Multi-source data assimilation for physically based hydrological modeling of an experimental hillslope

Data assimilation has recently been the focus of much attention for integrated surface–subsurface hydrological models, whereby joint assimilation of water table, soil moisture, and river discharge measurements with the ensemble Kalman filter (EnKF) has been extensively applied. Although the EnKF has been specifically developed to deal with nonlinear models, integrated hydrological models based on the Richards equation still represent a challenge, due to strong nonlinearities that may significantly affect the filter performance. Thus, more studies are needed to investigate the capabilities of the EnKF to correct the system state and identify parameters in cases where the unsaturated zone dynamics are dominant, as well as to quantify possible tradeoffs associated with assimilation of multi-source data. Here, the CATHY (CATchment HYdrology) model is applied to reproduce the hydrological dynamics observed in an experimental two-layered hillslope, equipped with tensiometers, water content reflectometer probes, and tipping bucket flow gages to monitor the hillslope response to a series of artificial rainfall events. Pressure head, soil moisture, and subsurface outflow are assimilated with the EnKF in a number of scenarios and the challenges and issues arising from the assimilation of multi-source data in this real-world test case are discussed. Our results demonstrate that the EnKF is able to effectively correct states and parameters even in a real application characterized by strong nonlinearities. However, multi-source data assimilation may lead to significant tradeoffs: the assimilation of additional variables can lead to degradation of model predictions for other variables that are otherwise well reproduced. Furthermore, we show that integrated observations such as outflow discharge cannot compensate for the lack of well-distributed data in heterogeneous hillslopes.</p

Numerical Modeling and Data Assimilation of Soil Water Flow

Soil water flow is a key process in Earth's hydrological cycle and an essential part of many ecosystem services. Soils are porous media and exhibit a heterogeneous, multi-scale architecture. Their non-linear material properties have a significant influence on the soil water dynamics, which poses difficulties for numerical models. These material properties cannot be measured directly, but data assimilation methods can estimate them by combining information from measurements of soil hydraulic states and from numerical models. The validity of the estimation results can be strongly affected by model errors. This dissertation (i) presents a versatile software package for modeling soil water flow and analyzes the accuracy and efficiency of its numerical discretization schemes, and (ii) employs this software in synthetic data assimilation tasks to investigate the effects of unrepresented dynamics, topography, and small-scale heterogeneity on estimated material properties and forecasts conducted with them. The results reveal that favoring low-order numerical methods over more accurate ones can be justified for use cases in soil hydrology. Moreover, the findings indicate that one-dimensional models with estimated effective material properties can reasonably replicate the dynamics of heterogeneous, two-dimensional domains with complicated topography, if boundary conditions are represented correctly

A wildland fire model with data assimilation

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version available from http://www-math.cudenver.edu/ccm/report

Kalman filters for assimilating near-surface observations into the Richards equation – Part 3: Retrieving states and parameters from laboratory evaporation experiments

Abstract. The purpose of this work is to evaluate the performance of a dual Kalman filter procedure in retrieving states and parameters of a one-dimensional soil water budget model based on the Richards equation, by assimilating near-surface soil water content values during evaporation experiments carried out under laboratory conditions. The experimental data set consists of simultaneously measured evaporation rates, soil water content and matric potential profiles. The parameters identified by assimilating the data measured at 1 and 2 cm soil depths are in very good agreement with those obtained by exploiting the observations carried out in the entire soil profiles. A reasonably good correspondence has been found between the parameter values obtained from the proposed assimilation technique and those identified by applying a non-sequential parameter estimation method. The dual Kalman filter also performs well in retrieving the water state in the porous system. Bias and accuracy of the predicted state profiles are affected by observation depth changes, particularly for the experiments involving low state vertical gradients. The assimilation procedure proved flexible and very stable in both experimental cases, independently from the selected initial conditions and the involved uncertainty

