Data source and method of analysis

The European Center for Medium-Range Weather Forecasting (ECMWF) twice-daily analyses of 1000 hPa winds and surface air temperature (SAT) for the period 1980-87 are used as a surrogate for surface marine data. The original ECMWF analyses are interpolated from their 2.5° 2.5° grid to the same 1° 1° UWM/COADS grid. Each twice-daily interpolated value is considered to be an individual observation. Raw monthly means are computed by sampling this ECMWF data in three different ways:

Full sampling:

all the available data are included to compute our best estimate of the monthly means in each 1° box.

Ship-based sampling:

only includes data for which at least one ship observation was made in the 12 hour period within the boundaries of the 1° box. This sampling method is intended to closely simulate COADS data coverage, and should reflect ship fair weather bias.

Random sampling:

the total number of observations for each month in each 1° box is first recorded based on the actual COADS data availability. Subsequently, the same number of observations are randomly drawn from each 1° box in that month. This sampling method uses the same number of observations to compute monthly means as does the ship-based sampling method above, but by construction it is unbiased. By comparing results from ship-based and random sampling one can obtain an estimate of the effects of the fair weather bias.

Let us denote by the ``observations'' based on the interpolated ECMWF analysis for wind speed, for example. The number of grid-points is denoted by n. The analyses based on ship-based and random sampling are given by

where and denote the time-average with the ship-based and the random sampling methods; stands for the objective analysis with the Barnes' weighting function described in section 8. Because of the smoothing introduced by the successive correction scheme, the estimates / only resolve scales larger than approximately 770 km. In order to estimate error at these scales we define the ground truth as

where denotes the time-average with full sampling. Gridded error fields are now defined in terms of ,

Notice that we are ignoring observational errors, both in the form of instrument errors and errors of representativeness (Daley 1991). The discussion below will be centered on spatially averaged root-mean-square errors, e.g., , where

In order to quantify the effects of fair weather bias in the analyzed fields, we define

The plausibility of this heuristic definition follows from the fact that the random sampling, as defined above, is not affected by the current weather condition