Solar radiation is the primary energy source for physical, biological and chemical processes in the Earth’s surface system (Allen, 1997). Solar radiation can penetrate through the sea surface and heat a few meters of the upper ocean water column, which thus affects the stratification and mixing in the upper ocean. In addition, solar radiation provides energy for photosynthesis and helps fix carbon dioxide in the presence of chlorophyll in phytoplankton. The ecological processes in the ocean are more complex than those on land, because they are affected by the geofluid dynamic processes in the marine physical environment. For example, the ocean stratification causes the retention of phytoplankton in the upper layer, wherein light is more readily available with inorganic nutrients being limited (Mann and Lazier, 2006). In addition, chlorophyll-a is the main light-absorbing constituent in the ocean (Mobley, 2001), acting to trap more solar radiation in the surface layer, which in turn alters the vertical distribution of light and heat in the ocean (Mann and Lazier, 2006).

In the tropical upper ocean, phytoplankton is usually not light-limited (Shell et al., 2003; Mann and Lazier, 2006; Jochum et al., 2010). In particular, in the eastern equatorial Pacific, as the strong equatorial upwelling brings abundant nutrients, there is a triangular region with higher phytoplankton biomass expressed as the chlorophyll concentration (Lewis et al., 1990; Lin et al., 2007; Khanna et al., 2009). In the equatorial Pacific, the impact of chlorophyll on SST can be further amplified through the ocean-atmosphere interaction and then can influence SST interannual variations in association with the El Niño-Southern Oscillation (ENSO) events (Philander, 1983; Zhang and Gao, 2016; Gao and Zhang, 2023; Gao et al., 2022; Zhang et al., 2020, 2022, 2024). In addition to interactions among the hydrosphere, biosphere and atmosphere, there are also inter-basin linkages between the tropical Pacific and Indian Ocean, which may cause inter-basin effects through the Walker circulation in the atmosphere (Latif and Barnett, 1995) and the Indonesian Throughflow in the ocean (Sprintall et al., 2014). Thus, it is necessary to take into account chlorophyll variability and its effect in the Indo-Pacific region (Murtugudde et al., 2002; Marzeion et al., 2005; Wetzel et al., 2006; Ballabrera-Poy et al., 2007; Lengaigne et al., 2007; Park et al., 2014; Kang et al., 2017; Zhang et al., 2019b; Tian et al., 2021). At present, it is difficult to quantify the effects of ocean biology-induced heating (OBH) on the climate through in situ observations. Fortunately, since the launch of the Coastal Zone Color Scanner in 1979, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), the Moderate-resolution Imaging Spectroradiometer and the Medium Resolution Imaging Spectrometer have been launched successively (Gordon and Morel, 1983; Mann and Lazier, 2006; Valiela, 2015). The development of satellite remote sensing makes it possible to obtain satellite color images of the ocean surface and to retrieve chlorophyll by inverse modeling techniques (Rast et al., 1999). With the mapping of chlorophyll concentrations over large areas, the influence of chlorophyll on shortwave radiation penetration in the vertical direction can be considered in large-scale ocean models.

Numerical models have been developed to study the bio-physical feedback induced by chlorophyll (CHL) in the tropical Pacific. Several types of ocean general circulation models (OGCMs) based on different vertical coordinate systems have been employed to study the ocean biology-induced heating effects, including the most popularly used level OGCMs developed by GFDL/NOAA (Sathyendranath et al., 1991; Sweeney et al., 2005; Park et al., 2014; Kang et al., 2017), and layer ocean model (e.g., Zhang, 2015a; Gao et al., 2020). Historically, CHL-induced heating effects in oceanic models have been differently represented, which evolves with different complexities, including horizontally uniform penetration depth of solar radiation (Wetzel et al., 2006; Ballabrera-Poy et al., 2007; Gnanadesikan and Anderson, 2009), the spatially-varying sea surface CHL from satellite observations (Anderson et al., 2007, 2009; Park et al., 2014), the empirical statistical model for CHL interannual anomalies (Zhang et al., 2009, 2011; Zhang, 2015b), and the interactive oceanic ecological models for horizontally and vertically varying chlorophyll depictions (Wetzel et al., 2006; Lengaigne et al., 2007; Patara et al., 2012; Park et al., 2014; Lim et al., 2018; Zhang et al., 2018, 2019a; Tian et al., 2021; Shi et al., 2023). For example, Zhang et al. (2009) coupled the Gent-Cane ocean general circulation model (OGCM) with an empirical statistical model for the penetration depth ( H p , defined as the inverse of the attenuation coefficient for the penetrative solar radiation), and diagnosed the impact of interannual H p variability on bio-heating. Previous studies indicated that chlorophyll can cause contrasting effects on sea surface temperature (SST) and its interannual variability through direct thermodynamic heating (Sweeney et al., 2005; Löptien et al., 2009; Park et al., 2014; Lim et al., 2018; Gera et al., 2020) or indirect dynamic cooling (Murtugudde et al., 2002; Marzeion et al., 2005; Zhang et al., 2009; Gera et al., 2020), respectively. Currently, the nature of the bio-effects in oceanic and coupled ocean-atmosphere models remains elusive and the underlying processes are controversial. Evidently, the results from previous modeling studies are quite inconsistent and strongly model-dependent in terms of the ocean biology-induced heating effects on mean SST and its variability in the eastern equatorial Pacific ( Table 1 ), underscoring the need for alternative modeling approaches.

