Synthetic time series created from historical streamflow data are thought of as substitute events with a similar likelihood of recurrence to the real event. This technique has the potential to greatly reduce the uncertainty surrounding measured streamflow. The goal of this study is to create a synthetic streamflow model using a combination of Markov chain and Fourier transform techniques based on long-term historical data for the Nile River. First, the Markov chain’s auto-regression is applied, in which the data’s trend and seasonality are discovered and eliminated before applying the Pearson III distribution function. The Pearson III distribution function is substituted by a discrete Fourier transform (DFT) technique in the second approach. The applicability of the two techniques to simulate the streamflow between 1900 and 1999 is evaluated. The ability of the generated series to maintain the four most important statistical properties of the samples of monthly flows, i.e., the mean, standard deviation, autocorrelation lag coefficient, and cumulative distribution, was used to assess the quality of the series. The results reveal that the two techniques, with small differences in accuracy, reflect the monthly variation in streamflow well in terms of the three mentioned parameters. According to the coefficient of determination (R2) and normalized root mean square error (NRMSE) statistics, the discrete Fourier transform (DFT) approach is somewhat superior for simulating the monthly predicted discharge.

Hydrological data in general and water quality (WQ) data in particular frequently suffer from missing records and/or short-gauged monitoring/sampling sites. Many statistical regression techniques are employed to substitute missing values or to extend records at short-gauged sites, such as the Kendall-Theil robust line (KTRL), its modified version (KTRL2), ordinary least squares regression (OLS), four MOVE techniques, and the robust line of organic correlation (RLOC). In this study, in aspiring to achieve better accuracy and precision, the À Trous-Haar wavelet transform (WT) was adopted as a data denoising preprocessing step prior to applying record extension techniques. An empirical study was performed using real WQ data, from the National WQ monitoring network in the Nile Delta in Egypt, to evaluate the performance of these eight record-extension techniques with and without the WT data preprocessing step. Evaluations included the accuracy and precision of the techniques when used for the restoration of WQ missing values and for the extension of the WQ short-gauged variable. The results indicated that for the restoration of missing values, the KTRL and WT-KTRL outperformed other techniques. However, for the extension of short-gauged variables, WT-KTRL2, WT-MOVE3, and WT-MOVE4 techniques showed more accurate and precise results compared with both other techniques and their counterparts without the WT.

Terrestrial Water Storage (TWS) monitoring is critical for understanding hydrological dynamics and ensuring sustainable water resource management in arid countries such as Egypt, where data scarcity and climate variability pose significant challenges. The Gravity Recovery and Climate Experiment (GRACE) data provides valuable insights into TWS variability by tracking temporal changes in Earth’s gravitational field. However, GRACE’s coarse spatial resolution (~0.5°) restricts its direct application for regional-scale hydrological assessments. This study addresses this limitation by developing a statistical downscaling framework to enhance GRACE-derived Terrestrial Water Storage Anomalies (TWSA) from 0.5° to 0.1° resolution over Egypt for the period April 2002 to October 2024. The framework integrates machine learning models, including Random Forest (RF), Boosted Regression Trees (BRT), and Extreme Gradient Boosting (XGBoost). ERA5 reanalysis climate data, comprising 13 variables, were evaluated, and the 10 most influential predictors, including soil moisture, total evaporation, and net solar radiation, were selected based on their correlation with monthly GRACE TWSA. Results demonstrate that the downscaling approach significantly improves spatial detail and captures localized TWS variations. Declining storage trends were observed in western and central Egypt, while relatively stable or increasing trends were identified in southeastern regions, including parts of Sinai. The models achieved strong predictive performance (R up to 0.91; RMSE up to 1.43), with residual kriging further enhancing spatial continuity and reducing local biases. The validated high-resolution TWSA dataset provides a valuable resource for groundwater monitoring, drought risk assessment, and sustainable water management. Future studies should integrate anthropogenic influences, such as groundwater extraction and land-use change, to further refine TWS assessments.