Bias correction on a grid point for a long period of time can be a complex task and there are several methods that you can use depending on the specific details of your analysis.

One common approach is to use a bias correction algorithm, such as the delta method, the bias correction factor (BCF) method or the quantile mapping method. These methods are commonly used to correct for systematic errors in climate models, and they can also be applied to other types of datasets.

The delta method (also known as the "delta change factor" or "delta factor" method) involves calculating the ratio of the model-simulated change in a variable to the observed change in that variable for a specific grid point and time period. The BCF method, on the other hand, involves estimating the ratio of the bias-corrected simulation to the original simulation for each grid point and time period.

The quantile mapping method is based on the empirical cumulative distribution function of the model output and the corresponding observational data. It maps the model output to the observational data distribution.

Another approach could be to use a Bayesian hierarchical model, which allows to incorporate information from multiple sources, such as observational data, reanalysis data, and model output. This approach allows to use information from all the available data to improve the estimation of the bias correction factor.

It is important to note that, regardless of the method used, bias correction should be done with caution and it is important to evaluate the performance of the bias corrected dataset in a robust way, through a validation process, and also to report the uncertainty associated with the bias correction.

I once faced the same problem and developed two different tools for it.

(1). The first (and slower) is the Python package python-cmethods (https://github.com/btschwertfeger/python-cmethods)

(2). The way faster command-line tool BiasAdjustCXX (https://github.com/btschwertfeger/BiasAdjustCXX) DOI: https://doi.org/10.1016/j.softx.2023.101379.

Both can be applied to interval- and ration-based variables on 1- and 3-dimensional data sets. The following bias correction techniques are available:

• Linear Scaling
• Variance Scaling
• Delta Method
• Quantile Mapping
• Quantile Delta Mapping

... both tools are free, open source and made by me. So in case there are any questions - feel free to contact me.

Benjamin Thomas Schwertfeger Osinachi Ekeagwu Thanks to both of you.