Uncertainty Decomposition Research Articles

Generalizing uncertainty decomposition theory in climate change impact assessments

Most studies of the uncertainties in climate change impact assessments focus on each stage independently without considering correlations between stages. Therefore, it is difficult to quantify the relative contribution of each stage to the total uncertainty and to identify how uncertainties are propagated as the stages proceed. In this study, we propose a new method for decomposing total uncertainty to components from individual stages. The proposed method is more theoretically sound compared to existing methods because the sum of the uncertainties from individual stages is always equal to the total uncertainty. In addition, the results of real data analysis indicate that our proposed method provides reasonable uncertainty decomposition.

Incomplete-Information Games in Large Populations with Anonymity

The paper provides theoretical foundations for models of strategic interdependence under uncertainty that have a continuum of agents and a decomposition of uncertainty into a macro component and an agent-specific micro component, with a law of large numbers for the latter. This macro-micro decomposition of uncertainty is implied by a condition of exchangeability of agents' types, which holds at the level of the prior if and only if it also holds at the level of agents' beliefs, i.e., posteriors. Under an additional condition of anonymity in payoffs, agents' behaviours are fully determined by their macro beliefs about the cross-section distribution of types and other macro variables and about the cross-section distribution of other agents' strategies. Any probability distribution over cross-section distributions of types and other macro variables is compatible with a fully specified belief system, but not every macro belief function is compatible with a common prior. The paper gives necessary and sufficient conditions for compatibility of a macro belief function with a common prior.

Effects of changes in land use and climate on aquatic ecosystems: Coupling of models and decomposition of uncertainties

To analyse the potential future ecological state of estuaries located in the temperate climate (here exemplified with the Odense Fjord estuary, Denmark), we combined end-of-the-century climate change projections from four different climate models, four contrasting land use scenarios (“Agriculture for nature”, “Extensive agriculture”, “High-tech agriculture” and “Market driven agriculture”) and two different eco-hydrological models. By decomposing the variance of the model-simulated output from all scenario and model combinations, we identified the key sources of uncertainties of these future projections. There was generally a decline in the ecological state of the estuary in scenarios with a warmer climate. Strikingly, even the most nature-friendly land use scenario, where a proportion of the intensive agricultural area was converted to forest, may not be enough to counteract the negative effects of a future warmer climate on the ecological state of the estuary. The different land use scenarios were the most significant sources of uncertainty in the projections of future ecological state, followed, in order, by eco-hydrological models and climate models, albeit all three sources caused high variability in the simulated outputs. Therefore, when projecting the future state of aquatic ecosystems in a global warming context, one should at the very least consider to evaluate an ensemble of land use scenarios (nutrient loads) but ideally also include multiple eco-hydrological models and climate change projections. Our study may set precedence for future attempts to predict and quantify uncertainties of model and model input ensembles, as this will likely be key elements in future tools for decision-making processes.

수자원 전망의 시나리오별 불확실성 분해

기후변화로 인한 수자원 전망은 배출 시나리오, 전지구적 순환모형, 상세화 기법, 수문 모형 등 여러 전망 단계를 거쳐 이루어지며, 각 단계는 수자원 전망의 총 불확실성의 원천이 된다. 근래에 들어 수자원 전망의 총 불확실성을 개별 전망 단계로, 이를 다시 전망 단계에 속하는 여러 시나리오의 불확실성으로 분해하는 방법의 필요성이 제기되고 있다. 그러나 그 필요성에 비하여 관련 연구는 전무한 실정이다. 본 연구에서는 수자원 전망의 총 불확실성을 시나리오의 불확실성으로 분해나는 방법을 제안한다. 제안하는 방법은 개별 시나리오의 불확실성이 총 불확실성에 기여하는 상대적 비중을 제시함으로써 시나리오 간의 불확실성 비교를 가능하게 한다. 제안한 방법을 이용하여 실제 수자원 전망 자료를 분석한 결과를 제시한다.

Decomposing the cascade of uncertainty in risk assessments for urban flooding reflecting critical decision-making issues

