Using Green's functions to calibrate an ocean general circulation model

Green's functions provide a simple yet effective method to test and to calibrate general circulation model (GCM) parameterizations, to study and to quantify model and data errors, to correct model biases and trends, and to blend estimates from different solutions and data products. The method is applied to an ocean GCM, resulting in substantial improvements of the solution relative to observations when compared to prior estimates: overall model bias and drift are reduced and there is a 10%-30% increase in explained variance. Within the context of this optimization, the following new estimates for commonly used ocean GCM parameters are obtained. Background vertical diffusivity is (15.1 +/- 0.1) X 10(-6) m(2) s(-2). Background vertical viscosity is (18 +/- 3) x 10(-6) m(2) s(-2). The critical bulk Richardson number, which sets boundary layer depth, is Ri(c), = 0.354 +/- 0.004. The threshold gradient Richardson number for shear instability vertical mixing is Rio = 0.699 +/- 0.008. The estimated isopycnal diffusivity coefficient ranges from 550 to 1350 m(2) s(-2), with the largest values occurring at depth in regions of increased mesoscale eddy activity. Surprisingly, the estimated isopycnal diffusivity exhibits a 5%-35% decrease near the surface. Improved estimates of initial and boundary conditions are also obtained. The above estimates are the backbone of a quasi-operational, global-ocean circulation analysis system.