Estimating uncertainty in terrestrial critical loads and their exceedances at four sites in the UK

Critical loads are the basis for policies controlling emissions of acidic substances in Europe and elsewhere. They are assessed by several elaborate and ingenious models, each of which requires many parameters, and have to be applied on a spatially-distributed basis. Often the values of the input parameters are poorly known, calling into question the validity of the calculated critical loads. This paper attempts to quantify the uncertainty in the critical loads due to this "parameter uncertainty", using examples from the UK. Models used for calculating critical loads for deposition of acidity and nitrogen in forest and heathland ecosystems were tested at four contrasting sites. Uncertainty was assessed by Monte Carlo methods. Each input parameter or variable was assigned a value, range and distribution in an objective a fashion as possible. Each model was run 5000 times at each site using parameters sampled from these input distributions. Output distributions of various critical load parameters were calculated. The results were surprising. Confidence limits of the calculated critical loads were typically considerably narrower than those of most of the input parameters. This may be due to a "compensation of errors" mechanism. The range of possible critical load values at a given site is however rather wide, and the tails of the distributions are typically long. The deposition reductions required for a high level of confidence that the critical load is not exceeded are thus likely to be large. The implication for pollutant regulation is that requiring a high probability of non-exceedance is likely to carry high costs. The relative contribution of the input variables to critical load uncertainty varied from site to site: any input variable could be important, and thus it was not possible to identify variables as likely targets for research into narrowing uncertainties. Sites where a number of good measurements of input parameters were available had lower uncertainties, so use of in situ measurement could be a valuable way of reducing critical load uncertainty at particularly valuable or disputed sites. From a restricted number of samples, uncertainties in heathland critical loads appear comparable to those of coniferous forest, and nutrient nitrogen critical loads to those of acidity. It was important to include correlations between input variables in the Monte Carlo analysis, but choice of statistical distribution type was of lesser importance. Overall, the analysis provided objective support for the continued use of critical loads in policy development. (c) 2007 Elsevier B.V. All rights reserved.

Sampling uncertainty properties of cloud fraction estimates from random transect observations

[1] Cloud cover is conventionally estimated from satellite images as the observed fraction of cloudy pixels. Active instruments such as radar and Lidar observe in narrow transects that sample only a small percentage of the area over which the cloud fraction is estimated. As a consequence, the fraction estimate has an associated sampling uncertainty, which usually remains unspecified. This paper extends a Bayesian method of cloud fraction estimation, which also provides an analytical estimate of the sampling error. This method is applied to test the sensitivity of this error to sampling characteristics, such as the number of observed transects and the variability of the underlying cloud field. The dependence of the uncertainty on these characteristics is investigated using synthetic data simulated to have properties closely resembling observations of the spaceborne Lidar NASA-LITE mission. Results suggest that the variance of the cloud fraction is greatest for medium cloud cover and least when conditions are mostly cloudy or clear. However, there is a bias in the estimation, which is greatest around 25% and 75% cloud cover. The sampling uncertainty is also affected by the mean lengths of clouds and of clear intervals; shorter lengths decrease uncertainty, primarily because there are more cloud observations in a transect of a given length. Uncertainty also falls with increasing number of transects. Therefore a sampling strategy aimed at minimizing the uncertainty in transect derived cloud fraction will have to take into account both the cloud and clear sky length distributions as well as the cloud fraction of the observed field. These conclusions have implications for the design of future satellite missions. This paper describes the first integrated methodology for the analytical assessment of sampling uncertainty in cloud fraction observations from forthcoming spaceborne radar and Lidar missions such as NASA's Calipso and CloudSat.

Assessing the uncertainty associated with intermittent rainfall fields

[1] In many practical situations where spatial rainfall estimates are needed, rainfall occurs as a spatially intermittent phenomenon. An efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components: a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas. The final rainfall estimates are obtained as the product of the estimates of these two random functions. However the published approach does not contain a method for estimation of uncertainties. The contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach. From the conditional distribution, representations of uncertainty such as the estimation variance and confidence intervals can be obtained. An approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area. The methodology has been validated using simulated and real rainfall data sets. The results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data.

