Level Time Series Research Articles

Generalized Logistic Function: A Retracker to Improve the Accuracy of Water Level Time Series in Coastal Areas and Lakes

The efficiency of satellite altimetry in monitoring coastal areas and lakes is limited due to the contaminated waveform caused by non-water features included in the satellite footprint. Therefore, to mitigate these limitations, waveforms need to be retracked. In this research, the Generalized Logistic Function (GLF) has been introduced with Analytical (GLFA) and Numerical (GLFN) approaches to retrack the first sub-waveform. The results have been compared with those obtained from on-board retrackers existing in Level-2 altimetry data, the retracking of the full-waveform, the first sub-waveform, and the mean of the sub-waveforms using the threshold retracker. The Level-2 and Level-1B data of the Sentinel-3A (SRAL) mission for passes 141, 700, 244, and 311, respectively, passing over Vättern and Hjälmaren Lakes in Sweden, and 0–2 km distance from the coasts of the Bay of Alcudia and the Northeast Gulf of Bothnia from January 2019 to December 2022, were investigated. The results of the retracking approaches used in this study were evaluated against tide gauge data in terms of RMSE and its improvement percentage. The results demonstrate the superiority of the GLFA over the GLFN in coastal areas, while over lakes, the results are nearly equivalent. The improvement percentages of RMSE for the GLFA and GLFN compared to on-board retrackers, respectively, are as follows: for Vättern Lake, 53% and 58%; for Hjälmaren Lake, 40% and 33%; for the Bay of Alcudia, 81% and 46%; and for the Northeast Gulf of Bothnia, the GLFA shows a 36% improvement, while the GLFN yields results equivalent to on-board retrackers. The GLF has shown better performance compared to other approaches, except for Vättern Lake, which yields results almost equivalent to the first sub-waveform retracking approach. Additionally, the mean of the sub-waveform retracking approach by making use of the threshold algorithm has mostly demonstrated weaker performance compared to other methods.

Machine Learning-Based Reconstruction and Prediction of Groundwater Time Series in the Allertal, Germany

State-of-the-art hydrogeological investigations use transient calibrated numerical flow and transport models for multiple scenario analyses. However, the transient calibration of numerical flow and transport models still requires consistent long-term groundwater time series, which are often not available or contain data gaps, thus reducing the robustness and confidence of the numerical model. This study presents a data-driven approach for the reconstruction and prediction of gaps in a discontinuous groundwater level time series at a monitoring station in the Allertal (Saxony-Anhalt, Germany). Deep Learning and classical machine learning (ML) approaches (artificial neural networks (TensorFlow, PyTorch), the ensemble method (Random Forest), boosting method (eXtreme gradient boosting (XGBoost)), and Multiple Linear Regression) are used. Precipitation and groundwater level time series from two neighboring monitoring stations serve as input data for the prediction and reconstruction. A comparative analysis shows that the input data from one measuring station enable the reconstruction and prediction of the missing groundwater levels with good to satisfactory accuracy. Due to a higher correlation between this station and the station to be predicted, its input data lead to better adapted models than those of the second station. If the time series of the second station are used as model inputs, the results show slightly lower correlations for training, testing and, prediction. All machine learning models show a similar qualitative behavior with lower fluctuations during the hydrological summer months. The successfully reconstructed and predicted time series can be used for transient calibration of numerical flow and transport models in the Allertal (e.g., for the overlying rocks of the Morsleben Nuclear Waste Repository). This could lead to greater acceptance, reliability, and confidence in further numerical studies, potentially addressing the influence of the overburden acting as a barrier to radioactive substances.

Gap filling of water level time series with water area using remote sensing data: a comparative performance analysis of polynomial functions, XGBoost, Random Forest and Support Vector Machine

Freshwater resources are crucial in many fields, such as food and transportation; hence, monitoring and interpretation of inland waters are necessary. Nowadays, remote sensing enables the detection of both water level and surface area of inland waters. In this study, Rathbun and Murray lakes in the U.S.A. were selected to fill gaps in the time series of water levels. Three polynomial functions (1st, 2nd, and 3rd order) and XGBoost, Random Forest, and Support Vector Machine regression methods were used to fill the gaps. The results showed that the XGBoost method outperformed other methods for both lakes. The water level in Lake Murray was determined with an RMSE = 0.31 m and R2 = 0.92, while in Lake Rathbun, it was RMSE = 0.30 m and R2 = 0.95. Based on these results, the XGBoost method could be an important approach for filling gaps in the water level time series.

