1 Introduction

Interactions between multiple processes are prominent in the tropical Pacific and are responsible for seasonal and inter-annual variabilities. For example, ocean–atmosphere coupling in the region creates the El Niño Southern Oscillation (ENSO), which is a dominant inter-annual mode in the climate system (e.g. Philander 1983; Zebiak and Cane 1987; Zhang and Levitus 1997; Zhang and Gao 2016; Tang et al. 2018). Additionally, various feedbacks and couplings coexist in the tropical Pacific that involve interactions among ocean physics, ocean biology and the climate, which can significantly modulate the ENSO (Zhang and Busalacchi 2008, 2009; Zhang et al. 2012; Zhi et al. 2015; Kang et al. 2017a, b). In particular, ocean biology can influence ocean physics through its modulation of penetrative solar radiation in the upper ocean (Timmermann and Jin 2002; Marzeion et al. 2005; Wetzel et al. 2006; Lengaigne et al. 2007; Gnanadesikan and Anderson 2009; Zhang et al. 2009; Anderson et al. 2009; Jochum et al. 2010; Park et al. 2014). Indeed, recent studies revealed pronounced ocean biology-induced heating feedback on the ENSO over the tropical Pacific (Zhang 2015; Kang et al. 2017a). As a major driver that strongly affects the upwelling and mixing processes in the equatorial Pacific, the ENSO greatly changes the Chl in the region. At the same time, corresponding biological perturbations modulate the penetrative solar radiation in the upper ocean, which produces a feedback on the ENSO.

The solar radiation that arrives at the sea surface penetrates through the upper water column and its shortwave component decays exponentially with depth. Some is absorbed directly within the mixed layer (ML), while some penetrates through the bottom of the ML and into subsurface layers. The ML depth (Hm) is a major physical factor that determines the vertical partitioning of solar radiation between the mixed layer (ML) and subsurface layers. Additionally, phytoplankton, detritus and colored dissolved organic matter (CDOM) can absorb solar radiation mainly in the visible spectrum (380–700 nm), thus affecting the vertical penetration of the incoming solar radiation in the upper ocean (Lewis et al. 1990; Morel and Antoine 1994; Siegel et al. 2002; Strutton and Chavez 2004; Kang et al. 2017a). Among these components, chlorophyll is the main factor that attenuates shortwave radiation and consequently affects the ocean’s thermal conditions. Correspondingly, a penetration depth (Hp) can be defined to represent the extent to which the penetration of solar radiation in the upper ocean is affected by the Chl concentration. Thus, the depth of the mixed layer (Hm) and penetration depth (Hp) are two factors that affect the distribution of penetrative solar radiation in the ML and subsurface layers; the former (Hm) is controlled by physical processes and the latter (Hp) is determined by biological processes. Furthermore, bio-effects are realized through a few heating terms that are directly associated with Chl (and the corresponding Hp) and Hm, including the absorbed solar radiation flux within the ML (denoted as Qabs) and its directly related temporal rate of change in the ML temperature (denoted as Rsr), alongside the penetrated portion of solar radiation through the bottom of the ML (denoted as Qpen). These heating terms can be used to characterize and quantify the Chl-induced heating feedback effects on the SST because these terms act to modulate the thermodynamics in the upper ocean, which can further induce indirect dynamical effects on the SST.

Previously, bio-climate interactions were investigated by using coupled ocean–atmosphere models with different degrees of complexity. Large uncertainties exist in model representations of ocean biology-induced heating (OBH) feedback, and its simulated effects strongly depend on models used. Thus, modulations in SST from ocean biology are sensitive to the manner in which bio-effects are represented in models. Currently, models exhibit biases in terms of simulating Chl variability in the tropical Pacific. Additionally, the physical mechanisms that are involved in bio-effects significantly differ among various previous modeling studies because different dominant processes are apparently at work. What are the main factors that control ocean biology-induced effects and the involved physical processes? Why do large intermodal differences exist in bio-effect simulations? Clearly, observations are vital to reveal the physical mechanism for these ocean biology-induced effects and validate model-based simulations and related bio-effects.

Over the past decade, remote sensing has made great progress in providing time series of ocean color data and associated products. For example, chlorophyll (Chl) data are available from satellite measurements and have been used to describe and understand bio-climate interactions (McClain et al. 1998). As observed in the tropical Pacific, for example, the existence and variations of Chl affect surface-layer water turbidity and modify the vertical redistribution of solar radiation in the upper ocean. Correspondingly, the Chl concentration can be used to estimate Hp. Also, Argo profiles provide unprecedented temperature and salinity data in the upper ocean, which can be used to estimate ocean fields on basin scales, including the depth of the ML (Hm). Thus, sufficient observational data of Chl and physical fields have been accumulated in the last decade, which allows us to perform detailed analyses on Chl-induced heating effects in the tropical Pacific.

In this paper, we perform an observation-based analysis for the biological heating effect, with a focus on the inter-annual variability that is associated with the ENSO in the tropical Pacific. A diagnostic analysis method is developed that makes full use of observational data to reveal bio-effects from inter-annual Chl anomalies. More specifically, observed Chl data are combined with other derived fields to characterize the structural relationships of Chl-related heating terms with Hm and Hp. For example, observed Hm and Hp fields are used to quantify the combined effects on the penetration of solar radiation and related heating effects. The revealed relationships are used to infer the processes that are involved and understand the influence pathways through which the SST is modulated by inter-annual Chl anomalies.

This paper is organized as follows. Section 2 describes the heating terms that are associated with Chl and the observational data that are used for the analyses. The structural relationships of these heating terms with Hm and Hp are analyzed in Sect. 3. Section 4 provides a summary and discussion. An Appendix is provided for the analyses of the annual mean and seasonal variations in some related fields.

2 Ocean Chl-induced heating terms and observational data

Comprehensive data are used to diagnose Chl-induced heating terms and bio-effects on the SST, including ocean physical and biological fields that are derived from satellite-based observations and in situ Argo profiles. As shown below, these heating terms are determined by the ocean mixed-layer depth (Hm) and penetration depth (Hp); the former is determined by physical processes and the latter is determined by biological processes. Observational data are used to quantify these heating terms and structural relationships between physical and biological fields. The effects on these terms can be analyzed using observational data, which are defined below.

