Standardized test to evaluate numerical weather prediction algorithms

In order to assist in comparing the computational techniques used in different models, the authors propose a standardized set of one-dimensional numerical experiments that could be completed for each model. The results of these experiments, with a simplified form of the computational representation for advection, diffusion, pressure gradient term, Coriolis term, and filter used in the models, should be reported in the peer-reviewed literature. Specific recommendations are described in this paper.

Graph-based algorithms for comparison and prediction of household-level energy use profiles

We present an efficient graph-based algorithm for quantifying the similarity of household-level energy use profiles, using a notion of similarity that allows for small time–shifts when comparing profiles. Experimental results on a real smart meter data set demonstrate that in cases of practical interest our technique is far faster than the existing method for computing the same similarity measure. Having a fast algorithm for measuring profile similarity improves the efficiency of tasks such as clustering of customers and cross-validation of forecasting methods using historical data. Furthermore, we apply a generalisation of our algorithm to produce substantially better household-level energy use forecasts from historical smart meter data.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Estimation of sea surface temperature from the Spinning Enhanced Visible and Infra Red Imager, improved using numerical weather prediction

Most of the operational Sea Surface Temperature (SST) products derived from satellite infrared radiometry use multi-spectral algorithms. They show, in general, reasonable performances with root mean square (RMS) residuals around 0.5 K when validated against buoy measurements, but have limitations, particularly a component of the retrieval error that relates to such algorithms' limited ability to cope with the full variability of atmospheric absorption and emission. We propose to use forecast atmospheric profiles and a radiative transfer model to simulate the algorithmic errors of multi-spectral algorithms. In the practical case of SST derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard Meteosat Second Generation (MSG), we demonstrate that simulated algorithmic errors do explain a significant component of the actual errors observed for the non linear (NL) split window algorithm in operational use at the Centre de Météorologie Spatiale (CMS). The simulated errors, used as correction terms, reduce significantly the regional biases of the NL algorithm as well as the standard deviation of the differences with drifting buoy measurements. The availability of atmospheric profiles associated with observed satellite-buoy differences allows us to analyze the origins of the main algorithmic errors observed in the SEVIRI field of view: a negative bias in the inter-tropical zone, and a mid-latitude positive bias. We demonstrate how these errors are explained by the sensitivity of observed brightness temperatures to the vertical distribution of water vapour, propagated through the SST retrieval algorithm.

Reconstruction and prediction of variations in the open solar magnetic flux and interplanetary conditions

Historic geomagnetic activity observations have been used to reveal centennial variations in the open solar flux and the near-Earth heliospheric conditions (the interplanetary magnetic field and the solar wind speed). The various methods are in very good agreement for the past 135 years when there were sufficient reliable magnetic observatories in operation to eliminate problems due to site-specific errors and calibration drifts. This review underlines the physical principles that allow these reconstructions to be made, as well as the details of the various algorithms employed and the results obtained. Discussion is included of: the importance of the averaging timescale; the key differences between “range” and “interdiurnal variability” geomagnetic data; the need to distinguish source field sector structure from heliospherically-imposed field structure; the importance of ensuring that regressions used are statistically robust; and uncertainty analysis. The reconstructions are exceedingly useful as they provide calibration between the in-situ spacecraft measurements from the past five decades and the millennial records of heliospheric behaviour deduced from measured abundances of cosmogenic radionuclides found in terrestrial reservoirs. Continuity of open solar flux, using sunspot number to quantify the emergence rate, is the basis of a number of models that have been very successful in reproducing the variation derived from geomagnetic activity. These models allow us to extend the reconstructions back to before the development of the magnetometer and to cover the Maunder minimum. Allied to the radionuclide data, the models are revealing much about how the Sun and heliosphere behaved outside of grand solar maxima and are providing a means of predicting how solar activity is likely to evolve now that the recent grand maximum (that had prevailed throughout the space age) has come to an end.

