Uncertainty In Model Response Research Articles

Weighting climate models for hydrological projections: effects on contrasting hydroclimatic regions

Weighting climate models has recently become a more accepted approach. However, it remains a topic of ongoing discussion, especially for analyses needed at regional scales, such as hydrological assessments. Various studies have evaluated the weighting approaches for climate simulations. Yet, few case studies have assessed the impacts of weighting climate models on streamflow projections. Additionally, the methodological and location limitations of previous studies make it difficult to extrapolate their conclusions over regions with contrasting hydroclimatic regimes, highlighting the need for further studies. Thus, this study evaluates the effects of different climate model’s weighting approaches on hydrological projections over hydrologically diverse basins. An ensemble of 24 global climate model (GCM) simulations coupled with a lumped hydrological model is used over 20 North American basins to generate 24 GCM-driven streamflow projections. Six unequal-weighting approaches, comprising temperature-, precipitation-, and streamflow-based criteria, were evaluated using an out-of-sample approach during the 1976–2005 reference period. Moreover, the unequal-weighting approaches were compared against the equal-weighting approach over the 1976–2005, 2041–2070, and 2070–2099 periods. The out-of-sample assessment showed that unequally weighted ensembles can improve the mean hydrograph representation under historical conditions compared to the common equal-weighting approach. In addition, results revealed that unequally weighting climate models not only impacted the magnitude and climate change signal, but also reduced the model response uncertainty spread of hydrological projections, particularly over rain-dominated basins. These results underline the need to further evaluate the adequacy of equally weighting climate models, especially for variables with generally larger uncertainty at regional scale.

TRANSLATE: standardized climate projections for Ireland

The TRANSLATE project was established in 2021 by Met Éireann, the Irish national meteorological service, to provide standardized future climate projections for Ireland. This paper outlines the principles and main methods that were used to generate the first set of such projections and presents selected results to the end of the 21st century. Two separate ensembles of dynamically downscaled CMIP5 projections were analyzed. These produce very consistent results, increasing confidence in both, and in the methods used. Future projected fields show plenty of detail (depending on local geography), but the change maps relative to the base period are much smoother, reflecting the global climate change signal. Future forcing uncertainty is represented by 3 different emission scenarios, while model response uncertainty is represented by sub-ensembles corresponding to different climate sensitivities. The resulting matrix of distinct climate ensembles is complemented by ensembles of temperature threshold-based projections, drawn from the same underlying simulations.

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. A modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

Quantifying CMIP6 model uncertainties in extreme precipitation projections

Projected changes in precipitation extremes and their uncertainties are evaluated using an ensemble of global climate models from phase 6 of the Coupled Model Intercomparison Project (CMIP). They are scaled by corresponding changes either in global mean surface temperature (ΔGSAT) or in local surface temperature (ΔT) and are expressed in terms of 20-yr return values (RV20) of annual maximum one-day precipitation. Our main objective is to quantify the model response uncertainty and to highlight the regions where changes may not be consistent with the widely used assumption of a Clausius–Clapeyron (CC) rate of ≈7%/K. When using a single realization for each model, as in the latest report from the Intergovernmental Panel on Climate Change (IPCC), the assessed inter-model spread includes both model uncertainty and internal variability, which can be however assessed separately using a large ensemble. Despite the overestimated inter-model spread, our results show a robust enhancement of extreme precipitation with more than 90% of models simulating an increase of RV20. Moreover, this increase is consistent with the CC rate of ≈7%/K over about 83% of the global land domain when scaled by (ΔGSAT). Our results also advocate for producing multiple single model initial condition ensembles in the next CMIP projections, to better filter internal variability out in estimating the response of extreme events.

Does Regional Hydroclimate Change Scale Linearly With Global Warming?

AbstractMany aspects of climate change scale linearly with global warming. However, nonlinear changes are possible, especially in the context of hydroclimate, and under emissions scenarios with stabilized global temperature, as aspired to by current climate targets. In CMIP5 and 6, a progressively larger land area shows nonlinear changes as a function of global warming when considering precipitation, evaporation, and soil moisture, with the latter showing nonlinearity over ∼50% of global land. Using ensemble simulations with the Community Earth System Model 1, in which individual forcing factors are held constant, we illustrate how nonadditive responses to anthropogenic greenhouse gases and industrial and fire‐related aerosols can yield complex soil moisture changes in certain regions. This complexity contributes to uncertainty in regional soil moisture projections and suggests that the timing of, as well as model response uncertainty to, future aerosol reductions will have significant impacts on regional hydroclimate change as global temperatures stabilize.

