Comparison of climate time series – Part 5: Multivariate annual cycles

This paper develops a method for determining whether two vector time series originate from a common stochastic process. The stochastic process considered incorporates both serial correlations and multivariate annual cycles. Specifically, the process is modeled as a vector autoregressive model with periodic forcing, referred to as a VARX model (where X stands for exogenous variables). The hypothesis that two VARX models share the same parameters is tested using the likelihood ratio method. The resulting test can be further decomposed into a series of tests to assess whether disparities in the VARX models stem from differences in noise parameters, autoregressive parameters, or annual cycle parameters. A comprehensive procedure for compressing discrepancies between VARX models into a minimal number of components is developed based on discriminant analysis. Using this method, the realism of climate model simulations of monthly mean North Atlantic sea surface temperatures is assessed. As expected, different simulations from the same climate model cannot be distinguished stochastically. Similarly, observations from different periods cannot be distinguished. However, every climate model differs stochastically from observations. Furthermore, each climate model differs stochastically from every other model, except when they originate from the same center. In essence, each climate model possesses a distinct fingerprint that sets it apart stochastically from both observations and models developed by other research centers. The primary factor contributing to these differences is the difference in annual cycles. The difference in annual cycles is often dominated by a single component, which can be extracted and illustrated using discriminant analysis.</p

Adjoints and Low-rank Covariance Representation

Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system

Predictability of Recurrent Weather Regimes over North America during Winter from Submonthly Reforecasts

Four recurrent weather regimes are identified over North America from October to March through a k-means clustering applied to MERRA daily 500-hPa geopotential heights over the 1982–2014 period. Three regimes resemble Rossby wave train patterns with some baroclinicity, while one is related to an NAO-like meridional pressure gradient between eastern North America and western regions of the North Atlantic. All regimes are associated with distinct rainfall and surface temperature anomalies over North America. The four-cluster partition is well reproduced byECMWFweek-1 reforecasts over the 1995–2014 period in terms of spatial structures, daily regime occurrences, and seasonal regime counts. The skill in forecasting daily regime sequences and weekly regime counts is largely limited to 2 weeks. However, skill relationships with the MJO, ENSO, and SST variability in the Atlantic and Indian Oceans suggest further potential for subseasonal predictability based on wintertime large-scale weather regimes

Probabilistic Skill of Subseasonal Precipitation Forecasts for the East Africa–West Asia Sector during September–May

The skill of submonthly forecasts of rainfall over the East Africa–West Asia sector is examined for starts during the extended boreal winter season (September–April) using three ensemble prediction systems (EPSs) from the Subseasonal-to-Seasonal (S2S) project. Forecasts of tercile category probabilities over the common period 1999–2010 are constructed using extended logistic regression (ELR), and a multimodel forecast is formed by averaging individual model probabilities. The calibration of each model separately produces reliable prob- abilistic weekly forecasts, but these lack sharpness beyond a week lead time. Multimodel ensembling generally improves skill by removing negative skill scores present in individual models. In addition, the multimodel en- semble week-3–4 forecasts have a higher ranked probability skill score and reliability compared to week-3 or week-4 forecasts for starts in February–April, while skill gain is less pronounced for other seasons. During the 1999–2010 period, skill over continental subregions is the highest for starts in February–April and for starts during El Niño conditions and MJO phase 7, which coincides with enhanced forecast probabilities of above- normal rainfall. Overall, these results indicate notable opportunities for the application of skillful subseasonal predictions over the East Africa–West Asia sector during the extended boreal winter season

Subseasonal Predictability of Boreal Summer Monsoon Rainfall from Ensemble Forecasts

