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Anthony G. Barnston
and
Michael K. Tippett

Abstract

Canonical correlation analysis (CCA)-based statistical corrections are applied to seasonal mean precipitation and temperature hindcasts of the individual models from the North American Multimodel Ensemble project to correct biases in the positions and amplitudes of the predicted large-scale anomaly patterns. Corrections are applied in 15 individual regions and then merged into globally corrected forecasts. The CCA correction dramatically improves the RMS error skill score, demonstrating that model predictions contain correctable systematic biases in mean and amplitude. However, the corrections do not materially improve the anomaly correlation skills of the individual models for most regions, seasons, and lead times, with the exception of October–December precipitation in Indonesia and eastern Africa. Models with lower uncorrected correlation skill tend to benefit more from the correction, suggesting that their lower skills may be due to correctable systematic errors. Unexpectedly, corrections for the globe as a single region tend to improve the anomaly correlation at least as much as the merged corrections to the individual regions for temperature, and more so for precipitation, perhaps due to better noise filtering. The lack of overall improvement in correlation may imply relatively mild errors in large-scale anomaly patterns. Alternatively, there may be such errors, but the period of record is too short to identify them effectively but long enough to find local biases in mean and amplitude. Therefore, statistical correction methods treating individual locations (e.g., multiple regression or principal component regression) may be recommended for today’s coupled climate model forecasts. The findings highlight that the performance of statistical postprocessing can be grossly overestimated without thorough cross validation or evaluation on independent data.

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Timothy DelSole
and
Michael K. Tippett

Abstract

This paper proposes a new method for representing data in a general domain on a sphere. The method is based on the eigenfunctions of the Laplace operator, which form an orthogonal basis set that can be ordered by a measure of length scale. Representing data with Laplacian eigenfunctions is attractive if one wants to reduce the dimension of a dataset by filtering out small-scale variability. Although Laplacian eigenfunctions are ubiquitous in climate modeling, their use in arbitrary domains, such as over continents, is not common because of the numerical difficulties associated with irregular boundaries. Recent advances in machine learning and computational sciences are exploited to derive eigenfunctions of the Laplace operator over an arbitrary domain on a sphere. The eigenfunctions depend only on the geometry of the domain and hence require no training data from models or observations, a feature that is especially useful in small sample sizes. Another novel feature is that the method produces reasonable eigenfunctions even if the domain is disconnected, such as a land domain comprising isolated continents and islands. The eigenfunctions are illustrated by quantifying variability of monthly mean temperature and precipitation in climate models and observations. This analysis extends previous studies by showing that climate models have significant biases not only in global-scale spatial averages but also in global-scale dipoles and other physically important structures. MATLAB and R codes for deriving Laplacian eigenfunctions are available upon request.

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Michael K. Tippett
and
Alessandra Giannini

Abstract

An ensemble of general circulation model (GCM) integrations forced by observed sea surface temperature (SST) represents the climate response to SST forcing as well as internal variability or “noise.” Signal-to-noise analysis is used to identify the most reproducible GCM patterns of African summer precipitation related to the SST forcing. Two of these potentially predictable components are associated with the precipitation of the Guinea Coast and Sahel regions and correlate well with observations. The GCM predictable component associated with rainfall in the Sahel region reproduces observed temporal variability on both interannual and decadal time scales, though with reduced amplitude.

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Emily J. Becker
and
Michael K. Tippett

Abstract

The effect of the El Niño–Southern Oscillation (ENSO) teleconnection and climate change trends on observed North American wintertime daily 2-m temperature is investigated for 1960–2022 with a quantile regression model, which represents the variability of the full distribution of daily temperature, including extremes and changes in spread. Climate change trends are included as a predictor in the regression model to avoid the potentially confounding effect on ENSO teleconnections. Based on prior evidence of asymmetric impacts from El Niño and La Niña, the ENSO response is taken to be piecewise linear, and the regression model contains separate predictors for warm and cool ENSO. The relationship between these predictors and shifts in median, interquartile range, skewness, and kurtosis of daily 2-m temperature are summarized through Legendre polynomials. Warm ENSO conditions result in significant warming shifts in the median and contraction of the interquartile range in central-northern North America, while no opposite effect is found for cool ENSO conditions in this region. In the southern United States, cool ENSO conditions produce a warming shift in the median, while warm ENSO conditions have little impact on the median, but contracts the interquartile range. Climate change trends are present as a near-uniform warming in the median and across quantiles and have no discernable impact on interquartile range or higher-order moments. Trends and ENSO together explain a substantial fraction of the interannual variability of daily temperature distribution shifts across much of North America and, to a lesser extent, changes of the interquartile range.

