Fig. 1
2D correlation functions where the length scale parameters are L 1=10 and L 2=50 for c 2,1 and c 2,2, respectively, and ν 1=ν 2=3. The left panel shows a cross-section of c 2,1 (dashed black), c 2,2 (dotted black) and two different linearly combined functions: f 2,2 with (red), and with (blue). The right panel shows a cross-section at of their normalised spectrum. The black lines highlight the normalised spectrum values and . See text for details.
Fig. 2
Evolution of the ratio k/k 1 with respect to . k is the kurtosis of the 2D correlation function , with L 1=10 and L 2=50 for c 2,1 and c 2,2, respectively, and ν 1=ν 2=3. k 1 is the kurtosis of the function c 2,1 (and c 2,2).
Fig. 3
Surface temperature increments on 1 December 2010 with the original formulation (top left panel) and a combination of two functions (top right panel) for the Gulf Stream region. The increments are calculated from the same initial states and the same set of observations. The factor defining the amount of the large scale to be used in the combination is shown on the bottom panel.
Table 1. RMSE for SNGL and DUAL in different areas
VariableAreaSNGLDUAL%
SST in situGlobal0.4550.462+1.5North Atlantic0.5160.527+2.1Southern Ocean0.4680.484+3.4Temperature profileGlobal0.6140.616+0.3North Atlantic0.8120.806−0.7Southern Ocean0.5680.565−0.5Salinity profileGlobal0.1260.124−1.6North Atlantic0.2180.214−1.8Southern Ocean0.1080.103−4.6Mixed layer depthGlobal40.3537.08−8.1North Atlantic44.1342.94−2.7Southern Ocean63.7656.44−11.5SSHGlobal0.0710.075+5.6North Atlantic0.0750.074−1.3Southern Ocean0.0890.097+9.0
Fig. 4
Hovmoller plots of the observation minus background innovation mean for temperature profiles for SNGL (left panel) and DUAL (right panel) in Southern Ocean. Blue colours denote a warm model bias, whereas red colours represent a cold model bias.
Fig. 5
Hovmoller plots of the observation minus background innovation mean for salinity profiles for SNGL (left panel) and DUAL (right panel) in Southern Ocean. Blue colours denote a salty model bias, whereas red colours represent a fresh model bias.