Integrating remote sensing datasets into ecological modelling: a Bayesian approach

Process-based models have been used to simulate 3-dimensional complexities of forest ecosystems and their temporal changes, but their extensive data requirement and complex parameterisation have often limited their use for practical management applications. Increasingly, information retrieved using remote sensing techniques can help in model parameterisation and data collection by providing spatially and temporally resolved forest information. In this paper, we illustrate the potential of Bayesian calibration for integrating such data sources to simulate forest production. As an example, we use the 3-PG model combined with hyperspectral, LiDAR, SAR and field-based data to simulate the growth of UK Corsican pine stands. Hyperspectral, LiDAR and SAR data are used to estimate LAI dynamics, tree height and above ground biomass, respectively, while the Bayesian calibration provides estimates of uncertainties to model parameters and outputs. The Bayesian calibration contrasts with goodness-of-fit approaches, which do not provide uncertainties to parameters and model outputs. Parameters and the data used in the calibration process are presented in the form of probability distributions, reflecting our degree of certainty about them. After the calibration, the distributions are updated. To approximate posterior distributions (of outputs and parameters), a Markov Chain Monte Carlo sampling approach is used (25 000 steps). A sensitivity analysis is also conducted between parameters and outputs. Overall, the results illustrate the potential of a Bayesian framework for truly integrative work, both in the consideration of field-based and remotely sensed datasets available and in estimating parameter and model output uncertainties

Bayesian Calibration Tool

Fitting a model to data is common practice in many fields of science. The models may contain unknown parameters and often, the goal is to obtain good estimates of them. A variety of methods have been developed for this purpose. They often differ in complexity, efficiency and accuracy and some may have very limited applications. Bayesian inference methods have recently become popular for the purpose of calibrating model\u27s parameters. The way they treat unknown quantities is completely different from any classical methods. Even though the unknown quantity is a constant, it is treated as a random variable and the desired outcome is it\u27s probability distribution. Good estimates and confidence intervals can then be easily produced from probability distributions. Anohter important feature of Bayesian inference is the ability to include prior knowledge in the calculations. However, Bayesian inference has to be done computationally as it involves solving multidimensional integrals. The Bayesian Calibration tool is an easy-to-use, well documented tool to efficiently carry out the calculations of the calibration process. The tool is open-source and uses fast Markov Chain Monte Carlo (MCMC) algorithms. The tool is run on nanoHUB, making it easily accessible without installing any software, etc. Given data and a model, the tool performs MCMC simulation of the model and returns the Bayesian posterior probability distributions of the model\u27s unknown parameters

Credit Shocks and Cycles: a Bayesian Calibration Approach

This paper asks how well a general equilibrium agency cost model describes the dynamic relationship between credit variables and the business cycle. A Bayesian VAR is used to obtain probability intervals for empirical correlations. The agency cost model is found to predict the leading, countercyclical correlation of spreads with output when shocks arising from the credit market contribute to output fluctuations. The contribution of technology shocks is held at conventional RBC levels. Sensitivity analysis shows that moderate prior calibration uncertainty leads to significant dispersion in predictedcorrelations. Most predictive uncertainty arises from a single parameter.agency costs, credit cycles, calibration, shocks.

Business Cycle Implications of Habit Formation

The inability of a wide array of dynamic stochastic general equilibrium (DSGE) models to generate fluctuations that resemble actual business cycles has lead to the use of habit formation in consumption. For example, habit formation has been shown to help explain the negative response of labour input to a positive, permanent technology shock, several asset pricing puzzles, and the impact of monetary shocks on real variables. Investigating four different DSGE models with the Bayesian calibration approach, this paper observes that, especially in a new Keynesian monetary business cycle model with both staggered price and wage, habit formation fails to mimic the shape of output growth in the frequency domain: it counterfactually emphasizes low frequency fluctuations in output growth, compared to the U.S. data. On the other hand, habit formation has no clear implications on other business cycle aspects including impulse responses and forecast error variance decompositions of output to permanent and transitory shocks. These observations cast doubt on habit formation as an important ingredient of the DSGE model with a rich set of internal propagation mechanisms.Business Cycle; Habit Formation; Frequency Domain; Bayesian Calibration