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Balachandrudu Narapusetty
,
Timothy DelSole
, and
Michael K. Tippett

Abstract

This paper shows theoretically and with examples that climatological means derived from spectral methods predict independent data with less error than climatological means derived from simple averaging. Herein, “spectral methods” indicates a least squares fit to a sum of a small number of sines and cosines that are periodic on annual or diurnal periods, and “simple averaging” refers to mean averages computed while holding the phase of the annual or diurnal cycle constant. The fact that spectral methods are superior to simple averaging can be understood as a straightforward consequence of overfitting, provided that one recognizes that simple averaging is a special case of the spectral method. To illustrate these results, the two methods are compared in the context of estimating the climatological mean of sea surface temperature (SST). Cross-validation experiments indicate that about four harmonics of the annual cycle are adequate, which requires estimation of nine independent parameters. In contrast, simple averaging of daily SST requires estimation of 366 parameters—one for each day of the year, which is a factor of 40 more parameters. Consistent with the greater number of parameters, simple averaging poorly predicts samples that were not included in the estimation of the climatological mean, compared to the spectral method. In addition to being more accurate, the spectral method also accommodates leap years and missing data simply, results in a greater degree of data compression, and automatically produces smooth time series.

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Li Zhang
,
Ping Chang
, and
Michael K. Tippett

Abstract

A novel noise filter is used to effectively reduce internal atmospheric variability in the air–sea fluxes of a coupled model. This procedure allows for a test of the impact of the internal atmospheric variability on ENSO through its effect on the Pacific meridional mode (MM). Three 100-yr coupled experiments are conducted, where the filter is utilized to suppress internal atmospheric variability in 1) both the surface wind stress and the heat flux (fully filtered run), 2) only the surface heat flux (filtered-flux run), and 3) only the surface wind stress (filtered-wind run). The fully filtered run indicates that suppressing internal atmospheric variability weakens the MM, which in turn results in substantially reduced ENSO variability. ENSO is no longer phase locked to the boreal winter. The filtered-flux and filtered-wind experiments reveal that different types of noise affect ENSO in different ways. The noise in the wind stress does not have a significant impact on the MM and its relationship to ENSO. This type of noise, however, tends to broaden the spectral peak of ENSO while shifting it toward lower frequencies. The noise in the heat flux, on the other hand, has a direct impact on the strength of the MM and consequently its ability to influence ENSO. Reducing the effect of heat flux noise yields substantially weakened MM activity and a weakened relationship to ENSO, which leads to altered seasonal phase-locking characteristics.

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Liwei Jia
,
Timothy DelSole
, and
Michael K. Tippett

Abstract

An optimal projection for improving the skill of dynamical model forecasts is proposed. The proposed method uses statistical optimization techniques to identify the most skillful or most predictable patterns, and then projects forecasts onto these patterns. Applying the method to seasonal mean 2-m temperature from the Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) multimodel hindcast dataset reveals that the method improves skill only in South America and Africa, suggesting that the benefit of optimal projection is limited to certain regions, but can be substantial. Further investigation reveals that the improvement in skill comes not from optimal projection itself, but from the EOF prefiltering that is done to reduce the dimension of the optimization space. Thus, much of the improvement attributable to optimal projection can be achieved by suitable EOF filtering. Interestingly, models are found to generate patterns that project only weakly on observational datasets but are strongly correlated between models. An important by-product of the method is a concise summary of the skillful or predictable structures in a given forecast. For the ENSEMBLES dataset, the method convincingly demonstrates that most of the seasonal prediction skill over continents comes from two components, ENSO and the global warming trend. In addition, the method can be used to determine whether a pattern exists that is well predicted by one model but not by another model (complementary skill).

