Written by Dr. Yawen Shao

  • A new statistical time variability correction (TVC) method is developed to:
    • Quantify time series variance errors at various time scales.
    • And correct these errors in the post-processing mode.
  • CMIP6 (The Coupled Model Intercomparison Project Phase 6) models misrepresent variances of maximum temperatures at differing time scales, particularly seasonal ones.
  • TVC significantly improves the variance and time-lag correlation attributes of model times series.

Why is post-processing important?

Global and regional climate models serve as critical tools for predicting climate conditions over the coming decades and centuries. These models, while invaluable, inherently contain systematic errors due to their simplified representations of the earth’s complex systems. For individual models, to enhance the accuracy of climate predictions, statistical post-processing techniques are essential. Numerous bias adjustment methods have been developed and widely adopted in the climate modelling community. The importance of bias adjustment is underscored by the IPCC Sixth Assessment Report, which states that ‘Bias adjustment has proven beneficial as an interface between climate model projections and impact modelling in many different contexts (high confidence).’ 

What is the merit of the TVC method?

This paper by Shao et al. (2024) introduces a novel time variability correction (TVC) method designed to diagnose and rectify variance errors across a range of time scales, such as annual, seasonal, synoptic, and so on. Unlike existing bias adjustment and post-processing methods, TVC accomplishes the following:

1) Addresses variance and covariance errors within and across time scales.

2) Enhances the realism of the temporal correlation within the model series.

3) Preserves the sequence of events observed in the raw model data.

Conceptually, TVC represents today’s temperature by considering backward-looking time series averages at specific time scales. These averages are summed to represent today’s temperature, and the sum of timescale averages varies from one day to the next. In this work, we select nine different time scales to filter time series, ranging from 365 to 2 days. This approach enables the computation of covariances between time scale averages and reveals differences between model covariances and observed ones at various time scales for specific locations (Figure 1). Subsequently, TVC allows us to map a model series to a new one with more realistic inter-timescale covariances. Detailed information about the algorithm is available in the Methods section of the paper.

In our study, TVC is applied to CMIP6 global maximum temperature projections, demonstrating substantial improvements in variance, and time-lag correlations during the in-sample historical period. Notably, TVC also enhances projections in the out-of-sample ssp126 and ssp585 scenarios (Figure 2). When applied to future temperature projections using real observations, TVC results in increased temperature variance in most middle to high latitude land regions in the Northern Hemisphere, and decreased variance in most low to middle latitude land regions, in comparison to simple mean-corrected projections (Figure 3).

Figure 1: Heatmaps of matrix of covariance across time scales for a) observations and b) mean-corrected raw ACCESS-ESM1-5 simulations for maximum temperature at a grid cell (37.5°S 144.5°E) over 1950-2014.
Figure 2: Box plot showing the percentage of improvement in mean absolute errors of maximum temperature a) variance and b) lag-1 correlation for each model-as-truth and each experiment. The in-sample historical period is 1950-2014, and the out-of-sample projection period for ssp126 and ssp585 is 2015-2100. 
Figure 3: Difference in variance (a,b), lag-1 correlation (c,d), and lag-5 correlation (e,f) between TVC and mean-corrected raw predictions across the globe for in-sample historical over Dec 1951-2014 and out-of-sample ssp585 over Dec 2016 – Dec 2100. The variance is the averaged value across all CMIP6 models.

Who would benefit from using this technique?

The TVC method offers substantial benefits to climate-sensitive sectors, including agriculture, water resources and the energy industry. By applying TVC to various climate variables, these sectors can anticipate using climate change projections that exhibit improved climate variability, enhanced temporal correlations, and a more accurate representation of extreme events.

The TVC method is implemented on a point-by-point basis, making it adaptable for specific regions. Whether you are working with data from a single location, a few stations or national grid points, TVC can generate post-processed outputs. While this paper primarily focuses on post-processing daily time series data, the TVC method has theoretical applicability to monthly data as well.

How to access the TVC program?

The TVC codes, along with all other Python scripts for data analyses and figure plotting, have been published on Zenodo and can be accessed here.

To utilize these codes, users should have proficiency in Python programming and pre-install a few Python packages. The readers are free to reach out to me if they have any questions regarding program running.

Next step

Future research will extend the application of TVC to post-process daily precipitation data. Additionally, future work will explore the potential of combining TVC with a model weighting technique to better assess the uncertainty in multi-model projections.

Reference

Shao, Y. (2023). Time Variability Correction (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.10212122.

Shao, Y., Bishop, C. H., Hobeichi, S., Nishant, N., Abramowitz, G., & Sherwood, S. (2024). Time variability correction of CMIP6 climate change projections. Journal of Advances in Modeling Earth Systems, 16(2), e2023MS003640. https://doi.org/10.1029/2023MS003640.