Climate change risk assessments traditionally follow an analytical structure in which climate information is linked to impact models, and subsequently to damage models and decision-making tools. This structure generates a wide cascade of uncertainties that accumulate with each analytical step, consequently resulting in a wide range of risk estimates. This cascade of uncertainties can suggest that climate change risk assessments are not very useful in the context of decision-making regarding climate adaptation. However, many of the uncertainties revealed in traditionally structured climate risk assessments are not equally relevant to specific decisions, and presenting wide cascades of uncertainties can mask key decision-making parameters. In this paper, we show how the cascade of uncertainty relevant to decision-making can be reduced by applying an uncertainty decomposition approach, which, in study design, initially identifies the uncertainty cascade elements of particular relevance to the focal decision-making context. We compare the full cascade of uncertainties that emerge in a traditional risk assessment based on linked climate scenarios, impact modeling, and damage cost assessment with the uncertainty cascade generated by a detailed assessment of urban flooding risks where the focus is on key uncertainties in decision-making on climate change adaptation. A case study on flooding from extreme precipitation in the Danish city of Odense is used to decompose major sources of uncertainties in the climate modeling, the hydrological modeling, and the damage cost assessment. The decomposition approach reduces the focal range of damage cost estimates by 7–9 M EUR, which corresponds to a 20–24% reduction in the full uncertainty range without the application of the decomposition approach. Assuming that damage cost assessments can provide an indication of how much society should be willing to spend on climate adaptation, a decomposition approach as presented here could assist decision-makers in increasing the economic effectiveness when investing in protective measures.

The Importance of Spatiotemporal Variability in Irrigation Inputs for Hydrological Modeling of Irrigated Catchments

AbstractIrrigation contributes substantially to the water balance and environmental condition of many agriculturally productive catchments. This study focuses on the representation of spatiotemporal variability of irrigation depths in irrigation schedule models. Irrigation variability arises due to differences in farmers’ irrigation practices, yet its effects on distributed hydrological predictions used to inform management decisions are currently poorly understood. Using a case study of the Barr Creek catchment in the Murray Darling Basin, Australia, we systematically compare four irrigation schedule models, including uniform versus variable in space, and continuous‐time versus event‐based representations. We evaluate simulated irrigation at hydrological response unit and catchment scales, and demonstrate the impact of irrigation schedules on the simulations of streamflow, evapotranspiration, and potential recharge obtained using the Soil and Water Assessment Tool (SWAT). A new spatially variable event‐based irrigation schedule model is developed. When used to provide irrigation inputs to SWAT, this new model: (i) reduces the over‐estimation of actual evapotranspiration that occurs with spatially uniform continuous‐time irrigation assumptions (biases reduced from ~40% to ~2%) and (ii) better reproduces the fast streamflow response to rainfall events compared to spatially uniform event‐based irrigation assumptions (seasonally adjusted Nash‐Sutcliffe Efficiency improves from 0.15 to 0.56). The stochastic nature of the new model allows representing irrigation schedule uncertainty, which improves the characterization of uncertainty in simulated catchment streamflow and can be used for uncertainty decomposition. More generally, this study highlights the importance of spatiotemporal variability of inputs to distributed hydrological models and the importance of using multivariate response data to test and refine environmental models.

Uncertainty characterization of HOAPS 3.3 latent heat-flux-related parameters

Abstract. Latent heat flux (LHF) is one of the main contributors to the global energy budget. As the density of in situ LHF measurements over the global oceans is generally poor, the potential of remotely sensed LHF for meteorological applications is enormous. However, to date none of the available satellite products have included estimates of systematic, random, and sampling uncertainties, all of which are essential for assessing their quality. Here, the challenge is taken on by matching LHF-related pixel-level data of the Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite (HOAPS) climatology (version 3.3) to in situ measurements originating from a high-quality data archive of buoys and selected ships. Assuming the ground reference to be bias-free, this allows for deriving instantaneous systematic uncertainties as a function of four atmospheric predictor variables. The approach is regionally independent and therefore overcomes the issue of sparse in situ data densities over large oceanic areas. Likewise, random uncertainties are derived, which include not only a retrieval component but also contributions from in situ measurement noise and the collocation procedure. A recently published random uncertainty decomposition approach is applied to isolate the random retrieval uncertainty of all LHF-related HOAPS parameters. It makes use of two combinations of independent data triplets of both satellite and in situ data, which are analysed in terms of their pairwise variances of differences. Instantaneous uncertainties are finally aggregated, allowing for uncertainty characterizations on monthly to multi-annual timescales. Results show that systematic LHF uncertainties range between 15 and 50 W m−2 with a global mean of 25 W m−2. Local maxima are mainly found over the subtropical ocean basins as well as along the western boundary currents. Investigations indicate that contributions from qa (U) to the overall LHF uncertainty are on the order of 60 % (25 %). From an instantaneous point of view, random retrieval uncertainties are specifically large over the subtropics with a global average of 37 W m−2. In a climatological sense, their magnitudes become negligible, as do respective sampling uncertainties. Regional and seasonal analyses suggest that largest total LHF uncertainties are seen over the Gulf Stream and the Indian monsoon region during boreal winter. In light of the uncertainty measures, the observed continuous global mean LHF increase up to 2009 needs to be treated with caution. The demonstrated approach can easily be transferred to other satellite retrievals, which increases the significance of the present work.