A Water Mass Balance–Based Procedure Using ERA5 Land Reanalysis and Level Observation to Reconstruct the Past Level Changes of Closed Lakes toward Future Management

Abstract This paper aims to refine an effective procedure to reconstruct the past level changes of closed lakes, as a tool for future management. In most cases, such water bodies are overlooked (particularly when they are small), even if they play a significant role in local communities from the economic and social points of view. In this perspective, this study explores the potential of using reanalysis data, as a single source of data to compute the lake water mass balance, and water level observations. It focuses on some closed lakes with minimal anthropogenic influence in Europe, Africa, and the United States. The number of cases studied is limited by the fact that a significant time series of water levels is difficult to obtain for small lakes. The research leverages ERA5 Land (ERA5L), the land component of ERA5 reanalysis, incorporating the Freshwater Lake (FLake) model. FLake allows simulation of the interaction of inland water bodies with the atmosphere. The use of ERA5L is preceded by data validation by considering satellite observation. To simulate the water mass balance of the selected lakes, the proposed procedure combines precipitation, runoff, and evaporation from the lake, provided by ERA5L, and the lake water level observations. The results indicate that even with a short time series of water level observations, a good agreement (Pearson coefficient ranging from 50% to 90%) between the observed monthly variation of the lake level and the corresponding values of the water storage, computed by using ERA5L, is achieved. The procedure exhibits adaptability and robustness, with an accurate representation of the lake water level trends. However, occasional discrepancies are noted during specific periods, primarily attributed to ERA5L precipitation biases. The proposed procedure can be used only when lake water level observations are available. This limits the number of lakes that it can be applied to. However, the procedure can be applied even with a short time series of data, without the need for additional ground-based or remotely sensed data to compute the water mass balance. Significance Statement This study employs ERA5L reanalysis data and lake level observations to effectively reconstruct the natural variability of closed lake water levels in some monitored lakes in Europe, Africa, and the United States. Results demonstrate the adaptability and robustness of the proposed procedure in capturing the past level changes. Despite occasional discrepancies attributed to precipitation biases, the procedure proves reliable for assessing lake water level trends. Future studies could refine the procedure and extend its applicability, enhancing the ability to monitor environmental changes.

Weather- and climate-driven power supply and demand time series for power and energy system analyses

Reaching net-zero carbon emissions requires large shares of intermittent renewable energy and the electrification of end-use consumption, such as heating, making the future energy system highly dependent on weather variability and climate change. Weather exhibits fluctuations on temporal scales ranging from sub-hourly to yearly while climate variations occur on decadal scales. To investigate the intricate interplay between weather patterns, climate variations, and power systems, we developed a database of time series of wind and solar power generation, hydropower inflow, heating and cooling demand using an internally consistent modeling framework. Here we focused on the European continent and generated country level time series extending between 1940 and 2100. Our database can be used for analyses aimed at understanding and addressing the challenges posed by the evolving energy landscape in the face of deep decarbonization and climate change.

Coastal sea level rise at altimetry-based virtual stations in the Gulf of Mexico

A dedicated reprocessing of satellite altimetry data from the Jason-1/2/3 missions in the world coastal zones provides a large set of virtual coastal stations where sea level time series and associated trends over 2002-2021 can be estimated. In the Gulf of Mexico, we obtain a set of 32 virtual coastal sites, well distributed along the Gulf coastlines, completing the tide gauge network with long-term data that is currently limited to the northern part of the Gulf. Altimetry-based coastal sea level time series and associated sea level trends confirm previous published results that report a strong acceleration in tide-gauge based sea level rise along the US coast of the Gulf of Mexico since the early 2010s. In addition, our study shows that this acceleration also takes place along the western and southern coasts of the Gulf of Mexico. The coastal sea level trends estimated over 2012-2021 amounts to ∼10 mm/yr at most virtual stations. We note a slightly smaller rise on the western coast of Florida and at two sites of the Cuba Island. Good agreement in terms of sea level trends over 2002-2021 is found between coastal altimetry data and tide-gauge record corrected for vertical land motion. Good correlation is also found between coastal altimetry and tide gauge sea level time series at low-frequency time scales, with interannual fluctuations in sea level being indirectly linked to natural climate modes, in particular the El Nino Southern Oscillation (ENSO).

