Assessing Ocean Forcing on Sea Surface Temperature Variability from Surface Heat Budget
This paper compares three methods for quantifying stochastic ocean forcing to low frequency sea surface temperature (SST) variability from the surface heat budget in the framework of a simple stochastic climate model, especially in the case of red noise ocean forcing. The three methods are: PT21 (Patrizio and Thompson, 2021), PT22 (Patrizio and Thompson, 2022) and LGD23 (Liu et al., 2023). PT21 estimates the ratio of ocean over atmosphere forcing as the ratio of the covariance of SST tendency with ocean heat transport over the covariance with surface heat flux, while PT22 and LGD23 first derive the time series of oceanic and atmospheric forcing before estimating their ratio. The three methods are first applied to synthetic data of the stochastic climate model and then to the mid-latitude North Atlantic in observations. It is found that the LGD23 method provides an unbiased estimation of oceanic forcing with a modest sampling error at low frequency, if the persistence time of the sea surface salinity can be treated as a good approximation of that of SST associated with ocean heat transport. The PT22 method has the smallest sampling error, but tends to underestimate the ocean forcing modestly when the ocean forcing is a red noise process. The PT21 method gives the correct ratio of oceanic over atmospheric forcing in spectral density in theory, but suffers from a very large sampling error for practical application to a data set of a finite length of decades. We recommend the use of both LGD23 and PT22 as two complimentary methods for the estimation of ocean forcing, with the PT22 providing likely a lower bound for red noise ocean forcing.