Climate models are biased with respect to real-world observations. They usually need to be adjusted before being used in impact studies. The suite of statistical methods that enable such adjustments is called bias correction (BC). However, BC methods currently struggle to adjust temporal biases. Because they mostly disregard the dependence between consecutive time points. As a result, climate statistics with long-range temporal properties, such as the number of heatwaves and their frequency, cannot be corrected accurately. This makes it more difficult to produce reliable impact studies on such climate statistics. This article offers a novel BC methodology to correct temporal biases. This is made possible by rethinking the philosophy behind BC. We will introduce BC as a time-indexed regression task with stochastic outputs. Rethinking BC enables us to adapt state-of-the-art machine learning (ML) attention models and thereby learn different types of biases, including temporal asynchronicities. With a case study of number of heatwaves in Abuja, Nigeria and Tokyo, Japan, we show more accurate results than current climate model outputs and alternative BC methods.

Bias correction is a critical aspect of data-centric climate studies, as it aims to improve the consistency between observational data and simulations by climate models or estimates by remote sensing. Satellite-based estimates of climatic variables like precipitation often exhibit systematic bias when compared to ground observations. To address this issue, the application of bias correction techniques becomes necessary. This research work examines the use of deep learning to reduce the systematic bias of satellite estimations at each grid location while maintaining the spatial dependency across grid points. More specifically, we try to calibrate daily precipitation values of tropical rainfall measuring mission based TRMM_3B42_Daily precipitation data over Indian landmass with ground observations recorded by India Meteorological Department (IMD). We have focused on the precipitation estimates of the Indian Summer Monsoon Rainfall (ISMR) period (June–September) since India gets more than 75% of its annual rainfall in this period. We have benchmarked these deep learning methods against standard statistical methods like quantile mapping and quantile delta mapping on the above datasets. The comparative analysis shows the effectiveness of the deep learning architecture in bias correction.

Let ?(u) be the probability of eventual ruin in the classical Sparre Andersen model of risk theory if the initial risk reserve is u. For a large class of such models ?(u) behaves asymptotically like a multiple of exp (–Ru) where R is the adjustment coefficient; R depends on the premium income rate, the claim size distribution and the distribution of the time between claim arrivals. Estimation of R has been considered by many authors. In the present paper we deal with confidence bounds for R. A variety of methods is used, including jackknife estimation of asymptotic variances and the bootstrap. We show that, under certain assumptions, these procedures result in interval estimates that have asymptotically the correct coverage probabilities. We also give the results of a simulation study that compares the different techniques in some particular cases.