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S. Pezzulli, D. B. Stephenson, and A. Hannachi

Abstract

Seasons are the complex nonlinear response of the physical climate system to regular annual solar forcing. There is no a priori reason why they should remain fixed/invariant from year to year, as is often assumed in climate studies when extracting the seasonal component. The widely used econometric variant of Census Method II Seasonal Adjustment Program (X-11), which allows for year-to-year variations in seasonal shape, is shown here to have some advantages for diagnosing climate variability. The X-11 procedure is applied to the monthly mean Niño-3.4 sea surface temperature (SST) index and global gridded NCEP–NCAR reanalyses of 2-m surface air temperature. The resulting seasonal component shows statistically significant interannual variations over many parts of the globe. By taking these variations in seasonality into account, it is shown that one can define less ambiguous ENSO indices. Furthermore, using the X-11 seasonal adjustment approach, it is shown that the three cold ENSO episodes after 1998 are due to an increase in amplitude of seasonality rather than being three distinct La Niña events. Globally, variations in the seasonal component represent a substantial fraction of the year-to-year variability in monthly mean temperatures. In addition, strong teleconnections can be discerned between the magnitude of seasonal variations across the globe. It might be possible to exploit such relationships to improve the skill of seasonal climate forecasts.

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A. H. Manson, J. B. Gregory, and D. G. Stephenson

Abstract

Measurements of winds (60–110 km) for Saskatoon, Canada (52N, 107W), have been obtained from a partial reflection radiowave system. Closely spaced atmospheric soundings (12 per hour) for heights between 51–117 km with 3–km height resolution, were made between August 1972 and September 1973. The median of the wind profiles for a given hour has been identified mainly as the prevailing wind, and the irregular components from each profile as internal atmospheric gravity waves (30<τ<60 min, 12<λ<30 km). The amplitudes and shears of the irregular winds have their largest values in winter. A diurnal variation has been found, showing a minimum in amplitude and shear values near noon for all seasons; this variation is especially noticeable above 90 km.

Comparisons of seasonal variations in the prevailing zonal and meridional winds, with the amplitudes of the irregular winds, suggest interactions involving critical layers and momentum transfer. Tropospheric weather systems are considered in relation to the gravity wave amplitudes.

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A. H. Manson, J. B. Gregory, and D. G. Stephenson

Abstract

The results of radiowave, partial reflection drift (wind) measurements from 60–110 km, for the years 1973–74, at Saskatoon, Canada (52°N, 107°W), are presented. Intensive soundings (12 profiles per hour) have provided hourly, weekly and monthly profiles for the prevailing winds and also for the amplitudes of internal gravity (I.G.) waves (τ≈60 min).

A relationship between the heights of reversals of the mean flow and of maxima in the I. G. wave amplitude profiles is demonstrated for 1973 and 1974. Hourly changes in the flow are also shown to be consistent with the effects of longer period (τ≈120 min) I. G. waves and/or momentum deposition by I. G. waves (τ≲60 min). It is shown that gravity waves are a major contribution to the dynamical and energetic balance of the lower thermosphere (80–110 km).

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Edward C. D. Pope, David B. Stephenson, and David R. Jackson

Abstract

Categorical probabilistic prediction is widely used for terrestrial and space weather forecasting as well as for other environmental forecasts. One example is a warning system for geomagnetic disturbances caused by space weather, which are often classified on a 10-level scale. The simplest approach assumes that the transition probabilities are stationary in time—the homogeneous Markov chain (HMC). We extend this approach by developing a flexible nonhomogeneous Markov chain (NHMC) model using Bayesian nonparametric estimation to describe the time-varying transition probabilities. The transition probabilities are updated using a modified Bayes’s rule that gradually forgets transitions in the distant past, with a tunable memory parameter. The approaches were tested by making daily geomagnetic state forecasts at lead times of 1–4 days and were verified over the period 2000–19 using the rank probability score (RPS). Both HMC and NHMC models were found to be skillful at all lead times when compared with climatological forecasts. The NHMC forecasts with an optimal memory parameter of ~100 days were found to be substantially more skillful than the HMC forecasts, with an RPS skill for the NHMC of 10.5% and 5.6% for lead times of 1 and 4 days ahead, respectively. The NHMC is thus a viable alternative approach for forecasting geomagnetic disturbances and could provide a new benchmark for producing operational forecasts. The approach is generic and is applicable to other forecasts that include discrete weather regimes or hydrological conditions (e.g., wet and dry days).

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D. B. Stephenson, C. A. S. Coelho, and I. T. Jolliffe

Abstract

The Brier score is widely used for the verification of probability forecasts. It also forms the basis of other frequently used probability scores such as the rank probability score. By conditioning (stratifying) on the issued forecast probabilities, the Brier score can be decomposed into the sum of three components: uncertainty, reliability, and resolution. This Brier score decomposition can provide useful information to the forecast provider about how the forecasts can be improved.

Rather than stratify on all values of issued probability, it is common practice to calculate the Brier score components by first partitioning the issued probabilities into a small set of bins. This note shows that for such a procedure, an additional two within-bin components are needed in addition to the three traditional components of the Brier score. The two new components can be combined with the resolution component to make a generalized resolution component that is less sensitive to choice of bin width than is the traditional resolution component. The difference between the generalized resolution term and the conventional resolution term also quantifies how forecast skill is degraded when issuing categorized probabilities to users. The ideas are illustrated using an example of multimodel ensemble seasonal forecasts of equatorial sea surface temperatures.

