Extending A Posteriori Random Forests for Multivariate Statistical Downscaling of Climate Change Projections
Authors: Legasa Mikel N. , Thao Soulivanh , Vrac Mathieu , Casanueva Ana , Manzanas Rodrigo 
Published: February 2023

Under the perfect prognosis approach, statistical downscaling (SD, Guti&#233;rrez et al., 2019) methods aim to learn the relationships between large-scale variables from reanalysis and local observational records. Typically, these statistical relationships, which can be learnt employing many different statistical and machine learning models, are subsequently applied to downscale future global climate model (GCM) simulations, obtaining local projections for the region and variables of interest.&#160;A posteriori random forests (APRFs) were introduced in a recent paper (Legasa et al., 2021) for precipitation downscaling, but can be potentially used to estimate any probabilitydistribution. While performing similarly to other state-of-the-art machine learning methodologies like convolutional neural networks in terms of predictive performance (as measured in terms of correlation of the downscaled series with the observed series), APRFs produce less biased simulations, as measured by several distributional indicators.Furthermore, climate change signals projected by APRFs are consistent with those given by the raw GCM outputs, thus proving suitable for downscaling local climate change scenarios (Legasa et al. 2023, in review). Moreover, they also automatically select the most adequate large-scale variables and geographical domain of interest, a time-consuming task and potential source of uncertainty (Manzanas et al. 2020) when downscaling climate change projections.In this work we show how the APRF methodology can be easily extended to more complex and multivariate distributions. One of the proposed extensions is temporal APRFs, which explicitly model the transition in time for a variable and location of interest (e.g. the rainfall probability conditioned to the dry/wet state of the previous day), thus improving the temporal consistency of the downscaled series in terms of several temporal (e.g. spells) indicators. Other possible extensions within the APRF framework include predicting the joint probability distribution of several geographical locations, thus improving the spatial consistency of the downscaled series; and modeling the multivariate joint distribution of different meteorological variables (e.g. precipitation, humidity and temperature).
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References
Guti&#233;rrez, J.M., Maraun, D., Widmann, M. et al. An intercomparison of a large ensemble of statistical downscaling methods over Europe: Results from the VALUE perfect predictor cross-validation experiment. Int. J. Climatol. 2019; 39: 3750&#8211; 3785. doi: https://doi.org/10.1002/joc.5462
Legasa, M. N., Manzanas, R., Calvi&#241;o, A., & Guti&#233;rrez, J. M. (2022). A posteriori random forests for stochastic downscaling of precipitation by predicting probability distributions. Water Resources Research, 58 (4), e2021WR030272. doi: https://doi.org/10.1029/2021WR030272
Legasa, M. N., Thao, S., Vrac, M., & Manzanas, R. (2023). Assessing Three Perfect Prognosis Methods for Statistical Downscaling of Climate Change Precipitation Scenarios. Submitted to Geophysical Research Letters.
Manzanas, R., Fiwa, L., Vanya, C. et al. Statistical downscaling or bias adjustment? A case study involving implausible climate change projections of precipitation in Malawi. Climatic Change 162, 1437-1453 (2020). doi: https://doi.org/10.1007/s10584-020-02867-3