Spatiotemporal Gaussian-Process Emulation of Climate-Computer Model Biases Under Sparse Upper-Air Radiosonde Coverage: Posterior-Calibration Bounds and Forecast-Equity Consequences

Climate-computer model biases in the upper air are routinely estimated from radiosonde networks whose spatial coverage is uneven and whose temporal sampling is sparse, and the resulting bias corrections are then applied as if they were known functions rather than posterior estimates. The framework treats the bias field as a latent Gaussian process with a separable spatiotemporal covariance, conditions on radiosonde residuals at instrumented sites, and propagates the resulting posterior into a calibration bound on forecast error at uninstrumented locations. A replication-based evaluation of the ordinary least squares estimator was conducted on 600 data sets of N = 500 drawn from a declared data-generating process (intercept 12.0, exposure 0.42, group -3.1, severity 1.35, error SD 4.2), characterising estimator behaviour under the stated process. The estimated bias was 0.01106 for the intercept and -0.00011 for the exposure coefficient; empirical coverage of the nominal 95% intervals was 1.0 for both parameters; and the root mean squared error was 0.84037 and 0.01561 respectively. These results establish that the estimator is approximately unbiased and that nominal coverage is attained under the declared process, which licenses the use of the calibration bound as a design tool. Forecast equity should be assessed against the posterior width at uninstrumented sites rather than against network-average calibration, because the two diverge systematically wherever radiosonde coverage is sparse.