  Time evolving surfaces can be modeled as two-dimensional Functional time
series, exploiting the tools of Functional data analysis. Leveraging this
approach, a forecasting framework for such complex data is developed. The main
focus revolves around Conformal Prediction, a versatile nonparametric paradigm
used to quantify uncertainty in prediction problems. Building upon recent
variations of Conformal Prediction for Functional time series, a probabilistic
forecasting scheme for two-dimensional functional time series is presented,
while providing an extension of Functional Autoregressive Processes of order
one to this setting. Estimation techniques for the latter process are
introduced and their performance are compared in terms of the resulting
prediction regions. Finally, the proposed forecasting procedure and the
uncertainty quantification technique are applied to a real dataset, collecting
daily observations of Sea Level Anomalies of the Black Sea
