Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity

2013 ◽  
Vol 28 (19) ◽  
pp. 5131-5139 ◽  
Author(s):  
James Knighton ◽  
Eric White ◽  
Edward Lennon ◽  
Rajesh Rajan
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Monte Carlo Analysis ◽  
Hydrologic Model ◽  
Model Parameters ◽  
Model Sensitivity

Probabilistic High-Cycle Fatigue Risk Assessment of an Integrally Bladed Rotor

2011 ◽  
Author(s):  
Benjamin D. Hall ◽  
Lauren Gray
Keyword(s):  
Risk Assessment ◽  
Monte Carlo ◽  
High Cycle Fatigue ◽  
Probability Distributions ◽  
Direct Monte Carlo Simulation ◽  
Model Parameters ◽  
Cycle Fatigue ◽  
Turbine Engine ◽  
Engineering Models ◽  
Mcmc Simulation

A fully probabilistic high-cycle fatigue (HCF) risk assessment methodology for application to turbine engine blades is described. The assessment uses the Bayesian paradigm of probability theory in which probability distributions are used to encode states of knowledge. Multi-level (or hierarchical) models are employed to capture engineering knowledge of the factors important for assessing HCF risk. This structure allows us to use standard probability distributions to adequately represent uncertainties in model parameters. The model accounts for engine-to-engine, run-to-run, and blade-to-blade variability as well as uncertainty in material capability, usage (flight conditions, time at resonance), and steady and vibratory stresses. Markov chain Monte Carlo (MCMC) simulation is used to fit observed data to the engineering models, then direct Monte Carlo simulation is used to assess the HCF risk.

Sensitivity analysis of an urban stormwater microorganism model

2010 ◽  
Vol 62 (6) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. T. McCarthy ◽  
A. Deletic ◽  
V. G. Mitchell ◽  
C. Diaper
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Analysis ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Urban Stormwater ◽  
Urban Catchments ◽  
Two Parameters

This paper presents the sensitivity analysis of a newly developed model which predicts microorganism concentrations in urban stormwater (MOPUS—MicroOrganism Prediction in Urban Stormwater). The analysis used Escherichia coli data collected from four urban catchments in Melbourne, Australia. The MICA program (Model Independent Markov Chain Monte Carlo Analysis), used to conduct this analysis, applies a carefully constructed Markov Chain Monte Carlo procedure, based on the Metropolis-Hastings algorithm, to explore the model's posterior parameter distribution. It was determined that the majority of parameters in the MOPUS model were well defined, with the data from the MCMC procedure indicating that the parameters were largely independent. However, a sporadic correlation found between two parameters indicates that some improvements may be possible in the MOPUS model. This paper identifies the parameters which are the most important during model calibration; it was shown, for example, that parameters associated with the deposition of microorganisms in the catchment were more influential than those related to microorganism survival processes. These findings will help users calibrate the MOPUS model, and will help the model developer to improve the model, with efforts currently being made to reduce the number of model parameters, whilst also reducing the slight interaction identified.

scholarly journals Constraining subglacial processes from surface velocity observations using surrogate-based Bayesian inference

2021 ◽  
pp. 1-19
Author(s):  
Douglas Brinkerhoff ◽  
Andy Aschwanden ◽  
Mark Fahnestock
Keyword(s):  
Probability Distributions ◽  
Water Pressure ◽  
Model Development ◽  
Computational Cost ◽  
Hydrologic Model ◽  
Surface Velocity ◽  
Small Scale ◽  
Model Parameters ◽  
Stress Regime ◽  
Ice Dynamics

Abstract Basal motion is the primary mechanism for ice flux in Greenland, yet a widely applicable model for predicting it remains elusive. This is due to the difficulty in both observing small-scale bed properties and predicting a time-varying water pressure on which basal motion putatively depends. We take a Bayesian approach to these problems by coupling models of ice dynamics and subglacial hydrology and conditioning on observations of surface velocity in southwestern Greenland to infer the posterior probability distributions for eight spatially and temporally constant parameters governing the behavior of both the sliding law and hydrologic model. Because the model is computationally expensive, characterization of these distributions using classical Markov Chain Monte Carlo sampling is intractable. We skirt this issue by training a neural network as a surrogate that approximates the model at a sliver of the computational cost. We find that surface velocity observations establish strong constraints on model parameters relative to a prior distribution and also elucidate correlations, while the model explains 60% of observed variance. However, we also find that several distinct configurations of the hydrologic system and stress regime are consistent with observations, underscoring the need for continued data collection and model development.

