Automatic estimation of parameter transfer functions for distributed hydrological models - a case study with the mHM model

2020 ◽  
Author(s):  
Moritz Feigl ◽  
Stephan Thober ◽  
Mathew Herrnegger ◽  
Luis Samaniego ◽  
Karsten Schulz
Keyword(s):  
Transfer Function ◽  
Function Space ◽  
Hydrological Model ◽  
Transfer Functions ◽  
Dimensional Space ◽  
Model Parameters ◽  
Hydrological Models ◽  
Estimation Of Parameters ◽  
General Applicability ◽  
Distributed Hydrological Models

<p>The estimation of parameters for spatially distributed rainfall runoff models is a long-studied, complex and ill-posed problem. Relating parameters of distributed hydrological models to geophysical properties of catchments could potentially solve some of the major difficulties connected to it.</p><p>One way to define this relationship is by the use of explicit equations called parameter transfer functions, which relate geophysical catchment properties to the model parameters. Computing parameter fields using transfer functions would result in spatially consistent parameter fields and the potential to extrapolate to other catchments. A further advantage is that the dimensionality of the parameter space is reduced because the transfer function parameters are applied to all computational units (i.e., grid cells). However, the structure and parameterization of transfer functions is often only implicitly assumed or needs to be derived by a laborious literature guided trial and error process.</p><p>For this reason we use Function Space Optimization (FSO), a symbolic regression approach which automatically estimates the structure and parameterization of transfer functions from catchment data. FSO transfers the search of the optimal function to a searchable continuous vector space. To create this space, a text generating neural network with a variational autoencoder (VAE) architecture is used. It is trained to map possible transfer functions and their distributions to a 6-dimensional space. After training, a continuous optimization is applied to search for the optimal transfer function in this function space. FSO was already tested in a virtual experiment using a parsimonious hydrological model, where its ability to solve the problem of transfer function estimation was shown.</p><p>Here, we further test FSO by applying it in a real world setting to the mesoscale hydrological model (mHM). mHM is a widely applied distributed hydological model, which uses transfer functions for all its parameters. For this study, we estimate transfer functions for the parameters porosity and field capacity, which both influence a range of hydrologic processes, e.g. infiltration and evapotranspiration. We compare the FSO estimated transfer functions with the already existing mHM transfer functions and examine their influence on the model performance.</p><p>In summary, we show the general applicability of FSO for distributed hydrological models and the advantages and capabilities of automatically defining parameter transfer functions.</p>

Catchment to model space mapping – learning transfer functions from data by symbolic regression

2021 ◽  
Author(s):  
Moritz Feigl ◽  
Robert Schweppe ◽  
Stephan Thober ◽  
Mathew Herrnegger ◽  
Luis Samaniego ◽  
...  
Keyword(s):  
Transfer Function ◽  
Function Space ◽  
Transfer Functions ◽  
Continuous Optimization ◽  
Model Space ◽  
Symbolic Regression ◽  
Regression Method ◽  
Hydrological Models ◽  
Distributed Hydrological Model ◽  
Distributed Hydrological Models

<p>The Function Space Optimization (FSO) method, recently developed by Feigl et al. (2020), automatically estimates the transfer function structure and coefficients to parameterize spatially distributed hydrological models. FSO is a symbolic regression method, searching for an optimal transfer function in a continuous optimization space, using a text generating neural network (variational autoencoder).</p><p>We apply our method to the distributed hydrological model mHM (www.ufz.de/mhm), which is based on a priori defined transfer functions. We estimate mHM transfer functions for the parameters “saturated hydraulic conductivity” and “field capacity”, which both influence a range of hydrologic processes, e.g. infiltration and evapotranspiration.</p><p>The FSO and standard mHM approach are compared using data from 229 basins, including 7 large training basins and 222 smaller validation basins, distributed across Germany. For training, 5 years of data of 7 gauging stations is used, while up to 35 years, with a median of 32 years, are used for validation. This setup is adopted from a previous study by Zink et al. (2017), testing mHM in the same basins and which is used as a benchmark. Maps of soil properties (sand/clay percentage, bulk density) and topographic properties (aspect, slope, elevation) are used as possible inputs for transfer functions.</p><p>FSO estimated transfer functions improved the mHM model performance in the validation catchments significantly when compared to the benchmark results, and only show a small decrease in performance compared to the training results. Results demonstrate that an automatic estimation of parameter transfer functions by FSO is beneficial for the parameterization of distributed hydrological models and allows for a robust parameter transfer to other locations.</p><p> </p><p>Feigl, M., Herrnegger, M., Klotz, D., & Schulz, K. (2020). Function Space Optimization: A symbolic regression method for estimating parameter transfer functions for hydrological models. Water resources research, 56(10), e2020WR027385.</p><p>Zink, M., Kumar, R., Cuntz, M., & Samaniego, L. (2017). A high-resolution dataset of water fluxes and states for Germany accounting for parametric uncertainty. Hydrol. Earth Syst. Sci, 21, 1769-1790.</p>

scholarly journals Identifying Key Hydrological Processes in Highly Urbanized Watersheds for Flood Forecasting with a Distributed Hydrological Model

