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Petra Friederichs
and
Andreas Hense

Abstract

To encourage the use of the standard parametric test procedures in canonical correlation analysis, the tests are applied to investigate the influence of northern Atlantic SST on the Euro–Atlantic atmospheric circulation.

A comparison with a Monte Carlo testing procedure shows that the parametric tests perform properly given that at least one of the two multivariate variates is normally distributed. In this case the parametric tests are even superior to a Monte Carlo test procedure, when the estimation of the error level relies on relatively small Monte Carlo samples, which is often the case in climate studies. Even if the parametric test procedures fail due to departures from the independency assumption, they provide qualified variables to perform the more costly Monte Carlo testing procedure.

A significant influence of the northern Atlantic tripole on the atmospheric circulation was detected in ensemble simulations with the Hamburg ECHAM3 model forced with prescribed SST. Another signal already described by Czaja and Frankignoul exhibits a lagged influence of the SST on the atmosphere.

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Petra Friederichs
and
Andreas Hense

Abstract

Commonly, postprocessing techniques are employed to calibrate a model forecast. Here, a probabilistic postprocessor is presented that provides calibrated probability and quantile forecasts of precipitation on the local scale. The forecasts are based on large-scale circulation patterns of the 12-h forecast from the NCEP high-resolution Global Forecast System (GFS). The censored quantile regression is used to estimate selected quantiles of the precipitation amount and the probability of the occurrence of precipitation. The approach accounts for the mixed discrete-continuous character of daily precipitation totals. The forecasts are verified using a new verification score for quantile forecasts, namely the censored quantile verification (CQV) score.

The forecast approach is as follows: first, a canonical correlation is employed to correct systematic deviations in the GFS large-scale patterns compared with the NCEP–NCAR reanalysis or the 40-yr ECMWF Re-Analysis (ERA-40). Second, the statistical quantile model between the large-scale circulation and the local precipitation quantile is derived using NCEP and ERA-40 reanalysis data. Then, the statistical quantile model is applied to 12-h forecasts provided by the GFS forecast system. The probabilistic forecasts are reliable and the relative gain in performance of the quantile as well as the probability forecasts compared to the climatological forecasts range between 20% and 50%. The importance of the various parts of the postprocessing is assessed, and the performance is compared to forecasts based on the direct precipitation output from the ECMWF forecast system.

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Andreas Röpnack
,
Andreas Hense
,
Christoph Gebhardt
, and
Detlev Majewski

Abstract

Forecasts of convective precipitation have large uncertainties. To consider the forecast uncertainties of convection-permitting models, a convection-permitting ensemble prediction system (EPS) based on the Consortium for Small-scale Modeling (COSMO) model with a horizontal resolution of 2.8 km covering all of Germany is being developed by the Deutscher Wetterdienst (DWD). The deterministic model is named COSMO-DE. Vertical structures of temperature and humidity affect the potential for convective instability. For verification of vertical model profiles, radiosonde data are used. However, the observed state is uncertain by itself because of the well-known limits in observing the atmosphere. In this work the authors use a probabilistic approach, which considers the observation error as well as the model uncertainty to validate multidimensional state vectors (e.g., temperature profiles) of the COSMO-DE-EPS and of two mesoscale ensembles with horizontal resolution of 10 km and parameterized convection. The mesoscale ensembles are the COSMO short-range EPS (COSMO-SREPS) and the COSMO limited-area EPS (COSMO-LEPS). The approach is based on Bayesian statistics and allows for both verification and comparison of ensembles. The investigation period comprises August 2007 for a comparison of the COSMO-DE-EPS with the COSMO-SREPS. A period of 5 days in July 2007 is used to demonstrate the potential of the Bayesian approach for verification by evaluating the COSMO-SREPS and COSMO-LEPS against COSMO-EU analyses. Based on the Bayesian approach, it is shown that the temperature profiles modeled by the COSMO-DE-EPS are more consistent with the observed profiles than those of COSMO-SREPS.