Hydrologic Model Sensitivity to Temporal Aggregation of Meteorological Forcing Data: a Case Study for the Contiguous USA

2021 ◽  
Author(s):  
Ashley E. Van Beusekom ◽  
Lauren E. Hay ◽  
Andrew R. Bennett ◽  
Young-Don Choi ◽  
Martyn P. Clark ◽  
...  
Keyword(s):  
Longwave Radiation ◽  
Latin Hypercube Sampling ◽  
Temporal Variations ◽  
Hydrologic Model ◽  
Specific Humidity ◽  
Shortwave Radiation ◽  
Model Parameters ◽  
Model Output ◽  
Regional Variability ◽  
Model Sensitivity

Abstract Surface meteorological analyses are an essential input (termed ‘forcing’) for hydrologic modeling. This study investigated the sensitivity of different hydrologic model configurations to temporal variations of seven forcing variables (precipitation rate, air temperature, longwave radiation, specific humidity, shortwave radiation, wind speed, and air pressure). Specifically, the effects of temporally aggregating hourly forcings to hourly daily-average forcings were examined. The analysis was based on 14 hydrological outputs from the Structure for Unifying Multiple Modeling Alternatives (SUMMA) model for the 671 Catchment Attributes and MEteorology for Large-sample Studies (CAMELS) basins across the contiguous United States (CONUS). Results demonstrated that the hydrologic model sensitivity to temporally aggregating the forcing inputs varies across model output variables and model locations. We used Latin Hypercube sampling to sample model parameters from eight combinations of three influential model physics choices (three model decisions with two options for each decision, i.e., eight model configurations). Results showed that the choice of model physics can change the relative influence of forcing on model outputs and the forcing importance may not be dependent on the parameter space. This allows for model output sensitivity to forcing aggregation to be tested prior to parameter calibration. More generally, this work provides a comprehensive analysis of the dependence of modeled outcomes on input forcing behavior, providing insight into the regional variability of forcing variable dominance on modeled outputs across CONUS.

scholarly journals A hydro-climatological approach to predicting regional landslide probability using Landlab

2017 ◽  
Author(s):  
Ronda Strauch ◽  
Erkan Istanbulluoglu ◽  
Sai Siddhartha Nudurupati ◽  
Christina Bandaragoda ◽  
Nicole M. Gasparini ◽  
...  
Keyword(s):  
Soil Depth ◽  
Probability Distributions ◽  
Probability Model ◽  
Subsurface Flow ◽  
Grid Cell ◽  
Bimodal Distribution ◽  
Shallow Landslide ◽  
Hydrologic Model ◽  
Model Parameters ◽  
Infinite Slope Stability Model

Abstract. We develop a hydro-climatological approach to modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation. The physically-based model couples the infinite slope stability model with a steady-state subsurface flow representation and operates on a digital elevation model. Spatially distributed raster data for soil properties and a soil evolution model and vegetation classification from National Land Cover Data are used to derive parameters for probability distributions to represent input uncertainty. Hydrologic forcing to the model is through annual maximum recharge to subsurface flow obtained from a macroscale hydrologic model, routed on raster grid to develop subsurface flow. A Monte Carlo approach is used to generate model parameters at each grid cell and calculate probability of shallow landsliding. We demonstrate the model in a steep mountainous region in northern Washington, U.S.A., using 30-m grid resolution over 2,700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting uncertainty of soil depth and its potential long-term variability. We found elevation dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests in low elevations, an increased landslide probability with forest decline at mid elevations (1,400 to 2,400 m), and soil limitation and steep topographic controls at high alpine elevations and post-glacial landscapes. These dominant controls manifest in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similar model confidence for the three hazard maps, suggesting suitable use as relative hazard products. Validation of the model with observed landslides is hindered by the completeness and accuracy of the inventory, estimation of source areas, and unmapped landslides. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.