Water ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1641 ◽  
Author(s):  
Huanyu Wang ◽  
Yangbo Chen
Keyword(s):  
Water Content ◽  
Parameter Uncertainty ◽  
Hydrological Model ◽  
Flood Forecasting ◽  
Hydrological Processes ◽  
Model Parameters ◽  
Hydrological Models ◽  
Distributed Hydrological Model ◽  
Physically Based ◽  
Distributed Hydrological Models

The world has experienced large-scale urbanization in the past century, and this trend is ongoing. Urbanization not only causes land use/cover (LUC) changes but also changes the flood responses of watersheds. Lumped conceptual hydrological models cannot be effectively used for flood forecasting in watersheds that lack long time series of hydrological data to calibrate model parameters. Thus, physically based distributed hydrological models are used instead in these areas, but considerable uncertainty is associated with model parameter derivation. To reduce model parameter uncertainty in physically based distributed hydrological models for flood forecasting in highly urbanized watersheds, a procedure is proposed to control parameter uncertainty. The core concept of this procedure is to identify the key hydrological and flood processes in the highly urbanized watersheds and the sensitive model parameters related to these processes. Then, the sensitive model parameters are adjusted based on local runoff coefficients to reduce the parameter uncertainty. This procedure includes these steps: collecting the latest LUC information or estimating this information using satellite remote sensing images, analyzing LUC spatial patterns and identifying dominant LUC types and their spatial structures, choosing and establishing a distributed hydrological model as the forecasting tool, and determining the initial model parameters and identifying the key hydrological processes and sensitive model parameters based on a parameter sensitivity analysis. A highly urbanized watershed called Shahe Creek in the Pearl River Delta area was selected as a case study. This study finds that the runoff production processes associated with both the ferric luvisol and acric ferralsol soil types and the runoff routing process on urban land are key hydrological processes. Additionally, the soil water content under saturated conditions, the soil water content under field conditions and the roughness of urban land are sensitive parameters.

scholarly journals Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization

2016 ◽  
Vol 20 (1) ◽  
pp. 375-392 ◽  
Author(s):  
Y. Chen ◽  
J. Li ◽  
H. Xu
Keyword(s):  
Parameter Optimization ◽  
Hydrological Model ◽  
Pso Algorithm ◽  
Flood Forecasting ◽  
Model Parameters ◽  
Hydrological Models ◽  
Distributed Hydrological Model ◽  
Inertia Weight ◽  
Physically Based ◽  
Distributed Hydrological Models

Abstract. Physically based distributed hydrological models (hereafter referred to as PBDHMs) divide the terrain of the whole catchment into a number of grid cells at fine resolution and assimilate different terrain data and precipitation to different cells. They are regarded to have the potential to improve the catchment hydrological process simulation and prediction capability. In the early stage, physically based distributed hydrological models are assumed to derive model parameters from the terrain properties directly, so there is no need to calibrate model parameters. However, unfortunately the uncertainties associated with this model derivation are very high, which impacted their application in flood forecasting, so parameter optimization may also be necessary. There are two main purposes for this study: the first is to propose a parameter optimization method for physically based distributed hydrological models in catchment flood forecasting by using particle swarm optimization (PSO) algorithm and to test its competence and to improve its performances; the second is to explore the possibility of improving physically based distributed hydrological model capability in catchment flood forecasting by parameter optimization. In this paper, based on the scalar concept, a general framework for parameter optimization of the PBDHMs for catchment flood forecasting is first proposed that could be used for all PBDHMs. Then, with the Liuxihe model as the study model, which is a physically based distributed hydrological model proposed for catchment flood forecasting, the improved PSO algorithm is developed for the parameter optimization of the Liuxihe model in catchment flood forecasting. The improvements include adoption of the linearly decreasing inertia weight strategy to change the inertia weight and the arccosine function strategy to adjust the acceleration coefficients. This method has been tested in two catchments in southern China with different sizes, and the results show that the improved PSO algorithm could be used for the Liuxihe model parameter optimization effectively and could improve the model capability largely in catchment flood forecasting, thus proving that parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological models. It also has been found that the appropriate particle number and the maximum evolution number of PSO algorithm used for the Liuxihe model catchment flood forecasting are 20 and 30 respectively.