Reduced Order Models and Data Assimilation for Hydrological Applications

The present thesis work concerns the study of Monte Carlo (MC)-based data assimilation methods applied to the numerical simulation of complex hydrological models with stochastic parameters. The ensemble Kalman filter (EnKF) and the sequential importance resampling (SIR) are implemented in the CATHY model, a solver that couples the subsurface water flow in porous media with the surface water dynamics. A detailed comparison of the results given by the two filters in a synthetic test case highlights the main benefits and drawbacks associated to these techniques. A modification of the SIR update is suggested to improve the performance of the filter in case of small ensemble sizes and small variances of the measurement errors. With this modification, both filters are able to assimilate pressure head and streamflow measurements and correct model errors, such as biased initial and boundary conditions. SIR technique seems to be better suited for the simulations at hand as they do not make use of the Gaussian approximation inherent the EnKF method. Further research is needed, however, to assess the robustness of the particle filters methods in particular to ensure accuracy of the results even when relatively small ensemble sizes are employed. In the second part of the thesis the focus is shifted to reducing the computational burden associated with the construction of the MC realizations (which constitutes the core of the EnKF and SIR). With this goal, we analyze the computational saving associated to the use of reduced order models (RM) for the generation of the ensemble of solutions. The proper orthogonal decomposition (POD) is applied to the linear equations of the groundwater flow in saturated porous media with a randomly distributed recharge and random heterogeneous hydraulic conductivity. Several test cases are used to assess the errors on the ensemble statistics caused by the RM approximation. Particular attention is given to the efficient computation of the principal components that are needed to project the model equations in the reduced space. The greedy algorithm selects the snapshots in the set of the MC realizations in such a way that the final principal components are parameter independent. An innovative residual-based estimation of the error associated to the RM solution is used to assess the precision of the RM and to stop the iterations of the greedy algorithm. By way of numerical applications in synthetic and real scenarios, we demonstrate that this modified greedy algorithm determines the minimum number of principal components to use in the reduction and, thus, leads to important computational savings

Reconstructing saturated hydraulic conductivity at the LEO-biosphere hillslope via data assimilation

A data assimilation process is fulfilled to estimate the spatial distribution of hydraulic conductivity of LEO soil, assimilating the volumetric water content data collected during the first experiment at LEO hillslope. The chosen assimilation methods are EnKF and SIR, and the simulations are fulfilled by means of the coupled hydrological model CATHY. The hillslope is modeled with different degrees of heterogeneity. The results may be improved by assimilating other geophysical dat

Final Report of the DAUFIN project

DAUFIN = Data Assimulation within Unifying Framework for Improved river basiN modeling (EC 5th framework Project

Parameter Estimation of Cancer Cell Dynamics

The goal of this project is to model cancer cell dynamics and their sensitivity to cancer drugs, and use parameter estimation techniques to provide experimental insights. We introduce several variations of a model developed by our team to capture the interactions between cancer cells and different drugs, as well as the methods utilized for parameter estimation. All variations of our model include a natural growth rate, cell-induced and drug-induced death rates, which are immeasurable and potentially time-varying. We utilize the Ensemble Kalman Filter for estimation as it accommodates noisy data noise by producing distribution estimations. Long term, estimation of parameters may lead to insight with regards to the drug-induced cell death mechanisms and proper data collection methods

Fusing Loop and GPS Probe Measurements to Estimate Freeway Density

In an age of ever-increasing penetration of GPS-enabled mobile devices, the potential of real-time "probe" location information for estimating the state of transportation networks is receiving increasing attention. Much work has been done on using probe data to estimate the current speed of vehicle traffic (or equivalently, trip travel time). While travel times are useful to individual drivers, the state variable for a large class of traffic models and control algorithms is vehicle density. Our goal is to use probe data to supplement traditional, fixed-location loop detector data for density estimation. To this end, we derive a method based on Rao-Blackwellized particle filters, a sequential Monte Carlo scheme. We present a simulation where we obtain a 30\% reduction in density mean absolute percentage error from fusing loop and probe data, vs. using loop data alone. We also present results using real data from a 19-mile freeway section in Los Angeles, California, where we obtain a 31\% reduction. In addition, our method's estimate when using only the real-world probe data, and no loop data, outperformed the estimate produced when only loop data were used (an 18\% reduction). These results demonstrate that probe data can be used for traffic density estimation