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Michael K. Tippett
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Michael K. Tippett

Abstract

The Madden–Julian oscillation (MJO) is the leading mode of tropical variability on subseasonal time scales and has predictable impacts in the extratropics. Whether or not the MJO has a discernible influence on U.S. tornado occurrence has important implications for the feasibility of extended-range forecasting of tornado activity. Interpretation and comparison of previous studies is difficult because of differing data periods, methods, and tornado activity metrics. Here, a previously described modulation of the frequency of violent tornado outbreaks (days with six or more tornadoes reported rated EF2 or greater) by the MJO is shown to be fairly robust to the addition or removal of years to the analysis period and to changes in the number of tornadoes used to define outbreak days, but is less robust to the choice of MJO index. Earlier findings of a statistically significant MJO signal in the frequency of days with at least one tornado report are shown to be incorrect. The reduction of the frequency of days with tornadoes rated EF1 and greater when MJO convection is present in the Maritime Continent and western Pacific is statistically significant in April and robust across varying thresholds of reliably reported tornado numbers and MJO indices.

Open access
Michael K. Tippett
and
Anthony G. Barnston

Abstract

The cross-validated hindcast skills of various multimodel ensemble combination strategies are compared for probabilistic predictions of monthly SST anomalies in the ENSO-related Niño-3.4 region of the tropical Pacific Ocean. Forecast data from seven individual models of the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) project are used, spanning the 22-yr period of 1980–2001. Skill of the probabilistic forecasts is measured using the ranked probability skill score and rate of return, the latter being an information theory–based measure. Although skill is generally low during boreal summer relative to other times of the year, the advantage of the model forecasts over simple historical frequencies is greatest at this time. Multimodel ensemble predictions, even those using simple combination methods, generally have higher skill than single model predictions, and this advantage is greater than that expected as a result of an increase in ensemble size. Overall, slightly better performance was obtained using combination methods based on individual model skill relative to methods based on the complete joint behavior of the models. This finding is attributed to the comparatively large expected sampling error in the estimation of the relations between model errors based on the short history. A practical conclusion is that, unless some models have grossly low skill relative to the others, and until the history is much longer than two to three decades, equal, independent, or constrained joint weighting are reasonable courses.

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Timothy DelSole
and
Michael K. Tippett

Abstract

A basic question in forecasting is whether one prediction system is more skillful than another. Some commonly used statistical significance tests cannot answer this question correctly if the skills are computed on a common period or using a common set of observations, because these tests do not account for correlations between sample skill estimates. Furthermore, the results of these tests are biased toward indicating no difference in skill, a fact that has important consequences for forecast improvement. This paper shows that the magnitude of bias is characterized by a few parameters such as sample size and correlation between forecasts and their errors, which, surprisingly, can be estimated from data. The bias is substantial for typical seasonal forecasts, implying that familiar tests may wrongly judge that differences in seasonal forecast skill are insignificant. Four tests that are appropriate for assessing differences in skill over a common period are reviewed. These tests are based on the sign test, the Wilcoxon signed-rank test, the Morgan–Granger–Newbold test, and a permutation test. These techniques are applied to ENSO hindcasts from the North American Multimodel Ensemble and reveal that the Climate Forecast System, version 2, and the Canadian Climate Model, version 3 (CanCM3), outperform other models in the sense that their squared error is less than that of other single models more frequently. It should be recognized that while certain models may be superior in a certain sense for a particular period and variable, combinations of forecasts are often significantly more skillful than a single model alone. In fact, the multimodel mean significantly outperforms all single models.

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Michael K. Tippett
and
Timothy DelSole

Abstract

The constructed analog procedure produces a statistical forecast that is a linear combination of past predictand values. The weights used to form the linear combination depend on the current predictor value and are chosen so that the linear combination of past predictor values approximates the current predictor value. The properties of the constructed analog method have previously been described as being distinct from those of linear regression. However, here the authors show that standard implementations of the constructed analog method give forecasts that are identical to linear regression forecasts. A consequence of this equivalence is that constructed analog forecasts based on many predictors tend to suffer from overfitting just as in linear regression. Differences between linear regression and constructed analog forecasts only result from implementation choices, especially ones related to the preparation and truncation of data. Two particular constructed analog implementations are shown to correspond to principal component regression and ridge regression. The equality of linear regression and constructed analog forecasts is illustrated in a Niño-3.4 prediction example, which also shows that increasing the number of predictors results in low-skill, high-variance forecasts, even at long leads, behavior typical of overfitting. Alternative definitions of the analog weights lead naturally to nonlinear extensions of linear regression such as local linear regression.

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Timothy DelSole
and
Michael K. Tippett

Abstract

This paper proposes a procedure based on random walks for testing and visualizing differences in forecast skill. The test is formally equivalent to the sign test and has numerous attractive statistical properties, including being independent of distributional assumptions about the forecast errors and being applicable to a wide class of measures of forecast quality. While the test is best suited for independent outcomes, it provides useful information even when serial correlation exists. The procedure is applied to deterministic ENSO forecasts from the North American Multimodel Ensemble and yields several revealing results, including 1) the Canadian models are the most skillful dynamical models, even when compared to the multimodel mean; 2) a regression model is significantly more skillful than all but one dynamical model (to which it is equally skillful); and 3) in some cases, there are significant differences in skill between ensemble members from the same model, potentially reflecting differences in initialization. The method requires only a few years of data to detect significant differences in the skill of models with known errors/biases, suggesting that the procedure may be useful for model development and monitoring of real-time forecasts.