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Seung-Ki Min
and
Andreas Hense

Abstract

A Bayesian approach is applied to the observed regional and seasonal surface air temperature (SAT) changes using single-model ensembles (SMEs) with the ECHO-G model and multimodel ensembles (MMEs) of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) simulations. Bayesian decision classifies observations into the most probable scenario out of six available scenarios: control (CTL), natural forcing (N), anthropogenic forcing (ANTHRO), greenhouse gas (G), sulfate aerosols (S), and natural plus anthropogenic forcing (ALL). Space–time vectors of the detection variable are constructed for six continental regions (North America, South America, Asia, Africa, Australia, and Europe) by combining temporal components of SATs (expressed as Legendre coefficients) from two or three subregions of each continental region.

Bayesian decision results show that over most of the regions observed SATs are classified into ALL or ANTHRO scenarios for the whole twentieth century and its second half. Natural forcing and ALL scenarios are decided during the first half of the twentieth century, but only in the low-latitude region (Africa and South America), which might be related to response patterns to solar forcing. Overall seasonal decisions follow annual results, but there are notable seasonal dependences that differ between regions. A comparison of SME and MME results demonstrates that the Bayesian decisions for regional-scale SATs are largely robust to intermodel uncertainties as well as prior probability and temporal scales, as found in the global results.

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Seung-Ki Min
and
Andreas Hense

Abstract

A Bayesian approach is applied to the observed global surface air temperature (SAT) changes using multimodel ensembles (MMEs) of the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) simulations and single-model ensembles (SMEs) with the ECHO-G coupled climate model. A Bayesian decision method is used as a tool for classifying observations into given scenarios (or hypotheses). The prior probability of the scenarios, which represents a degree of subjective belief in the scenarios, is changed into the posterior probability through the likelihood where observations enter, and the posterior is used as a decision function. In the identical prior case the Bayes factor (or likelihood ratio) becomes a decision function and provides observational evidence for each scenario against a predefined reference scenario. Four scenarios are used to explain observed SAT changes: “CTL” (control or no change), “Nat” (natural forcing induced change), “GHG” (greenhouse gas–induced change), and “All” (natural plus anthropogenic forcing–induced change). Observed and simulated global mean SATs are decomposed into temporal components of overall mean, linear trend, and decadal variabilities through Legendre series expansions, coefficients of which are used as detection variables. Parameters (means and covariance matrices) needed to define the four scenarios are estimated from SMEs or MMEs. Taking the CTL scenario as reference one, application results for global mean SAT changes for the whole twentieth century (1900–99) show “decisive” evidence (logarithm of Bayes factor >5) for the All scenario only. While “strong” evidence (log of Bayes factor >2.5) for both the Nat and All scenarios are found in SAT changes for the first half (1900–49), there is decisive evidence for the All scenario for SAT changes in the second half (1950–99), supporting previous results. It is demonstrated that the Bayesian decision results for global mean SATs are largely insensitive to both intermodel uncertainties and prior probabilities.

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Jessica Keune
,
Christian Ohlwein
, and
Andreas Hense

Abstract

Ensemble weather forecasting has been operational for two decades now. However, the related uncertainty analysis in terms of probabilistic postprocessing still focuses on single variables, grid points, or stations. Inevitable dependencies in space and time and between variables are often ignored. To address this problem, two probabilistic postprocessing methods are presented, which are multivariate versions of Gaussian fit and kernel dressing, respectively. The multivariate case requires the estimation of a full rank, invertible covariance matrix. For this purpose, a Graphical Least Absolute Shrinkage and Selection Operators (GLASSO) estimator has been employed that is based on sparse undirected graphical models regularized by an L1 penalty term in order to parameterize the full rank inverse covariance. In all cases, the result is a multidimensional probability density. The forecasts used to test the approach are station forecasts of 2-m temperature and surface pressure from four main global ensemble prediction systems (EPS) with medium-range weather forecasts: the NCEP Global Ensemble Forecast System (GEFS), the Met Office Global and Regional Ensemble Prediction System (MOGREPS), the Canadian Meteorological Centre (CMC) Global Ensemble Prediction System (GEPS), and the ECMWF EPS. To evaluate the multivariate probabilistic postprocessing, especially the uncertainty estimates, common verification methods such as the analysis rank histogram and the continuous ranked probability score (CRPS) are applied. Furthermore, a multivariate extension of the CRPS, the energy score, allows for the verification of a complete medium-range forecast as well as for determining its predictability. It is shown that the predictability is similar for all of the examined ensemble prediction systems, whereas the GLASSO proved to be a useful tool for calibrating the commonly observed underdispersion of ensemble forecasts during the first few lead days by using information from the full covariance matrix.