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

The predictability of extratropical storm tracks and the sensitivity of their prediction to the observing system

A new method for assessing forecast skill and predictability that involves the identification and tracking of extratropical cyclones has been developed and implemented to obtain detailed information about the prediction of cyclones that cannot be obtained from more conventional analysis methodologies. The cyclones were identified and tracked along the forecast trajectories, and statistics were generated to determine the rate at which the position and intensity of the forecasted storms diverge from the analyzed tracks as a function of forecast lead time. The results show a higher level of skill in predicting the position of extratropical cyclones than the intensity. They also show that there is potential to improve the skill in predicting the position by 1 - 1.5 days and the intensity by 2 - 3 days, via improvements to the forecast model. Further analysis shows that forecasted storms move at a slower speed than analyzed storms on average and that there is a larger error in the predicted amplitudes of intense storms than the weaker storms. The results also show that some storms can be predicted up to 3 days before they are identified as an 850-hPa vorticity center in the analyses. In general, the results show a higher level of skill in the Northern Hemisphere (NH) than the Southern Hemisphere (SH); however, the rapid growth of NH winter storms is not very well predicted. The impact that observations of different types have on the prediction of the extratropical cyclones has also been explored, using forecasts integrated from analyses that were constructed from reduced observing systems. A terrestrial, satellite, and surface-based system were investigated and the results showed that the predictive skill of the terrestrial system was superior to the satellite system in the NH. Further analysis showed that the satellite system was not very good at predicting the growth of the storms. In the SH the terrestrial system has significantly less skill than the satellite system, highlighting the dominance of satellite observations in this hemisphere. The surface system has very poor predictive skill in both hemispheres.

The prediction of extratropical storm tracks by the ECMWF and NCEP ensemble prediction systems

The prediction of extratropical cyclones by the European Centre for Medium Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) Ensemble Prediction Systems (EPS) has been investigated using an objective feature tracking methodology to identify and track the cyclones along the forecast trajectories. Overall the results show that the ECMWF EPS has a slightly higher level of skill than the NCEP EPS in the northern hemisphere (NH). However in the southern hemisphere (SH), NCEP has higher predictive skill than ECMWF for the intensity of the cyclones. The results from both EPS indicate a higher level of predictive skill for the position of extratropical cyclones than their intensity and show that there is a larger spread in intensity than position. Further analysis shows that the predicted propagation speed of cyclones is generally too slow for the ECMWF EPS and show a slight bias for the intensity of the cyclones to be overpredicted. This is also true for the NCEP EPS in the SH. For the NCEP EPS in the NH the intensity of the cyclones is underpredicted. There is small bias in both the EPS for the cyclones to be displaced towards the poles. For each ensemble forecast of each cyclone, the predictive skill of the ensemble member that best predicts the cyclones position and intensity was computed. The results are very encouraging showing that the predictive skill of the best ensemble member is significantly higher than that of the control forecast in terms of both the position and intensity of the cyclones. The prediction of cyclones before they are identified as 850 hPa vorticity centers in the analysis cycle was also considered. It is shown that an indication of extratropical cyclones can be given by at least 1 ensemble member 7 days before they are identified in the analysis. Further analysis of the ECMWF EPS shows that the ensemble mean has a higher level of skill than the control forecast, particularly for the intensity of the cyclones, 2 from day 3 of the forecast. There is a higher level of skill in the NH than the SH and the spread in the SH is correspondingly larger. The difference between the ensemble mean and spread is very small for the position of the cyclones, but the spread of the ensemble is smaller than the ensemble mean error for the intensity of the cyclones in both hemispheres. Results also show that the ECMWF control forecast has ½ to 1 day more skill than the perturbed members, for both the position and intensity of the cyclones, throughout the forecast.

Storm tracking and ensemble prediction

The prediction of extratropical cyclones by the European Centre for Medium Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) Ensemble Prediction Systems (EPS) is investigated using a storm-tracking forecast verifica-tion methodology. The cyclones are identified and tracked along the forecast trajectories so that statistics can be generated to determine the rate at which the position and intensity of the forecasted cyclones diverge from the corresponding analysed cyclones with forecast time. Overall the ECMWF EPS has a slightly higher level of performance than the NCEP EPS. However, in the southern hemisphere the NCEP EPS has a slightly higher level of skill for the intensity of the storms. The results from both EPS indicate a higher level of predictive skill for the position of extratropical cyclones than their intensity and show that there is a larger spread in intensity than position. The results also illustrate several benefits an EPS can offer over a deterministic forecast.