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Chiara Lepore
and
Michael K. Tippett

Abstract

The scaling of U.S. tornado frequency with enhanced Fujita (EF)-rated intensity is examined for the range EF1–EF3. Previous work has found that tornado frequency decreases exponentially with increasing EF rating and that many regions around the world show the same exponential rate of decrease despite having quite different overall tornado frequencies. This scaling is important because it relates the frequency of the most intense tornadoes to the overall tornado frequency. Here we find that U.S. tornado frequency decreases more sharply with increasing intensity during summer than during other times of the year. One implication of this finding is that, despite their rarity, when tornadoes do occur during the cool season, the relative likelihood of more intense tornadoes is higher than during summer. The environmental driver of this scaling variability is explored through new EF-dependent tornado environmental indices (TEI-EF) that are fitted to each EF class. We find that the sensitivity of TEI-EF to storm relative helicity (SRH) increases with increasing EF class. This increasing sensitivity to SRH means that TEI-EF predicts a slower decrease in frequency with increasing intensity for larger values of SRH (e.g., cool season) and a sharper decrease in tornado frequency in summer when wind shear plays a less dominant role. This explanation is also consistent with the fact that the fraction of supercell tornadoes is smaller during summer.

Open access
Kelsey Malloy
and
Michael K. Tippett

Abstract

Tornado outbreaks—when multiple tornadoes occur within a short period of time—are rare yet impactful events. Here we developed a two-part stochastic tornado outbreak index for the contiguous United States (CONUS). The first component produces a probability map for outbreak tornado occurrence based on spatially resolved values of convective precipitation, storm relative helicity (SRH), and convective available potential energy. The second part of the index provides a probability distribution for the total number of tornadoes given the outbreak tornado probability map. Together these two components allow stochastic simulation of location and number of tornadoes that is consistent with environmental conditions. Storm report data from the Storm Prediction Center for the 1979–2021 period are used to train the model and evaluate its performance. In the first component, the probability of an outbreak-level tornado is most sensitive to SRH changes. In the second component, the total number of CONUS tornadoes depends on the sum and gridpoint maximum of the probability map. Overall, the tornado outbreak index represents the climatology, seasonal cycle, and interannual variability of tornado outbreak activity well, particularly over regions and seasons when tornado outbreaks occur most often. We found that El Niño–Southern Oscillation (ENSO) modulates the tornado outbreak index such that La Niña is associated with enhanced U.S. tornado outbreak activity over the Ohio River Valley and Tennessee River Valley regions during January–March, similar to the behavior seen in storm report data. We also found an upward trend in U.S. tornado outbreak activity during winter and spring for the 1979–2021 period using both observations and the index.

Significance Statement

Tornado outbreaks are when multiple tornadoes happen in a short time span. Because of the rare, sporadic nature of tornadoes, it can be challenging to use observational tornado reports directly to assess how climate affects tornado and tornado outbreak activity. Here, we developed a statistical model that produces a U.S. map of the likelihood that an outbreak-level tornado would occur based on environmental conditions. In addition, using that likelihood map, the model predicts a range of how many tornadoes could occur in these events. We found that “storm relative helicity” (a proxy for potential rotation in a storm’s updraft) is especially important for predicting outbreak tornado likelihood, and the sum and maximum value of the likelihood map is important for predicting total numbers for an event. Overall, this model can represent the typical behavior and fluctuations in tornado outbreak activity well. Both the tornado outbreak model and observations agree that the state of sea surface temperature in the tropical Pacific (El Niño–Southern Oscillation) is linked to tornado outbreak activity over the Ohio River Valley and Tennessee River Valley in winter through early spring and that there are upward trends in tornado outbreak activity.

Restricted access
Kelsey Malloy
,
Michael K. Tippett
, and
William J. Koshak

Abstract

Cloud-to-ground (CG) lightning substantially impacts human health and property. However, the relations between U.S. lightning activity and the Madden–Julian oscillation (MJO) and El Niño–Southern Oscillation (ENSO), two predictable drivers of global climate variability, remain uncertain, in part because most lightning datasets have short records that cannot robustly reveal MJO- and ENSO-related patterns. To overcome this limitation, we developed an empirical model of 6-hourly lightning flash count over the contiguous United States (CONUS) using environmental variables (convective available potential energy and precipitation) and National Lightning Detection Network data for 2003–16. This model is shown to reproduce the observed daily and seasonal variability of lightning over most of CONUS. Then, the empirical model was applied to construct a proxy lightning dataset for the period 1979–2021, which was used to investigate the summer MJO–lightning relationship at daily resolution and the winter–spring ENSO–lightning relationship at seasonal resolution. Overall, no robust relationship between MJO phase and lightning patterns was found when seasonality was taken into consideration. El Niño is associated with increased lightning activity over the coastal Southeast United States during early winter, the Southwest during winter through spring, and the Northwest during late spring, whereas La Niña is associated with increased lightning activity over the Tennessee River valley during winter.

Significance Statement

Cloud-to-ground lightning is dangerous for humans via direct strikes or through triggering wildfires, generating air pollution, etc. How lightning activity can be affected by climate remains unclear, and it is challenging to study their links because the data record for lightning is short. With the available lightning record, we developed a model that relates lightning flash counts over the United States to environmental factors. This model well represents observed fluctuations in daily and seasonal lightning over most of the United States. Because the model only needs environmental information to predict lightning flash counts, we were able to construct a longer record of predicted lightning based on the longer data record of environmental variables. With this dataset, we investigated the links between lightning and climate and found that the state of sea surface temperatures in the tropical Pacific (El Niño–Southern Oscillation) is linked to changes in U.S. lightning patterns in winter and spring.

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Michael K. Tippett
,
Anthony G. Barnston
, and
Timothy DelSole
Full access