CALIBRO : an R package for the automatic calibration of building energy simulation models

Bayesian probability theory offers a powerful framework for the calibration of building energy models (Bayesian calibration). The major issues impeding its routine adoption are its steep learning curve, and the complicated setting up of the required calculation. This paper introduces CALIBRO, an R package which has the objective of facilitating the undertaking of Bayesian calibration of building energy models. An overview of the techniques and procedures involved in CALIBRO is given, as well as demonstrations of its capability and reliability through two examples

Bayesian calibration of AquaCrop model

The AquaCrop simulation model, modelling the dynamic change of crop growth status, is an important crop management tool for quantifying crop yield response to water. To effectively simulate the soil water balance and the crop growth process, a number of system parameters and canopy state variables are inevitably adopted. As a result, certain key parameters need to be calibrated so that the AquaCrop model can achieve a better performance of prediction for various scales of regions. This paper aims to apply Bayesian technique to calibrate the AquaCrop model. In this approach, the prior information regarding the system parameters is expressed in the form of a uniform probability distribution. Then with the advent of output variable measurement (e.g. biomass) by remote sensing techniques, the parameter distributions are iteratively updated by using Bayesian Markov Chain Monte Carlo (MCMC) method. The calibrated system parameters are expressed by the posterior distributions and gained by distribution mean value. Finally, the Bayesian calibration is compared with the conventional optimisation based calibration in terms of biomass and canopy cover, where simulated annealing is chosen as the optimisation approach, indicating a better calibration performance can be achieved by using Bayesian methods. Consequently, it is recommended that Bayesian calibration is one promising approach to the problem of crop model calibration

Parameter-induced uncertainty quantification of soil N 2 O, NO and CO 2 emission from Höglwald spruce forest (Germany) using the LandscapeDNDC model

Assessing the uncertainties of simulation results of ecological models is becoming increasingly important, specifically if these models are used to estimate greenhouse gas emissions on site to regional/national levels. Four general sources of uncertainty effect the outcome of process-based models: (i) uncertainty of information used to initialise and drive the model, (ii) uncertainty of model parameters describing specific ecosystem processes, (iii) uncertainty of the model structure, and (iv) accurateness of measurements (e.g., soil-atmosphere greenhouse gas exchange) which are used for model testing and development. The aim of our study was to assess the simulation uncertainty of the process-based biogeochemical model LandscapeDNDC. For this we set up a Bayesian framework using a Markov Chain Monte Carlo (MCMC) method, to estimate the joint model parameter distribution. Data for model testing, parameter estimation and uncertainty assessment were taken from observations of soil fluxes of nitrous oxide (N2O), nitric oxide (NO) and carbon dioxide (CO2) as observed over a 10 yr period at the spruce site of the Höglwald Forest, Germany. By running four independent Markov Chains in parallel with identical properties (except for the parameter start values), an objective criteria for chain convergence developed by Gelman et al. (2003) could be used. Our approach shows that by means of the joint parameter distribution, we were able not only to limit the parameter space and specify the probability of parameter values, but also to assess the complex dependencies among model parameters used for simulating soil C and N trace gas emissions. This helped to improve the understanding of the behaviour of the complex LandscapeDNDC model while simulating soil C and N turnover processes and associated C and N soil-atmosphere exchange. In a final step the parameter distribution of the most sensitive parameters determining soil-atmosphere C and N exchange were used to obtain the parameter-induced uncertainty of simulated N2O, NO and CO2 emissions. These were compared to observational data of an calibration set (6 yr) and an independent validation set of 4 yr. The comparison showed that most of the annual observed trace gas emissions were in the range of simulated values and were predicted with a high certainty (Root-mean-squared error (RMSE) NO: 2.4 to 18.95 g N ha−1 d−1, N2O: 0.14 to 21.12 g N ha−1 d−1, CO2: 5.4 to 11.9 kg C ha−1 d−1). However, LandscapeDNDC simulations were sometimes still limited to accurately predict observed seasonal variations in fluxes