Online climate change projections report Production of data
Here we summarise the computational procedure used to generate probabilistic projections for UKCP09 for the A1B scenario, from the elements described in the preceding sub-sections. Figure 3.12 gives a schematic overview of the main elements of the procedure, described in more detail below.
- Produce a large (106 members) of the parameter space of surface and atmospheric processes in HadSM3, using our emulator (Section 3.2.3) to estimate multiannual mean global fields of the set of the recent climate variables identified as observational constraints in Section 3.2.9, and of the equilibrium response to doubled CO2 for the set of variables for which future projections are required (Table 1.1), at UK land and marine points in our global climate model (downscaling is handled later in step (vi)). Uncertainties in emulated model output, observational errors and discrepancy are accounted for by sampling from their specified distributions, obtained respectively from calibration of the emulator against climate model simulations, estimates of observational errors statistics derived either from the use of alternative datasets or (where available) formal published estimates (Section 3.2.9), and the use of HadSM3 to predict the results of an ensemble of alternative climate models (see Section 3.2.8). At this stage, an interim weight is calculated for each Monte Carlo sample member, based on the recent climate observables but neglecting the Braganza et al (2003) indices of historical temperature change.
- Sub-sample 25,000 of the 106 members. This is necessary because step (iii) below involves running a simple climate model, which places computational restrictions on the sample size. In selecting the 25,000 members, we use the interim weights from (i) to ensure that different parts of parameter space are sampled with a likelihood approximately consistent with their likely final contribution to the final probabilistic projections.
- Obtain realisations of time-dependent climate changes for the 21st century (such as those shown in Figure 3.2) by applying our timescaling technique to each of the 25,000 members from (ii). This is done by forcing our simple climate model from 1860–2100 with time series of historical and future forcing agents, using emulated values of regional equilibrium responses and land and ocean climate sensitivities (see Section 3.2.4), and sampling values of timescaling error, ocean heat uptake, carbon cycle feedback and sulphate aerosol forcing from the distributions described in Sections 3.2.4 and 3.2.6. Calculate the final weight to be assigned to each point in parameter space, given by the emulated values of present-day climate observables from step (i), plus the Braganza et al. (2003) indices measuring changes in surface temperature patterns for the period 1970–1999 relative to 1910–1939 (see Section 3.2.9).
- Sub-sample the 25,000 points according to the ratio of the final weights from (iii) to the interim weights from (i). This produces a final sample of 10,000 points which can be treated as a set of individual estimates of equal likelihood, based on the final weights. This further restriction of the sample size is done in order to provide a dataset which can be processed by users without placing an excessive burden on their data processing facilities.
- Ideally, step (iv) would provide, for relevant GCM grid boxes, 10,000 samples of the joint variations between all the future variables of interest, at all times of the year (see Table 1.1), for all future periods of interest (Figure 1.3). However, such a large joint calculation is not computationally feasible, so the data are split into smaller batches. Each of the five GCM land boxes and nine marine boxes is treated separately, in two distinct batches containing different subsets of the required variables, making 28 batches in all. For a given grid box, the first batch includes all variables relating to temperature and precipitation in Table 1.1, and the additional variables required as input to the UKCP09 Weather Generator (with the exception of the correlation between successive daily precipitation amounts), for all times of the year and all future periods. The second batch covers the remaining variables. Within a given batch, the sampled values for different variables, months/seasons and future periods include a fully consistent treatment of covariances between both the best estimate values of the variables (driven by variations in the various climate and simple model parameters controlling the relevant physical and biogeochemical processes), and between their sampled errors. Many of these errors are actually assumed independent of one another (e.g. we assume no relationship between emulation errors, timescaling errors, observational errors or discrepancy values), however we do account for covariances between emulation errors for different variables, months (or seasons) and locations in parameter space, and between timescaling errors for different variables for a given month/season and future period. Data in different batches (e.g. projections of a given variable for a given month and future period, but at different GCM boxes), will account for physically-driven covariances between the variables, but not for the statistical error covariances identified above. The implications of handling variables from separate batches are discussed further in the UKCP09 User Guidance.
- Sampled climate changes for a given batch are then converted into 10,000 equiprobable estimates for UKCP09 target locations (i.e. 25 km squares or aggregated regions, see Figure 1.2) using our downscaling relationships, sampling values for the regression coefficients and residuals assuming Gaussian distributions with means and variances determined from the fitting procedure described in Section 3.2.11. Joint probabilities can be estimated from these downscaled samples for changes in two or more variables in the same batch.
- Marginal posterior probabilities for individual climate variables for each UKCP09 target location and period are generated by a slightly different procedure. In this case, we start from probabilistic projections of the relevant variable from the appropriate GCM grid box, adjusting values associated with different probability levels of the Cumulative Distribution Function (CDF) according to the slope and uncertainty in the appropriate downscaling relationship, and hence generating an updated CDF appropriate to the required 25 km grid box or administrative region. This procedure provides a robust numerical approximation to a full (but unfeasible) integration over the entire model parameter space.
- The sampled data were not considered robust either below the 1% probability level or above the 99% probability level, so we prevented the sampled data from going outside that range. That is, for a given combination of variable, location, time of year, future period and emissions scenario, the values of sampled data below the 1% probability level are set to the value of the 1% probability level from the corresponding CDF, and values above the 99% probability level are set to the value of the 99% probability level. Three variables used by the weather generator (variance and skewness of daily precipitation and variance of daily temperature) are higher order statistics than the other variables, and were considered less robust; for these three variables we set the limits at the 5% and 95% probability levels.