An efficient variance-based global sensitivity index based on C-DRM and Taylor expansion

Sensitivity analysis plays an important role in quantifying the impact of input uncertainty on model response uncertainty. Through sensitivity analysis, we can grasp the crucial parameters and gain a deeper understanding of the model behavior. In this paper, an effective analytical solution for solving the variance-based global sensitivity index is proposed. Firstly, the original performance function is approximated as the sum of a series of univariate functions using the conventional dimensional reduction method (C-DRM). Then, the Taylor series expansion is used to expand the univariate function as unary linear function and unary quadratic functions. Finally, the analytical solutions of the variance-based global sensitivity index based on unary linear function and unary quadratic functions are derived respectively. The computational cost of the proposed method is completely concentrated on the calculation of the partial derivative information of the performance function with respect to each variable. As long as the partial derivative information is obtained, the variance-based global sensitivity index can be obtained directly by the proposed method without any additional computational cost. For simple explicit performance functions, the derivative information can be directly derived analytically. For complex explicit or implicit performance functions, the derivative information can be estimated by some simple numerical difference methods. Five examples are studied to investigate the accuracy and efficiency of the proposed method.

Assessing natural variability in RCM signals: comparison of a multi model EURO-CORDEX ensemble with a 50-member single model large ensemble

Uncertainties in climate model ensembles are still relatively large. Besides scenario and model response uncertainty, natural variability is another important source of uncertainty. To study regional natural variability on timescales of several decades and more, observations are often too sparse and short. Regional Climate Models (RCMs) can be used to overcome this lack of useful data at high spatial resolutions. In this study, we compare a new 50-member single RCM large ensemble (CRCM5-LE) with an ensemble of 22 EURO-CORDEX models for seasonal temperature and precipitation at 0.11° grid size over Europe—all driven by the RCP 8.5 scenario. This setup allows us to quantify the contribution of natural/model-internal variability on the total uncertainty of a multi-model ensemble. The variability of climate change signals within the two ensembles is compared for three future periods (2020–2049, 2040–069 and 2070–2099). Results show that the single model spread is usually smaller than the multi-model spread for temperature. Similar variabilities can mostly be found in the near future (and to a lesser extent in the mid future) during winter and spring, especially for northern and central parts of Europe. The contribution of internal variability is generally higher for precipitation. In the near future almost all seasons and regions show similar variabilities. In the mid and far future only fall, summer and spring still show similar variabilites. There is a significant decrease of the contribution of internal variability over time for both variables. However, even in the far future for most regions and seasons 25–75% of the overall variability can be explained by internal variability.

Analyzing uncertainties in model response using the point estimate method: Applications from railway asset management

Predicting current and future states of rail infrastructure based on existing data and measurements is essential for optimal maintenance and operation of railway systems. Mathematical models are helpful tools for detecting failures and extrapolating current states into the future. This, however, inherently gives rise to uncertainties in the model response that must be analyzed carefully to avoid misleading results and conclusions. Commonly, Monte Carlo simulations are used for such analyses which often require a large number of sample points to be evaluated for convergence. Moreover, even if quite close to the exact distributions, the Monte Carlo approach necessarily provides approximate results only. In contrast to that, the present contribution reviews an alternative way of computing important statistical quantities of the model response. The so-called point estimate method, which can be shown to be exact under certain constraints, usually (i.e. depending on the number of input variables) works with only a few specific sample points. Thus, the point estimate method helps to reduce the computational load for model evaluation considerably in the case of complex models or large-scale applications. To demonstrate the point estimate method, five academic but typical examples of railway asset management are analyzed in more detail: (a) track degradation, (b) reliability analysis of composite systems, (c) terminal reliability in rail networks, (d) failure detection/identification using decision trees, and (e) track condition modeling incorporating maintenance. Advantages as well as limitations of the point estimate method in comparison with common Monte Carlo simulations are discussed.