2.1 Ocean Chl-induced heating terms

The incoming solar radiation that arrives at the sea surface tends to decay very sharply with depth in the upper ocean (a factor that reflects the effect of pure water on penetrative solar radiation); the depth of the mixed layer (Hm) is a major factor that determines the vertical partitioning of solar radiation between the mixed layer (ML) and subsurface layers. At the same time, the existence and variations of Chl can affect the penetrative solar radiation in the upper ocean; therefore, the penetration depth (Hp) can be introduced to quantify the extent to which solar radiation is affected by biological fields in the upper ocean.

Some heating-term fields are directly related to Hp and Hm, including the absorbed solar radiation flux within the ML (denoted as Qabs) and its directly related temporal rate of change in the ML temperature (denoted as Rsr), alongside the portion of solar radiation that penetrates the bottom of the ML (denoted as Qpen).

2.1.1 Penetration depth (Hp)

Ocean biological components (such as phytoplankton, detritus and colored dissolved organic matter (CDOM)) can absorb solar radiation in the visible spectrum (380–700 nm) and further modify the vertical penetration of the incoming solar radiation in the upper ocean (Lewis et al. 1990; Morel and Antoine 1994; Siegel et al. 2002; Strutton and Chavez 2004). The penetration of the solar shortwave radiation in the upper ocean follows the Beer-Lambert Law, which indicates that shortwave radiation decays exponentially with depth according to attenuation coefficients. Here, chlorophyll is considered to have attenuating effects on shortwave radiation.

Thus, the total attenuation coefficient can be computed as follows (Wang et al. 2008):

$$K_{A} (z) = K_{W} + K_{C} Chl(z),$$
(1)

where z is the depth; KW = 0.028 m−1 and KC = 0.058 m−1 (mg chl m−3)−1 represent the attenuation coefficients for pure water and chlorophyll, respectively; and Chl(z) is the chlorophyll concentration. In this study, we only consider the Chl effect on KA because Chl plays a dominant role in ocean biology-induced heating effects.

Then, a penetration depth (Hp) of the shortwave radiation is defined as the inverse of KA calculated from the satellite observations of the Chl field (Murtugudde et al. 2002; Zhang et al. 2011). This Hp field serves as a linkage between ocean biology and physics and can be used to quantify the ocean biology-induced heating effects on the related heating terms.

2.1.2 Absorbed solar radiation within the ML (Qabs and Rsr)

As expressed in Zhang (2015), Hp and Hm are explicitly associated with several ocean biology-induced heating terms. Qabs denotes the absorbed solar radiation flux within the ML, and Rsr denotes the temporal rate of change in the ML temperature that directly results from the Qabs effect on SST, both of which are written as follows

$$Q_{abs} (H_{m} ,H_{p} ) = Q_{sr} [1 - \gamma \exp ( - H_{m} /H_{p} )],$$
(2)
$$R_{sr} (H_{m} ,H_{p} ) = Q_{sr} [1 - \gamma \exp ( - H_{m} /H_{p} )]/(\rho_{0} c_{p} H_{m} ) = Q_{abs} /(\rho_{0} c_{p} H_{m} ),$$
(3)

where Qsr is the incoming solar radiation flux at the sea surface, γ is a constant (= 0.33) that denotes the fraction of the available radiation to penetrate to depths beyond the first few centimeters of the sea surface, Cp is the heat capacity, and ρ0 is the density of sea water.

As expressed above, Qabs, which is a function of both Hm and Hp, is determined by changes in Hm and Hp. On the one hand, Qabs increases exponentially with Hm. The deeper the ML, the more solar radiation that is directly absorbed within the ML. On the other hand, Qabs also decreases exponentially with Hp; the larger the Hp value, the less solar radiation that is directly absorbed within the ML, producing more penetration through the bottom of the ML. Therefore, changes in Hm and Hp tend to have an opposite effect on Qabs. That is, a negative (positive) perturbation in Hm reduces (increases) Qabs, whereas a negative (positive) perturbation in Hp increases (reduces) Qabs.

Furthermore, the absorbed solar radiation within the ML (Qabs) directly changes Rsr, thus further changing the SST, which represents a direct thermal effect. Rsr is proportional to Qabs (which has an exponential relationship with Hm and Hp) and inversely proportional to Hm (appearing as a denominator). Thus, Rsr can be affected by Hm in two fashions, whose effects tend to be of opposite signs. On the one hand, Hm is exponentially related to Qabs, so a deepening (shoaling) of the ML (which increases (decreases) Qabs) can increase (decrease) Rsr. On the other hand, Hm is inversely proportional to Rsr (appearing as a denominator), so the deepening (shoaling) of the ML can decrease (increase) Rsr. These two effects on Rsr that are induced by Hm and Hp have implications for how this term is modulated by Hp.

2.1.3 Penetrative solar radiation flux through the bottom of the ML (Qpen)

The solar radiation flux that penetrates the bottom of the ML (Qpen) is written as

$$Q_{pen} (H_{m} ,H_{p} ) = Q_{sr} [\gamma \exp ( - H_{m} /H_{p} )] = Q_{sr} - Q_{abs} .$$
(4)

As expressed, Qpen has exponential relationships with Hm and Hp, which tend to have opposite signs relative to Qabs. For example, Qpen decreases exponentially with Hm but increases exponentially with Hp; that is, the deeper the ML, the less solar radiation that directly penetrates through the bottom of the ML. Similarly, the larger the Hp value, the deeper that the solar radiation directly penetrates into the subsurface layer. Therefore, changes in Hm and Hp tend to have opposite effects on Qpen.