The Regional Ocean Modeling System (ROMS) is an ocean model which is based on free-surface, terrain-following and primitive-equations, which is widely utilized among oceanographers (Shchepetkin and McWilliams, 2005; Hedström, 2018). The ROMS offers flexible vertical coordinate systems that incorporate two kinds of vertical transformation equations and a variety of vertical stretching functions. The stretched coordinates allow higher resolution in the areas of interest, such as the upper mixed layer (Song and Haidvogel, 1994; Shchepetkin and McWilliams, 2005). The ROMS includes several vertical mixing parameterization schemes for turbulence closure and modules for ecological, sediment and sea ice applications. Although the ROMS offers various ecosystem sub-models with varying levels of complexity (Haidvogel et al., 2008), the coupling between its physical and ecological sub-models is in one way from the physics to ecological state, in which the scheme of Paulson and Simpson (1977) is adopted for solar radiation penetration parameterization. For example, in current ROMS setting, a simplified empirical formula is adopted to represent this intricate radiation transfer process. The bimodal-exponential function of Paulson and Simpson (1977) is a traditional parameterization scheme to represent the attenuation of shortwave radiation with depth (z, which is defined to be negative below the ocean surface). The formula is expressed as follows:

where I and I 0 denote the shortwave radiation at depth z and the sea surface, respectively. The proportion of I to I 0 represents the decay rate of shortwave radiation. A 1 , A 2 , B 1 and   B 2 are tunable parameters determined empirically by fitting the function to downward irradiance observations according to the water types of Jerlov (1968). The descriptive classification scheme defines five types of water based on the ocean transparency that can be considered as a proxy for chlorophyll concentration. For example, a clear open ocean is classified as Type I (Jerlov, 1968). In such a way, when the water type is given, the decay rate at a particular depth is identical everywhere regardless of the distribution of chlorophyll. Clearly, this parameterization scheme for the penetration of solar radiation in the upper ocean cannot represent the effects of temporal and spatial variations in chlorophyll concentrations; only the impacts of ocean dynamics on ecological processes are taken into account, while the impacts of chlorophyll on the physical fields are not considered. So, there is no feedback from ocean ecological processes to physical processes. Note that Liu et al. (2020) previously tested four shortwave radiation transmission schemes using an idealized one-dimensional ROMS model, and they found that the simulation results with chlorophyll-based schemes exhibit obvious differences in the vertical temperature and upper mixing when compared with the default water-type scheme, with SST differences reaching 1.5–2.0°C. These results clearly indicate the importance of incorporating chlorophyll-based shortwave radiation parameterization schemes into the ROMS. Despite its capabilities and wide applications to regional oceanic problems, the ROMS has not yet been extensively utilized in simulating and understanding large-scale ocean circulations. Previous studies using ROMS-based ecological models have been limited by their shortwave radiation scheme. The ocean biology-induced heating effects have not been adequately explored.

