Towards the sequential assimilation of SAR-derived water stages into hydraulic models using the Particle Filter: proof of concept

Abstract. With the onset of new satellite radar constellations (e.g. Sentinel-1) and advances in computational science (e.g. grid computing) enabling the supply and processing of multi-mission satellite data at a temporal frequency that is compatible with real-time flood forecasting requirements, this study presents a new concept for the sequential assimilation of Synthetic Aperture Radar (SAR)-derived water stages into coupled hydrologic-hydraulic models. The proposed methodology consists of adjusting storages and fluxes simulated by a coupled hydrologic-hydraulic model using a Particle Filter-based data assimilation scheme. Synthetic observations of water levels, representing satellite measurements, are assimilated into the coupled model in order to investigate the performance of the proposed assimilation scheme as a function of both accuracy and frequency of water level observations. The use of the Particle Filter provides flexibility regarding the form of the probability densities of both model simulations and remote sensing observations. We illustrate the potential of the proposed methodology using a twin experiment over a widely studied river reach located in the Grand-Duchy of Luxembourg. The study demonstrates that the Particle Filter algorithm leads to significant uncertainty reduction of water level and discharge at the time step of assimilation. However, updating the storages of the model only improves the model forecast over a very short time horizon. A more effective way of updating thus consists in adjusting both states and inputs. The proposed methodology, which consists in updating the biased forcing of the hydrodynamic model using information on model errors that is inferred from satellite observations, enables persistent model improvement. The present schedule of satellite radar missions is such that it is likely that there will be continuity for SAR-based operational water management services. This research contributes to evolve reactive flood management into systematic or quasi-systematic SAR-based flood monitoring services.

Download Full-text

Assimilating SAR-derived water level data into a hydraulic model: a case study

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-8-2103-2011 ◽

2011 ◽

Vol 8 (1) ◽

pp. 2103-2144 ◽

Cited By ~ 4

Author(s):

L. Giustarini ◽

P. Matgen ◽

R. Hostache ◽

M. Montanari ◽

D. Plaza ◽

...

Keyword(s):

Particle Filter ◽

Water Level ◽

Cross Sections ◽

Hydraulic Model ◽

Water Levels ◽

Hydraulic Models ◽

Level Data ◽

Water Level Data ◽

Assimilation Scheme

Abstract. Satellite-based active microwave sensors not only provide synoptic overviews of flooded areas, but also offer an effective way to estimate spatially distributed river water levels. If rapidly produced and processed, these data can be used for updating hydraulic models in near real-time. The usefulness of such approaches with real event data sets provided by currently existing sensors has yet to be demonstrated. In this case study, a Particle Filter-based assimilation scheme is used to integrate ERS-2 SAR and ENVISAT ASAR-derived water level data into a one-dimensional (1-D) hydraulic model of the Alzette River. Two variants of the Particle Filter assimilation scheme are proposed with a global and local particle weighting procedure. The first option finds the best water stage line across all cross sections, while the second option finds the best solution at individual cross sections. The variant that is to be preferred depends on the level of confidence that is attributed to the observations or to the model. The results show that the Particle Filter-based assimilation of remote sensing-derived water elevation data provides a significant reduction to the model forecast uncertainty. Moreover, it is shown that the periodical updating of hydraulic models through the proposed assimilation scheme leads to an improvement of model predictions over several time steps. However, the performance of the assimilation depends on the skill of the hydraulic model and the quality of the observation data.

Download Full-text

Assimilating SAR-derived water level data into a hydraulic model: a case study

Hydrology and Earth System Sciences ◽

10.5194/hess-15-2349-2011 ◽

2011 ◽

Vol 15 (7) ◽

pp. 2349-2365 ◽

Cited By ~ 89

Author(s):

L. Giustarini ◽

P. Matgen ◽

R. Hostache ◽

M. Montanari ◽

D. Plaza ◽

...