scholarly journals Uncertainties in model predictions of nitrogen fluxes from agro-ecosystems in Europe

2012 ◽  
Vol 9 (5) ◽  
pp. 6051-6094 ◽  
Author(s):  
J. Kros ◽  
G. B. M. Heuvelink ◽  
G. J. Reinds ◽  
J. P. Lesschen ◽  
V. Ioannidi ◽  
...  
Keyword(s):  
Probability Distributions ◽  
Spatial Scales ◽  
Uncertainty Propagation ◽  
Correlation Coefficients ◽  
Monte Carlo Analysis ◽  
N Leaching ◽  
Model Parameters ◽  
Country Level ◽  
Uncertain Model ◽  
Relative Errors

Abstract. To assess the responses of nitrogen and greenhouse gas emissions to pan-European changes in land cover, land management and climate, an integrated dynamic model, INTEGRATOR, has been developed. This model includes both simple process-based descriptions and empirical relationships, and uses detailed GIS-based environmental and farming data in combination with various downscaling methods. This paper analyses the propagation of uncertainties in model inputs and model parameters to outputs of INTEGRATOR, using a Monte Carlo analysis. Uncertain model inputs and parameters were represented by probability distributions, while spatial correlation in these uncertainties was taken into account by assigning correlation coefficients at various spatial scales. The uncertainty propagation was analysed for the emissions of NH3, N2O and NOx and N leaching to groundwater and N surface runoff to surface water for the entire EU27 and for individual countries. Results show large uncertainties for N leaching and N runoff (relative errors of ~19 % for Europe as a whole), and smaller uncertainties for emission of N2O, NH3 and NOx (relative errors of ~12 %). Uncertainties for Europe as a whole were much smaller compared to uncertainties at Country level, because errors partly cancelled out due to spatial aggregation.

scholarly journals Probabilistic Inference Coupled with Possibilistic Reasoning for Robust Estimation of Hydrologic Parameters and Piecewise Characterization of Interactive Uncertainties

2016 ◽  
Vol 17 (4) ◽  
pp. 1243-1260 ◽  
Author(s):  
S. Wang ◽  
G. H. Huang ◽  
B. W. Baetz ◽  
W. Huang
Keyword(s):  
Expert Knowledge ◽  
Probability Distributions ◽  
Statistical Significance ◽  
Probabilistic Inference ◽  
Hydrologic Model ◽  
Factorial Analysis ◽  
Model Parameters ◽  
Xiangxi River ◽  
Parametric Interactions

Abstract This paper presents a factorial possibilistic–probabilistic inference (FPI) framework for estimation of hydrologic parameters and characterization of interactive uncertainties. FPI is capable of incorporating expert knowledge into the parameter adjustment procedure for enhancing the understanding of the nature of the calibration problem. As a component of the FPI framework, a Monte Carlo–based fractional fuzzy–factorial analysis (MFA) method is also proposed to identify the best parameter set and its underlying probability distributions in a fuzzy probability space. Factorial analysis of variance (ANOVA) coupled with its multivariate extensions are performed to explore potential interactions among model parameters and among hydrological metrics in a systematic manner. The proposed methodology is applied to the Xiangxi River watershed by using the conceptual hydrological model (HYMOD) to demonstrate its validity and applicability. Results reveal that MFA is capable of deriving probability density functions (PDFs) of hydrologic model parameters. Moreover, the sequential inferences derived from the F test and its multivariate approximations disclose the statistical significance of parametric interactions affecting individual and multiple hydrological metrics, respectively. The findings presented here indicate that parametric interactions are complex in a fuzzy stochastic environment, and the magnitude and direction of interaction effects vary in different regions of the parameter space as well as vary temporally because of the dynamic behavior of hydrologic systems.

Sign in / Sign up

Export Citation Format

Share Document