2.2 Observational data

Various observational data are used to describe the inter-annual variability and relationships among some physical and biological fields. The SST fields are obtained from Reynolds et al. (2002). The shortwave solar radiation data are from the MERRA re-analysis product (Rienecker et al. 2011). The surface chlorophyll datasets are obtained from the GlobColour project from 1998 to 2007, which supplied continuous datasets for merged Level-3 Ocean Color products (including the SeaWIFS, MODIS, MERIS and VIIRS sensors; see details at http://hermes.acri.fr/index.php; Maritorena et al. 2010). Then, monthly CHL-1 data (chlorophyll concentration (mgm−3) for case-1 waters) are interpolated from 0.25° × 0.25° grids to our analysis grids (1.0° × 1.0°).

The Argo-based dataset is provided by the International Pacific Research Center (IPRC)/Asia–Pacific Data-Research Center (APDRC). This product includes the MLD and three-dimensional gridded fields for temperature and salinity with a 1° horizontal resolution at the standard depths. The MLD is defined as the depth at which the density increases from 10 m to a value that is equivalent to a temperature drop of 0.2 °C.

These data during 2005–2015 are averaged to form climatological monthly fields, which are used to calculate their inter-annual anomalies. In addition to these directly observed data, some related heating fields are estimated, including a penetration depth (Hp), Qabs, Rsr, and Qpen.

3 Structural relationships associated with the bio-effects on ENSO

Figures 1, 2, and 3 display the evolution along the Equator for various related total fields; the corresponding annual-mean and seasonal variations are presented in the Appendix. The inter-annual variabilities of these physical and biological fields are dominated by ENSO signals in the tropical Pacific. Note that full quantity and its variability exhibit differences in their magnitudes between physical and biological fields. For example, seasonal and inter-annual variabilities of physical fields are generally one order of magnitude smaller than its total field. However, the magnitudes of seasonal and inter-annual Chl variabilities are comparable to those of its total value, and the total Qabs field is one order of magnitude larger than its seasonal and inter-annual variability.

Fig. 1
figure 1

Time-longitude sections along the Equator during 2005–2015 for the a SST and b Chl fields from the GlobColour Project. The contour interval is 1 °C in a and 0.05 mg m−3 in b

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Fig. 2
figure 2

Time-longitude sections along the Equator during 2005–2015 for the a shortwave radiation, b Hm, and c Hp fields. The contour interval is 10 W m−2 in a, 5 m in b, and 1 m in c

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Fig. 3
figure 3

Time-longitude sections along the Equator during 2005–2015 for the ocean Chl-related total heating terms: a Qabs, b Qpen, and c Rsr. The contour interval is 10 W m−2 in a, 5 W m−2 in b and 1 °C month−1 in c

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3.1 Inter-annual variations in SST and Chl

The total SST field (Fig. 1a) is characterized by a warm pool in the western tropical Pacific and a cold tongue in the eastern equatorial Pacific. The warm pool in the west and cold tongue in the east exhibit large zonal displacements during ENSO cycles. During La Niña, the warm pool retreats to the west, whereas the cold tongue in the east develops and expands westward along the Equator, with the 25 °C SST isotherm located west of 150°W. During El Niño, the warm waters in the west extend eastward along the Equator (e.g., the 27 °C SST isotherm extends eastward to the east of 150°W), while the cold tongue shrinks in the east.

As a major driver, the ENSO induces pronounced perturbations to ocean physical and biological fields in the tropical Pacific (Figs. 1, 2). For example, shortwave radiation exhibited a pronounced inter-annual variation associated with ENSO (Fig. 2a); one interesting feature is the large shift for shortwave radiation around 2010. We speculate that the eastward migration of atmospheric convection center during El Niño is responsible for a decrease in shortwave radiation near the dateline. During 2009-2010, a record-breaking warm sea surface temperature emerged in the central Pacific, which is the strongest Central Pacific type of El Niño in the 21th century (Lee and McPhaden 2010). In terms of biological field, a well-defined pattern of inter-annual Chl variability is seen during El Niño and La Niña cycles. The main characteristics of the mean Chl field and variability have been previously described (e.g. Ballabrera-Poy et al. 2007). Climatologically (see Fig. 1b and the Appendix), Chl exhibits elevated values from the west to the east across the tropical Pacific: its concentration is low (< 0.1 mg m−3) in the western equatorial Pacific in association with the warm waters but is high (> 0.2 mg m−3) in the eastern equatorial region, where the cold tongue develops. Additionally, the Chl concentration is very high in the eastern coastal regions.

Inter-annually, the Chl concentration in the equatorial Pacific significant increases during La Niña events and drops during El Niño events. Detailed examinations indicate that the inter-annual Chl variability exhibits different characteristics in the west and east. In the western-central equatorial Pacific, the Chl field has a clear east–west migration along the Equator during ENSO cycles. Regions with large values extend to the date line during El Niño. In the eastern equatorial Pacific, large variations are associated with local oceanic processes (e.g., upwelling).

The inter-annual variability features of the SST and Chl fields can be more clearly seen in their anomaly fields (Fig. 4). The magnitude of the inter-annual Chl variability is comparable to that of the total Chl field. ENSO is a major source for inter-annual variability of Chl, with negative anomaly during El Niño events and positive anomaly during La Niña events. The inter-annual Chl variations in the east do not exhibit obvious propagation along the Equator (i.e., they are almost in phase in terms of time), but those in the west have zonal migration along the Equator (Fig. 1). The inter-annual Chl variability is quantified by calculating its standard deviations (Fig. 5a). Two large Chl variability centers are seen: one in the western equatorial Pacific to the west of the date line and another in the eastern equatorial and coastal regions.