Statistical and Machine Learning Methods for River Water Level Time Series Construction Using Satellite Altimetry

Statistical and Machine Learning Methods for River Water Level Time Series Construction Using Satellite Altimetry

A CNN-BiGRU sea level height prediction model combined with bayesian optimization algorithm

Traditional linear models are insufficient for capturing the complex dynamics of sea level changes. This paper aims to predict sea level time series using neural network models adapted for nonlinear data. Currently, few researchers use a combination of convolutional neural networks and bidirectional gated recurrent units (CNN-BiGRU) optimized with hyperparameter tuning for sea level prediction. There is also a lack of detailed discussion on the randomness of neural network initialization in prediction domains. Therefore, this study employs the bayesian optimization algorithm (BO) to optimize the CNN-BiGRU model, resulting in the BO-CNN-BiGRU model. Experiments initially compared the BO-CNN-BiGRU model with five other models using data from ten tidal stations in the US, showing that the model outperformed the others. To address initialization randomness, we used ten random seeds for statistical analysis, which demonstrated that the BO-CNN-BiGRU model performed well in terms of predictive performance and robustness. Finally, the BO-CNN-BiGRU model was applied to satellite altimetry grid data from the Bohai and Yellow Seas in China, yielding a linear trend of 3.92 ± 0.63 mm/a from 1993 to 2023, consistent with the China Sea Level Bulletin, further validating the model's effectiveness. This model can be used to predict regional sea level change.

Analysis of Optimal Water Levels in the Great Lakes Based on A Comprehensive Satisfaction Function

The purpose of this paper is to analyze the optimal water levels in the Great Lakes to meet the needs of multiple stakeholders and thus achieve sustainable development in the region. The Weight-Function-Synthesis-Optimization (WFSO) model was used in this study. By classifying the water level needs of different interest groups, their respective satisfaction functions are established, and the overall satisfaction function is formed by weighting. In addition, the quadratic polynomial function is used to fit the optimal monthly water level time series of Lake Ontario, and the fitting effect is good, fully reflecting the periodic and seasonal changes in the water level of Lake Ontario. By considering the priorities of various stakeholders, this paper defines an overall satisfaction metric, "allsa," and identifies a time series of monthly optimal water levels for Lake Ontario and beyond. The ideal water level was determined to be 74.9 meters. The study results suggest that maintaining this water level can maximize the satisfaction of ecosystems, transportation, real estate, terminals, and hydropower companies, and promote sustainable development of the region.

Spatial-temporal graph neural networks for groundwater data.

This paper introduces a novel application of spatial-temporal graph neural networks (ST-GNNs) to predict groundwater levels. Groundwater level prediction is inherently complex, influenced by various hydrological, meteorological, and anthropogenic factors. Traditional prediction models often struggle with the nonlinearity and non-stationary characteristics of groundwater data. Our study leverages the capabilities of ST-GNNs to address these challenges in the Overbetuwe area, Netherlands. We utilize a comprehensive dataset encompassing 395 groundwater level time series and auxiliary data such as precipitation, evaporation, river stages, and pumping well data. The graph-based framework of our ST-GNN model facilitates the integration of spatial interconnectivity and temporal dynamics, capturing the complex interactions within the groundwater system. Our modified Multivariate Time Graph Neural Network model shows significant improvements over traditional methods, particularly in handling missing data and forecasting future groundwater levels with minimal bias. The model's performance is rigorously evaluated when trained and applied with both synthetic and measured data, demonstrating superior accuracy and robustness in comparison to traditional numerical models in long-term forecasting. The study's findings highlight the potential of ST-GNNs in environmental modeling, offering a significant step forward in predictive modeling of groundwater levels.