Systematic Sensitivity Analysis of the Full Economic Impacts of Sea Level Rise

The potential impacts of sea level rise (SLR) due to climate change have been widely studied in the literature. However, the uncertainty and robustness of these estimates has seldom been explored. Here we assess the model input uncertainty regarding the wide effects of SLR on marine navigation from a global economic perspective. We systematically assess the robustness of computable general equilibrium (CGE) estimates to model’s inputs uncertainty. Monte Carlo (MC) and Gaussian quadrature (GQ) methods are used for conducting a Systematic sensitivity analysis (SSA). This design allows to both explore the sensitivity of the CGE model and to compare the MC and GQ methods. Results show that, regardless whether triangular or piecewise linear Probability distributions are used, the welfare losses are higher in the MC SSA than in the original deterministic simulation. This indicates that the CGE economic literature has potentially underestimated the total economic effects of SLR, thus stressing the necessity of SSA when simulating the general equilibrium effects of SLR. The uncertainty decomposition shows that land losses have a smaller effect compared to capital and seaport productivity losses. Capital losses seem to affect the developed regions GDP more than the productivity losses do. Moreover, we show the uncertainty decomposition of the MC results and discuss the convergence of the MC results for a decomposed version of the CGE model. This paper aims to provide standardised guidelines for stochastic simulation in the context of CGE modelling that could be useful for researchers in similar settings.

Eliciting Second-Order Beliefs

We study elicitation of subjective beliefs of an agent facing ambiguity (model uncertainty): the agent has a non-singleton set of (first-order) priors on an event and a second-order prior on these first-order belief-states. Such a two-stage decomposition of uncertainty and non-reduction of compound lotteries resulting from non-neutrality to the second-order distribution plays an important role in resolving the Ellsberg Paradox. The problem of eliciting beliefs on unobservable belief-states with ambiguity-sensitive agents is novel, and we introduce new elicitation techniques using report-dependent prize variations. We construct a direct revelation mechanism that induces truthful reporting of the first-order belief states as well as the second-order distribution on the belief-states as the unique best response. The technique requires knowledge of the sensitivity function to second-order distribution (capturing ambiguity attitude) and the vN-M utility function, which we also elicit.

Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method

Summary Because of groundwater conceptualization uncertainty, multi-model methods are usually used and the corresponding uncertainties are estimated by integrating Markov Chain Monte Carlo (MCMC) and Bayesian model averaging (BMA) methods. Generally, the variance method is used to measure the uncertainties of BMA prediction. The total variance of ensemble prediction is decomposed into within-model and between-model variances, which represent the uncertainties derived from parameter and conceptual model, respectively. However, the uncertainty of a probability distribution couldn’t be comprehensively quantified by variance solely. A new measuring method based on information entropy theory is proposed in this study. Due to actual BMA process hard to meet the ideal mutually exclusive collectively exhaustive condition, BMA predictive uncertainty could be decomposed into parameter, conceptual model, and overlapped uncertainties, respectively. Overlapped uncertainty is induced by the combination of predictions from correlated model structures. In this paper, five simple analytical functions are firstly used to illustrate the feasibility of the variance and information entropy methods. A discrete distribution example shows that information entropy could be more appropriate to describe between-model uncertainty than variance. Two continuous distribution examples show that the two methods are consistent in measuring normal distribution, and information entropy is more appropriate to describe bimodal distribution than variance. The two examples of BMA uncertainty decomposition demonstrate that the two methods are relatively consistent in assessing the uncertainty of unimodal BMA prediction. Information entropy is more informative in describing the uncertainty decomposition of bimodal BMA prediction. Then, based on a synthetical groundwater model, the variance and information entropy methods are used to assess the BMA uncertainty of groundwater modeling. The uncertainty assessments of groundwater BMA prediction are consistent with that of analytical function examples.