Keyword(s):

Particle Filter ◽

Water Level ◽

Cross Sections ◽

Hydraulic Model ◽

Water Levels ◽

Hydraulic Models ◽

Level Data ◽

Water Level Data ◽

Assimilation Scheme

Abstract. Satellite-based active microwave sensors not only provide synoptic overviews of flooded areas, but also offer an effective way to estimate spatially distributed river water levels. If rapidly produced and processed, these data can be used for updating hydraulic models in near real-time. The usefulness of such approaches with real event data sets provided by currently existing sensors has yet to be demonstrated. In this case study, a Particle Filter-based assimilation scheme is used to integrate ERS-2 SAR and ENVISAT ASAR-derived water level data into a one-dimensional (1-D) hydraulic model of the Alzette River. Two variants of the Particle Filter assimilation scheme are proposed with a global and local particle weighting procedure. The first option finds the best water stage line across all cross sections, while the second option finds the best solution at individual cross sections. The variant that is to be preferred depends on the level of confidence that is attributed to the observations or to the model. The results show that the Particle Filter-based assimilation of remote sensing-derived water elevation data provides a significant reduction in the uncertainty at the analysis step. Moreover, it is shown that the periodical updating of hydraulic models through the proposed assimilation scheme leads to an improvement of model predictions over several time steps. However, the performance of the assimilation depends on the skill of the hydraulic model and the quality of the observation data.

Download Full-text

Assimilation of inundation extent observations into a flood forecasting system: a tempered particle filter for combatting degeneracy and sample impoverishment.

10.5194/egusphere-egu21-10878 ◽

2021 ◽

Author(s):

Concetta Di Mauro ◽

Renaud Hostache ◽

Patrick Matgen ◽

Peter Jan van Leeuwen ◽

Nancy Nichols ◽

...

Keyword(s):

Particle Filter ◽

Main Idea ◽

Water Levels ◽

Smooth Transition ◽

Observation Data ◽

Flood Inundation ◽

State Variables ◽

Time Step ◽

Radar Images ◽

Forecasting System

Data assimilation uses observation for updating model variables and improving model output accuracy. In this study, flood extent information derived from Earth Observation data (namely Synthetic Aperture Radar images) are assimilated into a loosely coupled flood inundation forecasting system via a Particle Filter (PF). A previous study based on a synthetic experiment has shown the validity and efficiency of a recently developed PF-based assimilation framework allowing to effectively integrate remote sensing-derived probabilistic flood inundation maps into a coupled hydrologic-hydraulic model. One of the main limitations of this recent framework based on sequential importance sampling is the sample degeneracy and impoverishment, as particles loose diversity and only few of them keep a substantial importance weight in the posterior distribution. In order to circumvent this limitation, a new methodology is adopted and evaluated: a tempered particle filter. The main idea is to update a set of state variables, namely through a smooth transition (iterative and adaptative process). To do so, the likelihood is factorized using small tempering factors. Each iteration includes subsequent resampling and mutation steps using a Monte Carlo Metropolis Hasting algorithm. The mutation step is required to regain diversity between the particles after the resampling. The new methodology is tested using synthetic twin experiments and the results are compared to the one obtained with the previous approach. The new proposed method enables to substantially improve the predictions of streamflow and water levels within the hydraulic domain at the assimilation time step. Moreover, the preliminary results show that these improvements are longer lasting. The proposed tempered particle filter also helps in keeping more diversity within the ensemble.

Download Full-text

Adaptive forecast of multi-month lake level elevations

Canadian Journal of Civil Engineering ◽

10.1139/l94-084 ◽

1994 ◽

Vol 21 (5) ◽

pp. 778-788 ◽

Cited By ~ 4

Author(s):

Saad Bennis ◽

Gabriel J. Assaf

Keyword(s):