Fig. 4
figure 4

Time-longitude sections along the Equator during 2005–2015 for inter-annual anomalies of a SST and b Chl. The contour interval is 0.5 °C in a and 0.02 mg m−3 in b

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Fig. 5
figure 5

Standard deviations for inter-annual anomalies of a Chl, b Hp and c Hm. The contour interval is 0.02 mg m−3 in a, 0.2 m in b and 1 m in c

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Clear relationships exist between the inter-annual variations in SST and Chl; the latter closely follows the former, characterized by their out-of-phase fluctuations during ENSO cycles (Fig. 4). Thus, the ENSO induces bio-responses that are quick and coherent at large scales. In addition, the Chl and SST exhibit spatial shifts in their large variability regions. While the largest SST anomalies occur in the central and eastern equatorial Pacific (Fig. 4a), a pronounced inter-annual variability of Chl is located in the western-central equatorial Pacific (Fig. 4b). During La Niña events, for example, a cold SST anomaly is located in the central-eastern equatorial Pacific, but regions with positive Chl concentration are seen in the western-central equatorial region. In contrast, during El Niño events, a warm SST anomaly in the east is associated with a negative Chl concentration in the west. Quantitatively, the correlations between SST and Chl are shown in Fig. 6a. The inter-annual variability of Chl closely follows that of SST, so the inter-annual variations in Chl tend to be negatively correlated with those in the SST over the tropical Pacific, with large negative values in the western equatorial Pacific near the date line.

Fig. 6
figure 6

Correlations during 2005–2015 between inter-annual anomalies of a Chl and SST, b Chl and Hm, and c Hp and Hm. The contour interval is 0.2

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3.2 Inter-annual variations in Hm and Hp

The characteristics of the Hm structure and its variability are seen in Fig. 2b and the Appendix. The ML is relatively shallow (< 30 m) in the western tropical Pacific because of the weak surface friction velocity and stabilizing surface buoyancy flux. Regions with values larger than 50 m are found in the central basin, which exhibit energetic surface wind and strong surface buoyancy losses. During La Niña, the ML is unusually deep in the western-central equatorial Pacific but shallow in the eastern regions. During El Niño, the ML becomes shallower in the west but deeper in the east. The inter-annual variations in Hm exhibit a see-saw pattern, with two large anomaly regions in the western and eastern equatorial regions (Fig. 7b) and the zero-crossing line around 150°W. As such, inter-annual anomalies of Hm in the west tend to be out of phase with those in the east, a clear see-saw pattern that is associated with the ENSO’s evolution.

Fig. 7
figure 7

Time-longitude sections along the Equator during 2005–2015 for inter-annual anomalies: a shortwave radiation, b Hm, and c Hp. The contour interval is 5 W m−2 in a, 5 m in b, and 1 m in c

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The above Chl field is used to estimate the penetration depth (Hp). As shown in Fig. 2c and the Appendix, the penetration of solar radiation is deep in the western equatorial Pacific but shallow in the east, with a low Hp value (< 19 m) in the east and high Hp value (> 20 m) in the west. Seasonally (see the Appendix), the penetration of solar radiation is deep in spring but shallow in fall. Inter-annually, the penetration depth in the equatorial Pacific exhibits large variations during ENSO cycles (Fig. 7c). Inter-annual Hp anomalies have a uniform pattern across the equatorial Pacific. For example, Hp has positive anomalies in the equatorial Pacific during El Niño (corresponding to a reduced Chl concentration with a deeper penetration of solar radiation) but negative anomalies during La Niña (corresponding to an increased Chl concentration with a shallower penetration of solar radiation).

As a response to ENSO cycles, the inter-annual variations in Hm and Hp indicate a coherent space–time structure (Figs. 7b, c, 8, 9) clearly display their horizontal patterns during La Niña conditions as represented in August 2010 and during El Niño conditions in August 2015, respectively. One striking feature is that the inter-annual variations in Hp and Hm tend to be out of phase in the western-central equatorial Pacific during ENSO cycles but in phase in the east (Figs. 8b, c, 9b, c). That is, in the western equatorial Pacific, positive (negative) Hm anomalies are accompanied by negative (positive) Hp anomalies during La Niña (El Niño). However, in the eastern equatorial Pacific, Hp anomalies are weak and Hm has positive and negative anomalies during El Niño and La Niña, respectively.

Fig. 8
figure 8

Horizontal patterns of inter-annual anomaly fields for La Niña conditions as represented in August 2010: a SST, b Hm, c Hp, d Qpen when estimated with the inter-annual Hp effect considered, e Qpen when estimated with the inter-annual Hp effect excluded, and f the differences (the Qpen fields estimated with the inter-annual Hp effect included minus those excluded). The contour interval is 0.5 °C in a, 5 m in b, 1 m in c, 2 W m−2 in d and e, and 1 W m−2 in f

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Fig. 9
figure 9

Same as in Fig. 8 but for El Niño conditions as represented in August 2015

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The standard deviations for the inter-annual anomalies of Hp and Hm are shown in Fig. 5b, c. Regions with large inter-annual Hp variability are seen in the western Pacific west of the date line. Hm has a large-variability region in the western equatorial region. In the western-central equatorial Pacific near the date line, the magnitude of the inter-annual variability of Hp is approximately 20% that of Hm, indicating that the effect of Hp on the heating terms is not negligible compared to that of Hm. Quantitatively, the correlations between Hm and Hp are shown in Fig. 6c. Corresponding to the negative correlations between Hp and Chl, positive correlations exist between Hp and Hm in the western equatorial Pacific. The regions with large positive correlation near the date line are consistent with those where the amplitude of Hp is approximately 20% that of Hm, indicating that Hp can have pronounced effects. The effects on the heating terms from the inter-annual variability of Hp will be analyzed below.

3.3 Inter-annual variations in the bio-induced heating terms

Hm and Hp are two factors that determine the distribution of solar radiation between the mixed layer and underlying subsurface layers. As mathematically expressed above, the three heating terms are directly associated with Hm and Hp. To understand the bio-effects in the tropical Pacific, a diagnostic analysis is performed to quantify the structural relationships of these heating terms with Hm and Hp, with emphasis placed on the ENSO. Then, the manner in which these related fields are affected by Hp can be inferred to reveal how the SST is modulated by the bio-effects and underlying processes that are involved.

Figures 3, 10, 11, and 12 display the space–time evolution of some related fields along the Equator; examples for the horizontal patterns of inter-annual Qpen anomalies are demonstrated in Fig. 8 during La Niña conditions and Fig. 9 El Niño conditions, respectively. All these fields exhibit large variability that is associated with the ENSO. The inter-annual variations in Hm and Hp exhibit well-defined structures during ENSO cycles, so their effects on the vertical distributions of solar radiation between the ML and subsurface layers are expected, which can be quantified by calculating the modulating effects on these heating terms. For example, the structural relationships of Qpen with Hm and Hp can be clearly seen in the horizontal distributions of their inter-annual anomaly fields during El Niño (Fig. 8) and La Niña (Fig. 9), respectively.