Climate models and hydrological parameter uncertainties in climate change impacts on monthly runoff and daily flow duration curve of a Mediterranean catchment

ABSTRACTClimate models and hydrological parameter uncertainties were quantified and compared while assessing climate change impacts on monthly runoff and daily flow duration curve (FDC) in a Mediterranean catchment. Simulations of the Soil and Water Assessment Tool (SWAT) model using an ensemble of behavioural parameter sets derived from the Generalized Likelihood Uncertainty Estimation (GLUE) method were approximated by feed-forward artificial neural networks (FF-NN). Then, outputs of climate models were used as inputs to the FF-NN models. Subsequently, projected changes in runoff and FDC were calculated and their associated uncertainty was partitioned into climate model and hydrological parameter uncertainties. Runoff and daily discharge of the Chiba catchment were expected to decrease in response to drier and warmer climatic conditions in the 2050s. For both hydrological indicators, uncertainty magnitude increased when moving from dry to wet periods. The decomposition of uncertainty demonstrated that climate model uncertainty dominated hydrological parameter uncertainty in wet periods, whereas in dry periods hydrological parametric uncertainty became more important.Editor M.C. Acreman; Associate editor S. Kanae

Publisher's Note: Uncertainty decomposition method and its application to the liquid drop model [Phys. Rev. C93, 034310 (2016)

Received 11 March 2016DOI:https://doi.org/10.1103/PhysRevC.93.039901©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBinding energy & massesTechniquesCollective modelsNuclear Physics

Uncertainty decomposition method and its application to the liquid drop model

A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the standard statistical fitting procedures. The present work concentrates on the decomposition of the total uncertainty, of which the distribution corresponds to that of the residues. The distribution of the total uncertainty is considered as two normal distributions, statistical and systematic uncertainties. The standard deviation of the statistical part, ${\ensuremath{\sigma}}_{\mathrm{stat}}$, is estimated through random parameters distributed around their best fitted values. The two normal distributions are obtained by minimizing the moments of the distribution of the residues with the fixed ${\ensuremath{\sigma}}_{\mathrm{stat}}$. The method is applied to the liquid drop model (LD). The statistical and systematic uncertainties are decomposed from the residues of the nuclear binding energies with and without the consideration of the shell effect in LD. The estimated distributions of the statistical and systematic uncertainties can well describe that of the residues. The normal assumption of the distribution of the statistical and systematic uncertainties is examined through various approaches. The comparison between the distributions of the specific nuclei and those of the statistical and systematic uncertainties are consistent with the physical considerations, although the latter two can be obtained without the knowledge of these considerations. Such as, the LD are more suitable to describe the heavy nuclei. The light and heavy nuclei are indeed distributed mostly inside the distributions of the systematic and statistical uncertainties, respectively. A similar situation is also found for the nuclei close to and far from shell. The present method is also performed for nuclei around the stability line. The results are used to investigate all measured nuclei, which show the usefulness of the uncertainty decomposition method in the exploration of the unmeasured nuclei.

Adaptive Actuator Failure Identification for Microsatellites Under Closed-Loop Control

This paper addresses the actuator failure identification problem of microsatellites in a stabilized feedback framework. An adaptive failure identification scheme is developed using multiple estimators and cost functions to identify the failed actuators for understanding vehicle health and protecting microsatellites. For the implementation of failure identification, an adaptive failure compensation scheme is developed using an uncertainty decomposition to guarantee the system stability and asymptotic tracking properties, and a special reference motion is also provided using a linearly independent condition. After some actuators have failed, both identification and control are applied, and the control, while stabilizing the system, makes the microsatellite engage in the provided special motion so that the failed actuators can be identified by the identification algorithm. Simulation results illustrate the effectiveness of the proposed adaptive failure identification and compensation schemes.

Uncertainty decomposition-based fault-tolerant adaptive control of flexible spacecraft

A fault-tolerant adaptive control scheme is developed for attitude tracking of flexible spacecraft with unknown inertia parameters, external disturbance, and actuator faults. The uncertainties of flexibility and dynamics are parameterized, and the control gain matrix uncertainty is handled using an uncertainty decomposition. The control scheme, with adaptive laws of the overall system uncertain parameter estimates, guarantees the system stability and asymptotic attitude tracking properties. Simulation results illustrate the effectiveness of the proposed control scheme.

Uncertainty decomposition and reduction in river flood forecasting: Belgian case study

AbstractUncertainty is a key factor to be taken into account in river flood forecasting. Every forecast is subject to several sources of uncertainty. Knowledge on the relative importance of the different sources would be useful to determine the most effective improvement actions to reduce the uncertainty. In this paper, three key uncertainty sources are studied for hydrological flood forecasting in the Belgian case study of the Rivierbeek: model uncertainty, forecasted rainfall uncertainty and uncertainty in the initial conditions. A non‐parametric data‐based approach is used to quantify the total uncertainty in the forecasts. By resimulating in the model historical forecasts with optimal initial conditions and observed rainfall, the uncertainty generated by each of the key sources could be identified. In order to reduce the model uncertainty, which was primarily identified as the most important source of uncertainty, a step‐wise physically based calibration technique was suggested. After recalibration of the model with this technique, a significant reduction of the contribution of the model uncertainty to the total forecast uncertainty could be achieved. Further improvement of the initial conditions, identified as the second most important uncertainty source for short lead times, could be obtained by applying data assimilation. Both uncertainty reduction techniques combined led to a reduction of the total forecast uncertainty with 30% to 40%.

