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Many estimates of uncorrelated observational error uncertainty have been made. Although thermometers issued to ships by many port meteorological officers are calibrated, such calibration information is not routinely published, nor is there any guarantee that the temperature of a water sample measured by a well calibrated thermometer is equal to the actual SST when the sample has spent time in a bucket, or passed through the pipe work of a ship. Consequently, estimates of measurement uncertainty from the literature are typically estimates derived from considerations of the variance of the data: for example, using spatial [Lindau, 2003; Kent and Challenor, 2006; Emery et al., 2001] and temporal [Stubbs, 1965] semivariograms, by comparing collocated observations [O'Carroll et al., 2008, Lean and Saunders 2013], by resampling [Shen et al., 2007], by using the variation of the variance with the number of observations [Rayner et al., 2006], or by comparison with a background field [Kent and Berry, 2008; Xu and Ignatov, 2010, 2014; Ingleby, 2010; Kennedy et al., 2011a; Atkinson et al., 2013]. Some of the analyses did not distinguish between uncorrelated observational errors and systematic observational errors, tending to combine them into one estimate. In addition it is not always easy to separate the effects of spatial sampling from measurement errors particularly in regions of high SST variability [Castro et al., 2012].
A single SST measurement from a ship has a typical combined uncorrelated and systematic error uncertainty of around 1 K to 1.5 K. Results from individual analyses are summarized in Table 1. The studies are mostly based on data from 1970 onwards.
| References | Estimated measurement uncertainty for ship measurements |
|---|---|
| Stubbs [1965] | 0.11±0.01K for canvas bucket measurements from an Ocean Weather Ship |
| Strong and McLean [1984] | 1.8K RMS difference between ship and AVHRR data |
| Bernstein and Chelton [1985] pg 11620 | 1.1K |
| Sarachik [1984], Weare [1989] pg 359 | 1K |
| Wilkerson and Earle [1990] pg 3381 | 3.5K |
| Cummings [2005] Table 1, pg 3592 | 1.3 K (ERI) 0.6 K (Hull sensor) 1.2 K (bucket) |
| Kent and Challenor [2006] pg 484 | 1.2±0.4 K or 1.3±0.3 K depending on how measurements were weighted |
| Kent et al. [1999] abstract | 1.5±0.1 K |
| Kent and Berry [2005] Table 2 pg 853 | 1.3±0.1 K and 1.2±0.1 K |
| Reynolds et al. [2002] pg 1613 | 1.3K |
| Kennedy et al. [2011a] pg 83 | 1.0K |
| Ingleby [2010] Table 10 pg 1487 | 0.9 K for automatic systems 1.2 K for manual measurements |
| Kent and Berry [2008] Table 5a pg 11 | 1.1K |
| Xu and Ignatov [2010] pg 16 of 18 | 1.16K |
| Xu and Ignatov [2016] abstract | 0.75K |
Table 1: List of estimates of measurement error uncertainties for ships where uncorrelated and systematic errors were not dealt with separately.
Measurements are not all of identical quality. Kent and Challenor [2006] showed that in the period 1970-1997 the uncertainties of measurements from ships varied with location, time, measurement method and the country that recruited the ship. Uncertainties were estimated to be larger in the mid-1970s probably due to data being incorrectly transmitted in the early days of the Global Telecommunication System. Their estimated uncertainty for engine room measurements was larger than for bucket measurements. Tabata [1978a] noted that bucket measurements could be accurate to 0.15 K, but that ERI measurements were nearly an order of magnitude worse (1.16 K). Ingleby [2010] estimated uncertainties for different subsets of the data and noted that manual VOSclim (a high-quality subset of the VOS fleet) measurements and automated measurements were of slightly higher quality than manual ship measurements in general. Beggs et al. [2012] showed that Australia Integrated Marine Observing System ships had uncertainties comparable to those from data buoys. Analyses that have looked at statistics for individual ships and buoys have found that some ships and buoys take much higher quality measurements than others [Kent and Berry, 2008; Brasnett, 2008; Kennedy et al., 2011a; Atkinson et al., 2013]. The subset of ships (around 40-50% of ship observations) that passed the more stringent quality control procedures of Atkinson et al. [2013] had significantly lower measurement uncertainties assessed using the method of Kennedy et al. [2011a] than did the full fleet of ships. Early results on hull sensors reported by Emery et al. [1997] indicated the potential for these sensors to make accurate measurements. Indeed, Kent et al. [1993] found that hull sensors installed on ships in the Voluntary Observing Ships Special Observing Project for the North Atlantic (VSOP-NA) gave consistent measurements during the two year observing period.
