Statistical constraints on El Niño Southern Oscillation reconstructions using individual foraminifera: A sensitivity analysis


  • Kaustubh Thirumalai,

    Corresponding author
    1. Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    2. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    • Corresponding author: K. Thirumalai, Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, J. J. Pickle Research Campus, Building 196, 10100 Burnet Road (R2200), Austin, TX 78758, USA. (

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  • Judson W. Partin,

    1. Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
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  • Charles S. Jackson,

    1. Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
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  • Terrence M. Quinn

    1. Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
    2. Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA
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Recent investigations of submillennial paleoceanographic variability have attempted to resolve high-frequency climate signals such as the El Niño Southern Oscillation (ENSO) using the population statistics of individual planktic foraminiferal δ18O analyses. This approach is complicated by the relatively short lifespan of individual foraminifers (~2–4 weeks) compared to the time represented by a typical marine sediment sample (~decades to millennia). Here, we investigate the uncertainty associated with individual foraminiferal analyses (IFA) through simulations on forward modeled δ18Ocarbonate. First, focusing on the Niño3.4 region of the tropical Pacific Ocean, a bootstrap Monte Carlo algorithm is developed to constrain the uncertainty on IFA-statistics. Subsequently, to test the sensitivity of IFA to changes in seasonal cycle amplitude, ENSO amplitude, and ENSO frequency, synthetic time series of δ18Ocarbonate with differing variability are constructed and tested with our algorithm. The probabilities of the IFA technique in detecting changes in ENSO amplitude and seasonal cycle amplitude (or a combination of both) for the surface ocean and thermocline at different locations in the tropical Pacific are quantified. We find that the uncertainty in the standard deviation is smaller than the range, that the IFA-signal is insensitive to ENSO frequency, and at certain locations the seasonal cycle may dominate ENSO. IFA sensitivity towards ENSO is highest at the central equatorial Pacific surface ocean and the eastern equatorial Pacific (EEP) thermocline whereas sensitivity towards the seasonal cycle is highest at the EEP surface ocean. Our results suggest that rigorous uncertainty quantification should become standard practice for accurately interpreting IFA-data.

1 Introduction

Paleoceanographic reconstructions are crucial in understanding past changes in the El Niño Southern Oscillation (ENSO) system due to the brevity of the instrumental record. Thus far, coral skeletons [Cobb et al., 2003; Cole et al., 1993; Hereid et al., 2012; Kilbourne et al., 2004; Quinn et al., 2006] and lacustrine sediments [Moy et al., 2002; Conroy et al., 2008] have proven to be insightful archives of past ENSO variability. However, reconstructing long-term ENSO variability using these proxies is complicated due to the dearth of long records. Recently, the stable isotopic composition of oxygen (δ18O) of individual planktic foraminiferal tests has been used to investigate interannual ENSO variability on submillennial scales. This method infers past ENSO variability by comparing the statistics (standard deviation, range, skewness) of the population of individual foraminiferal analyses (IFA) of samples from discrete depths in marine sediment cores (i.e., related to different time periods) [Khider et al., 2011; Koutavas and Joanides, 2012; Koutavas et al., 2006; Leduc et al., 2009; Scroxton et al., 2011].

The potential uncertainty associated with reconstructions of past ENSO variability using the δ18O of individual foraminiferal analyses (IFA-δ18O) is assessed in this work. We build on initial studies that utilized IFA-δ18O to investigate the signal-to-noise ratio of conventional, multitest foraminiferal analysis (MFA) of planktic specimens. Ideally, for a large number of foraminifers analyzed from the same sediment sample, the IFA population mean should equal the δ18O of MFA. To test the validity of this assumption for conventional numbers of foraminifera analyzed (≤100), the first IFA-δ18O study was performed on box core sediments (ERDC 83 Bx; 1°24.1′N, 157°18.6′E) from the Ontong-Java Plateau [Killingley et al., 1981]. A large range of variability was observed and attributed to intraspecific depths of calcification and metabolic effects. Schiffelbein and Hills [1984] used these data to constrain uncertainty on MFA arising from sampling variability (i.e., δ18O variability from individual to individual living at a different subset of the time represented by the sediment sample) and analytical precision as a function of the number of total foraminifera analyzed. Subsequent studies used IFA-δ18O to assess the uncertainty associated with factors such as calcification depths [Oba, 1991], bioturbation [Billups and Spero, 1996; Stott and Tang, 1996], interspecific shell ontogeny [Spero and Williams, 1990], photosymbiont influences [Houston et al., 1999; Spero and Lea, 1993], and discrepancies between living and recently fossil individuals [Waelbroeck et al., 2005] in MFA-based reconstructions. Apart from a tool to assess uncertainty in MFA reconstructions, populations of IFA-data have been used to infer paleoceanographic variability across the time represented by the sampling resolution of the sediment core [Billups and Spero, 1996; Spero and Williams, 1990]. For example, IFA-data have been used to constrain changes across the Paleocene-Eocene Thermal Maximum [Stott, 1992; Thomas et al., 2002; Zachos et al., 2007], resolve changes in past seasonality [Spero and Williams, 1989; Wit et al., 2010], and to extract information on past monsoonal systems [Ganssen et al., 2010; Ramesh and Tiwari, 2005; Tang and Stott, 1993; Weldeab, 2012]. Koutavas et al. [2006] were the first group to attempt reconstructing the interannual variability of ENSO and used individual specimens of mixed layer dweller Globigerinoides ruber (White variety) from a sediment core (V21–30; 1°13′S, 89°41′W) in the eastern equatorial Pacific (EEP). They inferred that ENSO variability in the mid-Holocene (~6 ka) was reduced by ~50% compared to the late Holocene based on their IFA-δ18O results. Other studies in the EEP [Leduc et al., 2009; Scroxton et al., 2011] and western equatorial Pacific (WEP) [Khider et al., 2011] have applied the IFA method to thermocline dwelling foraminifers to investigate past ENSO variability over different time periods.