The phenology and water level time-series mangrove index for improved mangrove monitoring

Mangroves face decline and degradation due to human activities and natural forces, making their accurate mapping and dynamic monitoring essential. However, most of the existing mangrove indices that rely on multispectral image spectral characteristics suffer from limitations in terms of recognition accuracy and universality. Therefore, this study aimed to develop a robust and efficient Phenology and Water level Time-series Mangrove Index (PWTMI) for mangrove monitoring. PWTMI is constructed by combining spectral and temporal characteristics from dense time-series multispectral data, wherein phenology and water level time-series characteristics are extracted from NDVI and MNDWI time series. The results show that PWTMI outperforms existing multispectral-based mangrove indices and has an accuracy similar to a hyperspectral-based mangrove index, with overall accuracy ranging from 91.49% to 98.83% and F1 score ranging from 0.91 to 0.98 in four typical areas in China, indicating great potential for long time-series and large-scale mangrove monitoring.

Guardians of the aquifers: ehancing Rome’s groundwater monitoring network

This paper proposes a methodology for managing groundwater monitoring directly in the field through a specific data entry system installed on mobile devices and a relational geographic database that allows the visualization and querying of data via a specific web interface. The study area is the city of Rome, where a monitoring system of approximately 150 piezometers and wells, currently manually monitored twice a year. The proposed method uses the Enterprise cloud platform (ESRI, 2024) managed by ISPRA-SNPA, which guarantees the repository of the data collected in an online cloud system and the use of Web applications. The data of the time series of levels and chemical-physical parameters such as temperature, pH, conductivity are freely accessible through attribute tables, graphs, and viewer elements. The results highlight numerous possibilities for expanding the network of active wells, enabling the use of groundwater resources for adaptation measures to address ongoing climate change.

A machine learning approach to nearshore wave modeling in large lakes using land-based wind observations

This study presents a novel machine learning-based (ML) framework that utilizes the ConvLSTM-1D model to simulate wave heights at a nearshore location in Lake Michigan using a nonuniform land-based array of wind observations from a broad geographic region as an input. This approach was applied to Lake Michigan to perform a 70-year ice-free hindcast of waves near Chicago, IL (USA). Because of annual winter gaps in Great Lakes buoy observations, output from the Wave Information System model (WIS) was used for the training, validation, and testing of the ML model. Models with different numbers of wind stations were tested, showing that a single wind station as an input feature produced a reasonably accurate wave height. However, the wave height model accuracy increased as more wind input data was included from around the lake, largely plateauing beyond the inclusion of four stations that spanned Lake Michigan’s southern basin. The optimized model lookback period was found to be 10 h for all models, suggestive of a fetch-limited temporal coupling between the wind observations and nearshore waves. The extended time series showed a statistically significant increase in the interannual standard deviation of the storm wave height and the storm height over the mean wave height while no correlation was found with the annual water level time series. The ML framework offers a promising avenue for utilizing historical wind records to extend wave height time series for nearshore locations, particularly in enclosed and semi-enclosed basins where waves are strongly linked to local winds.

Influence of data source and copula statistics on estimates of compound flood extremes in a river mouth environment

Abstract. Coastal and riverine floods are major concerns worldwide as they can impact highly populated areas and result in significant economic losses. In a river mouth environment, interacting hydrological and oceanographical processes can enhance the severity of floods. The compound flood hazards from high sea levels and high river discharge are often estimated using copulas, among other methods. Here, we systematically investigate the influence of different data sources coming from observations and models as well as the choice of copula on extreme water level estimates. While we focus on the river mouth at the city of Halmstad (Sweden), the approach presented is easily transferable to other sites. Our results show that the choice of data sources can considerably impact the results up to 10 % and 15 % for the river time series and 3 % to 4.6 % for the sea level time series under the 5- and 30-year return periods, respectively. The choice of copula can also strongly influence the outcome of such analyses up to 13 % and 9.5 % for the 5-year and 30-year return periods. Each percentage refers to the normalized difference in return level results we can expect when choosing a certain copula or input dataset. The copulas found to statistically best fit our datasets are the Clayton, BB1, and Gaussian (once) ones. We also show that the compound occurrence of high sea levels and river runoff may lead to heightened flood risks as opposed to considering them independent processes and that, in the current study, this is dominated by the hydrological driver. Our findings contribute to framing existing studies, which typically only consider selected copulas and datasets, by demonstrating the importance of considering uncertainties.