Drifting buoy measurements are generally more accurate and consistent than ship measurements, but there is a greater relative spread between the estimates which are summarized in Table 2. In part these differences are likely to arise from the level of pre-screening that is applied to the observations. Where quality control is more stringent, estimated uncertainties are likely to be lower and, where the error variance of the observations is low already, the effects of quality control and processing choices are likely to be more pronounced [Xu and Ignatov, 2012]. Castro et al. [2012] considered differences between drifting buoys and two different satellite products and found that there was little difference between buoys produced by different manufacturers. There is some evidence that the quality of drifting buoy observations has improved slightly over time [Merchant et al., 2012, Lean and Saunders, 2013]. As a comparison, temperature measurements from Argo have been reckoned to have an uncertainty of around 0.002K [Abraham et al., 2013].
| References | Estimated measurement uncertainty for drifting buoy measurements |
|---|---|
| Strong and Mclean [1984] | 0.6K RMS difference between drifter and AVHRR |
| Reynolds et al. [2002] pg 1613 | 0.5K |
| Emery et al. [2001] pg 2393 | 0.3K |
| Cummings [2005] Table 1, pg 3592 | 0.12K |
| O'Carroll et al. [2008] abstract | 0.23K |
| Kent and Berry [2008] Table 5c pg 12 | 0.67K |
| Ingleby [2010] Table 10 pg 1487 | 0.33K |
| Kennedy et al. [2011a] pg 83 | 0.2-0.4K |
| Xu and Ignatov [2010] pg 16 of 18 | 0.26K |
| Merchant et al. [2012] Table 2 pg 8 of 18 | 0.15-0.19K |
| Lean and Saunders [2013] abstract | 0.19-0.15K |
| Xu and Ignatov [2016] abstract | 0.21-0.22K |
Table 2: List of estimates of measurement error uncertainties for drifting buoys where uncorrelated and systematic errors were not dealt with separately.
Moored buoys have received less attention. Estimates of the measurement uncertainties are summarized in Table 3. The two studies [Kennedy et al., 2011a; Xu and Ignatov, 2010] that examined moorings from the GTMBA separately from other moorings found that they had lower measurement error uncertainties. Castro et al. [2012] found that the standard deviations of differences between moorings and satellite data were lower for tropical moorings than for coastal moorings. They noted that in coastal waters there can be large local variations in temperature, which satellites cannot resolve. Some moorings along coastlines are located in estuaries and river mouths and are therefore less likely to be representative of open ocean areas. This is perhaps one reason why Wilkerson and Earl [1990], who studied US coastal buoys, found such large standard deviations between ships and moorings (Table 1). Merchant et al. [2012] found that few coastal moorings met their required stability criteria.
| References | Estimated measurement uncertainty for moored buoy measurements |
|---|---|
| Cummings [2005] Table 1, pg 3592 | 0.05K |
| Kent and Berry [2008] Table 5b pg 11 | 0.4K |
| Kennedy et al. [2011a] pg 83 | tropical moorings, 0.12 K; all moorings, 0.21 K |
| Xu and Ignatov [2010] pg 16 of 18 | tropical moorings, 0.30 K; coastal moorings, 0.39 K |
| Gilhousen [1987] Table 6 pg 104 | 0.22K |
| Xu and Ignatov [2016] abstract | tropical moorings, 0.17K; all moorings, 0.40K |
Table 3: List of estimates of measurement error uncertainties for moored buoys where uncorrelated and systematic errors were not dealt with separately.
As noted in section 2, uncorrelated observational errors are of relatively minor importance in large-scale averages (see Figure 8 and section 3.5), particularly in the modern period when observations are numerous. For an uncertainty of 1.0 K for a single observation due to uncorrelated observational error, the resulting uncertainty of a global annual average based on 10000 observations would be of order 0.01 K.
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