However, there are multiple sources of uncertainty associated with inferring paleoceanographic variability on relatively short timescales (e.g., interannual) from IFA-δ18O. The short lifespan of a planktic foraminifer spanning ~2–4 weeks (~a month) [Bijma et al., 1990; Spero, 1998] is much less than the decades to millennia represented by the typical marine sediment sample. Thus, aside from biological and environmental factors, the uncertainty in the variability of IFA-δ18O in reconstructing paleoceanographic (temperature and δ18Oseawater) variability is mainly dependent on sampling factors: (1) the number of foraminifera analyzed, limited by availability, and (2) the time represented by the sediment sample, limited by the sedimentation rate at the core site. Analytical uncertainty also limits the accuracy and precision of IFA-based reconstructions. Consequently, the statistics of a discrete subset of individual foraminifera may not be representative of the time period represented by the sediment sample. Further complications arise when extracting an interannual signal (such as ENSO) using the IFA technique due to the superimposition of other oceanographic signals within the time period represented by the sediment sample (e.g., changes in the seasonal cycle or decadal to centennial variability etc.). It is therefore essential to understand the relative roles of these sources of uncertainty on the statistics of IFA-δ18O when comparing populations from different time periods. Here, we use instrumental data to build a forward model of foraminiferal δ18Ocarbonate, simulate the random process of sampling foraminifera and then apply the algorithm on constructed synthetic time series with varying seasonality and ENSO variability (amplitude, frequency) in order to quantify uncertainty in IFA-based ENSO reconstructions. In doing so, a suite of code generated in MATLAB® that performs the aforementioned functions, which we term Individual Foraminiferal Approach Uncertainty Analysis (INFAUNAL), is presented. The goal of this article is twofold: (1) to quantify the uncertainty in IFA-statistics (accuracy and precision in the range and standard deviation of an IFA δ18O population due to intrasample variability) and (2) to investigate the resolving capability of IFA in detecting changes in past ENSO variability at different locations in the tropical Pacific Ocean.

2 Methods

2.1 IFA Uncertainty Quantification

To better understand the uncertainty associated with the signals derived from IFA, we used a δ18Ocarbonate-forward model to produce an idealized virtual sediment sample utilizing the instrumental record [Schmidt, 1999]. Employing the monthly 1°×1° Hadley Centre Sea Ice and Sea Surface Temperature (HadISST1) data set [Rayner et al., 2003], sea surface temperatures (SSTs) in the Niño3.4 region (5°N–5°S, 120°W–170°W) were obtained for the interval 1910–2009. The Niño3.4 region was chosen for this exercise as ENSO is canonically defined here due to its ability to accurately record ENSO-related SST variability [Trenberth, 1997]. The monthly SST (°C) values were transformed to foraminiferal δ18Ocarbonate (‰, VPDB) using an established equation ([Bemis et al., 1998]; δ18Oseawater was neglected: for details, see Text S1.1 in supporting information). This transformation is the basis of the virtual sediment sample which represents 100 years of sedimentation, based on 100 years of instrumental SST data (Figure 1). We generated IFA-δ18Ocarbonate populations from the monthly, instrumental pseudo-δ18Ocarbonate time series with the underlying assumptions: (1) Monthly pseudo-δ18Ocarbonate accurately reflects δ18Ocarbonate of individual foraminifera that calcified during that month. (2) There is an equal probability of repeating monthly values as picking a different month, i.e., more than one sampled individual could have grown in the same month, of the same year for the given sediment sample.

Figure 1.

