A sensitivity analysis of soil moisture retrieval from the t-w microwave emission model

The potential of the τ-ω model for retrieving the volumetric moisture content of bare and vegetated soil from dual polarisation passive microwave data acquired at single and multiple angles is tested. Measurement error and several additional sources of uncertainty will affect the theoretical retrieval accuracy. These include uncertainty in the soil temperature, the vegetation structure and consequently its microwave singlescattering albedo, and uncertainty in soil microwave emissivity based on its roughness. To test the effects of these uncertainties for simple homogeneous scenes, we attempt to retrieve soil moisture from a number of simulated microwave brightness temperature datasets generated using the τ-ω model. The uncertainties for each influence are estimated and applied to curves generated for typical scenarios, and an inverse model used to retrieve the soil moisture content, vegetation optical depth and soil temperature. The effect of each influence on the theoretical soil moisture retrieval limit is explored, the likelihood of each sensor configuration meeting user requirements is assessed, and the most effective means of improving moisture retrieval indicated.

The potential to narrow uncertainty in projections of regional precipitation change

We separate and quantify the sources of uncertainty in projections of regional (*2,500 km) precipitation changes for the twenty-first century using the CMIP3 multi-model ensemble, allowing a direct comparison with a similar analysis for regional temperature changes. For decadal means of seasonal mean precipitation, internal variability is the dominant uncertainty for predictions of the first decade everywhere, and for many regions until the third decade ahead. Model uncertainty is generally the dominant source of uncertainty for longer lead times. Scenario uncertainty is found to be small or negligible for all regions and lead times, apart from close to the poles at the end of the century. For the global mean, model uncertainty dominates at all lead times. The signal-to-noise ratio (S/N) of the precipitation projections is highest at the poles but less than 1 almost everywhere else, and is far lower than for temperature projections. In particular, the tropics have the highest S/N for temperature, but the lowest for precipitation. We also estimate a ‘potential S/N’ by assuming that model uncertainty could be reduced to zero, and show that, for regional precipitation, the gains in S/N are fairly modest, especially for predictions of the next few decades. This finding suggests that adaptation decisions will need to be made in the context of high uncertainty concerning regional changes in precipitation. The potential to narrow uncertainty in regional temperature projections is far greater. These conclusions on S/N are for the current generation of models; the real signal may be larger or smaller than the CMIP3 multi-model mean. Also note that the S/N for extreme precipitation, which is more relevant for many climate impacts, may be larger than for the seasonal mean precipitation considered here.

Recent changes in solar outputs and the global mean surface temperature. III. Analysis of contributions to global mean air surface temperature rise

A multivariate fit to the variation in global mean surface air temperature anomaly over the past half century is presented. The fit procedure allows for the effect of response time on the waveform, amplitude and lag of each radiative forcing input, and each is allowed to have its own time constant. It is shown that the contribution of solar variability to the temperature trend since 1987 is small and downward; the best estimate is -1.3% and the 2sigma confidence level sets the uncertainty range of -0.7 to -1.9%. The result is the same if one quantifies the solar variation using galactic cosmic ray fluxes (for which the analysis can be extended back to 1953) or the most accurate total solar irradiance data composite. The rise in the global mean air surface temperatures is predominantly associated with a linear increase that represents the combined effects of changes in anthropogenic well-mixed greenhouse gases and aerosols, although, in recent decades, there is also a considerable contribution by a relative lack of major volcanic eruptions. The best estimate is that the anthropogenic factors contribute 75% of the rise since 1987, with an uncertainty range (set by the 2sigma confidence level using an AR(1) noise model) of 49–160%; thus, the uncertainty is large, but we can state that at least half of the temperature trend comes from the linear term and that this term could explain the entire rise. The results are consistent with the intergovernmental panel on climate change (IPCC) estimates of the changes in radiative forcing (given for 1961–1995) and are here combined with those estimates to find the response times, equilibrium climate sensitivities and pertinent heat capacities (i.e. the depth into the oceans to which a given radiative forcing variation penetrates) of the quasi-periodic (decadal-scale) input forcing variations. As shown by previous studies, the decadal-scale variations do not penetrate as deeply into the oceans as the longer term drifts and have shorter response times. Hence, conclusions about the response to century-scale forcing changes (and hence the associated equilibrium climate sensitivity and the temperature rise commitment) cannot be made from studies of the response to shorter period forcing changes.

