However, the analysis of the discrepancies between the two models cannot be limited here to the differences between the velocity magnitudes, as different flow directions are obtained in some conditions. The same parameters of the previous analysis were hence also correlated to the absolute values of the difference between the depth-averaged velocity directions obtained from the 2D and the 3D models, |Δdir(V)_2D−3D| = |dir(V_2D)−dir(V_3D)|, as listed in Table 3. The highest correlation coefficients are obtained to |Δdir_s-b|, proving that the error in the depth-averaged velocity estimation by the 2D model is significant where the differences in the velocity direction along the flow depth are relevant. In addition, correlation coefficients to ⁠, despite being much lower than those for the velocity magnitude differences, are still higher than those to (except for the no-wind case). This suggests once again that the inaccuracy of the 2D model is mostly linked to turbulent processes in the vertical plane, in particular to the shear produced by varying velocity direction along the water column.

Table 3

Correlation coefficients between |Δdir(V)_2D−3D| and the selected variables from the 3D simulations on the Superior Lake of Mantua (all values are significant with p < 0.01)

Wind .	Null .	Standard .	Storm .	Standard .	Storm .	Standard .	Storm .
Q [m3/s] .	20 .	20 .	20 .	5 .	5 .	0 .	0 .
I	0.040	0.122	0.359	0.144	0.177	0.239	0.374
νT	−0.157	0.297	0.120	0.365	0.134	0.150	0.081
	0.136	0.215	0.412	0.121	0.379	0.295	0.232
	0.162	0.130	0.283	0.115	0.232	0.253	0.153
|Δdirs-b|	0.461	0.576	0.694	0.545	0.706	0.526	0.689

Wind .	Null .	Standard .	Storm .	Standard .	Storm .	Standard .	Storm .
Q [m3/s] .	20 .	20 .	20 .	5 .	5 .	0 .	0 .
I	0.040	0.122	0.359	0.144	0.177	0.239	0.374
νT	−0.157	0.297	0.120	0.365	0.134	0.150	0.081
	0.136	0.215	0.412	0.121	0.379	0.295	0.232
	0.162	0.130	0.283	0.115	0.232	0.253	0.153
|Δdirs-b|	0.461	0.576	0.694	0.545	0.706	0.526	0.689

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