Subseasonal forecast skill over the broadly defined North American (NAM), West African (WAM) and Asian (AM) summer monsoon regions is investigated using three Ensemble Prediction Systems (EPS) at sub-monthly lead times. Extended Logistic Regression (ELR) is used to produce probabilistic forecasts of weekly and week 3–4 averages of precipitation with starts in May–Aug, over the 1999–2010 period. The ELR tercile category probabilities for each model gridpoint are then averaged together with equal weight. The resulting Multi-Model Ensemble (MME) forecasts exhibit good reliability, but have generally low sharpness for forecasts beyond 1 week; Multi-model ensembling largely removes negative values of the Ranked Probability Skill Score (RPSS) seen in individual forecasts, and broadly improves the skill obtained in any of the three individual models except for the AM. The MME week 3–4 forecasts have generally higher RPSS and comparable reliability over all monsoon regions, compared to week 3 or week 4 forecast separately. Skill is higher during La Niña compared to El Niño and ENSO-neutral conditions over the 1999–2010 period, especially for the NAM. Regionally averaged RPSS is significantly correlated with the Maden-Julian Oscillation (MJO) for the AM and WAM. Our results indicate potential for skillful predictions at subseasonal time-scales over the three summer monsoon regions of the Northern Hemisphere

Multimodel Ensembling of Subseasonal Precipitation Forecasts over North America

Probabilistic forecasts of weekly and week 3–4 averages of precipitation are constructed using extended logistic regression (ELR) applied to three models (ECMWF, NCEP, and CMA) from the Subseasonal-to- Seasonal (S2S) project. Individual and multimodel ensemble (MME) forecasts are verified over the common period 1999–2010. The regression parameters are fitted separately at each grid point and lead time for the three ensemble prediction system (EPS) reforecasts with starts during January–March and July–September. The ELR produces tercile category probabilities for each model that are then averaged with equal weighting. The resulting MME forecasts are characterized by good reliability but low sharpness. A clear benefit of multimodel ensembling is to largely remove negative skill scores present in individual forecasts. The forecast skill of weekly averages is higher in winter than summer and decreases with lead time, with steep decreases after one and two weeks. Week 3–4 forecasts have more skill along the U.S. East Coast and the southwestern United States in winter, as well as over west/central U.S. regions and the intra-American sea/east Pacific during summer. Skill is also enhanced when the regression parameters are fit using spatially smoothed ob- servations and forecasts. The skill of week 3–4 precipitation outlooks has a modest, but statistically significant, relation with ENSO and the MJO, particularly in winter over the southwestern United States

Association of U.S. tornado occurrence with monthly environmental parameters

Monthly U.S. tornado numbers are here related to observation-based monthly averaged atmospheric parameters. Poisson regression is used to form an index which captures the climatological spatial distribution and seasonal variation of tornado occurrence, as well as year-to-year variability, and provides a framework for extended range forecasts of tornado activity. Computing the same index with predicted atmospheric parameters from a comprehensive forecast model gives some evidence of the predictability of monthly tornado activity

A Poisson Regression Index for Tropical Cyclone Genesis and the Role of Large-Scale Vorticity in Genesis

A Poisson regression between the observed climatology of tropical cyclogenesis (TCG) and large-scale climate variables is used to construct a TCG index. The regression methodology is objective and provides a framework for the selection of the climate variables in the index. Broadly following earlier work, four climate variables appear in the index: low-level absolute vorticity, relative humidity, relative sea surface temperature (SST), and vertical shear. Several variants in the choice of predictors are explored, including relative SST versus potential intensity and satellite-based column-integrated relative humidity versus reanalysis relative humidity at a single level; these choices lead to modest differences in the performance of the index. The feature of the new index that leads to the greatest improvement is a functional dependence on low-level absolute vorticity that causes the index response to absolute vorticity to saturate when absolute vorticity exceeds a threshold. This feature reduces some biases of the index and improves the fidelity of its spatial distribution. Physically, this result suggests that once low-level environmental vorticity reaches a sufficiently large value, other factors become rate limiting so that further increases in vorticity (at least on a monthly mean basis) do not increase the probability of genesis. Although the index is fit to climatological data, it reproduces some aspects of interannual variability when applied to interannually varying data. Overall, the new index compares positively to the genesis potential index (GPI), whose derivation, computation, and analysis is more complex in part because of its dependence on potential intensity