## 4 Discussion
### The Model Comparison
Regarding the applicability of the methods, the linear bias correction (dbERA model) is the simplified and cost-effective approach to constructing a continuous time series. The dbERA method can be applied for the gap-filling of spatially correlated meteorological variables, such as atmospheric pressure or air temperature and humidity. The performance of the dbERA model is far from perfect. Meteorological characteristics formed under the essential impacts of local conditions (wind speed and direction, soil temperature) are the most sensitive to selection of the model type and training dataset. High-cost computation models (NN or GPRexp) should be used for simulation of these variables. NN models are widely used for gap-filling of meteorological time series [27; 28; 29; 30; 42; 43]. Air temperature, pressure and relative humidity, wind, and irradiance characteristics were  
Figure 9: The comparison of observed (x) and modelled (y) meteorological variables from the GPRexp model based on the ERA dataset. 1—air surface pressure (hPa), 2—air temperature (°C), 3—incoming photosynthetically active radiation (\(\mu\)mol/m\({}^{2}\)/s), 4—relative air humidity (%), 5—wind speed (m/s), 6—wind direction (deg), 7—net radiation (W/m\({}^{2}\)), 8—soil temperature at 5 cm (°C); blue—training subset; red—validation subset, (a) observed (y) vs. modelled (x), (b) error (y \(-\) x) vs. modelled (x). successfully simulated by the bilayer NN model. The hidden and nonlinear interrelations in the climate system were revealed and reproduced by the NN model with an efficient number of hidden layers. The increased number of hidden layers and neurons do not result in an increase in the model's performance, hence a relatively simple NN model is recommended for further application. The benefit of the GPR models in comparison to the others is the best performance metrics obtained for the training dataset. The volume of training dataset is critically important for the model identification. Actually, the best strategy for application of the GPRexp model is the use of the full dataset to retrain the model after the validation phase. The model parameters estimated after model retraining should be used for application of the model for construction of a continuous time series of meteorological variables. A simulated dataset will have neglectable difference with in situ measured values. The decomposition of initial input variables into principal components and the subsequent decrease in number of inputs (PCA dataset) lead to improvement (decline) of the computation costs, and reduction of the model's performance. The first 25 principal components describe more than 99% of the variability of the initial dataset, but results in lower _CC_ and _KGE_ metrics for all studied target variables and models. The NN model is less sensitive to change of the input dataset from PCA to ERA. In summary, the performance of all studied models is good enough except raw ERA5-Land data. Any method of correction of raw reanalysis data results in an improvement of representation of local meteorological characteristics. Optimized parameters for gap-filling models estimated from the training model using in situ observations are related to the target variable, and very likely should be site specific. An attempt at spatial interpolation of linear bias correction coefficient for sums of atmospheric precipitation was performed for South Siberia [21]. Spatial structure of the model coefficients for other meteorological variables and complex models is not obvious and can be studied in future research. The further application of the studied gap-filling models will be performed for a full dataset of the 67 observed meteorological variables available at the Mukhrino Field Station [49]. A routine procedure for annual data records should be developed and used after annual replenishment of the in situ observation database. Implementation of new data into the model training process will result in a change of the model parameters and refinement of gap-filled data records.