Representation of the picking procedure employed for the uncertainty algorithm INFAUNAL: (a) Instrumental Niño3.4 time series (black) with picked months (green circles with red fill) for one Monte Carlo simulation with #IFA = 30 for the 100 year time slice. (b) Comparison of picked range (green bar) and standard deviation (red bar) for #IFA = 30 and corresponding actual statistics for the overall population (orange bars).

We develop an algorithm to determine the uncertainty associated with the number of individual foraminifera analyzed (# IFA) by simulating the random process of sampling foraminifers (or randomly picking monthly pseudo-δ18Ocarbonate values) from the virtual sediment sample using a bootstrap Monte Carlo approach [Efron, 1979; Hall and Martin, 1988]. Each #IFA case (1–200) is composed of 5000 Monte Carlo realizations. A value of 0.1‰ (2σ) as a Gaussian distribution is incorporated in the picking procedure to simulate analytical uncertainty. Figure 1 depicts an example of one realization for #IFA = 30 for the 100 year virtual sediment sample. The standard deviation and range were calculated for each of the 5000 realizations for all #IFA (1–200). We ascribe the 2σ Monte Carlo spread of the 5000 standard deviations and ranges as the standard error on those parameters for that particular #IFA (Figure 2).

Figure 2.

Departures from actual range and standard deviation for a 100 year time period of the instrumental Niño3.4 time series. The gray envelopes depict the 2σ spread in 5000 Monte Carlo realizations for a given number of IFA. The purple, inverted triangle represents the #IFA we utilized for subsequent tests (#IFA = 70), which is used as a subjective approximation for the number of analyses where the uncertainty does not appreciably decrease and additional analyses could be cost prohibitive. Dotted line depicts zero departure or actual value (i.e., 100% accuracy). Neither IFA standard deviation nor range converges to the actual value, even at #IFA = 200 due to the presence of analytical uncertainty (2σanalytical = ±0.1‰).

We emphasize that the purpose of this initial statistical exercise is purely illustrative: to determine IFA uncertainty that arises due to sampling a subset of data in the continuous time period represented by the discrete sediment sample and to demonstrate the application of our algorithm to a time series of oceanic variability (in this case, Niño3.4 SSTs). In the subsequent IFA-modeling exercises, we attempt to more accurately represent real foraminifera in sediment cores by using instrumental data from a single point (0.5°N, 150.5°W) in the central equatorial Pacific (CEP) instead of spatially averaged instrumental data from the entire Niño3.4 box. Additionally, we incorporate the influence of sea surface salinity (SSS) on δ18Oseawater using salinity observations into our forward model as SSS can contribute significantly to interannual δ18Ocarbonate variability.

2.2 Synthetic Time Series

After developing an algorithm that can simulate the uncertainty associated with IFA sampling, we explore the sensitivity of the methodology to changes in climate variability. The probabilities of the IFA approach in detecting changes in ENSO variability and seasonal cycle changes are quantified by constructing synthetic δ18O time series using SST and SSS at three different locations in the tropical Pacific Ocean: WEP - 0.5°N, 159.5°E; CEP - 0.5°N, 150.5°W; and EEP - 1.5°S, 89.5°W. The influence of SSS on δ18Oseawater and hence foraminiferal δ18Ocarbonate was incorporated into our forward modeling scheme by utilizing monthly, 1°×1° SSS observations from the LEGOS data set [Delcroix et al., 2011]. Since accurate SSS observations in the tropical Pacific are relatively brief, the climatological seasonal cycle, average El Niño and La Niña deviations used as input for constructing synthetic time series at each site (Figure 3) were based on 39 years of SSS and SST observations (1970–2008). The transformation to foraminiferal δ18Ocarbonate-space (‰, VPDB) was based on a site-specific SSS-δ18Oseawater relationship [Hut, 1987; LeGrande and Schmidt, 2006] and the previously used SST equation [Bemis et al., 1998] (Text S1.1).

Figure 3.

The pseudo-δ18Ocarbonate (= f (SST,SSS); ‰, VPDB) climatology (bold, black) and average ENSO deviations (El Niño - bold, red; La Niña - bold, purple) from 1970 to 2008 for sites in: (a) WEP (0.5°N, 159.5°E), (b) CEP (0.5°N, 150.5°W), and (c) EEP (1.5°S, 89.5°W). The thinner lines indicate the mean El Niño (red) and La Niña (blue) events for synthetic time series where ENSO amplitude is doubled (AENSO = 2Elocation). For perspective, anomalies of a large El Niño event (1997–1998, thin dashed red line) and a large La Niña event (1988–1989, thin dashed blue line) at the different locations are plotted.

