## 1. Introduction

## 2. Results

#### 2.1. Estimating the Long-Memory Exponent for the GMST-Response

#### 2.2. Instrumental GMST Explained

#### 2.3. The Recent Hiatus and Warming Trend

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Data and Its Use

#### 4.2. Methods

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Forcing signals used in the regression analysis. (

**a**) The sum of volcanic, solar and anthropogenic forcing. (

**b**) The blue curve depicts the volcanic forcing, the yellow curve depicts the solar forcing and the green curve depicts the total anthropogenic forcing, including greenhouse gases, land use change and anthropogenic aerosols. (

**c**) The Atlantic Multidecadal Oscillation (AMO) index. (

**d**) the Niño3.4 index. These indices are not in units of forcing, but the corresponding forcing is assumed to be proportional to the indices.

**Figure 2.**(

**a**) The blue curve is $\widehat{\beta}$ plotted against $\beta $ which was estimated from the variogram of the residual signal obtained after regression using fingerprints obtained from filtering forcing signals by the response function, $G\left(t\right)=c{t}^{\beta /2-1}$. The yellow curve is the straight line through the origin with unit slope. (

**b**) The blue curve is ${R}^{2}$ of the regression plotted against $\beta $ which was used in the response function. The yellow curve is $1+AIC/1000$ versus $\beta $, where $AIC$ is the Akaike information criterion.

**Figure 3.**In all four panels, the red curve is the total explained global mean surface temperature (GMST, or the total footprint) from the regression. (

**a**) The black, dashed curve is the HadCrut4 GMST signal. (

**b**) The brown curve is the signal obtained after the AMO footprint is subtracted from the total footprint. (

**c**) The blue curve is the signal obtained after the El Niño Southern Oscillation (ENSO) footprint is subtracted from the total footprint. (

**d**) The green curve is the signal obtained after the anthropogenic footprint issubtracted from the total footprint.

**Figure 5.**(

**a**) The red curve is the total explained GMST (or the total footprint) from the regression when the only predictor (fingerprint) is the unfiltered sum of solar, volcanic and anthropogenic forcing (the total forcing). The black, dashed curve is the HadCrut4 GMST signal. (

**b**) The same as (

**a**) with the long-memory filtered ($\beta =0.6$) forcing as a predictor.

**Figure 6.**(

**a**) The red curve is the total explained GMST (or the total footprint) from the regression where the fingerprints are the unfiltered total forcing and ENSO index. The black, dashed curve is the HadCrut4 GMST signal. (

**b**) The individual footprints whose sum is the red curve in panel (

**a**). The blue curve is the total forcing and the yellow curve represents the ENSO footprints, respectively. Panels (

**c**,

**d**) show the results of the same analysis as panels (

**a**,

**b**), but with fingerprints filtered with $\beta =0.6$.

**Figure 7.**(

**a**) The red curve is the total explained GMST (or the total footprint) from the regression when the fingerprints are the unfiltered total forcing and the ENSO and AMO indices. The black, dashed curve is the HadCrut4 GMST signal. (

**b**) The individual footprints, whose sum is the red curve in panel (

**a**). The blue curve is the total forcing, the yellow curve is the ENSO, and the green curve is the AMO footprints, respectively. Panels (

**c**,

**d**) show the results of the same analysis as panels (

**a**,

**b**), but with fingerprints filtered with $\beta =0.6$.

**Figure 8.**(

**a**) The red curve is the total explained GMST (or the total footprint) from the regression when the fingerprints are the unfiltered solar and anthropogenic forcing, the unfiltered volcanic forcing, and the unfiltered ENSO and AMO indices. The black, dashed curve is the HadCrut4 GMST signal. (

**b**) The individual footprints, whose sum is the red curve in panel (

**a**). The blue curve is the total forcing, the yellow curve is the ENSO, and the green curve is the AMO footprints, respectively. Panels (

**c**,

**d**) show the results of the same analysis as panels (

**a**,

**b**), but with fingerprints filtered with $\beta =0.6$.

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