Invasive-Weed-Optimization-Based Extreme Learning Machine for Prediction of Lake Water Level Using Major Atmospheric–Oceanic Climate Scenarios

Fresh water lakes are vulnerable assets that need to be protected against manmade/natural challenges like climate change and anthropogenesis activities. This study addresses the predictability of the lake water level changes based on the knowledge acquired directly from the climate data. Two fresh water lakes named Lake Iznik and Uluabat, located in Turkey, are addressed. Time series of the lake water levels during October 1990–September 2019 at a monthly scale, along with the corresponding anomalies of 24 Large-Scale Atmospheric–Oceanic Oscillations (LSAOOs) from around the globe, are used in the analysis. The relationship between variables and the structure of the models are initially acquired based on the significance of the dependence between climate indices and lake water levels with consideration of the significance of the Spearman rank-order coefficient. Then, the time series are divided into training (80%) and testing (20%) sets. The Extreme Learning Method (ELM), enhanced with the genetic algorithm (ELM-GA) and Invasive Weed Optimization (ELM-IWO), is then used in the predictive models. Based on the results, Lake Uluabat showed a stronger teleconnection with LSAOOs, while the ELM-GA for Lake Iznik and ELM-IWA for Lake Uluabat depicted the best performance in the prediction of lake water levels. Comparison of the enhanced ELM-IWO to the corresponding ELM-GA illustrates that the ELM-IWO reveals more acceptable results owing to its flexible nature.

Deep Neural Networks for Predicting the Settlement of Earth Dams Based on the InSAR Outputs

Earth dams play a crucial role in water resource management, necessitating effective maintenance to ensure prolonged functionality and safety. Monitoring these dams traditionally involves methods such as surveying and instrumentation. However, challenges arise from equipment malfunctions and absences, especially in dams affected by environmental changes. In response to these challenges, the cost-effective and adaptable nature of Interferometric Synthetic Aperture Radar (InSAR) has made it a preferred choice for monitoring. Despite their advantages, traditional numerical models like finite element methods have limitations in predicting deformation comprehensively, particularly due to intricate, non-linear correlations involving material type and environmental conditions. To overcome these limitations, this research employs deep learning techniques, specifically Long Short-Term Memory (LSTM) network, to capture intricate relationships and accurately predict dam behavior. Time series data from InSAR, representing settlement, are decomposed into trend and seasonal components using Artificial Neural Networks (ANN) for trend prediction. Furthermore, an LSTM network is utilized to handle the complexity of the seasonal component and its correlation with environmental factors. This network incorporates settlement, precipitation, temperature, and reservoir water level time series as inputs, thereby enhancing prediction accuracy. The research outcome presents a robust solution that holds the promise of increased accuracy and efficiency in predicting, monitoring, and serving as an early warning system for earth dam deformations over time. Such advancements are crucial for ensuring the safety and integrity of critical infrastructure in the face of evolving environmental conditions.

Filling the ponds of Hattuşa - a geohydrological approach to determine inflows by time and volume

In the ruins of Hattuşa, the capital of the Hittite Empire more than 3,000 years ago, large, sedimented water storage ponds have been uncovered since 1998. An investigation based on time series of measured groundwater levels, showed that the ponds were supplied from layered aquifers which were opened at their source horizons directly at the uphill edge of the pond. When the groundwater level at the pond exceeds a threshold given by the geology at that edge, water pours into the pond. The principles and the path of filling become clear, but not the volumes and time distribution of the transfers. These results of the previous studies were amply published and are shortly summarized. The present investigation is also based on the time series of groundwater levels and of the discharge of a modern fountain as well as the local hydrogeological properties. The approach is simple but shows the effect of storage in the aquifer which delays the outflow into the pond, so that water from the rainy season was available in the dry season. Also, the annual outflow values are determined. Besides gaining knowledge it is an aim of the article to encourage interdisciplinary and process-oriented thinking.