Influences of increasing temperature on Indian wheat: quantifying limits to predictability

As climate changes, temperatures will play an increasing role in determining crop yield. Both climate model error and lack of constrained physiological thresholds limit the predictability of yield. We used a perturbed-parameter climate model ensemble with two methods of bias-correction as input to a regional-scale wheat simulation model over India to examine future yields. This model configuration accounted for uncertainty in climate, planting date, optimization, temperature-induced changes in development rate and reproduction. It also accounts for lethal temperatures, which have been somewhat neglected to date. Using uncertainty decomposition, we found that fractional uncertainty due to temperature-driven processes in the crop model was on average larger than climate model uncertainty (0.56 versus 0.44), and that the crop model uncertainty is dominated by crop development. Simulations with the raw compared to the bias-corrected climate data did not agree on the impact on future wheat yield, nor its geographical distribution. However the method of bias-correction was not an important source of uncertainty. We conclude that bias-correction of climate model data and improved constraints on especially crop development are critical for robust impact predictions.

Application of variance decomposition approach in the uncertainty analysis of a hydrological model

Decomposition of uncertainty into individual sources is important for understanding the risks of decisions made under the modelling uncertainty. This paper has applied the predictive uncertainty analysis and variance decomposition (VD) approach for quantifying hydrological modelling uncertainty. The VD analysis is used for quantifying the contribution of various sources of uncertainty to total modelling uncertainty. The goal is to increase the reliability of predictive uncertainty analysis by the inclusion of the results of VD analysis. The approach is evaluated by analyzing uncertainty of the Soil and Water Assessment Tool (SWAT) model for a watershed of Southwestern Ontario, Canada. Three uncertainty analyzing frameworks are employed for quantifying modelling uncertainty by both predictive uncertainty analysis and VD approach. The contribution of parameter uncertainty to total error variance is expressed by the percentage of total variance explained by parameter uncertainty and this contribution is quantified for three uncertainty analyzing frameworks. The contributions of other uncertainties excluding model parameters and precipitation uncertainties to total error variance are quantified by applying the VD approach. The results obtained from predictive uncertainty and VD analyses are observed to be consistent. The underlying hypotheses of each uncertainty framework are also verified for the reliability of the uncertainty analysis.

The uncertainty about the social cost of carbon: A decomposition analysis using fund

We report the results of an uncertainty decomposition analysis of the social cost of carbon as estimated by FUND, a model that has a more detailed representation of the economic impact of climate change than any other model. Some of the parameters particularly influence impacts in the short run whereas other parameters are important in the long run. Some parameters are influential in some regions only. Some parameters are known reasonably well, but others are not. Ethical values, such as the pure rate of time preference and the rate of risk aversion, therefore affect not only the social cost of carbon, but also the importance of the parameters that determine its value. Some parameters, however, are consistently important: cooling energy demand, migration, climate sensitivity, and agriculture. The last two are subject to a large research effort, but the first two are not.

Decomposition of Uncertainties between Coarse MM5–Noah-Simulated and Fine ASAR-Retrieved Soil Moisture over Central Tibet

Abstract Understanding the sources of uncertainty that cause deviations between simulated and satellite-observed states can facilitate optimal usage of these products via data assimilation or calibration techniques. A method is presented for separating uncertainties following from (i) scale differences between model grid and satellite footprint, (ii) residuals inherent to imperfect model and retrieval applications, and (iii) biases in the climatologies of simulations and retrievals. The method is applied to coarse (10 km) soil moisture simulations by the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5)–Noah regional climate model and 2.5 years of high-resolution (100 m) retrievals from the Advanced Synthetic Aperture Radar (ASAR) data collected over central Tibet. Suppression of the bias is performed via cumulative distribution function (CDF) matching. The other deviations are separated by taking the variance of the ASAR soil moisture at the coarse MM5 model grid as measure for the deviations caused by scale differences. Via decomposition of the uncertainty sources it is shown that the bias and the spatial-scale difference explain the majority (>70%) of the deviations between the two products, whereas the contribution of model–observation residuals is less than 30% on a monthly basis. Consequently, this study demonstrates that accounting for uncertainties caused by bias as well as spatial-scale difference is imperative for meaningful assimilation of high-resolution soil moisture products. On the other hand, the large uncertainties following from spatial-scale differences suggests that high-resolution soil moisture products have a potential of providing observation-based input for the subgrid spatial variability parameterizations within large-scale models.