By Hans Roelofsen
Abstract
A design based approach to estimate global mean temperature and temporal differences in global mean temperature was developed, as an alternative to to existing datasets of mean annual temperature which are model-based. A Stratified Simple Random Sampling design was employed. A sample consists of n measurements of mean annual temperature on random locations, but optimally distributed over 34 strata according to a fixed sample fraction fK, with a minimum of 2 measurements per stratum. The sample size was determined by the available budget, whilst the relative area, sampling costs and internal variance of mean annual temperature determine the sample fraction fK of each stratum.
To construct the strata, seven cost- and eleven temperature strata were combined to give 34 unique combinations. The cost strata are areas where costs for measuring temperature are similar; temperature strata are internally relatively homogeneous with respect to mean annual temperature according to the Köppen climate classification. Besides the Köppen classification, which only covers land, a Sea Surface Temperature dataset was to create strata in the oceans. The range of SST values of the World Ocean Atlas Dataset v.2 was classified into six equidistant classes, where the corresponding areas formed the six sea temperature strata. Projecting the strata using an equal area projection allowed the area calculation of each stratum.
The variance of mean annual temperature within each temperature stratum was calculated from meteorological stations around the globe and SST observations from ships and buoys. With known internal variance, area and costs per stratum, the number of measurements per stratum was calculated and corrected to the nearest integer 2. The standard deviation of the estimated global average was set as a measure for the accuracy and was calculated for a range of budgets. With increasing budget -> sample size -> true costs, the standard deviation decreased towards its asymptote at 0, i.e. the accuracy increased. Comparison with currently used datasets revealed that this method can produce a more accurate estimate of the global mean annual temperature if at least 310 million euro is spent on sampling temperature.
To assess the accuracy of mean temperature differences over one, two. five and ten years, four variables dT1, dT2, dT5 and dT10 were defined. Calculation of the accuracy of the estimated mean for each variable was similar to the procedure given above,, but the within stratum variance needed to be redefined for each variable. Therefore, each record in the datasets was updated with 10 dT1, 9 dT2, 6 dT5 and 1 dT10 values. The variance was calculated in each stratum for all differences of a specific pair of years. The within stratum variance was computed as the average of those variances. The sample size fraction and the accuracy was calculated for all four variables and showed that the accuracy of the estimated difference decreased with increasing temporal difference, but increased with a larger sample size.
To conclude, it was shown that a design based approach can be used for estimating global mean temperature with predicted accuracy. The approach lacks any assumptions or model parameters, so the outcome is valid by construction and cannot be subject to discussion about models being used. Fine-tuning the strata and finding a better estimate of the within stratum variance are matters for future research which will improve the accuracy of the estimated mean.
Keywords: climate change, design-based, stratified simple random sampling, annual global mean temperature, accuracy, difference in annual global mean temperature.