Formulating generalised 'goal games' against nature: An illustration from decision-making under uncertainty in agriculture

The games-against-nature approach to the analysis of uncertainty in decision-making relies on the assumption that the behaviour of a decision-maker can be explained by concepts such as maximin, minimax regret, or a similarly defined criterion. In reality, however, these criteria represent a spectrum and, the actual behaviour of a decision-maker is most likely to embody a mixture of such idealisations. This paper proposes that in game-theoretic approach to decision-making under uncertainty, a more realistic representation of a decision-maker's behaviour can be achieved by synthesising games-against-nature with goal programming into a single framework. The proposed formulation is illustrated by using a well-known example from the literature on mathematical programming models for agricultural-decision-making. (c) 2005 Elsevier Inc. All rights reserved.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Recent developments in genetic data analysis: what can they tell us about human demographic history?

Over the last decade, a number of new methods of population genetic analysis based on likelihood have been introduced. This review describes and explains the general statistical techniques that have recently been used, and discusses the underlying population genetic models. Experimental papers that use these methods to infer human demographic and phylogeographic history are reviewed. It appears that the use of likelihood has hitherto had little impact in the field of human population genetics, which is still primarily driven by more traditional approaches. However, with the current uncertainty about the effects of natural selection, population structure and ascertainment of single-nucleotide polymorphism markers, it is suggested that likelihood-based methods may have a greater impact in the future.

An entropy-based financial decision support system (e-FDSS) for project analysis in construction SMEs

Uncertainty contributes a major part in the accuracy of a decision-making process while its inconsistency is always difficult to be solved by existing decision-making tools. Entropy has been proved to be useful to evaluate the inconsistency of uncertainty among different respondents. The study demonstrates an entropy-based financial decision support system called e-FDSS. This integrated system provides decision support to evaluate attributes (funding options and multiple risks) available in projects. Fuzzy logic theory is included in the system to deal with the qualitative aspect of these options and risks. An adaptive genetic algorithm (AGA) is also employed to solve the decision algorithm in the system in order to provide optimal and consistent rates to these attributes. Seven simplified and parallel projects from a Hong Kong construction small and medium enterprise (SME) were assessed to evaluate the system. The result shows that the system calculates risk adjusted discount rates (RADR) of projects in an objective way. These rates discount project cash flow impartially. Inconsistency of uncertainty is also successfully evaluated by the use of the entropy method. Finally, the system identifies the favourable funding options that are managed by a scheme called SME Loan Guarantee Scheme (SGS). Based on these results, resource allocation could then be optimized and the best time to start a new project could also be identified throughout the overall project life cycle.

Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase.

Entropic risk analysis by a high level decision support system (e-FDSS) for construction SMEs

The method of entropy has been useful in evaluating inconsistency on human judgments. This paper illustrates an entropy-based decision support system called e-FDSS to the solution of multicriterion risk and decision analysis in projects of construction small and medium enterprises (SMEs). It is optimized and solved by fuzzy logic, entropy, and genetic algorithms. A case study demonstrated the use of entropy in e-FDSS on analyzing multiple risk criteria in the predevelopment stage of SME projects. Survey data studying the degree of impact of selected project risk criteria on different projects were input into the system in order to evaluate the preidentified project risks in an impartial environment. Without taking into account the amount of uncertainty embedded in the evaluation process; the results showed that all decision vectors are indeed full of bias and the deviations of decisions are finally quantified providing a more objective decision and risk assessment profile to the stakeholders of projects in order to search and screen the most profitable projects.