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Timothy DelSole
,
Xiaoqin Yan
, and
Michael K. Tippett

Abstract

Hydrological sensitivity is the change in global-mean precipitation per degree of global-mean temperature change. This paper shows that the hydrological sensitivity of the response to anthropogenic aerosol forcing is distinct from that of the combined response to all other forcings and that this difference is sufficient to infer the associated cooling in global-mean temperature. This result is demonstrated using temperature and precipitation data generated by climate models and is robust across different climate models. Remarkably, greenhouse gas warming and aerosol cooling can be estimated in a model without using any spatial or temporal gradient information in the response, provided temperature data are augmented by precipitation data. Over the late twentieth century, the hydrological sensitivities of climate models differ significantly from that of observations. Whether this discrepancy can be attributed to observational error, which is substantial as different estimates of global-mean precipitation are not even significantly correlated with each other, or to model error is unclear. The results highlight the urgency to construct accurate estimates of global precipitation from past observations and for reducing model uncertainty in hydrological sensitivity. This paper also clarifies that previous estimates of hydrological sensitivity are limited in that standard regression methods neglect temperature–precipitation relations that occur through internal variability. An alternative method for estimating hydrological sensitivity that overcomes this limitation is presented.

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Xiaoqin Yan
,
Timothy DelSole
, and
Michael K. Tippett

Abstract

This paper shows that joint temperature–precipitation information over a global domain provides a more accurate estimate of aerosol forced responses in climate models than does any other combination of temperature, precipitation, or sea level pressure. This fact is demonstrated using a new quantity called potential detectability, which measures the extent to which a forced response can be detected in a model. In particular, this measure can be evaluated independently of observations and therefore permits efficient exploration of a large number of variable combinations before performing optimal fingerprinting on observations. This paper also shows that the response to anthropogenic aerosol forcing can be separated from that of other forcings using only spatial structure alone, leaving the time variation of the response to be inferred from data, thereby demonstrating that temporal information is not necessary for detection. The spatial structure of the forced response is derived by maximizing the signal-to-noise ratio. For single variables, the north–south hemispheric gradient and equator-to-pole latitudinal gradient are important spatial structures for detecting anthropogenic aerosols in some models but not all. Sea level pressure is not an independent detection variable because it is derived partly from surface temperature. In no case does sea level pressure significantly enhance potential detectability beyond that already possible using surface temperature. Including seasonal or land–sea contrast information does not significantly enhance detectability of anthropogenic aerosol responses relative to annual means over global domains.

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Timothy DelSole
,
Liwei Jia
, and
Michael K. Tippett

Abstract

This paper proposes a new approach to linearly combining multimodel forecasts, called scale-selective ridge regression, which ensures that the weighting coefficients satisfy certain smoothness constraints. The smoothness constraint reflects the “prior assumption” that seasonally predictable patterns tend to be large scale. In the absence of a smoothness constraint, regression methods typically produce noisy weights and hence noisy predictions. Constraining the weights to be smooth ensures that the multimodel combination is no less smooth than the individual model forecasts. The proposed method is equivalent to minimizing a cost function comprising the familiar mean square error plus a “penalty function” that penalizes weights with large spatial gradients. The method reduces to pointwise ridge regression for a suitable choice of constraint. The method is tested using the Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) hindcast dataset during 1960–2005. The cross-validated skill of the proposed forecast method is shown to be larger than the skill of either ordinary least squares or pointwise ridge regression, although the significance of this difference is difficult to test owing to the small sample size. The model weights derived from the method are much smoother than those obtained from ordinary least squares or pointwise ridge regression. Interestingly, regressions in which the weights are completely independent of space give comparable overall skill. The scale-selective ridge is numerically more intensive than pointwise methods since the solution requires solving equations that couple all grid points together.

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