The mean squared error of rˆ is equivalent to 1/η  2. Assuming the normal distribution for rˆk, each σk   is approximated as ¼ of the 95% confidence interval of rˆk (in brackets below) by: equation(3) σk(rˆk,Nk)=14tanhz+1.96Nk-3-tanhz-1.96Nk-3,where equation(4) z=12log1+rˆk1-rˆk,( this website David, 1938) and Nk   is the number of degrees of freedom for a time series of length n  , reduced by the band pass filter to: equation(5) Nk=2ΔTTc1-ΔTTc2(nk-2),( Yan et al., 2004) where ΔTΔT is the time step and Tc  1 and Tc  2 are the band pass times (40 and 160 h, respectively). Although there is autocorrelation in the time series, subsampling at the decorrelation

time causes a negligible change in N  . Each σk  , η  2, rˆk, and rˆ is a function of l, the lead or lag time

between τ and SST. For model correlation Rˆ (model terms represented by capital letters), Eq. (2) reduces because there is a single complete time series, i.e. K   = 1. When comparing between observations and model, the greatest magnitude of the lagged observed and modeled correlation ( rˆ and Rˆ respectively) is selected and denoted r and R, and their associated lead times l and L. For all buoys, r is negative ( Figs. 3 and 4) meaning that increased wind stress leads decreased SST. Lead selleck kinase inhibitor time l   has an observational uncertainty ηl2, calculated by an application of Eq. (2) to lead time where equation(6) ηl2=∑k=1k1σlk2,and the standard deviation for lead time, σl  , has to be estimated empirically. In order to examine σl   for the buoy observations, each lead time l   associated with an individual time series k   (i.e. the time at which rˆk is greatest in magnitude) is subtracted from the mean l   at buoys along its longitude. Shorter time series tend to result in higher deviations

from meridional mean of l  , and the relationship between time series length and lead time variability is even more clear when analyzing artificially truncated model runs ( Fig. 5). Assuming that the record length and standard http://www.selleck.co.jp/products/erastin.html deviation relationship from the observational data is approximated by the model, an exponential fit to the model relationship between standard deviation in l   and record length ( Fig. 5) is used as an approximation of σl   for lead time uncertainty ηl2 (Eq. (6)). Because all model time series have a record length of 2 years, the standard deviation of the estimated error in model lead time, σL, is a constant 2.16 h ( Fig. 5). The uncertainty in forcing is estimated by the sensitivity of model to the blended wind product at each buoy, using the twenty experiments with different wind products and the same model physics (Table 2): equation(7) φ2=1n∑i=120(Ri-μR)2,φ2=1n∑i=120(Li-μL)2,where each i is an experiment forced with a different blended wind, and μ is a mean value over years 1.5–3.5 of the 20 blended wind experiments.