Fig. 10
figure 10

Time-longitude sections along the Equator during 2005-2015 for inter-annual anomalies: a Qpen when estimated with the inter-annual Hp effect considered, b Qpen when estimated with the inter-annual Hp effect excluded, and c their differences (the Qpen fields estimated with the inter-annual Hp effect included minus those excluded). The contour interval is 2 W m−2 in a and b and 0.5 W m−2 in c

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Fig. 11
figure 11

Time-longitude sections along the Equator during 2005-2015 for inter-annual anomalies: a Qabs when estimated with the inter-annual Hp effect considered, b Qabs when estimated with the inter-annual Hp effect excluded, and c their differences (the Qabs fields estimated with the inter-annual Hp effect included minus those excluded). The contour interval is 5 W m−2 in a and b and 0.5 W m−2 in c

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Fig. 12
figure 12

Time-longitude sections along the Equator for inter-annual anomalies: a Rsr when estimated with the inter-annual Hp effect considered, b Rsr when estimated with the inter-annual Hp effect excluded, and c their differences (the Rsr fields estimated with the inter-annual Hp effect included minus those excluded). The contour interval is 0.5 °C month−1 in a and b and 0.02 °C month−1 in c

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As indicated in the Hm structure (Fig. 2b), most of the solar radiation is absorbed within the ML (Qabs; Fig. 3a), with some penetrating through the bottom of the ML (Qpen; Fig. 3b). When the ML changes during ENSO cycles, the amount of solar radiation that is absorbed within the ML (Qabs) and penetrates through the bottom of the ML (Qpen) also changes. The absorbed component within the ML directly changes the Rsr value (Fig. 3c), thus modulating the SST, a way to directly change SST. Additionally, Hp can have a modulating effect on these terms, which is analyzed in detail below.

3.3.1 Modulating effect on Qpen

The total Qpen field and corresponding inter-annual Qpen anomalies along the Equator (Figs. 3b, 10a) indicate their well-defined structure during ENSO cycles. Large Qpen anomalies are observed in the equatorial regions with a see-saw pattern in the west and east, which is characterized by a positive Qpen anomaly during El Niño and a negative anomaly during La Niña. In the east, an opposite pattern is seen during ENSO cycles.

Qpen is affected by Hm and Hp (Fig. 3), and Hm’s effect on Qpen can be clearly seen in the horizontal distributions of the inter-annual anomaly fields during El Niño (Fig. 8) and La Niña (Fig. 9). In the western-central equatorial region, for example, the negative Qpen anomaly during La Niña is accompanied by a positive Hm anomaly. An opposite pattern is seen during El Niño (Fig. 9), with a positive Qpen anomaly accompanied by a negative Hm anomaly in the western-central region near the date line. The similarity between the space–time evolutions of Hm (Fig. 7b) and Qpen (Fig. 10a) indicates that Hm is a main factor that determines the mean state and variations of Qpen in the tropical Pacific.

Qpen is also a function of Hp, so we expect that Qpen can be modulated by Hp. As shown in Figs. 7c and 10a, negative and positive Qpen anomalies have a clear signature of the inter-annual Hp effects. Thus, a close relationship exists between the inter-annual variations in Hp and Qpen in the western-central equatorial basin. A negative Hp anomaly is observed during La Niña events, which causes less sunlight to penetrate through the bottom of the mixed layer, but become trapped more within the mixed layer. Thus, this negative Hp anomaly makes the negative Qpen anomaly during La Niña more negative. During El Niño, when Hp becomes a positive anomaly, sunlight can penetrate deeper into subsurface layers, so the positive Hp anomaly makes the positive Qpen anomaly more positive.

Clearly, the large observed inter-annual anomalies of Qpen (e.g., Fig. 10a) represent a combined effect from both Hm and Hp during ENSO cycles. Although the inter-annual variability of Qpen in this region is mainly determined by that of Hm, the inter-annual variability of Hp can also make a substantial contribution, enhancing inter-annual anomalies of Qpen during El Niño-La Niña cycles.

3.3.2 Modulating effects on Qabs and Rsr

Next, similar calculations are shown in Figs. 3a and 11 for Qabs. Similar to Qpen, the inter-annual variability in Qabs exhibits a well-defined pattern during ENSO cycles. As defined above, the space–time structural relationships of Qabs’s variability with Hm and Hp are similar to those of Qpen but with the opposite sign. For example, in the western-central equatorial Pacific, Qabs exhibits a positive anomaly during La Niña (more gain in solar radiation within the ML) but a negative anomaly during El Niño (loss of solar radiation within the ML), which is determined collectively by Hm and Hp. The inter-annual variability of Qabs (Fig. 11a) almost mirrors that of Hm (Fig. 7b), so Hm is a major factor that controls the structure and variability of Qabs. Additionally, Qabs can be modulated by Hp because the former is a function of Hp. Similar to Qpen, a change in Hp significantly modulates Qabs in the western-central equatorial Pacific, and the observed inter-annual variability of Qabs also represents the combined effects of Hm and Hp. During La Niña conditions, a positive Hm anomaly is mainly responsible for a positive Qabs anomaly in the region; at the same time, Hp exhibits a negative anomaly, which increases the absorption of solar radiation within the ML (a corresponding positive Qabs anomaly). Thus, the negative Hp anomaly makes the positive Qabs anomaly more positive. The combined effects of the positive Hm anomaly and negative Hp anomaly enhance the positive Qabs anomaly. During El Niño events, the negative Hm anomaly is responsible for a negative Qabs anomaly in the western-central equatorial Pacific; then, the positive Hp anomaly makes the negative Qabs anomaly more negative. Thus, the inter-annual variability of Hp tends to enhance inter-annual anomalies of Qabs during ENSO cycles.

