The aim of this study is to investigate the capability of three machine learning models, including Gaussian Process Regression (GPR), Gradient Boosted Decision Trees (GBDT), and Long Short-Term Memory (LSTM) neural networks, for short-term prediction of precipitable water vapor (PWV) using a limited amount of training data and to determine the minimum training period required to achieve acceptable prediction accuracy at the local scale. For this purpose, hourly PWV data derived from GNSS observations at five stations, HSHG, MRGD, PKDT, SPHR, and TNGO, in Tehran were used over a 36-day period corresponding to days of year (DOY) 312 to 347 of 2021. To investigate the effect of training-period length on model performance, three scenarios were defined. In each scenario, one, two, and three consecutive days of data were used for training, respectively, followed by the subsequent three days for evaluation, using six separate time windows with a six-day interval between consecutive windows.

Prior to modeling, considering the presence of periodic components in the PWV time series, a peak-to-background ratio (PBR) analysis was performed to examine the relative prominence of the 12- and 24-hour periods. The mean PBR values across the five stations were 3.63 and 3.24 for the 24- and 12-hour periods, respectively. These results confirmed the importance of the dominant periodic variations in the PWV time series. Accordingly, the periodic components were first extracted using a harmonic model including 12- and 24-hour periods. The residual component was then obtained by subtracting the periodic component from the observed PWV values. The residual component at time t was used as the input to predict the periodic and residual components at time t+1. Finally, the PWV values for the test period were obtained by summing the predicted periodic and residual components.

The performance of the models was evaluated using RMSE and the Pearson correlation coefficient, together with a statistical pairwise comparison of the models. In addition to the GNSS data, ERA5 estimates and radiosonde-derived values transferred to the elevations of the GNSS stations were used as complementary reference datasets. To determine the statistical significance of differences in model performance, a paired t-test was applied to the mean RMSE values of each pair of models. Furthermore, to evaluate the capability of the machine learning models against an empirical model for estimating PWV, their errors were compared with those of ERA5. For an independent evaluation, radiosonde-derived values from the Mehrabad station in Tehran were transferred to the elevations of three nearby GNSS stations, namely MRGD, PKDT, and TNGO. The predictions obtained from the three models were then evaluated against the corresponding radiosonde-derived values.

The results showed that increasing the training period generally reduced the prediction error of all three models. The overall mean RMSE decreased from 2.04 mm in the first scenario to 1.00 and 0.69 mm in the second and third scenarios, respectively. Under the same conditions, the mean RMSE values of GBDT decreased from 3.43 to 2.20 and 1.65 mm, while those of LSTM decreased from 3.56 to 1.85 and 1.55 mm. Therefore, GPR achieved the lowest mean RMSE among the three models in all three scenarios, demonstrating its superior performance under limited training-data conditions.

Furthermore, the RMSE of GPR in the second and third scenarios was lower than that of ERA5, with RMSE values of 1.15 and 1.25 mm, respectively. The Pearson correlation analysis showed that, in the first scenario, the correlation between the GPR predictions and the GNSS reference values ranged from 0.80 to 0.91. This range increased to 0.94–0.98 in the second and third scenarios, indicating the higher capability of GPR to reproduce the temporal variations of PWV with an increase in the amount of training data. In the independent evaluation against radiosonde-derived values, the mean RMSE of GPR decreased from 2.09 mm in the first scenario to 1.31 and 1.25 mm in the second and third scenarios, respectively.

Overall, the results showed that GPR provided more accurate and consistent performance than GBDT and LSTM under limited training-data conditions. Increasing the training period, particularly from one to two days, resulted in a notable improvement in prediction accuracy and correlation. Based on the findings of this study, GPR can be considered a suitable option for short-term PWV prediction at the local scale and for near-real-time applications.