Regionalization of rainfall-runoff model parameters using Markov Chain Monte Carlo samples

2001 ◽  
Vol 37 (3) ◽  
pp. 731-739 ◽  
Author(s):  
Edward P. Campbell ◽  
Bryson C. Bates
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Model Parameters ◽  
Rainfall Runoff ◽  
Rainfall Runoff Model ◽  
Runoff Model

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

scholarly journals Regionalizing rainfall–runoff model parameters to predict the daily streamflow of ungauged catchments in the dry tropics

2009 ◽  
Vol 40 (5) ◽  
pp. 433-444 ◽  
Author(s):  
David A. Post
Keyword(s):  
Input Data ◽  
Water Yield ◽  
Model Parameters ◽  
Rainfall Runoff ◽  
Wet Season ◽  
Daily Streamflow ◽  
Total Length ◽  
Dry Tropics ◽  
Rainfall Runoff Model ◽  
Runoff Model

A methodology has been derived which allows an estimate to be made of the daily streamflow at any point within the Burdekin catchment in the dry tropics of Australia. The input data requirements are daily rainfall (to drive the rainfall–runoff model) and mean average wet season rainfall, total length of streams, percent cropping and percent forest in the catchment (to regionalize the parameters of the rainfall–runoff model). The method is based on the use of a simple, lumped parameter rainfall–runoff model, IHACRES (Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data). Of the five parameters in the model, three have been set to constants to reflect regional conditions while the other two have been related to physio-climatic attributes of the catchment under consideration. The parameter defining total catchment water yield (c) has been estimated based on the mean average wet season rainfall, while the streamflow recession time constant (τ) has been estimated based on the total length of streams, percent cropping and percent forest in the catchment. These relationships have been shown to be applicable over a range of scales from 68–130,146 km2. However, three separate relationships were required to define c in the three major physiographic regions of the Burdekin: the upper Burdekin, Bowen and Suttor/lower Burdekin. The invariance of the relationships with scale indicates that the dominant processes may be similar across a range of scales. The fact that different relationships were required for each of the three major regions indicates the geographic limitations of this regionalization approach. For most of the 24 gauged catchments within the Burdekin the regionalized rainfall–runoff models were nearly as good as or better than the rainfall–runoff models calibrated to the observed streamflow. In addition, models often performed better over the simulation period than the calibration period. This indicates that future improvements in regionalization should focus on improving the quality of input data and rainfall–runoff model conceptualization rather than on the regionalization procedure per se.

scholarly journals Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

2017 ◽  
Vol 14 (18) ◽  
pp. 4295-4314 ◽  
Author(s):  
Dan Lu ◽  
Daniel Ricciuto ◽  
Anthony Walker ◽  
Cosmin Safta ◽  
William Munger
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Likelihood Function ◽  
Terrestrial Ecosystem ◽  
Error Model ◽  
Model Parameters ◽  
Posterior Distributions ◽  
Ecosystem Models ◽  
Bayesian Calibration

Abstract. Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. The result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

scholarly journals Bayesian estimation of parameters in a regional hydrological model

2002 ◽  
Vol 6 (5) ◽  
pp. 883-898 ◽  
Author(s):  
K. Engeland ◽  
L. Gottschalk
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Hydrological Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Daily Streamflow ◽  
Likelihood Model ◽  
Simulation Errors

Abstract. This study evaluates the applicability of the distributed, process-oriented Ecomag model for prediction of daily streamflow in ungauged basins. The Ecomag model is applied as a regional model to nine catchments in the NOPEX area, using Bayesian statistics to estimate the posterior distribution of the model parameters conditioned on the observed streamflow. The distribution is calculated by Markov Chain Monte Carlo (MCMC) analysis. The Bayesian method requires formulation of a likelihood function for the parameters and three alternative formulations are used. The first is a subjectively chosen objective function that describes the goodness of fit between the simulated and observed streamflow, as defined in the GLUE framework. The second and third formulations are more statistically correct likelihood models that describe the simulation errors. The full statistical likelihood model describes the simulation errors as an AR(1) process, whereas the simple model excludes the auto-regressive part. The statistical parameters depend on the catchments and the hydrological processes and the statistical and the hydrological parameters are estimated simultaneously. The results show that the simple likelihood model gives the most robust parameter estimates. The simulation error may be explained to a large extent by the catchment characteristics and climatic conditions, so it is possible to transfer knowledge about them to ungauged catchments. The statistical models for the simulation errors indicate that structural errors in the model are more important than parameter uncertainties. Keywords: regional hydrological model, model uncertainty, Bayesian analysis, Markov Chain Monte Carlo analysis

Analysis of parameter uncertainty of a flow and quality stormwater model

2009 ◽  
Vol 60 (3) ◽  
pp. 717-725 ◽  
Author(s):  
C. B. S. Dotto ◽  
A. Deletic ◽  
T. D. Fletcher
Keyword(s):  
Water Quality ◽  
Bayesian Methods ◽  
Flow Model ◽  
Model Parameters ◽  
Rainfall Runoff ◽  
Sources Of Uncertainty ◽  
Music Model ◽  
Rainfall Runoff Model ◽  
Water Quality Models ◽  
Runoff Model

Uncertainty is intrinsic to all monitoring programs and all models. It cannot realistically be eliminated, but it is necessary to understand the sources of uncertainty, and their consequences on models and decisions. The aim of this paper is to evaluate uncertainty in a flow and water quality stormwater model, due to the model parameters and the availability of data for calibration and validation of the flow model. The MUSIC model, widely used in Australian stormwater practice, has been investigated. Frequentist and Bayesian methods were used for calibration and sensitivity analysis, respectively. It was found that out of 13 calibration parameters of the rainfall/runoff model, only two matter (the model results were not sensitive to the other 11). This suggests that the model can be simplified without losing its accuracy. The evaluation of the water quality models proved to be much more difficult. For the specific catchment and model tested, we argue that for rainfall/runoff, 6 months of data for calibration and 6 months of data for validation are required to produce reliable predictions. Further work is needed to make similar recommendations for modelling water quality.

Effect of rainfall data errors on the optimized values of model parameters

Soil Research ◽  
1982 ◽  
Vol 20 (1) ◽  
pp. 15
Author(s):  
WC Boughton ◽  
FT Sefe
Keyword(s):  
Storage Capacity ◽  
Rainfall Data ◽  
Model Parameters ◽  
Similar Magnitude ◽  
Rainfall Runoff ◽  
Data Errors ◽  
Cast Doubt ◽  
Rainfall Runoff Model ◽  
Induced Changes ◽  
Runoff Model

The rainfall input to a rainfall-runoff model was arbitrarily increased and decreased in order to determine the magnitude of corresponding changes in optimized values of the model parameters. The optimized capacities of moisture stores representing surface storage capacity of a catchment changed by average amounts of +24% and -20% as rainfall input was changed by +10% and -10%, respectively. Values of other parameters showed changes of similar magnitude, but there was no uniformity in the magnitude of induced changes from catchment to catchment. The results cast doubt on the validity of relating optimized values of model parameters to physical characteristics of catchments.

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