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C. A. S. Coelho, C. A. T. Ferro, D. B. Stephenson, and D. J. Steinskog

Abstract

This study presents various statistical methods for exploring and summarizing spatial extremal properties in large gridpoint datasets. Extremal properties are inferred from the subset of gridpoint values that exceed sufficiently high, time-varying thresholds. A simple approach is presented for how to choose the thresholds so as to avoid sampling biases from nonstationary differential trends within the annual cycle. The excesses are summarized by estimating parameters of a flexible generalized Pareto model that can account for spatial and temporal variation in the excess distributions. The effect of potentially explanatory factors (e.g., ENSO) on the distribution of extremes can be easily investigated using this model. Smooth spatially pooled estimates are obtained by fitting the model over neighboring grid points while accounting for possible spatial variation across these points. Extreme value theory methods are also presented for how to investigate the temporal clustering and spatial dependency (teleconnections) of extremes. The methods are illustrated using Northern Hemisphere monthly mean gridded temperatures for June–August (JJA) summers from 1870 to 2005.

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M. R. P. Sapiano, D. B. Stephenson, H. J. Grubb, and P. A. Arkin

Abstract

A physically motivated statistical model is used to diagnose variability and trends in wintertime (October–March) Global Precipitation Climatology Project (GPCP) pentad (5-day mean) precipitation. Quasigeostrophic theory suggests that extratropical precipitation amounts should depend multiplicatively on the pressure gradient, saturation specific humidity, and the meridional temperature gradient. This physical insight has been used to guide the development of a suitable statistical model for precipitation using a mixture of generalized linear models: a logistic model for the binary occurrence of precipitation and a Gamma distribution model for the wet day precipitation amount.

The statistical model allows for the investigation of the role of each factor in determining variations and long-term trends. Saturation specific humidity qs has a generally negative effect on global precipitation occurrence and with the tropical wet pentad precipitation amount, but has a positive relationship with the pentad precipitation amount at mid- and high latitudes. The North Atlantic Oscillation, a proxy for the meridional temperature gradient, is also found to have a statistically significant positive effect on precipitation over much of the Atlantic region. Residual time trends in wet pentad precipitation are extremely sensitive to the choice of the wet pentad threshold because of increasing trends in low-amplitude precipitation pentads; too low a choice of threshold can lead to a spurious decreasing trend in wet pentad precipitation amounts. However, for not too small thresholds, it is found that the meridional temperature gradient is an important factor for explaining part of the long-term trend in Atlantic precipitation.

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C. A. S. Coelho, S. Pezzulli, M. Balmaseda, F. J. Doblas-Reyes, and D. B. Stephenson

Abstract

This study presents a new simple approach for combining empirical with raw (i.e., not bias corrected) coupled model ensemble forecasts in order to make more skillful interval forecasts of ENSO. A Bayesian normal model has been used to combine empirical and raw coupled model December SST Niño-3.4 index forecasts started at the end of the preceding July (5-month lead time). The empirical forecasts were obtained by linear regression between December and the preceding July Niño-3.4 index values over the period 1950–2001. Coupled model ensemble forecasts for the period 1987–99 were provided by ECMWF, as part of the Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER) project. Empirical and raw coupled model ensemble forecasts alone have similar mean absolute error forecast skill score, compared to climatological forecasts, of around 50% over the period 1987–99. The combined forecast gives an increased skill score of 74% and provides a well-calibrated and reliable estimate of forecast uncertainty.

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J. B. Gregory, C. E. Meek, A. H. Manson, and D. G. Stephenson

Abstract

The drifts technique derives wind vectors from correlation analysis of spatial and temporal sequences of radiowave field strength at ground level. The paper examines the bases of the analysis, and presents a new method (simplified Gaussian correlation analysis) suitable for large-scale processing. Evaluation of the quality of derived winds vectors by means of internal consistency measurements is described. Methods of editing are surveyed, and a new method, based on the normalized time discrepancy, is demonstrated. Methods for securing maximum yield of winds vectors from raw data are described. The use of microprocessors for immediate data processing is outlined. Comparisons of winds obtained by the partial reflection technique with other experimental techniques are examined.

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A. H. Manson, J. B. Gregory, C. E. Meek, and D. G. Stephenson

Abstract

The behavior of the daily noon winds at 52°N, 107° W (Saskatoon, Canada) at altitudes from 52 km to about 110 km are studied for the interval September 1974–Apzil 1975. These data are compared with ROCOB temperatures and winds (≲55 km) for Churchill (94°N, 59°W). The thermal wind equation and running cross-correlation analysis are used to demonstrate the seasonal variations of the meridional temperature gradient, and of coupling, within the stratosphere, mesosphere and thermosphere. The effects of the stratospheric warming of January 1975 are also investigated. The correlations were dominated by this event, and show that coupling occurred between the stratosphere (20–30 mb) and mesosphere/thermosphere (≲100 km) during the first half of January. Spectral analysis for two intervals before and after the stratwarm show that coupling was more significant during the late winter; periods near 2–3, 4–5 and ≳20 days were involved.

Comparisons between daily mean winds and daily noon winds show that up to 100 km the daily variations are well represented by the noon data; above 100 km the daily variations are less reliable but trends are well represented by the noon data.

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