scholarly journals Improving flood forecasting capability of physically based distributed hydrological model by parameter optimization

2015 ◽  
Vol 12 (10) ◽  
pp. 10603-10649 ◽  
Author(s):  
Y. Chen ◽  
J. Li ◽  
H. Xu
Keyword(s):  
Parameter Optimization ◽  
Hydrological Model ◽  
Pso Algorithm ◽  
Flood Forecasting ◽  
Model Parameters ◽  
Hydrological Models ◽  
Distributed Hydrological Model ◽  
Inertia Weight ◽  
Physically Based ◽  
Distributed Hydrological Models

Abstract. Physically based distributed hydrological models discrete the terrain of the whole catchment into a number of grid cells at fine resolution, and assimilate different terrain data and precipitation to different cells, and are regarded to have the potential to improve the catchment hydrological processes simulation and prediction capability. In the early stage, physically based distributed hydrological models are assumed to derive model parameters from the terrain properties directly, so there is no need to calibrate model parameters, but unfortunately, the uncertanties associated with this model parameter deriving is very high, which impacted their application in flood forecasting, so parameter optimization may also be necessary. There are two main purposes for this study, the first is to propose a parameter optimization method for physically based distributed hydrological models in catchment flood forecasting by using PSO algorithm and to test its competence and to improve its performances, the second is to explore the possibility of improving physically based distributed hydrological models capability in cathcment flood forecasting by parameter optimization. In this paper, based on the scalar concept, a general framework for parameter optimization of the PBDHMs for catchment flood forecasting is first proposed that could be used for all PBDHMs. Then, with Liuxihe model as the study model, which is a physically based distributed hydrological model proposed for catchment flood forecasting, the improverd Particle Swarm Optimization (PSO) algorithm is developed for the parameter optimization of Liuxihe model in catchment flood forecasting, the improvements include to adopt the linear decreasing inertia weight strategy to change the inertia weight, and the arccosine function strategy to adjust the acceleration coefficients. This method has been tested in two catchments in southern China with different sizes, and the results show that the improved PSO algorithm could be used for Liuxihe model parameter optimization effectively, and could improve the model capability largely in catchment flood forecasting, thus proven that parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological model. It also has been found that the appropriate particle number and the maximum evolution number of PSO algorithm used for Liuxihe model catchment flood forcasting is 20 and 30, respectively.

Individualized Transfer Functions for the Noninvasive Estimation of Central Pressure From Brachial Pressure Readings

2009 ◽  
Author(s):  
Ashis Mookerjee ◽  
Ahmed M. Al-Jumaily ◽  
Andrew Lowe
Keyword(s):  
Blood Pressure ◽  
Transfer Function ◽  
Brachial Artery ◽  
Transfer Functions ◽  
Patient Characteristics ◽  
Patient Specific ◽  
Model Parameters ◽  
Brachial Blood Pressure ◽  
Noninvasive Estimation ◽  
Artery Segment

A model-based investigation is carried out with the aim of developing an ab-initio methodology for the patient-specific estimation of central pressures from brachial blood pressure readings. The subclavian root-brachial artery segment is modeled as a 1-D tube with all model parameters linked to patient characteristics. A simulation is also run with typical physiological parameters, which gives a “first estimate” of the transfer function (TF). The TF derived using the patient characteristics is studied in detail to investigate the change in the arterial TF occurring with changes in patient characteristics. This TF is compared with the “first estimate” to evaluate the feasibility of using standard arterial properties.

scholarly journals Calibration of hydrological model parameters for ungauged catchments

2007 ◽  
Vol 11 (2) ◽  
pp. 703-710 ◽  
Author(s):  
A. Bárdossy
Keyword(s):  
Hydrological Model ◽  
Model Performance ◽  
Model Parameters ◽  
Hydrological Models ◽  
Rainfall Runoff ◽  
Ungauged Catchments ◽  
Rainfall Runoff Model ◽  
Climate Statistics ◽  
Runoff Model ◽  
German Part

Abstract. The parameters of hydrological models for catchments with few or no discharge records can be estimated using regional information. One can assume that catchments with similar characteristics show a similar hydrological behaviour and thus can be modeled using similar model parameters. Therefore a regionalisation of the hydrological model parameters on the basis of catchment characteristics is plausible. However, due to the non-uniqueness of the rainfall-runoff model parameters (equifinality), a workflow of regional parameter estimation by model calibration and a subsequent fit of a regional function is not appropriate. In this paper a different approach for the transfer of entire parameter sets from one catchment to another is discussed. Parameter sets are considered as tranferable if the corresponding model performance (defined as the Nash-Sutclife efficiency) on the donor catchment is good and the regional statistics: means and variances of annual discharges estimated from catchment properties and annual climate statistics for the recipient catchment are well reproduced by the model. The methodology is applied to a set of 16 catchments in the German part of the Rhine catchments. Results show that the parameters transfered according to the above criteria perform well on the target catchments.

