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.

Probabilistic simulations of crop yield over western India using the DEMETER seasonal hindcast ensembles

Process-based integrated modelling of weather and crop yield over large areas is becoming an important research topic. The production of the DEMETER ensemble hindcasts of weather allows this work to be carried out in a probabilistic framework. In this study, ensembles of crop yield (groundnut, Arachis hypogaea L.) were produced for 10 2.5 degrees x 2.5 degrees grid cells in western India using the DEMETER ensembles and the general large-area model (GLAM) for annual crops. Four key issues are addressed by this study. First, crop model calibration methods for use with weather ensemble data are assessed. Calibration using yield ensembles was more successful than calibration using reanalysis data (the European Centre for Medium-Range Weather Forecasts 40-yr reanalysis, ERA40). Secondly, the potential for probabilistic forecasting of crop failure is examined. The hindcasts show skill in the prediction of crop failure, with more severe failures being more predictable. Thirdly, the use of yield ensemble means to predict interannual variability in crop yield is examined and their skill assessed relative to baseline simulations using ERA40. The accuracy of multi-model yield ensemble means is equal to or greater than the accuracy using ERA40. Fourthly, the impact of two key uncertainties, sowing window and spatial scale, is briefly examined. The impact of uncertainty in the sowing window is greater with ERA40 than with the multi-model yield ensemble mean. Subgrid heterogeneity affects model accuracy: where correlations are low on the grid scale, they may be significantly positive on the subgrid scale. The implications of the results of this study for yield forecasting on seasonal time-scales are as follows. (i) There is the potential for probabilistic forecasting of crop failure (defined by a threshold yield value); forecasting of yield terciles shows less potential. (ii) Any improvement in the skill of climate models has the potential to translate into improved deterministic yield prediction. (iii) Whilst model input uncertainties are important, uncertainty in the sowing window may not require specific modelling. The implications of the results of this study for yield forecasting on multidecadal (climate change) time-scales are as follows. (i) The skill in the ensemble mean suggests that the perturbation, within uncertainty bounds, of crop and climate parameters, could potentially average out some of the errors associated with mean yield prediction. (ii) For a given technology trend, decadal fluctuations in the yield-gap parameter used by GLAM may be relatively small, implying some predictability on those time-scales.

Synthesis, crystal structure and hydrolysis of a dinuclear copper(II) complex constructed by N2O donor Schiff base and 4,4 '-bipyridine: discrete supra-molecular ensembles vs. oligomers

The tridentate Schiff base ligand, 7-amino-4-methyl-5-aza-3-hepten-2-one (HAMAH), prepared by the mono-condensation of 1,2diaminoethane and acetylacetone, reacts with Cu(BF4)(2) center dot 6H(2)O to produce initially a dinuclear Cu(II) complex, [{Cu(AMAH)}(2) (mu-4,4'-bipyJ](BF4)(2) (1) which undergoes hydrolysis in the reaction mixture and finally produces a linear polymeric chain compound, [Cu(acac)(2)(mu-4,4'-bipy)](n) (2). The geometry around the copper atom in compound 1 is distorted square planar while that in compound 2 is essentially an elongated octahedron. On the other hand, the ligand HAMAH reacts with Cu(ClO4)(2) center dot 6H(2)O to yield a polymeric zigzag chain, [{Cu(acac)(CH3OH)(mu-4,4'-bipy)}(ClO4)](n) (3). The geometry of the copper atom in 3 is square pyramidal with the two bipyridine molecules in the cis equatorial positions. All three complexes have been characterized by elemental analysis, IR and UV-Vis spectroscopy and single crystal X-ray diffraction studies. A probable explanation for the different size and shape of the reported polynuclear complexes formed by copper(II) and 4,4'-bipyridine has been put forward by taking into account the denticity and crystal field strength of the blocking ligand as well as the Jahn-Teller effect in copper(II). (c) 2007 Elsevier Ltd. All rights reserved.

Large vibrational variational calculations using 'multimode' and an iterative diagonalization technique

We have favoured the variational (secular equation) method for the determination of the (ro-) vibrational energy levels of polyatomic molecules. We use predominantly the Watson Hamiltonian in normal coordinates and an associated given potential in the variational code 'Multimode'. The dominant cost is the construction and diagonalization of matrices of ever-increasing size. Here we address this problem, using pertubation theory to select dominant expansion terms within the Davidson-Liu iterative diagonalization method. Our chosen example is the twelve-mode molecule methanol, for which we have an ab initio representation of the potential which includes the internal rotational motion of the OH group relative to CH3. Our new algorithm allows us to obtain converged energy levels for matrices of dimensions in excess of 100 000.

Predicting fault inflow in iterative software development processes: an industrial evaluation

This paper addresses the need for accurate predictions on the fault inflow, i.e. the number of faults found in the consecutive project weeks, in highly iterative processes. In such processes, in contrast to waterfall-like processes, fault repair and development of new features run almost in parallel. Given accurate predictions on fault inflow, managers could dynamically re-allocate resources between these different tasks in a more adequate way. Furthermore, managers could react with process improvements when the expected fault inflow is higher than desired. This study suggests software reliability growth models (SRGMs) for predicting fault inflow. Originally developed for traditional processes, the performance of these models in highly iterative processes is investigated. Additionally, a simple linear model is developed and compared to the SRGMs. The paper provides results from applying these models on fault data from three different industrial projects. One of the key findings of this study is that some SRGMs are applicable for predicting fault inflow in highly iterative processes. Moreover, the results show that the simple linear model represents a valid alternative to the SRGMs, as it provides reasonably accurate predictions and performs better in many cases.