The synthetic time series were constructed with three degrees of freedom:

  1. Number of ENSO (El Niño and La Niña) events in a century (ENSO frequency, N)

  2. Change in the amplitude of mean ENSO events (ENSO amplitude, AENSO)

  3. Change in the amplitude of the climatological seasonal cycle (seasonal cycle, Aseasonal)

First, we utilize the climatological seasonal cycle (1970–2008) at a location as the basis for a 39 year long synthetic time series, i.e., black line in Figure 3 is repeatedly spliced. Next, we calculate climatologically averaged (or mean) δ18Ocarbonate values for El Niño and La Niña years. This is achieved by averaging monthly δ18Ocarbonate values at a location from April to March for all El Niño and La Niña years which are canonically defined at Niño3.4 [Trenberth, 1997]. Hence, we obtain mean El Niño and La Niña events which are allowed to grow and peak in phase with the seasonal cycle (Figure 3 red and purple bold lines, respectively). These events are inserted at different intervals into the initial time series to vary ENSO frequency (N). The monthly difference between mean ENSO events and the seasonal cycle at a location (defined as monthly residuals; AENSO = E) are altered to vary the ENSO amplitude of the synthetic time series (AENSO = kE; k ∈ {0.1:0.1:2} in subsequent experiments). For example, in a k = 2 scenario or a doubling of ENSO-related δ18Ocarbonate amplitude at that location (100% increase), the monthly ENSO residuals are doubled and added to the seasonal cycle to produce the event (AENSO = 2E; Figure 3 dashed lines). INFAUNAL suitably handles the phasing of an ENSO year for a given alteration in ENSO amplitude depending on the location, e.g., an increase in ENSO amplitude would yield warmer/depleted δ18Oseawater in a central Pacific site and cooler/enriched δ18Oseawater in a southwestern Pacific site during an El Niño event.

The amplitude of the seasonal cycle at the location (Aseasonal = SC) is varied by altering the amplitude of the quasi-sinusoidal climatology at a location, i.e., winters get cooler and summers get warmer for an increase in seasonal cycle amplitude and vice versa for a decrease (Aseasonal = kSC; k ∈ {0.1:0.1:2} in subsequent experiments; Note: the mean of the seasonal cycle is held constant). Finally, red and white noise is added to the preliminary time series in order to produce a record that has the same characteristics as the instrumental record, both visually as well as in frequency space. A comparison of the power spectra between the synthetic time series and the instrumental time series indicates that the synthetic noise approximates the noise found in the real time series, and that the character of the modeled time series accurately depicts observations at a given site (Figure S1 in supporting information). The 39 year long time series are spliced together to obtain synthetic time series of required time periods (depending on the length of time represented by the sediment sample at a location) ensuring that the characteristics of the initial time series were not altered. We fix the length of the synthetic time series at 100 years for all further exercises in this article. Thus, the frequency of ENSO events was varied compared to the canonically defined Niño3.4 SST record, where there are 52 events from 1909 to 2008 (N = 52; [Rasmusson and Carpenter, 1982; Trenberth, 1997]).

We assess the resolving ability of IFA by comparing the statistics of periods with differing ENSO and seasonal variability using our uncertainty algorithm (analogous to a “down-core” comparison). The synthetic δ18Ocarbonate time series representing the instrumental record at a location (Figure 4a; N = 52, AENSO = E, Aseasonal = SC; hereafter Modeled Modern Variability) was used as the basis for “down-core” comparison such that we define it as “modern variability.” By comparing the statistics of an altered synthetic time series to that of the Modeled Modern Variability (with #IFA = 70), we computed a probability of detection (Pdetection; Text S1.2). The basis of this lies in an explicit paired difference test: the probability that a random sample taken from a synthetic IFA-data distribution (5000 realizations) is significantly different from IFA-data taken from the Modeled Modern Variability (5000 realizations) within the standard error of measurement obtained from our uncertainty algorithm [Lanzante, 2005; Wilks, 2006]. Pdetection contour plots with concurrent ENSO and seasonal cycle changes (compared to the Modeled Modern Variability) were produced by simultaneously varying ENSO and seasonal cycle amplitudes at the three sites in the tropical Pacific Ocean (Figure 5).

Figure 4.

Selected synthetic time series with differing pseudo-δ18Ocarbonate (= f (SST,SSS); ‰, VPDB) variability for the CEP site with corresponding IFA range (green) and standard deviations (red) with error bars (#IFA = 70), where the length of the bars indicate the average statistic from the Monte Carlo analysis and the error bars are the 2σ standard deviation of the 5000 simulations. The orange stars depict the actual statistics for the continuous, overall time series. (a) Modeled Modern Variability at the CEP (N = 52; AENSO = ECEP; Aseasonal = SCCEP), (b) Doubled ENSO Amplitude (N = 52; AENSO = 2*ECEP; Aseasonal = SCCEP), (c) Halved ENSO Amplitude (N = 52; AENSO = 0.5*ECEP; Aseasonal = SCCEP), and (d) Doubled Seasonal Cycle (N = 52; AENSO = ECEP; Aseasonal = 2*SCCEP). Note the scale difference between range and standard deviation, as the range and associated error are larger in magnitude than the standard deviation.

