Toward improved identifiability of hydrologic model parameters: The information content of experimental data

We have developed a sequential optimization methodology, entitled the parameter identification method based on the localization of information (PIMLI) that increases information retrieval from the data by inferring the location and type of measurements that are most informative for the model parameters. The PIMLI approach merges the strengths of the generalized sensitivity analysis (GSA) method [Spear and Hornberger, 1980], the Bayesian recursive estimation (BARE) algorithm [Thiemann et al., 2001], and the Metropolis algorithm [Metropolis et al., 1953]. Three case studies with increasing complexity are used to illustrate the usefulness and applicability of the PIMLI methodology. The first two case studies consider the identification of soil hydraulic parameters using soil water retention data and a transient multistep outflow experiment (MSO), whereas the third study involves the calibration of a conceptual rainfall-runoff model

A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters

Markov Chain Monte Carlo (MCMC) methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models. However, MCMC methods require the a priori definition of a proposal or sampling distribution, which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the Markov Chain and its rate of convergence. In this paper we present an MCMC sampler entitled the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), which is well suited to infer the posterior distribution of hydrologic model parameters. The SCEM-UA algorithm is a modified version of the original SCE-UA global optimization algorithm developed by Duan et al. [1992]. The SCEM-UA algorithm operates by merging the strengths of the Metropolis algorithm, controlled random search, competitive evolution, and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution. Three case studies demonstrate that the adaptive capability of the SCEM-UA algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional Metropolis-Hastings samplers

Effective and efficient algorithm for multiobjective optimization of hydrologic models

Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity

Inverse modeling of cloud-aerosol interactions – Part 1: Detailed response surface analysis

This is the final version of the article. Available from EGU via the DOI in this record.New methodologies are required to probe the sensitivity of parameters describing cloud droplet activation. This paper presents an inverse modeling-based method for exploring cloud-aerosol interactions via response surfaces. The objective function, containing the difference between the measured and model predicted cloud droplet size distribution is studied in a two-dimensional framework, and presented for pseudo-adiabatic cloud parcel model parameters that are pair-wise selected. From this response surface analysis it is shown that the susceptibility of cloud droplet size distribution to variations in different aerosol physiochemical parameters is highly dependent on the aerosol environment and meteorological conditions. In general the cloud droplet size distribution is most susceptible to changes in the updraft velocity. A shift towards an increase in the importance of chemistry for the cloud nucleating ability of particles is shown to exist somewhere between marine average and rural continental aerosol regimes. We also use these response surfaces to explore the feasibility of inverse modeling to determine cloud-aerosol interactions. It is shown that the "cloud-aerosol" inverse problem is particularly difficult to solve due to significant parameter interaction, presence of multiple regions of attraction, numerous local optima, and considerable parameter insensitivity. The identifiability of the model parameters will be dependent on the choice of the objective function. Sensitivity analysis is performed to investigate the location of the information content within the calibration data to confirm that our choice of objective function maximizes information retrieval from the cloud droplet size distribution. Cloud parcel models that employ a moving-centre based calculation of the cloud droplet size distribution pose additional difficulties when applying automatic search algorithms for studying cloud-aerosol interactions. To aid future studies, an increased resolution of the region of the size spectrum associated with droplet activation within cloud parcel models, or further development of fixed-sectional cloud models would be beneficial. Despite these improvements, it is demonstrated that powerful search algorithms remain necessary to efficiently explore the parameter space and successfully solve the cloud-aerosol inverse problem.We gratefully acknowledge the financial support of the Bert Bolin Centre for Climate research. We gratefully appreciate G. J. Roelofs, IMAU, Utrecht, the Netherlands, for providing us with the pseudo-adiabatic cloud parcel model used in this study. We gratefully acknowledge Hamish Struthers valuable discussions and his help to improve the readability of the manuscript. Some of the calculations made during the course of this study have been made possible using the LISA cluster from the SARA centre for parallel computing at the University of Amsterdam, the Netherlands. AS acknowledges support from an Office of Naval Research YIP award (N00014-10-1-0811).The authors acknowledge the Swedish Environmental Monitoring Program a

Identification of key parameters controlling demographically structured vegetation dynamics in a land surface model: CLM4.5(FATES)

Vegetation plays an important role in regulating global carbon cycles and is a key component of the Earth system models (ESMs) that aim to project Earth's future climate. In the last decade, the vegetation component within ESMs has witnessed great progress from simple "big-leaf" approaches to demographically structured approaches, which have a better representation of plant size, canopy structure, and disturbances. These demographically structured vegetation models typically have a large number of input parameters, and sensitivity analysis is needed to quantify the impact of each parameter on the model outputs for a better understanding of model behavior. In this study, we conducted a comprehensive sensitivity analysis to diagnose the Community Land Model coupled to the Functionally Assembled Terrestrial Simulator, or CLM4.5(FATES). Specifically, we quantified the first- and second-order sensitivities of the model parameters to outputs that represent simulated growth and mortality as well as carbon fluxes and stocks for a tropical site with an extent of 1×1°. While the photosynthetic capacity parameter (Vc;max25) is found to be important for simulated carbon stocks and fluxes, we also show the importance of carbon storage and allometry parameters, which determine survival and growth strategies within the model. The parameter sensitivity changes with different sizes of trees and climate conditions. The results of this study highlight the importance of understanding the dynamics of the next generation of demographically enabled vegetation models within ESMs to improve model parameterization and structure for better model fidelity

Comparative run-time performance of evolutionary algorithms on multi-objective interpolated continuous optimisation problems.

We propose a new class of multi-objective benchmark problems on which we analyse the performance of four well established multi-objective evolutionary algorithms (MOEAs) – each implementing a different search paradigm – by comparing run-time convergence behaviour over a set of 1200 problem instances. The new benchmarks are created by fusing previously proposed single-objective interpolated continuous optimisation problems (ICOPs) via a common set of Pareto non-dominated seeds. They thus inherit the ICOP property of having tunable fitness landscape features. The benchmarks are of intrinsic interest as they derive from interpolation methods and so can approximate general problem instances. This property is revealed to be of particular importance as our extensive set of numerical experiments indicates that choices pertaining to (i) the weighting of the inverse distance interpolation function and (ii) the problem dimension can be used to construct problems that are challenging to all tested multi-objective search paradigms. This in turn means that the new multi-objective ICOPs problems (MO-ICOPs) can be used to construct well-balanced benchmark sets that discriminate well between the run-time convergence behaviour of different solvers

Use of the q-Gaussian mutation in evolutionary algorithms

Copyright @ Springer-Verlag 2010.This paper proposes the use of the q-Gaussian mutation with self-adaptation of the shape of the mutation distribution in evolutionary algorithms. The shape of the q-Gaussian mutation distribution is controlled by a real parameter q. In the proposed method, the real parameter q of the q-Gaussian mutation is encoded in the chromosome of individuals and hence is allowed to evolve during the evolutionary process. In order to test the new mutation operator, evolution strategy and evolutionary programming algorithms with self-adapted q-Gaussian mutation generated from anisotropic and isotropic distributions are presented. The theoretical analysis of the q-Gaussian mutation is also provided. In the experimental study, the q-Gaussian mutation is compared to Gaussian and Cauchy mutations in the optimization of a set of test functions. Experimental results show the efficiency of the proposed method of self-adapting the mutation distribution in evolutionary algorithms.This work was supported in part by FAPESP and CNPq in Brazil and in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant EP/E060722/1 and Grant EP/E060722/2