Defining an exposure index along the Schleswig-Holstein Baltic Sea coast

A wind exposure index (EI), which indicates the main physical driver of a coastal system, was developed along the Schleswig-Holstein Baltic Sea (SH) coast – Germany, to demonstrate the highly dynamic coastal stretches (i.e., potential erosion hotspots). The approach used three steps to define more accurate EIs. Initially, a representative wind year (RWY), which has similar physical characteristics as in the long-term data, was defined by analysing measured wind data from 2000 to 2019 at four stations distributed in the entire area of interest. The RWY was identified by a statistical comparison of wind speeds in 5 classes and 36 directional sectors between summer to summer yearly wind and the overall data. The selected RWY spanned from 01.09.2016 to 31.08.2017 and showed a reasonable agreement with the overall data (Skill = 0.77 and rmsd = 0.56 m/s). Next, high spatiotemporal nearshore hydrodynamics over the RWY were predicted using a model nesting approach of two domains in Delft3D. The predicted nearshore hydrodynamics indicated fair agreements with the measured data (R2: 0.87–0.90 for water levels and 0.75–0.86 for wave heights). Finally, the predicted water level and wave height time series in the nearshore area (∼ 5 m MSL depth) were used for the analysis of the EI adopting a 2-step procedure capturing short- and long-term correlations as well as seasonal long-range dependencies of the time series. This approach allows to model the clustering behaviour of extreme values of both parameters and provides reasonable EIs along the SH coast. The exposed areas display high EIs (e.g., 1 at the east of Fehmarn), while sheltered areas and bays have low values (e.g., 0 at Eckernförde Bay). The higher the EI the stronger the coastal dynamics and thus strong erosion can be expected. Interestingly, the EI varies considerably even along the exposed coastal stretches with long fetches, which indicates the sensitivity of the EI to the local morphology, which determines the nearshore hydrodynamics. Therefore, a definition of the EI based on nearshore hydrodynamics provides an accurate index of local physical drivers of a coastal system. The developed approach can be adopted to any coast, and provides useful information on the potential erosion areas for the coastal managers.

Global assessment of linear trend and seasonal variations of GNSS-IR sea level retrievals with nearby tide gauges

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) sea level retrievals and tide gauges at 40 globally distributed stations spanning from about 4.5 to 18 years are compared on a site-by-site basis, in terms of noise background, rate and seasonal variations by using the weighted least squares estimation (LSE) along with the Maximum likelihood estimation (MLE). The result shows that monthly GNSS-IR data agree well with tide gauges for most stations except the site Tuktoyaktuk, Canada. The mean correlation is 0.95 and the mean root mean square difference is 2.9 cm, respectively. The discrepancies of rate and seasonal amplitude estimates are within ± 1 cm for most stations. We confirm both the two sea level data exhibit temporal correlation, which has a great effect on the rate uncertainty estimates. Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) favor Matérn and first-order autoregressive (AR1) the preferred stochastic model for the daily and monthly mean sea level time series, respectively. Owing to the data span dependence for the rate uncertainty estimates, to get an accuracy of sub-mm/yr in linear rate using the weighted LSE, at least 30 years of data (depends on data quality) is required. We recommend using long time series and a proper stochastic model for the rate estimation of sea level.

Drivers of Daily Water Level Fluctuation of Shallow Groundwater in the Inner Delta of the River Danube

Groundwater flow systems are influenced by the changes in surface waters as well as climatic factors. These teleconnections significantly increase in cases of extreme weather conditions. To prepare and mitigate the effect of such phenomena, the background factors that create and influence natural processes must be recognized. In the present study, 94 shallow groundwater (SGW) wells’ water level time series were analyzed in the inner delta of the River Danube (Europe) the Szigetköz region to explore which factors contribute to the development of diurnal periodicity of SGW and what its drivers are. The relationship between surface meteorological processes and SGW dynamics in the Szigetköz region was investigated using hourly data from monitoring wells. Hourly water temperature data exhibited weak correlations with meteorological parameters. However, daily averaged data revealed stronger correlations, particularly between SGW levels and air temperature and potential evapotranspiration. Diurnal periodicity in SGW fluctuations correlated strongly with potential evapotranspiration. The study also demonstrated the role of capillary fringe dynamics in linking surface evapotranspiration with SGW fluctuations. Changes in groundwater levels, even small, can significantly affect soil moisture, vegetation, and ecosystem functioning, highlighting the sensitivity of the unsaturated zone to SGW fluctuations driven by surface processes.