Figure 5.

Probabilities of detecting (Pdetection; %) a change from Modeled Modern Variability (AENSO = Elocation, Aseasonal = SClocation, N = 52) using the IFA approach for synthetic time series with concurrent changes in ENSO amplitude (%, abscissa) and seasonal cycle amplitude (%, ordinate) variability at (a) WEP, (b) CEP, and (c) EEP. The IFA-signal is controlled by ENSO amplitude changes in the WEP and CEP, though it is more sensitive to ENSO changes in the CEP. Changes in seasonal cycle amplitude are the dominant influence in the EEP.

To increase the practical applicability of this study, we also tested the sensitivity of IFA for planktic foraminifera that may have a seasonal bias in productivity (e.g., a summer bias in G. ruber [Mortyn et al., 2011]) and those that potentially dwell and calcify in the thermocline (e.g., Pulleniatina obliquiloculata [Khider et al., 2011] and Neogloboquadrina dutertrei [Leduc et al., 2009; Scroxton et al., 2011]). For the seasonal bias case, we modified our uncertainty algorithm such that the preferred months of productivity were weighted higher in the procedure of random sampling. For the thermocline case, we extracted temperature and salinity at a depth of 60 m from the ECMWF ORA-S4 reanalysis data set for 1970–2008 [Balmaseda et al., 2012] and employed a thermocline-specific δ18Oseawater-salinity conversion [Benway and Mix, 2004] (Text S1.1). It should be noted that we have not accounted for species migration along the thermocline and assume a narrow depth range, both of which could potentially complicate the IFA-signal. As described above, we constructed synthetic time series with differing variability and produced Pdetection contour plots to assess the relative influences of ENSO and seasonal cycle amplitude changes in the IFA-signal.

3 Results

3.1 Uncertainty in IFA-Statistics

Figure 2 displays the departure of IFA-statistics from actual (or overall) statistics with the application of our picking algorithm on the Niño3.4 SST-based virtual sediment sample. Expectedly, the departure from the true statistic and associated uncertainty decreases with an increase in the number of foraminifera analyzed. We fix #IFA at 70 (purple triangle) for subsequent tests of comparison based on the average #IFA used in previous studies [Khider et al., 2011; Koutavas et al., 2006; Leduc et al., 2009; Scroxton et al., 2011] where the uncertainty associated with the standard deviation (red line, light gray envelope) is 0.04‰ and range (green line, dark gray envelope) is 0.27‰. The uncertainty in standard deviation is significantly smaller than that of the range even at #IFA = 200 and the Monte Carlo averages of both statistical parameters do not converge around the zero departure line (100% accuracy).

3.2 ENSO Frequency

To investigate the sensitivity of the IFA approach to changes in ENSO frequency, we held the amplitude of the seasonal cycle and ENSO amplitude constant (AENSO = E, Aseasonal = SC) and varied the number of ENSO events (N = 30 and N = 75) for constructed synthetic time series of δ18Ocarbonate at the WEP, CEP, and EEP surface ocean sites. Unlike section 3.1, δ18Ocarbonate for these results is a function of both SST and δ18Oseawater (a proxy for SSS). We find that the IFA-signal is mostly insensitive to large changes in ENSO frequency at the selected locations, with low probabilities of detection (<20%) for both statistical parameters (Table 1). Based on this result, we fixed ENSO frequency at modern variability (N = 52) for further tests where we varied the seasonal cycle and ENSO amplitude.

Table 1. Probabilities of Detecting (Pdetection) a Change From Modeled Modern Variability (AENSO = Elocation, Aseasonal = SClocation, N = 52) at a Location Using the IFA Approach for Synthetic Time Series With Two End-Member Cases of ENSO Frequency (N = 30 and N = 75) but Constant ENSO and Seasonal Cycle Amplitude (AENSO = Elocation, Aseasonal = SClocation)
Synthetic Time SeriesNo. of ENSO Events per Century (N)Pdetection*
RangeStd. Dev.
  • * Monte Carlo standard error on Pdetection is ±3%.
Modeled Modern Variability (at all locations)52-na--na-
Reduced ENSO FrequencyWEP305%7%
Increased ENSO FrequencyWEP757%15%

