Timothy DelSole

A Significant Component of Unforced Multidecadal Variability in the Recent Acceleration of Global Warming

Abstract The problem of separating variations due to natural and anthropogenic forcing from those due to unforced internal dynamics during the twentieth century is addressed using state-of-the-art climate simulations and observations. An unforced internal component that varies on multidecadal time scales is identified by a new statistical method that maximizes integral time scale. This component, called the internal multidecadal pattern (IMP), is stochastic and hence does not contribute to trends on long time scales; however, it can contribute significantly to short-term trends. Observational estimates indicate that the trend in the spatially averaged “well observed” sea surface temperature (SST) due to the forced component has an approximately constant value of 0.1 K decade−1, while the IMP can contribute about ±0.08 K decade−1 for a 30-yr trend. The warming and cooling of the IMP matches that of the Atlantic multidecadal oscillation and is of sufficient amplitude to explain the acceleration in warming d...

Predictability and Information Theory. Part I: Measures of Predictability

Abstract This paper gives an introduction to the connection between predictability and information theory, and derives new connections between these concepts. A system is said to be unpredictable if the forecast distribution, which gives the most complete description of the future state based on all available knowledge, is identical to the climatological distribution, which describes the state in the absence of time lag information. It follows that a necessary condition for predictability is for the forecast and climatological distributions to differ. Information theory provides a powerful framework for quantifying the difference between two distributions that agrees with intuition about predictability. Three information theoretic measures have been proposed in the literature: predictive information, relative entropy, and mutual information. These metrics are discussed with the aim of clarifying their similarities and differences. All three metrics have attractive properties for defining predictability, i...

Artificial skill due to predictor screening.

Abstract This paper shows that if predictors are selected preferentially because of their strong correlation with a prediction variable, then standard methods for validating prediction models derived from these predictors will be biased. This bias is demonstrated by screening random numbers and showing that regression models derived from these random numbers have apparent skill, in a cross-validation sense, even though the predictors cannot possibly have the slightest predictive usefulness. This result seemingly implies that random numbers can give useful predictions, since the sample being predicted is separate from the sample used to estimate the regression model. The resolution of this paradox is that, prior to cross validation, all of the data had been used to evaluate correlations for selecting predictors. This situation differs from real-time forecasts in that the future sample is not available for screening. These results clarify the fallacy in assuming that if a model performs well in cross-valida...

A Predictable AMO-Like Pattern in the GFDL Fully Coupled Ensemble Initialization and Decadal Forecasting System

The decadal predictability of sea surface temperature (SST) and 2-m air temperature (T2m) in the Geophysical Fluid Dynamics Laboratory (GFDL) decadal hindcasts, which are part of the Fifth Coupled Model Intercomparison Project experiments, has been investigated using an average predictability time (APT) analysis. Comparison of retrospective forecasts initialized using the GFDL Ensemble Coupled Data Assimilation system with uninitialized historical forcing simulations using the same model allows identification of the internal multidecadal pattern (IMP) for SST and T2m. The IMP of SST is characterized by an interhemisphere dipole, with warm anomalies centered in the North Atlantic subpolar gyre region and North Pacific subpolar gyre region, and cold anomalies centered in the Antarctic Circumpolar Current region. The IMP of T2m is characterized by a general bipolar seesaw, with warm anomalies centered in Greenland and cold anomalies centered in Antarctica. The retrospective prediction skill of the initialized system, verified against independent observational datasets, indicates that the IMP of SST may be predictable up to 4 (10) yr lead time at 95% (90%) significance level, and the IMP of T2m may be predictable up to 2 (10) yr at the 95% (90%) significance level. The initialization of multidecadal variations of northward oceanic heat transport in the North Atlantic significantly improves the predictive skill of the IMP. The dominant roles of oceanic internaldynamicsin decadalpredictionare furtherelucidated byfixed-forcing experimentsin which radiative forcing is returned abruptly to 1961 values. These results point toward the possibility of meaningful decadal climateoutlooksusingdynamicalcoupledmodelsiftheyareappropriatelyinitializedfromasustainedclimate observing system.

Linear Prediction of Indian Monsoon Rainfall

Abstract This paper proposes a strategy for selecting the best linear prediction model for Indian monsoon rainfall. In this strategy, a cross-validation procedure first screens out all models that perform poorly on independent data, then the error variance of every remaining model is compared to that of every other model to test whether the difference in error variances is statistically significant. This strategy is shown to produce better forecasts on average than selecting either the model that utilizes all predictors, the model that explains the most variance in the independent data, or the model with the most favorable statistic suggested by Mallow. All of the model selection criteria suggest that regression models based on two to three predictors produce better forecasts on average than regression models using a larger number of predictors. For the period up to 1967, the forecast strategy selected the prior climatology as the best predictor. For the period 1967 to the present, the strategy performed ...