Water Level ◽

Lake Erie ◽

Flood Control ◽

Ordinary Least Squares ◽

Water Levels ◽

Control Measures ◽

Type Model ◽

Model Parameters ◽

Time Step ◽

Kalman Predictor

The early and precise prediction of the water levels in lakes is a major concern for public authorities. Such predictions describe the evolution of the water levels and are essential for appropriate flood control measures. In this paper, a new ARMAX-type model is developed to predict, months in advance, the monthly fluctuations of the water level of Lake Erie. The predictive variables used in the model are the past monthly water levels of Lakes Erie, Superior, and Michigan–Huron along with the estimated response times between water flow entries and exits. Two scenarios are compared. The first scenario is based on the ordinary least squares (OLS) technique in order to identify the parameters of the ARMAX-type model, to filter measurement and model noises, using the ARMAX Kalman predictor (AKP), and to optimize predictions. In this scenario, the model parameters remain unchanged throughout the simulation. The second scenario is based on the mutually interactive state parameter (MISP) technique in order to readjust the parameters of the model at each time step and to filter measurement and modelling noises through the Kalman predictor. In this scenario, the parameters of the model change with time. The analysis shows that the MISP–AKP framework has a slightly higher Nash coefficient than the OLS–AKP framework for the first month. In subsequent months, however, the quality of the predictions based on the OLS–AKP technique improves significantly. This observation also applies to the persistence and extrapolation coefficients as well as to the sample autocorrelation functions for the residuals of the Lake Erie water level forecast. It was therefore decided to apply the MISP–AKP technique to obtain the first prediction of the Lake Erie level, and the OLS–AKP technique to compute subsequent predictions. Key words: adaptive, forecast, Kalman's filter, lake levels, MISP algorithm, Great Lakes.

Download Full-text

Groundwater modelling for time periods of up to hundreds of thousands of years.

10.5194/egusphere-egu2020-5177 ◽

2020 ◽

Author(s):

Gerrit H. de Rooij ◽

Thomas Mueller

Keyword(s):

Surface Water ◽

Water Level ◽

Coastal Plain ◽

Land Surface ◽

Hydraulic Head ◽

Water Levels ◽

Analytical Models ◽

Time Interval ◽

Mountain Range ◽

Time Step

Occasionally, there is an interest in groundwater flows over many millennia. The input parameter requirement of numerical groundwater flow models and their calculation times limit their usefulness for such studies.Analytical models require considerable simplifications of the properties and geometry of aquifers and of the forcings. On the other hand, they do not appear to have an inherent limitation on the duration of the simulated period. The simplest models have explicit solutions, meaning that the hydraulic head at a given time and location can be calculated directly, without the need to incrementally iterate through the entire preceding time period like their numerical counterparts.We developed an analytical solution for a simple aquifer geometry: a strip aquifer between a no flow boundary and a body of surface water with a prescribed water level. This simplicity permitted flexible forcings: The non-uniform initial hydraulic head in the aquifer is arbitrary and the surface water level can vary arbitrarily with time. Aquifer recharge must be uniform in space but can also vary arbitrarily with time.We also developed a modification that verifies after prescribed and constant time intervals if the hydraulic head is such that the land surface is covered with water. This excess water then infiltrates in areas where the groundwater level is below the surface and the remainder is discharged into the surface water. The hydraulic head across the aquifer is modified accordingly and used as the initial condition for the next time interval. This modification models the development of a river network during dry periods. The increased flexibility of the model comes at the price of the need to go through the entire simulation period one time step at a time. For very long time records, these intervals will typically be one year.Given the uncertainty of the aquifer parameters and the forcings, the models are expected to be used in a stochastic framework. We are therefore working on a shell that accepts multiple values for each parameter as well as multiple scenarios of surface water levels and groundwater recharge rates, along with an estimate of their probabilities. The shell will generate all possible resulting combinations, the number of which can easily exceed 10000, then runs the model for each combination, and computes statistics of the average hydraulic head and the aquifer discharge into the surface water at user-specified times.A case study will tell if this endeavor is viable. We will model the aquifer below the mountain range north of Salalah in Oman, which separates the desert of the Arabian Peninsula from the coastal plain at its southern shore. Rainfall estimates from the isotopic composition of stalactites in the area indicate distinct dry and wet periods in the past 300 000 years. In combination with estimated sea level fluctuations over that period, this provides an interesting combination of forcings. We examine the dynamics of the total amount of water stored in the aquifer, and of the outflow of water from the aquifer into the coastal plain.