Predictability of the western North Pacific summer climate demonstrated by the coupled models of ENSEMBLES

The Asian monsoon system, including the western North Pacific (WNP), East Asian, and Indian monsoons, dominates the climate of the Asia-Indian Ocean-Pacific region, and plays a significant role in the global hydrological and energy cycles. The prediction of monsoons and associated climate features is a major challenge in seasonal time scale climate forecast. In this study, a comprehensive assessment of the interannual predictability of the WNP summer climate has been performed using the 1-month lead retrospective forecasts (hindcasts) of five state-of-the-art coupled models from ENSEMBLES for the period of 1960–2005. Spatial distribution of the temporal correlation coefficients shows that the interannual variation of precipitation is well predicted around the Maritime Continent and east of the Philippines. The high skills for the lower-tropospheric circulation and sea surface temperature (SST) spread over almost the whole WNP. These results indicate that the models in general successfully predict the interannual variation of the WNP summer climate. Two typical indices, the WNP summer precipitation index and the WNP lower-tropospheric circulation index (WNPMI), have been used to quantify the forecast skill. The correlation coefficient between five models’ multi-model ensemble (MME) mean prediction and observations for the WNP summer precipitation index reaches 0.66 during 1979–2005 while it is 0.68 for the WNPMI during 1960–2005. The WNPMI-regressed anomalies of lower-tropospheric winds, SSTs and precipitation are similar between observations and MME. Further analysis suggests that prediction reliability of the WNP summer climate mainly arises from the atmosphere–ocean interaction over the tropical Indian and the tropical Pacific Ocean, implying that continuing improvement in the representation of the air–sea interaction over these regions in CGCMs is a key for long-lead seasonal forecast over the WNP and East Asia. On the other hand, the prediction of the WNP summer climate anomalies exhibits a remarkable spread resulted from uncertainty in initial conditions. The summer anomalies related to the prediction spread, including the lower-tropospheric circulation, SST and precipitation anomalies, show a Pacific-Japan or East Asia-Pacific pattern in the meridional direction over the WNP. Our further investigations suggest that the WNPMI prediction spread arises mainly from the internal dynamics in air–sea interaction over the WNP and Indian Ocean, since the local relationships among the anomalous SST, circulation, and precipitation associated with the spread are similar to those associated with the interannual variation of the WNPMI in both observations and MME. However, the magnitudes of these anomalies related to the spread are weaker, ranging from one third to a half of those anomalies associated with the interannual variation of the WNPMI in MME over the tropical Indian Ocean and subtropical WNP. These results further support that the improvement in the representation of the air–sea interaction over the tropical Indian Ocean and subtropical WNP in CGCMs is a key for reducing the prediction spread and for improving the long-lead seasonal forecast over the WNP and East Asia.

On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations

This paper considers two-stage iterative processes for solving the linear system $Af = b$. The outer iteration is defined by $Mf^{k + 1} = Nf^k + b$, where $M$ is a nonsingular matrix such that $M - N = A$. At each stage $f^{k + 1} $ is computed approximately using an inner iteration process to solve $Mv = Nf^k + b$ for $v$. At the $k$th outer iteration, $p_k $ inner iterations are performed. It is shown that this procedure converges if $p_k \geqq P$ for some $P$ provided that the inner iteration is convergent and that the outer process would converge if $f^{k + 1} $ were determined exactly at every step. Convergence is also proved under more specialized conditions, and for the procedure where $p_k = p$ for all $k$, an estimate for $p$ is obtained which optimizes the convergence rate. Examples are given for systems arising from the numerical solution of elliptic partial differential equations and numerical results are presented.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.

Trends in Austral jet position in ensembles of high- and low-top CMIP5 models

Trends in the position of the DJF Austral jet have been analysed for multi-model ensemble simulations of a subset of high- and low-top models for the periods 1960-2000, 2000-2050, and 2050-2098 under the CMIP5 historical, RCP4.5, and RCP8.5 scenarios. Comparison with ERA-Interim, CFSR and the NCEP/NCAR reanalysis shows that the DJF and annual mean jet positions in CMIP5 models are equatorward of reanalyses for the 1979-2006 mean. Under the RCP8.5 scenario, the mean jet position in the high-top models moves 3 degrees poleward of its 1860-1900 position by 2098, compared to just over 2 degrees for the low-top models. Changes in jet position are linked to changes in the meridional temperature gradient. Compared to low-top models, the high-top models predict greater warming in the tropical upper troposphere due to increased greenhouse gases for all periods considered: up to 0.28 K/decade more in the period 2050-2098 under the RCP8.5 scenario. Larger polar lower-stratospheric cooling is seen in high-top models: -1.64 K/decade compared to -1.40 K/decade in the period 1960-2000, mainly in response to ozone depletion, and -0.41 K/decade compared to -0.12 K/decade in the period 2050-2098, mainly in response to increases in greenhouse gases. Analysis suggests that there may be a linear relationship between the trend in jet position and meridional temperature gradient, even under strong forcing. There were no clear indications of an approach to a geometric limit on the absolute magnitude of the poleward shift by 2100.

Evaluating raw ensembles with the continuous ranked probability score

The continuous ranked probability score (CRPS) is a frequently used scoring rule. In contrast with many other scoring rules, the CRPS evaluates cumulative distribution functions. An ensemble of forecasts can easily be converted into a piecewise constant cumulative distribution function with steps at the ensemble members. This renders the CRPS a convenient scoring rule for the evaluation of ‘raw’ ensembles, obviating the need for sophisticated ensemble model output statistics or dressing methods prior to evaluation. In this article, a relation between the CRPS score and the quantile score is established. The evaluation of ‘raw’ ensembles using the CRPS is discussed in this light. It is shown that latent in this evaluation is an interpretation of the ensemble as quantiles but with non-uniform levels. This needs to be taken into account if the ensemble is evaluated further, for example with rank histograms.