA, with weaker winds at 60∘ S. The midlatitude cores are also slightly stronger during JJA in L20. At 80∘ S, the zero contour extends down to the surface, indicating a change in the mean wind direction from weak westerlies to weak easterlies.

Annual mean SST (Fig. a) shows maximum temperatures in the Indian and tropical Pacific and Atlantic oceans reach 26 ∘C. Compared with the EN3 climatology (, Fig. c), there is a cool anomaly of around 1 ∘C throughout the tropics (Fig. e). Regions immediately west of the major land masses (coincident with regions of coastal upwelling) show warm SST errors of 2–3 ∘C magnitude, probably arising from a known issue in many coupled climate models related to the poor representation of marine stratocumulus clouds . There is a substantial warm bias throughout the Southern Ocean and extending into the southern parts of the Pacific and Indian oceans, likely due to a combination of deficiencies in the physical representations of the ocean dynamics and cloud physics . The Nordic Seas are several degrees cooler and up to 1.5 PSU fresher (Fig. f) than EN3, possibly due in part to the crude representation of sea ice, and in part due to the inadequate representation of ocean circulation in the Arctic and Nordic seas in a 2∘ resolution ocean model. There is a positive salinity bias of around 3 PSU further east in the Arctic, north of Siberia. Although large, the size of the salinity bias in the Arctic is not uncommon, even for models that do not require a polar island to prevent issues arising from the convergence of the grid at the North Pole . Annual mean SSS is well represented throughout the Southern Hemisphere ocean, where errors are mainly confined to within ±0.5 PSU (Fig. f). Positive biases of the order of 1–1.5 PSU occur in the Bay of Bengal and around the Maritime Continent and the northeast Pacific. The Labrador Sea and the region extending along the US coastline as far south as Cape Hatteras show positive salinity biases between 0.5 and 2 PSU, the latter coincident with a positive temperature bias that exceeds 5 ∘C in a small region that is indicative of the Gulf Stream separating too far north, bringing tropical waters too far north and west. It is worth noting, though, that the L20 simulation exhibits smaller biases in both SST and SSS in the Labrador and Irminger seas (Fig. g and h). There is also a slight improvement in the Southern Ocean warm bias in L20 compared with L35. Some of the model biases will arise from the relatively coarse horizontal and vertical resolution and missing physical processes. However, as indicated by the differences between the L20 and L35 simulations, it is likely that a substantial reduction of biases would be achieved with the application of a rigorous calibration methodology such as history matching .

Sea surface height (SSH) provides insight into the wind-driven ocean circulation. The SSH from L35 and the Ocean Comprehensible Atlas (OCCA; Forget, 2010) climatology are shown in Fig. a and b, respectively. Gyre circulation in all the major ocean basins is highlighted by the contours, along with regions of intensified flow, such as the Gulf Stream, the Kuroshio, and along the northern boundary of the ACC. However, the coarse resolution of the ocean model results in flows that are too broad and diffuse, weakening the SSH gradient across these intensified flows. The North Atlantic subpolar gyre appears constrained to the west of the basin. Slumping of the SSH gradient across the ACC is evident in the anomaly of L35 with respect to OCCA (Fig. d) and corresponds to the weak ACC transport shown earlier (Fig. ). The slope in SSH is also weaker in the North Atlantic and extending into the Nordic Seas. Comparison with L20 (Fig. c) shows a slight steepening of the gradient across the ACC in L20, a small reduction in the bias compared with the OCCA climatology.

A latitude depth plot of the AMOC shows a maximum around 50∘ N and at 1000 m depth (Fig. ). Closely packed streamlines at the high northern latitudes indicate that much of the deep convection occurs abruptly in a narrow latitude band and southward North Atlantic Deep Water transport reaches around 2.5 km depth. The abrupt sinking at the high northern latitudes is characteristic of coarse-resolution ocean models where flow into the Nordic Seas is poorly represented. Winter mixed layer depths in the southern Labrador Sea reach 2500 m in a few grid cells, whilst winter mixed layer depths south of the Denmark Strait, Iceland and the Faroe Bank Channel can reach 1000 m (Fig. ). Wintertime convection is too shallow in the Nordic Seas, with mixed layer depths reaching 125–150 m in the central and eastern Nordic Seas. The AMOC transport through 30∘ S is 10 Sv in L35 and 6 Sv in L20, and is stronger (∼14 Sv (L35), ∼10 Sv (L20)) at 30∘ N. There is a strong AABW cell (∼6 Sv) centred at 3500 m depth, which weakens to about 2 Sv at 30∘ N. As mentioned earlier, the AABW cell in L20 is slightly stronger, and in Fig.  it is shown to extend further north. There is evidence of two-grid-point noise at the Equator, which has been identified previously in Bryan–Cox models . The structure of the AMOC is similar in both the L35 and L20 simulations, with the L20 configuration consistently around 30 % weaker.

Ocean meridional heat transport (OHT) in FORTE 2.0 is around 60 % of that expected based on observational estimates but consistent with the weaker-than-observed volume transport (Fig. ). Atlantic OHT at 26∘ N is 0.74 PW in L35 and 0.63 PW in L20, whilst observationally derived estimates suggest the current value is closer to 1.3 PW . Globally, the OHT reaches 1.4 PW, instead of the 2.1±0.3 PW computed by . Over the Southern Ocean (35–65∘ S), OHT is northward, a characteristic seen previously in MOM-based ocean models . This may be related to the strong warm SST bias present over the region at 40–60∘ S (Fig. ) and its consequent effect on surface heat fluxes.