Inferred Net Aerosol Forcing Based on Historical Climate Changes: a Review

This review summarizes the inverse methods used to estimate the net aerosol forcing inferred from the historical climate change records for the Earth. The available methods are similar in design while differing in their assumptions. Primary differences are (a) the complexity of the earth system model used for forward simulations of the historical period (~ 1850 to the present), (b) the uncertainty sampling methodology, and (c) the representation of internal climate variability in the statistical approach. All methods, in some fashion, include the net aerosol radiative forcing as a residual forcing that is scaled to find simulations that match the observed records of surface air and deep ocean temperatures. Inverse methods also require sampling the model response uncertainty in the equilibrium climate sensitivity and the transient climate response (i.e., the delay due to mixing heat into the deep ocean), and therefore, a joint probability distribution is estimated that includes uncertainty across multiple components. The resulting estimates of the net aerosol forcing and its uncertainty are, by construction, necessarily linked to the earth system model, its response characteristics, and the estimates of the internal chaotic variability. Summary results indicate that the net aerosol forcing during the late twentieth century was − 0.77 Wm−2 with a 5–95% range of − 1.15 to − 0.31 Wm−2 based on 19 results from simple- to full-complexity climate system models.

Analytic uncertainty and sensitivity analysis of models with input correlations

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated parameters are often happened in practical applications. In the present paper, an analytic method is built for the uncertainty and sensitivity analysis of models in the presence of input correlations. With the method, it is straightforward to identify the importance of the independence and correlations of input variables in determining the model response. This allows one to decide whether or not the input correlations should be considered in practice. Numerical examples suggest the effectiveness and validation of our analytic method in the analysis of general models. A practical application of the method is also proposed to the uncertainty and sensitivity analysis of a deterministic HIV model.

Global sensitivity analysis for developing biological models: Application to K+ channel model in mouse ventricular myocytes.

Mathematical models of cardiac myocytes are highly nonlinear and involve a large number of model parameters. The parameters are estimated using experimental data, which are often corrupted by noise and uncertainty. Such uncertainty can be propagated onto model parameters during model calibration, which further affects model reliability and credibility. In order to improve model accuracy, it is important to quantify and reduce the uncertainty in model response resulting from parametric uncertainty. Sensitivity analysis is a key technique to investigate the significance of parametric uncertainty and its effect on model responses. This can identify and rank most sensitive parameters, and evaluate the effect of uncertainty on model outputs. In this work, a global sensitivity analysis is developed to determine the significance of parametric uncertainty on model responses using Sobol indices. This method is applied to nonlinear K+ channel models of mouse ventricular myocytes to demonstrate the efficacy of the developed algorithm.

Uncertainty quantification and sensitivity analysis applied to the wind wave model SWAN

We report on measuring uncertainty in the computational results of the wind wave model SWAN (Simulating WAves Nearshore) on an unstructured mesh and exploring the sources of this uncertainty. We considered an area in the vicinity of the Saint Petersburg Flood Prevention Facility Complex and treat the results as risks on using the model results for the Facility gate operation.We found that model response uncertainty is significant for small waves (Hs<0.3m), and the results variability is moderate (≈10%) for the extreme values of the model prediction. Thus the risk on the use of model results to predict flood threats is low together with visible uncertainty about the prediction of flood start time.Uncertainty in wind velocity has a substantial influence on the model response. In addition, uncertainty in the bathymetry, water level, and breaker index affects model output. Therefore, result uncertainty can be decreased obtaining more certain values of these model inputs.

Transient Earth system responses to cumulative carbon dioxide emissions: linearities, uncertainties, and probabilities in an observation-constrained model ensemble

Abstract. Information on the relationship between cumulative fossil CO2 emissions and multiple climate targets is essential to design emission mitigation and climate adaptation strategies. In this study, the transient response of a climate or environmental variable per trillion tonnes of CO2 emissions, termed TRE, is quantified for a set of impact-relevant climate variables and from a large set of multi-forcing scenarios extended to year 2300 towards stabilization. An ∼ 1000-member ensemble of the Bern3D-LPJ carbon–climate model is applied and model outcomes are constrained by 26 physical and biogeochemical observational data sets in a Bayesian, Monte Carlo-type framework. Uncertainties in TRE estimates include both scenario uncertainty and model response uncertainty. Cumulative fossil emissions of 1000 Gt C result in a global mean surface air temperature change of 1.9 °C (68 % confidence interval (c.i.): 1.3 to 2.7 °C), a decrease in surface ocean pH of 0.19 (0.18 to 0.22), and a steric sea level rise of 20 cm (13 to 27 cm until 2300). Linearity between cumulative emissions and transient response is high for pH and reasonably high for surface air and sea surface temperatures, but less pronounced for changes in Atlantic meridional overturning, Southern Ocean and tropical surface water saturation with respect to biogenic structures of calcium carbonate, and carbon stocks in soils. The constrained model ensemble is also applied to determine the response to a pulse-like emission and in idealized CO2-only simulations. The transient climate response is constrained, primarily by long-term ocean heat observations, to 1.7 °C (68 % c.i.: 1.3 to 2.2 °C) and the equilibrium climate sensitivity to 2.9 °C (2.0 to 4.2 °C). This is consistent with results by CMIP5 models but inconsistent with recent studies that relied on short-term air temperature data affected by natural climate variability.