scholarly journals Dynamics of hydrological model parameters: calibration and reliability

2019 ◽  
Author(s):  
Tian Lan ◽  
Kairong Lin ◽  
Xuezhi Tan ◽  
Chong-Yu Xu ◽  
Xiaohong Chen
Keyword(s):  
Hydrological Model ◽  
Model Performance ◽  
Dynamic Parameter ◽  
Model Parameters ◽  
Hydrological Models ◽  
State Variables ◽  
Individual Parameter ◽  
Calibration Scheme ◽  
Response Modes ◽  
Abrupt Shifts

Abstract. It has been demonstrated that the dynamics of hydrological model parameters based on dynamic catchment behavior significantly improves the accuracy and robustness of conventional models. However, the calibration for the dynamization of parameter set involves critical components of hydrological models, including parameters, objective functions, state variables, and fluxes, which usually are ignored. Hence, it is essential to design a reliable calibration scheme regarding these components. In this study, we compared and evaluate five calibration schemes with respect to multi-metric evaluation, dynamized parameter values, fluxes, and state variables. Furthermore, a simple and effective tool was designed to assess the reliability of the dynamized parameter set. The tool evaluates the convergence processes for global optimization algorithms using violin plots (ECP-VP), effectively describes the convergence behaviour in individual parameter spaces. The different types of violin plots can well match to all possible properties of fitness landscapes. The results showed that the reasons for poor model performance included time-invariant parameters oversimplifying the dynamic response modes of the model, the high-dimensionality disaster of parameters, the abrupt shifts of the parameter set, and the complicated correlations among parameters. The proposed calibration scheme overcome these issues, characterized the dynamic behaviour of catchments, and improved the model performance. Additionally, the designed ECP-VP tool effectively assessed the reliability of the dynamic parameter set, providing an indication on recognizing the dominant response modes of hydrological models in different sub-periods or catchments with the distinguishing catchment characteristics.

scholarly journals Spatio-Temporal Discretization Uncertainty of Distributed Hydrological Models

2021 ◽  
Author(s):  
Siavash Pouryousefi-Markhali ◽  
Annie Poulin ◽  
Marie-Amélie Boucher
Keyword(s):  
Spatial Resolution ◽  
Temporal Variations ◽  
Minor Role ◽  
Model Parameters ◽  
Hydrological Models ◽  
Spatial Discretization ◽  
Ensemble Approach ◽  
Temporal Discretization ◽  
Spatio Temporal ◽  
Distributed Hydrological Models

Quantifying the uncertainty linked to the degree to which the spatio-temporal variability of the catchment descriptors (CDs), and consequently calibration parameters (CPs), represented in the distributed hydrology models and its impacts on the simulation of flooding events is the main objective of this paper. Here, we introduce a methodology based on ensemble approach principles to characterize the uncertainties of spatio-temporal variations. We use two distributed hydrological models (WaSiM and Hydrotel) and six catchments with different sizes and characteristics, located in southern Quebec, to address this objective. We calibrate the models across four spatial (100, 250, 500, 1000 $m^2$) and two temporal (3 hours and 24 hours) resolutions. Afterwards, all combinations of CDs-CPs pairs are fed to the hydrological models to create an ensemble of simulations for characterizing the uncertainty related to the spatial resolution of the modeling, for each catchment. The catchments are further grouped into large ($>1000 km^2$), medium (between 500 and 1000 $km^2$) and small ($<500km^2$) to examine multiple hypotheses. The ensemble approach shows a significant degree of uncertainty (over $100\%$ error for estimation of extreme streamflow) linked to the spatial discretization of the modeling. Regarding the role of catchment descriptors, results show that first, there is no meaningful link between the uncertainty of the spatial discretization and catchment size, as spatio-temporal discretization uncertainty can be seen across different catchment sizes. Second, the temporal scale plays only a minor role in determining the uncertainty related to spatial discretization. Third, the more physically representative a model is, the more sensitive it is to changes in spatial resolution. Finally, the uncertainty related to model parameters is dominant larger than that of catchment descriptors for most of the catchments. Yet, there are exceptions for which a change in spatio-temporal resolution can alter the distribution of state and flux variables, change the hydrologic response of the catchments, and cause large uncertainties.

Sign in / Sign up

Export Citation Format

Share Document