LPMLEn

A code for estimating heat transport parameters in 1D

About

This repository contains the MATLAB code and data corresponding to:

R. van Kampen, U. Schneidewind, C. Anibas, A. Bertagnoli, D. Tonina, G. Vandersteen, C. Luce, S. Krause, and M. van Berkel (2022), LPMLEn - A frequency domain method to estimate vertical streambed fluxes and sediment thermal properties in semi-infinite and bounded domains, Water Resour. Res., doi: 10.1029/2021WR030886.

The LPMLEn combines the local polynomial method (LP method) with a maximum likelihood estimator (MLE) to estimate 1D vertical streambed fluxes and thermal diffusivities using time-series from n temperature sensors. It operates in the frequency domain and can use multiple frequencies and sensors simultaneously for the parameter estimation. The LPMLEn is provided here with two models, (i) the semi-infinite domain model where only an upper temperature boundary condition is used to estimate the parameters and (ii) a bounded (finite) domain model where an additional lower local temperature boundary condition is assigned to estimate the parameters for a distinct section of the streambed.

Contents

The MATLAB scirpts that are used to create the figures in the paper are: - Estimation_with_synthetic_dataset1_and_2_SI_vs_BD.m for Table 1, Fig. S1 and S2. - Estimation_with_synthetic_dataset3_change_in_D.m for Fig. 1. - Estimation_with_synthetic_dataset4_change_in_D_from_low_to_high.m for Fig. S3. - Estimation_with_experimental_dataset.m for Fig. 2b, 2c, 3, 4, 5, S4 and S5. - ML1_90.txt contains the measurement data of the experimental dataset. The analysis performed on the dataset in Estimation_with_experimental_dataset.m is resource demanding. For this reason the computational results are saved in Estimation_experimental_dataset_workspace.mat, which can be loaded into MATLAB to bypass the computations.

To start using the LPMLEn, please check the simplified example Example_simplified_LPMLEn.m that uses the function MLEn_hydrology_time.m that only requires the time-series, measurement depths, and model choice as input. The more advance user may want to use the LP-method (LocalPolyAnal.m) and MLEn (MLEn.m) sepperatly for more control and advanced settings. For this, the Estimation_with_experimental_dataset.m can be used as an example.

Additional information

The LPMLEn builds on earlier work and still contains all the functionality presented in the following publications:

M. van Berkel, G. W. Oosterwegel, M. Anthonissen, H. J. Zwart, and G. Vandersteen, "A novel frequency domain maximum likelihood approach for estimating transport coefficients in cylindrical geometry for nuclear fusion devices", 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 3220-3226, doi: 10.1109/CDC40024.2019.9029992..

U. Schneidewind, M. van Berkel, C. Anibas, G. Vandersteen, C. Schmidt, I. Joris, P. Seuntjens, O. Batelaan, and H. J. Zwart (2016), "LPMLE3: A novel 1‐D approach to study water flow in streambeds using heat as a tracer", Water Resour. Res., 52, 6596-6610, doi: 10.1002/2015WR017453.

M. van Berkel, G. Vandersteen, E. Geerardyn, R. Pintelon, H. Zwart, and M. de Baar, "Frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in PDEs", Automatica, Volume 50, Issue 8, 2014, Pages 2113-2119, ISSN 0005-1098, doi: 10.1016/j.automatica.2014.05.027.