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.

HESS Opinions ``Ensembles, uncertainty and flood prediction''

Ensemble predictions are being used more frequently to model the propagation of uncertainty through complex, coupled meteorological, hydrological and coastal models, with the goal of better characterising flood risk. In this paper, we consider the issues that we judge to be important when designing and evaluating ensemble predictions, and make recommendations for the guidance of future research.

Global hydrology modelling and uncertainty: running multiple ensembles with a campus grid.

Uncertainties associated with the representation of various physical processes in global climate models (GCMs) mean that, when projections from GCMs are used in climate change impact studies, the uncertainty propagates through to the impact estimates. A complete treatment of this ‘climate model structural uncertainty’ is necessary so that decision-makers are presented with an uncertainty range around the impact estimates. This uncertainty is often underexplored owing to the human and computer processing time required to perform the numerous simulations. Here, we present a 189-member ensemble of global river runoff and water resource stress simulations that adequately address this uncertainty. Following several adaptations and modifications, the ensemble creation time has been reduced from 750 h on a typical single-processor personal computer to 9 h of high-throughput computing on the University of Reading Campus Grid. Here, we outline the changes that had to be made to the hydrological impacts model and to the Campus Grid, and present the main results. We show that, although there is considerable uncertainty in both the magnitude and the sign of regional runoff changes across different GCMs with climate change, there is much less uncertainty in runoff changes for regions that experience large runoff increases (e.g. the high northern latitudes and Central Asia) and large runoff decreases (e.g. the Mediterranean). Furthermore, there is consensus that the percentage of the global population at risk to water resource stress will increase with climate change.

Calibrating flood inundation models: identifying and addressing uncertainty in satellite observed flood extents

Improvements in the resolution of satellite imagery have enabled extraction of water surface elevations at the margins of the flood. Comparison between modelled and observed water surface elevations provides a new means for calibrating and validating flood inundation models, however the uncertainty in this observed data has yet to be addressed. Here a flood inundation model is calibrated using a probabilistic treatment of the observed data. A LiDAR guided snake algorithm is used to determine an outline of a flood event in 2006 on the River Dee, North Wales, UK, using a 12.5m ERS-1 image. Points at approximately 100m intervals along this outline are selected, and the water surface elevation recorded as the LiDAR DEM elevation at each point. With a planar water surface from the gauged upstream to downstream water elevations as an approximation, the water surface elevations at points along this flooded extent are compared to their ‘expected’ value. The pattern of errors between the two show a roughly normal distribution, however when plotted against coordinates there is obvious spatial autocorrelation. The source of this spatial dependency is investigated by comparing errors to the slope gradient and aspect of the LiDAR DEM. A LISFLOOD-FP model of the flood event is set-up to investigate the effect of observed data uncertainty on the calibration of flood inundation models. Multiple simulations are run using different combinations of friction parameters, from which the optimum parameter set will be selected. For each simulation a T-test is used to quantify the fit between modelled and observed water surface elevations. The points chosen for use in this T-test are selected based on their error. The criteria for selection enables evaluation of the sensitivity of the choice of optimum parameter set to uncertainty in the observed data. This work explores the observed data in detail and highlights possible causes of error. The identification of significant error (RMSE = 0.8m) between approximate expected and actual observed elevations from the remotely sensed data emphasises the limitations of using this data in a deterministic manner within the calibration process. These limitations are addressed by developing a new probabilistic approach to using the observed data.

Singular vector ensemble forecasting systems and the prediction of flow dependent uncertainty

The ECMWF ensemble weather forecasts are generated by perturbing the initial conditions of the forecast using a subset of the singular vectors of the linearised propagator. Previous results show that when creating probabilistic forecasts from this ensemble better forecasts are obtained if the mean of the spread and the variability of the spread are calibrated separately. We show results from a simple linear model that suggest that this may be a generic property for all singular vector based ensemble forecasting systems based on only a subset of the full set of singular vectors.