Independent uncertainty estimates for coefficient based sea surface temperature retrieval from the Along-Trck Scanning Radiometer instruments

We establish a methodology for calculating uncertainties in sea surface temperature estimates from coefficient based satellite retrievals. The uncertainty estimates are derived independently of in-situ data. This enables validation of both the retrieved SSTs and their uncertainty estimate using in-situ data records. The total uncertainty budget is comprised of a number of components, arising from uncorrelated (eg. noise), locally systematic (eg. atmospheric), large scale systematic and sampling effects (for gridded products). The importance of distinguishing these components arises in propagating uncertainty across spatio-temporal scales. We apply the method to SST data retrieved from the Advanced Along Track Scanning Radiometer (AATSR) and validate the results for two different SST retrieval algorithms, both at a per pixel level and for gridded data. We find good agreement between our estimated uncertainties and validation data. This approach to calculating uncertainties in SST retrievals has a wider application to data from other instruments and retrieval of other geophysical variables.

Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

An ensemble approach to uncertainty estimation for satellite-based rainfall estimates

The potential to narrow uncertainty in regional climate predictions

Faced by the realities of a changing climate, decision makers in a wide variety of organisations are increasingly seeking quantitative predictions of regional and local climate. An important issue for these decision makers, and for organisations that fund climate research, is what is the potential for climate science to deliver improvements - especially reductions in uncertainty - in such predictions? Uncertainty in climate predictions arises from three distinct sources: internal variability, model uncertainty and scenario uncertainty. Using data from a suite of climate models we separate and quantify these sources. For predictions of changes in surface air temperature on decadal timescales and regional spatial scales, we show that uncertainty for the next few decades is dominated by sources (model uncertainty and internal variability) that are potentially reducible through progress in climate science. Furthermore, we find that model uncertainty is of greater importance than internal variability. Our findings have implications for managing adaptation to a changing climate. Because the costs of adaptation are very large, and greater uncertainty about future climate is likely to be associated with more expensive adaptation, reducing uncertainty in climate predictions is potentially of enormous economic value. We highlight the need for much more work to compare: a) the cost of various degrees of adaptation, given current levels of uncertainty; and b) the cost of new investments in climate science to reduce current levels of uncertainty. Our study also highlights the importance of targeting climate science investments on the most promising opportunities to reduce prediction uncertainty.

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km2), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R 2) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.

Uncertainty in the estimation of potential evapotranspiration under climate change.

21st century climate change is projected to result in an intensification of the global hydrological cycle, but there is substantial uncertainty in how this will impact freshwater availability. A relatively overlooked aspect of this uncertainty pertains to how different methods of estimating potential evapotranspiration (PET) respond to changing climate. Here we investigate the global response of six different PET methods to a 2 °C rise in global mean temperature. All methods suggest an increase in PET associated with a warming climate. However, differences in PET climate change signal of over 100% are found between methods. Analysis of a precipitation/PET aridity index and regional water surplus indicates that for certain regions and GCMs, choice of PET method can actually determine the direction of projections of future water resources. As such, method dependence of the PET climate change signal is an important source of uncertainty in projections of future freshwater availability.

A comparison of diatom phosphorus transfer functions and export coefficient models as tools for reconstructing lake nutrient histories

1. We compared the baseline phosphorus (P) concentrations inferred by diatom-P transfer functions and export coefficient models at 62 lakes in Great Britain to assess whether the techniques produce similar estimates of historical nutrient status. 2. There was a strong linear relationship between the two sets of values over the whole total P (TP) gradient (2-200 mu g TP L-1). However, a systematic bias was observed with the diatom model producing the higher values in 46 lakes (of which values differed by more than 10 mu g TP L-1 in 21). The export coefficient model gave the higher values in 10 lakes (of which the values differed by more than 10 mu g TP L-1 in only 4). 3. The difference between baseline and present-day TP concentrations was calculated to compare the extent of eutrophication inferred by the two sets of model output. There was generally poor agreement between the amounts of change estimated by the two approaches. The discrepancy in both the baseline values and the degree of change inferred by the models was greatest in the shallow and more productive sites. 4. Both approaches were applied to two lakes in the English Lake District where long-term P data exist, to assess how well the models track measured P concentrations since approximately 1850. There was good agreement between the pre-enrichment TP concentrations generated by the models. The diatom model paralleled the steeper rise in maximum soluble reactive P (SRP) more closely than the gradual increase in annual mean TP in both lakes. The export coefficient model produced a closer fit to observed annual mean TP concentrations for both sites, tracking the changes in total external nutrient loading. 5. A combined approach is recommended, with the diatom model employed to reflect the nature and timing of the in-lake response to changes in nutrient loading, and the export coefficient model used to establish the origins and extent of changes in the external load and to assess potential reduction in loading under different management scenarios. 6. However, caution must be exercised when applying these models to shallow lakes where the export coefficient model TP estimate will not include internal P loading from lake sediments and where the diatom TP inferences may over-estimate TP concentrations because of the high abundance of benthic taxa, many of which are poor indicators of trophic state.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

Quantifying uncertainty in critical loads: (A) literature review

Critical loads are the basis for policies controlling emissions of acidic substances in Europe. The implementation of these policies involves large expenditures, and it is reasonable for policymakers to ask what degree of certainty can be attached to the underlying critical load and exceedance estimates. This paper is a literature review of studies which attempt to estimate the uncertainty attached to critical loads. Critical load models and uncertainty analysis are briefly outlined. Most studies have used Monte Carlo analysis of some form to investigate the propagation of uncertainties in the definition of the input parameters through to uncertainties in critical loads. Though the input parameters are often poorly known, the critical load uncertainties are typically surprisingly small because of a "compensation of errors" mechanism. These results depend on the quality of the uncertainty estimates of the input parameters, and a "pedigree" classification for these is proposed. Sensitivity analysis shows that some input parameters are more important in influencing critical load uncertainty than others, but there have not been enough studies to form a general picture. Methods used for dealing with spatial variation are briefly discussed. Application of alternative models to the same site or modifications of existing models can lead to widely differing critical loads, indicating that research into the underlying science needs to continue.

Quantifying uncertainty in critical loads: (B) acidity mass balance critical loads on a sensitive site

This paper reports an uncertainty analysis of critical loads for acid deposition for a site in southern England, using the Steady State Mass Balance Model. The uncertainty bounds, distribution type and correlation structure for each of the 18 input parameters was considered explicitly, and overall uncertainty estimated by Monte Carlo methods. Estimates of deposition uncertainty were made from measured data and an atmospheric dispersion model, and hence the uncertainty in exceedance could also be calculated. The uncertainties of the calculated critical loads were generally much lower than those of the input parameters due to a "compensation of errors" mechanism - coefficients of variation ranged from 13% for CLmaxN to 37% for CL(A). With 1990 deposition, the probability that the critical load was exceeded was > 0.99; to reduce this probability to 0.50, a 63% reduction in deposition is required; to 0.05, an 82% reduction. With 1997 deposition, which was lower than that in 1990, exceedance probabilities declined and uncertainties in exceedance narrowed as deposition uncertainty had less effect. The parameters contributing most to the uncertainty in critical loads were weathering rates, base cation uptake rates, and choice of critical chemical value, indicating possible research priorities. However, the different critical load parameters were to some extent sensitive to different input parameters. The application of such probabilistic results to environmental regulation is discussed.