Next, we move to the analysis for Rsr (the rate of the ML temperature change that is directly resulted from the heating effect associated with Qabs). Figures 3c and 12 display the total Rsr field and its inter-annual variability along the Equator. Rsr has high values in the west and east but relatively low values in the central basin (Fig. 3c and the Appendix). Rsr also exhibits large inter-annual variability that is associated with ENSO cycles. In the western-central equatorial regions, Rsr has a positive anomaly during El Niño events but a negative anomaly during La Niña events, which is determined by Hm and Hp. The inter-annual variability of Rsr (Fig. 12a) follows closely with that of Hm (Fig. 7b), so Hm is a major factor that determines the structure and variability of Rsr. Rsr is also a function of Hp, so we expect that Rsr can be modulated by Hp, as with Qabs and Qpen. However, the manner in which Rsr is affected by Hp is different from Qabs and Qpen, which is explained below.

As expressed by Rsr = Qabs/(ρ0CpHm), Rsr is determined by both Qabs and Hm. On the one hand, Qabs, which is a function of Hm and Hp, can be one factor that determines the Rsr value. That is, the absorbed solar radiation within the ML (Qabs) directly affects the rate of the ML temperature change, so Rsr and Qabs can have a coherent variation and can be modulated by Hp in a similar fashion. In the western-central region, for example, the positive Hp anomaly during El Niño decreases the absorption of solar radiation within the ML (a corresponding negative Qabs anomaly), which would produce a negative Rsr anomaly with a negative correlation between Hp and Rsr. However, this scenario does not occur. Examining the relationship among the inter-annual variations in Hp (Fig. 7c), Qabs (Fig. 11a), and Rsr (Fig. 12a) indicates that the inter-annual variations in Rsr do not follow those in Qabs. In fact, their variations in Qabs and Rsr tend to be out of phase in the western-central regions during ENSO cycles. This result indicates that Rsr is not determined by Qabs and that the manner in which Qabs is modulated by Hp is not reflected in Rsr. This relationship indicates that Rsr is not affected by Hp in a coherent fashion.

On the other hand, Rsr is closely related to Hm because of their inverse relationship. As such, the manner in which Rsr is modulated by Hp can be complicated, which is different from Qabs. Indeed, another factor (the inverse relationship of Rsr with Hm) must be considered, which can play an important role in determining the nature of the inter-annual variability of Rsr. We provide additional explanations below.

The mathematical expressions in Eq. 3 indicate that Rsr is proportional to Qabs (which increases exponentially with Hm but decreases exponentially with Hp); additionally, Rsr is inversely proportional to Hm (appearing as a denominator in Rsr = Qabs/(ρ0CpHm)). As such, Hm has two effects on Rsr: one is exponential through Qabs and the other is an inverse relationship with Hm. Thus, the manner in which Rsr is affected by Hp (which is explicitly represented through Qabs) is complicated by the effect of inter-annual Hm variations. During an El Niño event, for example, Hp exhibits a positive anomaly in the western-central regions, which decreases the solar radiation within the ML (a decrease in Qabs); at the same time, the ML tends to be anomalously shallow (a negative Hm anomaly, which decreases Qabs). This decreased Qabs field (which is caused by the effect from the positive Hp anomaly) now acts on this anomalously shallow ML, so the effect on Rsr (= Qabs/(ρ0CpHm)) from the reduced Qabs is offset by that from the shoaling ML. The combined net effects of the reduced Qabs component and negative Hm anomaly produce an Rsr value that does not change much. Therefore, Rsr is not modulated by positive Hp anomalies as significantly as Qabs is during El Niño, and the sign of induced changes in Rsr is not consistent with what can be expected from the inter-annual variability of Qabs.

The relationships among these fields are further quantified in Fig. 13, which presents the anomaly correlations between Hp and Qpen and those between Hp and Rsr, respectively. The correlation between Hp and Qabs is exactly the same as that with Qpen but with the opposite sign and is not shown here. Evidently, the extent to which Rsr is correlated with Hp is different from what could be inferred from the manner in which Qabs is modulated by Hp, whereas Hp and Qpen (Qabs) indicate a high positive correlation in the western-central equatorial Pacific. One striking feature of Hp and Rsr is that these terms are weakly positively correlated in the west, exhibiting the opposite sign to what is expected from the effect of Hp on Qabs (i.e., in terms of the relationship with Qabs, Rsr would have a negative correlation with Hp). These results indicate that the extent to which Rsr is affected by Hp is different from Qabs and Qpen. The fact that Rsr is not significantly modulated by Hp has implications for the manner in which SST is modulated by bio-effects.

Fig. 13
figure 13

Correlations during 2005–2015 between inter-annual anomalies of a Hp and Qpen and b Hp and Rsr. The contour interval is 0.2

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3.4 Further attributions to the inter-annual Hp effects

To more clearly understand the bio-effects, further analyses are performed by isolating the contribution from the inter-annual Hp anomalies. The Hp field can be separated into its seasonally varying climatological component (\(\overline{{H_{p} }}\)) and inter-annual component (\(H_{p}^{\prime }\)); their direct effects on the three heating terms are then explicitly quantified by re-calculating these heating terms (say, Qpen) in two manners, namely, with Hp taken as its seasonally varying climatology (denoted as \(Q_{pen} (H_{m} ,\overline{{H_{p} }} )\)) and with Hp considered as varying inter-annually (denoted as \(Q_{pen} (H_{m} ,H_{p} )\)). Correspondingly, the effects of the inter-annual Hp anomalies on Qpen can be estimated by calculating the differences between \(Q_{pen} (H_{m} ,H_{p} )\) and \(Q_{pen} (H_{m} ,\overline{{H_{p} }} )\).

Figure 10b, c display the time-longitude sections along the Equator for Qpen; the horizontal patterns for the Qpen difference during El Niño and La Niña are shown in Figs. 8 and 9. The effects of the inter-annual Hp anomalies on Qpen are mostly pronounced in the western-central equatorial Pacific. High similarities in the spatial patterns and temporal variations are seen between the inter-annual variations in Hp and the Qpen difference. Their relationships indicate that Qpen is significantly modulated by Hp in the western-central regions, where a large variability of Hp exists. The high similarity between Hp and the Qpen difference is consistent with the high positive correlations between the inter-annual variations in Hp and Qpen (Fig. 13).