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Rüdiger Hewer
,
Petra Friederichs
,
Andreas Hense
, and
Martin Schlather

Abstract

The integration of physical relationships into stochastic models is of major interest, for example, in data assimilation. Here, a multivariate Gaussian random field formulation is introduced that represents the differential relations of the two-dimensional wind field and related variables such as the streamfunction, velocity potential, vorticity, and divergence. The covariance model is based on a flexible bivariate Matérn covariance function for the streamfunction and velocity potential. It allows for different variances in the potentials, nonzero correlations between them, anisotropy, and a flexible smoothness parameter. The joint covariance function of the related variables is derived analytically. Further, it is shown that a consistent model with nonzero correlations between the potentials and positive definite covariance function is possible. The statistical model is fitted to forecasts of the horizontal wind fields of a mesoscale numerical weather prediction system. Parameter uncertainty is assessed by a parametric bootstrap method. The estimates reveal only physically negligible correlations between the potentials.

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Heiko Paeth
,
Robin Girmes
,
Gunter Menz
, and
Andreas Hense

Abstract

Seasonal forecast of climate anomalies holds the prospect of improving agricultural planning and food security, particularly in the low latitudes where rainfall represents a limiting factor in agrarian production. Present-day methods are usually based on simulated precipitation as a predictor for the forthcoming rainy season. However, climate models often have low skill in predicting rainfall due to the uncertainties in physical parameterization. Here, the authors present an extended statistical model approach using three-dimensional dynamical variables from climate model experiments like temperature, geopotential height, wind components, and atmospheric moisture. A cross-validated multiple regression analysis is applied in order to fit the model output to observed seasonal precipitation during the twentieth century. This model output statistics (MOS) system is evaluated in various regions of the globe with potential predictability and compared with the conventional superensemble approach, which refers to the same variable for predictand and predictors.

It is found that predictability is highest in the low latitudes. Given the remarkable spatial teleconnections in the Tropics, a large number of dynamical predictors can be determined for each region of interest. To avoid overfitting in the regression model an EOF analysis is carried out, combining predictors that are largely in-phase with each other. In addition, a bootstrap approach is used to evaluate the predictability of the statistical model. As measured by different skill scores, the MOS system reaches much higher explained variance than the superensemble approach in all considered regions. In some cases, predictability only occurs if dynamical predictor variables are taken into account, whereas the superensemble forecast fails. The best results are found for the tropical Pacific sector, the Nordeste region, Central America, and tropical Africa, amounting to 50% to 80% of total interannual variability. In general, the statistical relationships between the leading predictors and the predictand are physically interpretable and basically highlight the interplay between regional climate anomalies and the omnipresent role of El Niño–Southern Oscillation in the tropical climate system.

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Jan D. Keller
,
Andreas Hense
,
Luis Kornblueh
, and
Andreas Rhodin

Abstract

The key to the improvement of the quality of ensemble forecasts assessing the inherent flow uncertainties is the choice of the initial ensemble perturbations. To generate such perturbations, the breeding of growing modes approach has been used for the past two decades. Here, the fastest-growing error modes of the initial model state are estimated. However, the resulting bred vectors (BVs) mainly point in the phase space direction of the leading Lyapunov vector and therefore favor one direction of growing errors. To overcome this characteristic and obtain growing modes pointing to Lyapunov vectors different from the leading one, an orthogonalization implemented as a singular value decomposition based on the similarity between the BVs is applied. This transformation is similar to that used in the ensemble transform technique currently in operational use at NCEP but with certain differences in the metric used and in the implementation. In this study, results of this approach using BVs generated in the Ensemble Forecasting System (EFS) based on the global numerical weather prediction model GME of the German Meteorological Service are presented. The gain in forecast performance achieved with the orthogonalized BV initialization is shown by using different probabilistic forecast scores evaluating ensemble reliability, variance, and resolution. For a 3-month period in summer 2007, the results are compared to forecasts generated with simple BV initializations of the same ensemble prediction system as well as operational ensemble forecasts from ECMWF and NCEP. The orthogonalization vastly improves the GME–EFS scores and makes them competitive with the two other centers.

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