3.3 ENSO Amplitude vs. Seasonal Cycle Amplitude

Our results reveal that the ratio of interannual-to-annual variability of δ18Ocarbonate (function of SST and SSS) at a particular location determines whether the IFA-signal was controlled by changes in ENSO amplitude or changes in the seasonal cycle (or some combination of both). At the CEP, peak (or maximum) ENSO residuals are usually in December and are relatively large (El Niño years: −0.43‰; La Niña years: 0.33‰) compared to the amplitude of the seasonal cycle (0.23‰), leading to a high ratio of interannual-to-annual variability (Figure 3b and Figure S1). Here, the actual statistics for the synthetic time series with doubled ENSO amplitude (Range: 1.81‰, Std. Dev.: 0.39‰; Figure 4b orange stars) were observed to be larger than those of the Modeled Modern Variability (Range: 1.18‰, Std. Dev.: 0.24‰; Figure 4a orange stars). The difference in actual statistics between Modeled Modern Variability and the doubled seasonal cycle case was much smaller (Range: 1.22‰, Std. Dev.: 0.27‰; Figure 4d orange stars) implying a lower sensitivity towards changes in seasonal cycle amplitude. Ultimately, the structure of the Pdetection contours reflects the dominant influence of ENSO amplitude changes in the CEP-IFA-signal (Figure 5b). For example, a 50% reduction in ENSO amplitude without any change in the seasonal cycle (AENSO = 0.5*ECEP, Aseasonal = SCCEP) can successfully be distinguished from Modeled Modern Variability by IFA standard deviation (range) with a probability of ~80% (~50%). In the opposite scenario, where ENSO amplitude is unchanged and the seasonal cycle amplitude is reduced by 50% (AENSO = ECEP, Aseasonal = 0.5*SCCEP), it is highly improbable that IFA-statistics at the CEP can detect this change (Pdetection < 10%). We also determine that IFA achieves a Pdetection > 90% when ENSO amplitude was doubled (AENSO = 2*ECEP). For comparison, a 100% increase in ENSO amplitude is analogous to a century containing ENSO variability centered on the significantly large 1997–1998 El Niño and the 1988–1989 La Niña events at the CEP (Figure 3b).

The structure of the Pdetection contours changes dramatically when INFAUNAL is applied to different sites in the tropical Pacific Ocean (Figure 5). In the EEP, ENSO residuals (El Niño years: −0.37‰; La Niña years: 0.23‰) are small compared to the seasonal cycle (1.34‰), which results in a small ratio of interannual-to-annual variability in the time series (Figure 3c). Therefore, changes in seasonal cycle amplitude exert a dominant influence on the IFA-signal in the EEP rather than changes in ENSO amplitude (Figure 5c). For example, a 50% increase in seasonal cycle amplitude with unchanged ENSO amplitude compared to modern variability (AENSO = EEEP, Aseasonal = 1.5*SCEEP) has a Pdetection ~90% for standard deviation. However, when ENSO amplitude was increased by 50% and the seasonal cycle was not changed (AENSO = 1.5*EEEP, Aseasonal = SCEEP), the IFA approach has a Pdetection <10% for standard deviation.

For the site in the WEP, small peak ENSO residuals (El Niño years: −0.12‰; La Niña years: 0.2‰; Figure 3a) and a smaller seasonal cycle amplitude (0.13‰) result in Pdetection values lower than either the EEP or the CEP for both IFA-statistics (Figure 5a). Due to the ratio of interannual-to-annual variability in the WEP, the structure of the contours is similar to that of the CEP contours, with ENSO amplitude changes controlling the IFA-signal, although with lower sensitivity. We also observe that the IFA-signal is more sensitive to an increase in ENSO amplitude rather than a decrease for both range and standard deviation. Here, the ENSO the dynamic range of δ18Ocarbonate is relatively low and comparable in magnitude to the IFA methodological uncertainty, making signal detection of ENSO using IFA problematic.

3.4 Thermocline Dwellers and Seasonally Biased Planktic Foraminifera

Figure 6 displays the Pdetection contours for IFA-statistics along with the climatological averages for the thermocline at a depth of 60 m in the WEP and EEP. The structure of the Pdetection contours for the WEP thermocline (Figure 6a) is very similar to the WEP surface ocean case (Figure 5c), although lower in Pdetection magnitudes. Therefore, changes in ENSO amplitude control the IFA-signal in the WEP thermocline. This result is expected when comparing the climatological seasonal cycle and ENSO inputs for the Modeled Modern Variability for both WEP cases, as they are similar in magnitude. In the EEP, thermocline variability has a vastly different structure than surface ocean variability as evinced by the climatological averages in Figure 6b and Figure 3c. The amplitude of the thermocline seasonal cycle (0.45‰) is smaller in magnitude compared to that of the surface ocean (1.34‰) whereas the peak ENSO residuals in the thermocline are much larger (El NiñoEEP-Thermocline: 0.81‰, La NiñaEEP-Thermocline: 0.45‰; El NiñoEEP-Surface: 0.37‰; La NiñaEEP-Surface: 0.23‰). Therefore, this higher ratio of interannual-to-annual variability results in ENSO amplitude changes controlling the IFA-signal in the EEP thermocline, as shown by the structure of the Pdetection contours (Figure 6b).