Model Fidelity versus Skill in Seasonal Forecasting

Abstract The relation between skill and fidelity of seasonal mean hindcasts of surface temperature by seven coupled atmosphere–ocean models is investigated. By definition, fidelity measures the agreement between model and observational climatological distributions, and skill measures the agreement between hindcasts and their corresponding verifications. While a relation between skill and fidelity seems intuitively plausible, it has not been checked systematically, nor is it mandated mathematically. New measures of skill and fidelity based on information theory are proposed. Specifically, fidelity is measured by the area average relative entropy between the climatological distributions of the model and observations, and skill is measured by the area averaged mutual information between forecast and verification. The fidelity measure is found to be dominated by the term measuring mean bias; that is, the discrepancy in climatological means is much larger than the discrepancy in climatological variances. Moreo...

Predictability and Information Theory. Part II: Imperfect Forecasts

This paper presents a framework for quantifying predictability based on the behavior of imperfect forecasts. The critical quantity in this framework is not the forecast distribution, as used in many other predictability studies, but the conditional distribution of the state given the forecasts, called the regression forecast distribution. The average predictability of the regression forecast distribution is given by a quantity called the mutual information. Standard inequalities in information theory show that this quantity is bounded above by the average predictability of the true system and by the average predictability of the forecast system. These bounds clarify the role of potential predictability, of which many incorrect statements can be found in the literature. Mutual information has further attractive properties: it is invariant with respect to nonlinear transformations of the data, cannot be improved by manipulating the forecast, and reduces to familiar measures of correlation skill when the forecast and verification are joint normally distributed. The concept of potential predictable components is shown to define a lower-dimensional space that captures the full predictability of the regression forecast without loss of generality. The predictability of stationary, Gaussian, Markov systems is examined in detail. Some simple numerical examples suggest that imperfect forecasts are not always useful for joint normally distributed systems since greater predictability often can be obtained directly from observations. Rather, the usefulness of imperfect forecasts appears to lie in the fact that they can identify potential predictable components and capture nonstationary and/or nonlinear behavior, which are difficult to capture by low-dimensional, empirical models estimated from short historical records.

Optimally Persistent Patterns in Time-Varying Fields

Abstract A technique is described for determining the set of patterns in a time-varying field whose corresponding time series remain correlated for the longest times. The basic idea is to obtain patterns that, when projected on a time-varying field, produce time series that optimize a measure of decorrelation time. The decorrelation time is measured by one of the integrals where τ is the time lag and ρτ is the correlation function of the time series. These integrals arise naturally in sampling theory and power spectra analysis. Moreover, these integrals define the maximum lead time beyond which linear prediction models lose all forecast skill. Thus, an optimally persistent pattern is interesting because it optimizes a quantity that is of fundamental and practical importance. An orthogonal set of time series that optimize these integrals can be obtained from the lagged covariance matrix of the dataset. The corresponding patterns, called optimal persistence patterns (OPPs), may provide a useful basis set fo...

Can quasigeostrophic turbulence be modeled stochastically

Abstract Numerically generated data of quasigeostrophic turbulence in an equilibrated shear flow are analyzed to determine the extent to which they can be modeled by a Markov model. The time lagged covariances are collected into a matrix, Cτ, and are substituted into the fluctuation-dissipation relation for a first-order Markov model with white noise forcing CτC0−1 = exp (Aτ),to determine whether the relation is satisfied for a single dynamic operator A. The dynamic operator obtained by inverting the relation was found to depend on time lag. In particular, for small time lags (τ < 1 day), the eigenvectors and imaginary eigenvalues were independent of time lag, while the damping rates increased linearly with time lag. It is shown analytically that precisely this discrepancy occurs when the relation is applied to data generated by a red noise Markov model using a time lag that is small compared to the decorrelation time of the noise. Although a fourth-order Markov model with white noise can more accurately ...

A Fundamental Limitation of Markov Models

A basic question in turbulence theory is whether Markov models produce statistics that differ systematically from dynamical systems. The conventional wisdom is that Markov models are problematic at short time intervals, but precisely what these problems are and when these problems manifest themselves do not seem to be generally recognized. A barrier to understanding this issue is the lack of a closure theory for the statistics of nonlinear dynamical systems. Without such theory, one has difficulty stating precisely how dynamical systems differ from Markov models. It turns out, nevertheless, that certain fundamental differences between Markov models and dynamical systems can be understood from their differential properties. It is shown than any stationary, ergodic system governed by a finite number of ordinary differential equations will produce time-lagged covariances with negative curvature over short lags and produce power spectra that decay faster than any power of frequency. In contrast, Markov models (which necessarily include white noise terms) produce covariances with positive curvature over short lags, and produce power spectra that decay only with some integer power of frequency. Problems that arise from these differences in the context of statistical prediction and turbulence modeling are discussed.