A similar analysis is performed for Qabs, and the corresponding results are shown in Fig. 11b, c. As defined with Qabs and Qpen, the effects of the inter-annual Hp anomalies on Qabs are the same as for Qpen but with the opposite sign. Good agreement exists between the inter-annual variations in Hp and the Qabs difference, indicating that Qabs is significantly modulated by Hp in the western-central equatorial regions.

Next, we analyze Rsr, in which the effects on Rsr are estimated by taking Hp as its seasonally varying climatology (denoted as \(R_{sr} (H_{m} ,\overline{{H_{p} }} )\)) and varying inter-annually (denoted as \(R_{sr} (H_{m} ,H_{p} )\)). Figure 12b, c show the time-longitude sections along the Equator for inter-annual anomalies of \(R_{sr} (H_{m} ,\overline{{H_{p} }} )\) and the differences. The relationships between Hp and the difference field in Rsr are different from those in Qpen. A large inter-annual anomaly of Hp does not produce a correspondingly large difference in Rsr, indicating that the Hp-induced modulating effect on Rsr is weak. The sign of the Rsr difference is even opposite to what is expected from the inter-annual Hp effect on Qabs. This result is consistent with the low correlation between Hp and Rsr.

Table 1 quantifies the modulating effects of the inter-annual Hp anomalies by calculating the standard deviation of some related variables in the Niño4 region (160°E–150°W, 5°S–5°N). Although the amplitude of the inter-annual variability of Hp is approximately 13% that of Hm in the Niño4 region, its contribution to the inter-annual variability of Qpen is approximately 28%, whereas that to Rsr is only 3%. One interesting feature is that the extent to which Rsr is modulated by the inter-annual Hp variability is different from the extent to which Qpen and Qabs are. Quantitatively, the correlation between the inter-annual anomalies of Hp and Qpen is highly positive, and that between Hp and Rsr is weakly positive (Fig. 13), indicating that Rsr is not modulated as significantly as Qabs and Qpen. The differences in the extent to which these heating terms are modulated by Hp have important implications for the manner in which SST is modulated by bio-effects and the mechanism that is involved.

Table 1 Standard deviation of variables in the Niño4 region (160°E–150°W, 5°S–5°N)
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3.5 Mechanism by which SST is modulated by the OBH feedback

The effects of ocean biology-induced heating on the penetrative solar radiation are realized through the modulations of the three heating terms, which are explicitly related to Hm and Hp. The revealed relationships among these related fields hint at the processes that are involved in the effects of the OBH-related feedback. Two influence pathways are possible by which SST can be modulated by inter-annual variations in Hp in the equatorial Pacific, depending on which heating term is predominantly affected. One is a direct influence pathway by which SST can be modulated through a direct gain or loss in solar radiation within the ML, which is indicated by Qabs and Rsr. If a significant change to Rsr is induced from Qabs in association with inter-annual Hp anomalies, a direct modulating effect on SST is indicated to be important. In this case, the ML is warmed up or cooled down directly by the Hp-induced Qabs contribution. Then, the bio-feedback is considered to be realized primarily through a direct thermal effect on the SST, which should be reflected in Rsr.

Another is an indirect influence pathway, by which Qpen and Qabs are significantly modulated by Hp, but Rsr is not. Then, differential heating is produced by Hp vertically between the ML (Qabs) and subsurface layers (Qpen), which modifies the vertical thermal contrast, stratification and vertical mixing in the upper ocean, thus affecting the SST. In this case, Qpen and Qabs are significantly modulated by Hp but Rsr does not show a coherent change with Qabs, indicating that the direct thermal effect on the SST is not a predominant mechanism for SST modulation by Hp. As such, an indirect dynamical effect on the SST that is associated with Qpen and Qabs is the dominant process. Therefore, the extent to which these heating terms are modulated by Hp can indicate the importance of a direct thermal effect or indirect dynamical effect on the SST (Fig. 14).

Fig. 14
figure 14

Standard deviations for inter-annual anomalies of Qpen (left panels) and Rsr (right panels), which were estimated with the inter-annual Hp effect (a, d) considered and (b, e) excluded, alongside (e, f) their differences. The contour interval is 0.5 W m−2 in a–c, 0.1 °C month−1 in d and e, and 0.01 °C month−1 in f

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Here, one striking feature revealed from observational data is that inter-annual variations in Rsr are not significantly modulated by Hp. That is, Rsr does not exhibit a corresponding positive anomaly, as would be expected from the effect of inter-annual Hp anomalies on Qabs in the western-central regions. The effects of Hp on Rsr cannot explain the modulating effect on the SST because the sign of the modulating effect on Rsr is opposite to what is expected from the inter-annual Hp effect on Qabs. Thus, bio-effects on the SST are not realized through the Rsr term. Other processes that are involved in the effects on Qpen and Qabs must play a dominantly important role in modulating the SST. Indeed, the inter-annual variability of Hp acts to enhance that of Qabs and Qpen during ENSO cycles. The Hp-enhanced anomalies of Qabs and Qpen produce large differential heating between the ML and subsurface layers, which modulates the vertical thermal contrast, stratification and vertical mixing, which represent a dominant indirect ocean dynamical effect on the SST.

4 Summary and discussion

In this paper, observed data were used to characterize the inter-annual variabilities of related physical and biological oceanic fields in the tropical Pacific. In terms of ocean biology, Chl anomalies appeared very quickly and almost simultaneously as a response to ENSO cycles. For example, large inter-annual variations in Chl were concentrated in the western-central equatorial Pacific near the date line: low-Chl-concentration regions extended eastward across the date line during El Niño but retreated westward during La Niña. These inter-annual variations in Chl both represented a response to the ENSO and exhibited feedback onto the ENSO. Here, Chl was considered a major component that affected the vertical penetration of solar radiation in the upper ocean and represented the bio-heating feedback; then, Chl was used to derive the penetration depth (Hp) and quantify the effect on the penetrative solar radiation. In terms of physical factors, Hm was estimated from Argo products. As with Hp, Hm exhibited large inter-annual anomalies in response to ENSO cycles. The incoming shortwave radiation decayed exponentially with depth in the upper ocean, so Hm was a major factor that controlled the penetration of solar radiation in the upper ocean. Thus, Hm and Hp are two factors that affect the distribution of solar radiation between the ML and the underlying subsurface layers.