Figure 6.

Pdetection (%) contour plots and associated climatological averages for the thermocline pseudo-δ18Ocarbonate (depth = 60 m) at (a) WEP and (b) EEP. Note the dramatic change in structure of the contours and climatological averages in the EEP thermocline compared to the EEP surface ocean (Figure 5c).

We investigated seasonal biases in foraminiferal productivity by weighting the picking procedure in INFAUNAL to a preferred set of months. First, we focused on weighting the months of December, January, and February (DJF; austral summer/boreal winter), when the ENSO signal is strongest for the EEP surface ocean, since there is evidence that in some locations, G. ruber may be a summer-biased planktic foraminifer that has higher abundances in warmer waters [Farmer et al., 2007; Mortyn et al., 2011]. For this case, Pdetection contours similar in structure to the nonweighted case (Figure 5c) are observed, though they are lower in sensitivity (Figure 7a). Since changes in seasonal cycle amplitude are the dominant influence on the IFA-signal at the EEP surface ocean, preferentially weighting only 25% of the seasonal cycle reduces the overall sensitivity. Encouraged by the high sensitivity of IFA towards changes in ENSO amplitude at a depth of 60 m in the EEP (Figure 6b), we carried out an austral-summer-weighted experiment in the thermocline at the site. The resultant Pdetection contours are observed to be heightened in sensitivity towards ENSO amplitude changes than the nonweighted case. Since ENSO amplitude changes dominate the IFA-signal in the EEP thermocline and since ENSO anomalies are largest in austral summer (Figure 6b), weighting the picking procedure towards DJF results in higher Pdetection values (Figure 7b).

Figure 7.

Pdetection (%) contour plots for the austral-summer-weighted (DJF) scenario for the EEP at (a) surface ocean and (b) thermocline (depth = 60 m).

4 Discussion

Reconstructing the statistics of interannual variability (such as ENSO) using the IFA technique has multiple sources of uncertainty that should be considered when interpreting the statistics of IFA-δ18O. The methodological uncertainty in standard deviation (2σMC (70) = ±0.04) is smaller in magnitude than that of the range (2σMC (70) = ±0.24) for all IFA populations we tested due to the larger dependence of the latter on outliers (Figure 1). Instrumental precision causes nonconvergence of IFA values to actual values even at high numbers of foraminifera (#IFA = 200) as analytical uncertainty tends to make outliers more extreme, thereby inflating both statistical parameters.

The mean of the IFA populations, analogous to measuring one sample of the same number of crushed and homogenized foraminifer shells (i.e., MFA), converges at a number of foraminifera comparable to the standard deviation (N = 70) but with better accuracy (Figure S2). As determined in previous studies [Killingley et al., 1981; Schiffelbein and Hills, 1984], the total variance in MFA is the sum of analytical precision variance and intrasample variance math formula. INFAUNAL provides an easy method to obtain this measure of total uncertainty and hence has application constraining uncertainty in multitest analysis. It is worth noting that our trends in uncertainty (Figure 2 and Figure S3) are similar in structure to the jackknife-based resampling approach used by Schiffelbein and Hills [1984], though the variance is lower. We stress that MFA-based studies should additively incorporate the uncertainty associated with the number of foraminifera analyzed along with analytical uncertainty as the overall uncertainty.

The ratio of interannual-to-annual variability at a particular location plays an influential role in IFA-signal and its interpretation (Figure 3). As demonstrated above, for foraminifers recording surface ocean variability, ENSO amplitude changes control the IFA-signal at the CEP and WEP whereas changes in seasonal cycle exert the dominant influence in the EEP (Figure 5). The IFA approach has a higher probability in resolving changes in ENSO amplitude at the CEP than the WEP due to relatively large ENSO anomalies compared to the seasonal cycle in the CEP.

In the EEP, our results indicate that IFA on planktic foraminifera recording surface ocean variability (e.g., G. ruber) most likely reflect past changes in the amplitude of the seasonal cycle and have low sensitivity to changes in ENSO amplitude. A recent study of mid-Holocene (6 ka) climate utilizing a general circulation model (GCM) indicates a ~40% (~2 °C) reduction in the amplitude of the seasonal cycle at the EEP site chosen for this study [Luan et al., 2012]. However, recent IFA studies of G. ruber at the same site show a reduction in variance at the mid-Holocene and are interpreted to be a ~50% reduction in ENSO amplitude [Koutavas et al., 2006; Koutavas and Joanides, 2012]. In contrast to this interpretation, our statistical analysis indicates that a ~40% reduction in the seasonal cycle at the EEP at 6 ka has a ~90% probability of being resolved by the IFA approach whereas an unchanged seasonal cycle and any change in ENSO amplitude from a 90% reduction to a 100% increase results in a <20% Pdetection value indicating the sensitivity at the location. Thus, we provide an alternate explanation for the population of G. ruber δ18O, that they are largely insensitive to changes in ENSO amplitude and are indicative of a reduced seasonal cycle, consistent with the GCM study.