Download Full-text

Dynamic neural networks for real-time water level predictions of sewerage systems-covering gauged and ungauged sites

Hydrology and Earth System Sciences ◽

10.5194/hess-14-1309-2010 ◽

2010 ◽

Vol 14 (7) ◽

pp. 1309-1319 ◽

Cited By ~ 26

Author(s):

◽

Keyword(s):

Neural Networks ◽

Water Level ◽

Water Levels ◽

Network Dynamic ◽

Suitable Model ◽

Training Procedure ◽

Time Step ◽

Current Time ◽

Sewerage System ◽

Ungauged Sites

Abstract. In this research, we propose recurrent neural networks (RNNs) to build a relationship between rainfalls and water level patterns of an urban sewerage system based on historical torrential rain/storm events. The RNN allows signals to propagate in both forward and backward directions, which offers the network dynamic memories. Besides, the information at the current time-step with a feedback operation can yield a time-delay unit that provides internal input information at the next time-step to effectively deal with time-varying systems. The RNN is implemented at both gauged and ungauged sites for 5-, 10-, 15-, and 20-min-ahead water level predictions. The results show that the RNN is capable of learning the nonlinear sewerage system and producing satisfactory predictions at the gauged sites. Concerning the ungauged sites, there are no historical data of water level to support prediction. In order to overcome such problem, a set of synthetic data, generated from a storm water management model (SWMM) under cautious verification process of applicability based on the data from nearby gauging stations, are introduced as the learning target to the training procedure of the RNN and moreover evaluating the performance of the RNN at the ungauged sites. The results demonstrate that the potential role of the SWMM coupled with nearby rainfall and water level information can be of great use in enhancing the capability of the RNN at the ungauged sites. Hence we can conclude that the RNN is an effective and suitable model for successfully predicting the water levels at both gauged and ungauged sites in urban sewerage systems.

Download Full-text

Water Level Prediction of Rainwater Pipe Network Using an SVM-Based Machine Learning Method

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001420510027 ◽

2019 ◽

Vol 34 (02) ◽

pp. 2051002 ◽

Cited By ~ 2

Author(s):

Hao Wang ◽

Lixiang Song

Keyword(s):

Machine Learning ◽

Water Level ◽

Water Levels ◽

Machine Learning Method ◽

Learning Method ◽

Pipe Network ◽

Hydrodynamic Models ◽

Time Step ◽

Running Speed ◽

Machine Learning Model

Model accuracy and running speed are the two key issues for flood warning in urban areas. Traditional hydrodynamic models, which have a rigorous physical mechanism for flood routine, have been widely adopted for water level prediction of rainwater pipe network. However, with the amount of pipes increasing, both the running speed and data availability of hydrodynamic models would be decreased rapidly. To achieve a real-time prediction for the water level of the rainwater pipe network, a new framework based on a machine learning method was proposed in this paper. The spatial and temporal autocorrelation of water levels for adjacent manholes was revealed through theoretical analysis, and then a support vector machine (SVM)-based machine learning model was developed, in which the water levels of adjacent manholes and rivers-near-by-outlets at the last time step were chosen as the independent variables, and then the water levels at the current time step can be computed by the proposed machine learning model with calibrated parameters. The proposed framework was applied in Fuzhou city, China. It turns out that the proposed machine learning method can forecast the water level of the rainwater pipe network with good accuracy and running speed.

Download Full-text

Groundwater modelling for time periods of up to 105 years

10.5194/egusphere-egu21-7948 ◽

2021 ◽

Author(s):

Gerrit H. de Rooij ◽

Thomas Mueller

Keyword(s):