Impacts of pollution and climate change on ombrotrophic Sphagnum species in the UK: analysis of uncertainties in two empirical niche models

A significant challenge in the prediction of climate change impacts on ecosystems and biodiversity is quantifying the sources of uncertainty that emerge within and between different models. Statistical species niche models have grown in popularity, yet no single best technique has been identified reflecting differing performance in different situations. Our aim was to quantify uncertainties associated with the application of 2 complimentary modelling techniques. Generalised linear mixed models (GLMM) and generalised additive mixed models (GAMM) were used to model the realised niche of ombrotrophic Sphagnum species in British peatlands. These models were then used to predict changes in Sphagnum cover between 2020 and 2050 based on projections of climate change and atmospheric deposition of nitrogen and sulphur. Over 90% of the variation in the GLMM predictions was due to niche model parameter uncertainty, dropping to 14% for the GAMM. After having covaried out other factors, average variation in predicted values of Sphagnum cover across UK peatlands was the next largest source of variation (8% for the GLMM and 86% for the GAMM). The better performance of the GAMM needs to be weighed against its tendency to overfit the training data. While our niche models are only a first approximation, we used them to undertake a preliminary evaluation of the relative importance of climate change and nitrogen and sulphur deposition and the geographic locations of the largest expected changes in Sphagnum cover. Predicted changes in cover were all small (generally <1% in an average 4 m2 unit area) but also highly uncertain. Peatlands expected to be most affected by climate change in combination with atmospheric pollution were Dartmoor, Brecon Beacons and the western Lake District.

A simple, coherent framework for partitioning uncertainty in climate predictions

A simple and coherent framework for partitioning uncertainty in multi-model climate ensembles is presented. The analysis of variance (ANOVA) is used to decompose a measure of total variation additively into scenario uncertainty, model uncertainty and internal variability. This approach requires fewer assumptions than existing methods and can be easily used to quantify uncertainty related to model-scenario interaction - the contribution to model uncertainty arising from the variation across scenarios of model deviations from the ensemble mean. Uncertainty in global mean surface air temperature is quantified as a function of lead time for a subset of the Coupled Model Intercomparison Project phase 3 ensemble and results largely agree with those published by other authors: scenario uncertainty dominates beyond 2050 and internal variability remains approximately constant over the 21st century. Both elements of model uncertainty, due to scenario-independent and scenario-dependent deviations from the ensemble mean, are found to increase with time. Estimates of model deviations that arise as by-products of the framework reveal significant differences between models that could lead to a deeper understanding of the sources of uncertainty in multi-model ensembles. For example, three models are shown diverging pattern over the 21st century, while another model exhibits an unusually large variation among its scenario-dependent deviations.

Uncertainty in climate change impacts on basin-scale freshwater resources – preface to the special issue: the QUEST-GSI methodology and synthesis of results

This paper presents a preface to this Special Issue on the results of the QUEST-GSI (Global Scale Impacts) project on climate change impacts on catchment-scale water resources. A detailed description of the unified methodology, subsequently used in all studies in this issue, is provided. The project method involved running simulations of catchment-scale hydrology using a unified set of past and future climate scenarios, to enable a consistent analysis of the climate impacts around the globe. These scenarios include "policy-relevant" prescribed warming scenarios. This is followed by a synthesis of the key findings. Overall, the studies indicate that in most basins the models project substantial changes to river flow, beyond that observed in the historical record, but that in many cases there is considerable uncertainty in the magnitude and sign of the projected changes. The implications of this for adaptation activities are discussed.

A comparative analysis of projected impacts of climate change on river runoff from global and catchment-scale hydrological models