To quantify the effects from inter-annual Hp anomalies, three heating terms were explicitly expressed as a function of Hp and Hm (Zhang 2015). As previously demonstrated by modeling studies, the biological conditions can affect the mean climate and inter-annual variability over the tropical Pacific through modulating effects on these heating terms. The structural relationships of Hm and Hp with the related heating terms were analyzed to gain insight into Chl-induced heating effects on the ENSO in nature. Furthermore, the revealed relationships from observations could be inferred to determine the processes and mechanisms for ENSO modulations.

The ENSO can induce large perturbations to Hp and Hm, whose inter-annual variations exhibited a well-defined structure across the tropical Pacific. Hp and Hm directly affected the three heating terms (Qpen, Qabs and Rsr), which underwent inter-annual variations that were dominated by ENSO signals. A combined modulating effect from Hm and Hp was seen on Qpen. In the western-central equatorial region, the inter-annual variations in Hp were large and have an out-of-phase relationship with those in Hm during ENSO cycles. The effects on Qpen induced by inter-annual anomalies of Hp tended to be of the same sign as those of Hm, with a high positive correlation between Hp and Qpen. During El Niño, for example, Qpen exhibited a positive anomaly, which can be attributed to the negative Hm anomaly. At this time, Hp was positive. The effect of this positive Hp anomaly caused the positive Qpen anomaly during El Niño to become more positive. During La Niña, Qpen became a negative anomaly in association with a positive Hm anomaly. At the same time, Hp became a negative anomaly, which caused the negative Qpen anomaly to become more negative. So, the inter-annual anomalies of Hp enhanced those of Qpen. In terms of Qabs, the Hp effect was the same as with Qpen but with the opposite sign. That is, in the western-central equatorial Pacific, the effects of the positive Hp anomaly during El Niño made the negative Qabs more negative, whereas those of the negative Hp anomaly made the positive Qabs more positive during La Niña. Thus, the inter-annual Hp anomalies enhanced the differential heating between the ML (Qabs) and subsurface layers (Qpen). In terms of the effect on Rsr, the extent to which Rsr was modulated by Hp was strikingly different from Qpen and Qabs. Although Qabs and Qpen were significantly modulated by Hp, Rsr was not. So, the modulating effects of Hp on the SST were not realized through the Rsr term and a direct thermal effect from Hp through Qabs was not a major process that modulated the SSTs. In contrast, Qpen and Qabs were significantly modulated by Hp in the western-central equatorial Pacific. As such, the Hp-enhanced anomalies of Qpen and Qabs produced large differential heating between the ML and subsurface layers, which modified the vertical thermal contrast, stratification and vertical mixing, thus affecting the SST. Thus, the modulating effects of Hp on the SST can be traced to the Qpen and Qabs terms, and bio-modulations of the ENSO were realized through an indirect dynamical effect on the SST in association with inter-annual Hp anomalies. Furthermore, the structural relationships indicated a negative feedback on the ENSO.

In this study, satellite-based Chl data were combined with Argo data to estimate inter-annual variations in Hp and Hm. Furthermore, the derived Hp and Hm fields were used to reveal their effects on ocean biology-induced heating terms and the modulating effects on the SST. The added values of satellite-Chl observations were clearly demonstrated in association with the use of in situ data. This use of satellite and in situ data elucidated the observed structural relationships among the related fields and processes that were involved in the bio-effects. In particular, an indirect dynamical effect on the SST from the inter-annual Chl variability could explain a negative feedback on the ENSO in the tropical Pacific.

These structural relationships in nature provide an observational basis for validating model simulations (Gnanadesikan and Anderson 2009; Jochum et al. 2010; Kang et al. 2017a; Zhi et al. 2019). For example, in our previous modeling studies, a statistical approach was utilized to derive a model for the inter-annual variations in Hp from satellite observations of Chl and Hp. The observational analyses from this study indicated a good relationship between the inter-annual variations in Chl (Hp) and the SST, so adopting a statistical approach was justified here. Furthermore, the derived Hp statistical model was used for coupled ocean–atmosphere simulations, and the relationships among these fields and modulating effects on the ENSO in modeling studies were consistent with this observation-based analysis. The results from these observation-based analyses support our previous modeling studies using the statistical Hp approach. By combining these observations and previous modeling, the modulating effects of ocean biology-induced heating were clearly demonstrated with a negative feedback on the ENSO. Furthermore, an indirect dynamical effect from inter-annual anomalies of Hp was identified as the predominant mechanism for ENSO modulations. These analyses offer a clear method to trace the influence pathways through which the ENSO is modulated by Chl anomalies, and the methodology that was developed in this study can be used in other models to reveal bio-effects.

In this study, we demonstrated the relationships between inter-annual variability of Chl and ENSO modulations using observational data. A diagnostic analysis is performed to quantify the contribution of interannual Hp anomalies to the three heating terms in association with that of Hm. Note that large inter-annual variability of Chl is located in the western-central equatorial Pacific. As seen in this analysis, the ENSO is a clear source for the Chl variability that is strongly affected by the upwelling and mixing processes in the region. However, the detailed processes that can be responsible for inter-annual variability of Chl have not been analyzed from this observations-based analysis. Also, we present a clear explanation for understanding the feedback onto ENSO induced by inter-annual Chl variability. But, here we only considered the direct impact of Hp on interannual variations of these related heat items using a diagnostic method. In fact, through the modulating effects on stratification and mixing, Hp is expected to have an impact on Hm, and thus there exist interactions between interannual variations in Hp and Hm. These issues cannot be evaluated from this observational analysis, and thus need to be addressed further by modeling studies as shown in (Zhang et al. 2018a, b, 2019).