A Methodology for Sensitivity Analysis Based on Regression: Applications to Handle Uncertainty in Natural Resources Characterization

Uncertainty in a natural resource model represents risk that should be minimized for improved management. Natural resources are components of complex earth science systems, which can be exhaustively sampled, numerically modeled with Monte Carlo simulation, or both, to understand their underlying nature. A numerical model represents relationships between a response variable and predictor variables. Uncertainty in a response variable can be observed directly, but understanding the importance of each predictor variable requires further post-processing of the numerical model. A methodology of local sensitivity analysis, based on linear and quadratic regression models, is developed to help understand the uncertainty contribution of each predictor variable to the response model. Sensitivity coefficients, predicted response values, and summary statistics with model utility tests for the regression models are evaluated. The importance of standardized sensitivity coefficients and other measures are developed. Standardized sensitivity coefficients represent the contribution of uncertainty in the predictor variables to uncertainty in model response. Results of the sensitivity analysis are visually summarized in the form of extended tornado charts. The proposed methodology is applied to representative petroleum and mining case studies. The methodology is robust, efficient, descriptive, and straightforward. Understanding of the contribution of each predictor variable to the response variable is useful for minimization of model response uncertainty, decision-making, and further study.

Uncertainty in predictions of the climate response to rising levels of greenhouse gases

The range of possibilities for future climate evolution needs to be taken into account when planning climate change mitigation and adaptation strategies. This requires ensembles of multi-decadal simulations to assess both chaotic climate variability and model response uncertainty. Statistical estimates of model response uncertainty, based on observations of recent climate change, admit climate sensitivities--defined as the equilibrium response of global mean temperature to doubling levels of atmospheric carbon dioxide--substantially greater than 5 K. But such strong responses are not used in ranges for future climate change because they have not been seen in general circulation models. Here we present results from the 'climateprediction.net' experiment, the first multi-thousand-member grand ensemble of simulations using a general circulation model and thereby explicitly resolving regional details. We find model versions as realistic as other state-of-the-art climate models but with climate sensitivities ranging from less than 2 K to more than 11 K. Models with such extreme sensitivities are critical for the study of the full range of possible responses of the climate system to rising greenhouse gas levels, and for assessing the risks associated with specific targets for stabilizing these levels.

An intercomparison between four tropical ocean models. Thermocline variability

A multivariate model testing procedure is used to intercompare several tropical ocean models, using the evolution of the thermocline depth during the 1982-1984 FOCAL/SEQUAL experiment in the equatorial Atlantic as observational basis. Four models of increasing complexity are considered: Cane's linear multimode model, a nonlinear 2-layer model developed at LODYC, the KNMI GCM and the LODYC GCM. Some of the uncertainties in the atmospheric forcing are taken into account by forcing the models with 3 equally plausible windstress fields whose differences are consistent with the wind measurement and sampling errors, and the drag coefficient indeterminacy. Although the resulting uncertainties in model response are substantial, none of the models is fully consistent with the observations, i.e., within the error bars. The more complex models represent the thermocline depth variations significantly better than the simpler ones, in particular when the comparison is done over broad geographical areas. When the whole intercomparison domain (12°N-12°S) is considered, the LODYC GCM performs better than the KNMI GCM, both for the yearly mean conditions and for the variations around the 3-year mean, while the 2 models have comparable performance in the equatorial waveguide (3°N-3°S). In view of its simplicity, the linear model shows much skill, in particular for simulating the longterm mean. The 2-layer model poorly represents the long-term mean position of the thermocline, but represents well the variations around the 3-year mean, outperforming the linear model in the equatorial waveguide. Along meridional sections, model performance may be more variable, stressing the need for a global approach to model validation. Finally, a coarse investigation of the simulations of the thermocline depth anomalies with respect to the mean seasonal cycle suggests that, because of the small signal-to-noise ratio, most models have only little skill in the 12°N-12°S domain, but more in the equatorial waveguide. The linear model, however, does not seem to have predicative skill for these noisy anomalies