The dominant influence on the IFA-signal can be markedly different between the thermocline and the surface ocean at the same site. For example, the changes recorded in the surface ocean of the EEP are dominated by the seasonal cycle, whereas changes in the thermocline respond primarily to ENSO amplitude changes. This is due to the fact that the EEP surface ocean has a lower ratio of interannual-to-annual variability than the thermocline and reflects changes in the seasonal cycle (Figure 5c and Figure 6b). These results suggest that IFA-based studies in the EEP using thermocline dwellers can resolve ENSO with higher probabilities of detection [Leduc et al., 2009; Scroxton et al., 2011], although each site should be assessed independently before IFA application.

Regarding seasonal biases in foraminiferal productivity, our results show that these preferences can influence the sensitivity of the IFA approach depending on the dominant control of the signal. Preferentially weighting austral summer months (DJF) in the EEP surface ocean case, where the seasonal cycle is the dominant control, results in Pdetection contours with diminished sensitivity (Figure 6b) compared to the nonweighted, year-round scenario (Figure 5c). However, the Pdetection contours for the EEP thermocline are heightened in sensitivity towards changes in ENSO amplitude with a DJF-weight (Figure 7b) as the peak ENSO anomalies occur in these months (Figure 6b). Considering all our results, the CEP surface ocean case and the DJF-weighted thermocline case in the EEP had the highest skill in reconstructing past ENSO amplitude. Year-round planktic foraminifers recording surface ocean variability in the EEP appear to be best suited to reconstruct past changes in the seasonal cycle via IFA.

We acknowledge that we have not accounted for biological processes such as intraspecific and vital effects [Spero and Williams, 1990], local environmental sensitivity, and different methods of sample preparation [Waelbroeck et al., 2005]. Nor have we accounted for geochemical dating errors, changing sedimentation rates and bioturbation [Schiffelbein, 1986; Trauth et al., 1997], all of which could potentially increase the overall uncertainty in the interpretation of IFA-data. Further, decadal- to centennial-scale trends could influence IFA-based reconstructions by adding variance to the IFA-δ18O population that is not due to ENSO and would subsequently be misinterpreted as changes in interannual variability. We hypothesize that most of these factors would result in inflated errors and reduced skill when interpreting an IFA-signal as changes in the seasonal cycle or amplitude of interannual variability. Therefore, our results represent an idealized scenario for interpreting the IFA-signal considering inherent uncertainty. We hypothesize that IFA on modern core tops and sediment trap samples, validated with the instrumental record, can be used as a calibration measure for more accurate estimates of past annual and interannual variability [e.g., Haarmann et al., 2011].

5 Conclusions

We present a sensitivity analysis algorithm, INFAUNAL, that generates IFA-δ18O data and calculates the inherent uncertainty on IFA-statistics. We use the technique at different locations in the tropical Pacific Ocean to probabilistically disentangle the contribution of changes in ENSO variability and seasonal cycle variability to the IFA-signal. INFAUNAL can also be applied at different depths (mixed layer, thermocline) where the climatological seasonal cycle and associated ENSO anomalies of δ18Ocarbonate are known. The local seasonal cycle, relative ENSO anomalies, and analytical precision are assessed as sources of uncertainty in the interpretation of synthetic IFA-δ18O as a recorder of paleoceanographic variability. We determine that the IFA standard deviation is a more precise and accurate statistic than the IFA range. Our results show that the IFA approach is insensitive to ENSO frequency changes (<20% probability) but nevertheless indicate that changes in ENSO amplitude or seasonal cycle amplitude (or a combination of both) can be detected depending on the ratio of interannual-to-annual variability at the location of the study. Last, we find that the habitat and seasonal productivity of planktic foraminifers can influence the IFA-signal and, in case of the EEP, reverse the sensitivity of the site from recording changes in the seasonal cycle to recording changes in ENSO. We suggest that rigorous uncertainty analysis become standard practice for future individual and multitest foraminiferal-based reconstructions of paleoceanographic variability.


We acknowledge Deborah Khider and Veronica Anderson from UT Austin and Rengaswamy Ramesh from PRL, Ahmedabad for productive discussions. We are very grateful to two anonymous reviewers whose comments and critique significantly (p < 0.01) improved this work. We also thank the editor Christopher Charles. The INFAUNAL suite of code in MATLAB® format and an example data set are available from KT.