We present a comparative analysis of projected impacts of climate change on river runoff from two types of distributed hydrological model, a global hydrological model (GHM) and catchment-scale hydrological models (CHM). Analyses are conducted for six catchments that are global in coverage and feature strong contrasts in spatial scale as well as climatic and development conditions. These include the Liard (Canada), Mekong (SE Asia), Okavango (SW Africa), Rio Grande (Brazil), Xiangu (China) and Harper's Brook (UK). A single GHM (Mac-PDM.09) is applied to all catchments whilst different CHMs are applied for each catchment. The CHMs typically simulate water resources impacts based on a more explicit representation of catchment water resources than that available from the GHM, and the CHMs include river routing. Simulations of average annual runoff, mean monthly runoff and high (Q5) and low (Q95) monthly runoff under baseline (1961-1990) and climate change scenarios are presented. We compare the simulated runoff response of each hydrological model to (1) prescribed increases in global mean temperature from the HadCM3 climate model and (2)a prescribed increase in global-mean temperature of 2oC for seven GCMs to explore response to climate model and structural uncertainty. We find that differences in projected changes of mean annual runoff between the two types of hydrological model can be substantial for a given GCM, and they are generally larger for indicators of high and low flow. However, they are relatively small in comparison to the range of projections across the seven GCMs. Hence, for the six catchments and seven GCMs we considered, climate model structural uncertainty is greater than the uncertainty associated with the type of hydrological model applied. Moreover, shifts in the seasonal cycle of runoff with climate change are presented similarly by both hydrological models, although for some catchments the monthly timing of high and low flows differs.This implies that for studies that seek to quantify and assess the role of climate model uncertainty on catchment-scale runoff, it may be equally as feasible to apply a GHM as it is to apply a CHM, especially when climate modelling uncertainty across the range of available GCMs is as large as it currently is. Whilst the GHM is able to represent the broad climate change signal that is represented by the CHMs, we find, however, that for some catchments there are differences between GHMs and CHMs in mean annual runoff due to differences in potential evaporation estimation methods, in the representation of the seasonality of runoff, and in the magnitude of changes in extreme monthly runoff, all of which have implications for future water management issues.

Decision theory and real estate development: a note on uncertainty

Real estate development appraisal is a quantification of future expectations. The appraisal model relies upon the valuer/developer having an understanding of the future in terms of the future marketability of the completed development and the future cost of development. In some cases the developer has some degree of control over the possible variation in the variables, as with the cost of construction through the choice of specification. However, other variables, such as the sale price of the final product, are totally dependent upon the vagaries of the market at the completion date. To try to address the risk of a different outcome to the one expected (modelled) the developer will often carry out a sensitivity analysis on the development. However, traditional sensitivity analysis has generally only looked at the best and worst scenarios and has focused on the anticipated or expected outcomes. This does not take into account uncertainty and the range of outcomes that can happen. A fuller analysis should include examination of the uncertainties in each of the components of the appraisal and account for the appropriate distributions of the variables. Similarly, as many of the variables in the model are not independent, the variables need to be correlated. This requires a standardised approach and we suggest that the use of a generic forecasting software package, in this case Crystal Ball, allows the analyst to work with an existing development appraisal model set up in Excel (or other spreadsheet) and to work with a predetermined set of probability distributions. Without a full knowledge of risk, developers are unable to determine the anticipated level of return that should be sought to compensate for the risk. This model allows the user a better understanding of the possible outcomes for the development. Ultimately the final decision will be made relative to current expectations and current business constraints, but by assessing the upside and downside risks more appropriately, the decision maker should be better placed to make a more informed and “better”.

Uncertainty and feasibility studies: an Italian case study

Uncertainty affects all aspects of the property market but one area where the impact of uncertainty is particularly significant is within feasibility analyses. Any development is impacted by differences between market conditions at the conception of the project and the market realities at the time of completion. The feasibility study needs to address the possible outcomes based on an understanding of the current market. This requires the appraiser to forecast the most likely outcome relating to the sale price of the completed development, the construction costs and the timing of both. It also requires the appraiser to understand the impact of finance on the project. All these issues are time sensitive and analysis needs to be undertaken to show the impact of time to the viability of the project. The future is uncertain and a full feasibility analysis should be able to model the upside and downside risk pertaining to a range of possible outcomes. Feasibility studies are extensively used in Italy to determine land value but they tend to be single point analysis based upon a single set of “likely” inputs. In this paper we look at the practical impact of uncertainty in variables using a simulation model (Crystal Ball ©) with an actual case study of an urban redevelopment plan for an Italian Municipality. This allows the appraiser to address the issues of uncertainty involved and thus provide the decision maker with a better understanding of the risk of development. This technique is then refined using a “two-dimensional technique” to distinguish between “uncertainty” and “variability” and thus create a more robust model.