An intercomparison between four tropical ocean models Thermocline variability

A multivariate model testing procedure is used to intercompare several tropical ocean models, using the evolution of the thermocline depth during the 1982—1984 FOCAL/SEQUAL experiment in the equatorial Atlantic as observational basis. Four models of increasing complexity are considered: Cane’s linear multimode model, a nonlinear 2-layer model developed at LODYC, the KNMI GCM and the LODYC GCM. Some of the uncertainties in the atmospheric forcing are taken into account by forcing the models with 3 equally plausible windstress fields whose differences are consistent with the wind measurement and sampling errors, and the drag coefficient indeterminacy. Although the resulting uncertainties in model response are substantial, none of the models is fully consistent with the observations, i.e., within the error bars. The more complex models represent the thermocline depth variations significantly better than the simpler ones, in particular when the comparison is done over broad geographical areas. When the whole intercomparison domain (12°N-12°S) is considered, the LODYC GCM performs better than the KNMI GCM, both for the yearly mean conditions and for the variations around the 3-year mean, while the 2 models have comparable performance in the equatorial waveguide (3°N-3°S). In view of its simplicity, the linear model shows much skill, in particular for simulating the long-term mean. The 2-layer model poorly represents the long-term mean position of the thermocline, but represents well the variations around the 3-year mean, outperforming the linear model in the equatorial waveguide. Along meridional sections, model performance may be more variable, stressing the need for a global approach to model validation. Finally, a coarse investigation of the simulations of the thermocline depth anomalies with respect to the mean seasonal cycle suggests that, because of the small signal-to-noise ratio, most models have only little skill in the 12°N-12°S domain, but more in the equatorial waveguide. The linear model, however, does not seem to have predicative skill for these noisy anomalies.

An approach to estimating uncertainties in modeling transport of solutes through soils

The objective of this research was to determine the effect of uncertainty in model parameters and rainfall on uncertainty of model response and the impact of these uncertainties on sample size requirements for simulating solute transport through soils. The research was designed to demonstrate a methodology with general applicability. The approach should help one understand the model being used and the uncertainty in model response. The magnitude of uncertainty in the estimated solute transport resulting from parameter variability was found comparable to that resulting from rainfall variability. The combined parameter and rainfall variabilities appear to magnify overall uncertainty in estimated solute transport. The results of uncertainty analysis, in conjunction with the sampling theory, were used todetermine the minimum number of random soil samples required to achieve a given degree of certainty in the estimated solute transport. Increasing soil sample size offers diminishing return in improving estimated solute transport because of natural rainfall variability.

The uncertainty in forecasting trends of forest soil acidification

A Regional Soil Acidification Model (RESAM) has been developed to gain insight in long-term impacts of deposition scenarios on forest soils in The Netherlands. Model predictions of such large-scale environmental effects of acid deposition require extrapolation of site specific data to large geographical regions. The major aim of this study is to quantify the uncertainty in model response to a given deposition scenario, due to uncertainty and spatial variability in data. Furthermore, the uncertainty analysis was performed to determine which additional data will most likely improve the reliability of predictions. An efficient Monte Carlo technique was used in combination with regression analysis. The analysis was restricted to one forest soil ecosystem: a leptic podzol with Douglas fir, subject to a reducing deposition scenario. The investigated output variables were pH, Al/Ca ratio and NH4/K ratio in the root zone, which are generally used as indicators of forest soil acidification and of potential forest damage. Statistical analyses showed that in most cases the relation between the parameters and model output can be satisfactorily described by a linear regression model. The uncertainty contribution of various parameters depends on the considered output variable, soil compartment and time. The uncertainty, as measured by the coefficient of variation, appears to be high for the NH4/K and Al/Ca ratios, whereas it was relatively low for the pH. Results show that the uncertainty in the depositions of SOx, NOx, and NHx in a receptor area and the uncertainty in the parameters and variables determining the nitrogen and aluminium dynamics contribute most to the resulting uncertainty of the considered model output.