Surface Water ◽

Water Level ◽

Coastal Plain ◽

Land Surface ◽

Hydraulic Head ◽

Water Levels ◽

Analytical Models ◽

Time Interval ◽

Mountain Range ◽

Time Step

Occasionally, there is an interest in groundwater flows over many millennia. The input parameter requirement of numerical groundwater flow models and their calculation times limit their usefulness for such studies.Analytical models require considerable simplifications of the properties and geometry of aquifers and of the forcings. On the other hand, they do not appear to have an inherent limitation on the duration of the simulated period. The simplest models have explicit solutions, meaning that the hydraulic head at a given time and location can be calculated directly, without the need to incrementally iterate through the entire preceding time period like their numerical counterparts.We developed an analytical solution for a simple aquifer geometry: a strip aquifer between a no flow boundary and a body of surface water with a prescribed water level. This simplicity permitted flexible forcings: The non-uniform initial hydraulic head in the aquifer is arbitrary and the surface water level can vary arbitrarily with time. Aquifer recharge must be uniform in space but can also vary arbitrarily with time.We also developed a modification that verifies after prescribed and constant time intervals if the hydraulic head is such that the land surface is covered with water. This excess water then infiltrates in areas where the groundwater level is below the surface and the remainder is discharged into the surface water. The hydraulic head across the aquifer is modified accordingly and used as the initial condition for the next time interval. This modification models the development of a river network during dry periods. The increased flexibility of the model comes at the price of the need to go through the entire simulation period one time step at a time. For very long time records, these intervals will typically be one year.Given the uncertainty of the aquifer parameters and the forcings, the models are expected to be used in a stochastic framework. We are therefore working on a shell that accepts multiple values for each parameter as well as multiple scenarios of surface water levels and groundwater recharge rates, along with an estimate of their probabilities. The shell will generate all possible resulting combinations, the number of which can easily exceed 10000, then runs the model for each combination, and computes statistics of the average hydraulic head and the aquifer discharge into the surface water at user-specified times.A case study will tell if this endeavor is viable. We will model the aquifer below the mountain range north of Salalah in Oman, which separates the desert of the Arabian Peninsula from the coastal plain at its southern shore. Rainfall estimates from the isotopic composition of stalactites in the area indicate distinct dry and wet periods in the past 300 000 years. In combination with estimated sea level fluctuations over that period, this provides an interesting combination of forcings. We examine the dynamics of the total amount of water stored in the aquifer, and of the outflow of water from the aquifer into the coastal plain.

Download Full-text

Integrating a 2D Hydraulic Model and GIS Algorithms into a Data Assimilation Framework for Real Time Flood Forecasting and Mapping

10.29007/29nd ◽

2018 ◽

Author(s):

Antonio Annis ◽

Noemi Gonzalez-Ramirez ◽

Fernando Nardi ◽

Fabio Castelli

Keyword(s):

Data Assimilation ◽

Water Level ◽

Real Time ◽

Satellite Images ◽

Early Warning Systems ◽

Hydraulic Model ◽

Water Levels ◽

Data Types ◽

Flow Measurements ◽

The Impact

The intensification of flood-related damages and fatalities is challenging Early Warning Systems (EWS) to always better perform in predicting flood levels allowing decision makers to take the most effective decisions for mitigating the impact of extreme events. EWS require hydrologic and hydraulic modelling that are usually affected by uncertainties that can be extremely significant in data scarce regions. This work presents the implementation and application of a Data Assimilation (DA) framework, based on the Ensemble Kalman Filter, integrating the hydraulic model FLO-2D and geospatial algorithms for data post-processing and mapping. The hydraulic model is forced by both flow gages and simulated flow data produced by a simplified GIS-based hydrologic modelling for flood wave analysis tailored for small ungauged basins. The hydraulic code is adapted to assimilate different observation data types: flow measurements taken along the channel, water level observations captured within the floodplain, such as water signs on vegetation and buildings pictures by human sensors, and inundation extents obtained by processing satellite images. This DA framework required the development of significant novelties for incorporating the 2D hydraulic model and for integrating the different types of measurements considering the heterogeneous specifications and uncertainty of the various assimilated data types. Advanced GIS algorithms are implemented for improving the real time flood mapping taking advantage of the distributed output provided by the 2D inundation model. Results show improved model performances in terms of water level simulations and reduced uncertainties. The integrated hydraulic and geospatial modelling allows to empower the water levels correction on the flood extension prediction. Additionally, the capability of using the different available observations, from satellite images to crowdsourced data, is promising for the development of a flexible and scalable flood EWS model overcoming the limitations of standard DA working generally with 1D hydraulic models and traditional sensors.

Download Full-text