This study addresses this gap by implementing a two-way coupling between the physical and ecological processes within the ROMS, in which the default shortwave penetration parameterization scheme within the ROMS is substituted by a chlorophyll-based scheme. This modeling application to a basinwide Indo-Pacific region allows to represent the CHL-induced heating feedback onto physics, including SST, a field that is important to the climate system. Furthermore, processes underlying the bio-effects are analyzed based on the ROMS simulations for the Indo-Pacific region; the corresponding bio-heating effects are quantified by adopting a diagnostic scheme and separating the shortwave radiation part penetrating out of the base of the mixed layer (ML; Q_pen ), the portion absorbed within the ML (Q_abs ), and the rate of temperature change of the ML (R_sr ), respectively. These dedicated efforts provide a basis for further understanding of the thermodynamic and dynamic effects associated with ocean biology-induced heating within the ROMS. It is expected that the methodology and understanding developed in this study can help explore the CHL-related processes in the ocean and further the interactions with the atmosphere.

A detailed description of the model, experiments and data sources is provided in Section 2. The model results are described in Section 3, in which following the method of Zhang et al. (2011; Zhang, 2015a), three bio-heating terms are analyzed to isolate and quantify the direct OBH effects in association with the mixed layer depth (MLD) and chlorophyll. A brief discussion and conclusion are given in Sections 4 and 5. Table 2 presents the nomenclature and abbreviation adopted in this paper.

In this study, ocean-only experiments are performed using a basin-scale three-dimensional ocean circulation model and a simple ecological model. The former is the ROMS provided by the ROMS/Terrain-following Ocean Modeling System Group (https://www.myroms.org/). The latter is the Nutrient-Phytoplankton-Zooplankton-Detritus Model with Iron Limitation on Phytoplankton Growth (hereinafter referred to as the NPZD-IRON) developed by Fiechter et al. (2009). Some details are presented in this section.

The ROMS employs a stretched terrain-following coordinate system, which not only has the benefit of a σ-coordinate system, but also enables further refinement near the surface or the bottom boundary regions. The ROMS, as a state-of-the-art ocean dynamical model that allows higher resolution and better adaptability to coastal boundaries, has been extensively utilized by the scientific community, but it is often limited to regional-scale applications. Here, we apply the ROMS to a basinwide tropical Indo-Pacific Ocean to achieve a two-way coupling between its physical and ecological components, which can represent interactive impacts of the marine ecological fields on the physical fields.

As stated in the introduction, bio-modeling in the tropical Pacific with differently formulated OGCMs is clearly needed to explore interactions between ocean biogeochemistry and the climate system in the tropical Pacific. The ROMS supplies several ecological modules, including the NPZD-IRON ecological model, which can be activated in modeling experiments. Due to the simple variable selections of the ecological model, it is economical in terms of computations. It should be noted that the coupling between the ROMS and ecological model in its default setting is still one-way from physical side to ecological side, not the other way around. Thus, in most previous studies, ecological models based on the ROMS are often used to study marine ecological dynamics. In this study, the coupling between the ROMS and the NPZD-IRON has been expanded from one-way to two-way by modifying the default shortwave penetration parameterization to reflect the influences of the ocean ecological fields on the physical fields.

In order to simplify the conversion of phytoplankton biomass into chlorophyll concentration, this study still uses a fixed C:Chl ratio; the NPZD-IRON model used in this paper is still at a lower trophic level with only two limiting nutrients and one size class for phytoplankton and zooplankton (Fiechter et al., 2009). As noted by Wang et al. (2009), the C:Chl ratio can vary with the irradiance, temperature, nitrate and iron concentrations. Since the ROMS provides a variety of ecological modules, other more complex ecological models can be selected and tested in the future according to actual needs, including a way to represent a varying C: Chl ratio. Nevertheless, results from this modeling activity indicate that the model is sufficiently realistic for qualitative investigation since it can well reproduce the spatial pattern of chlorophyll, such as the triangular high-value region in the eastern Pacific. The ROMS-based ocean physical-ecological coupled model provides an alternative flexible vertical layering method for successful applications, and its results can be cross-validated with other ocean models (Nakamoto et al., 2001; Murtugudde et al., 2002; Manizza, 2005; Lin et al., 2007; Löptien et al., 2009; Zhang, 2015b).

Additionally, this study analyzes three heating terms that are related to chlorophyll and the MLD. It is generally recognized that chlorophyll absorbs solar radiation in seawater, but its impact on the ocean remains intricate and is not fully comprehended. For instance, the chlorophyll absorbs solar radiation and heats seawater directly. Nonetheless, the SST variation induced by the chlorophyll does not always increase (Nakamoto et al., 2001; Manizza, 2005; Anderson et al., 2007; Lin et al., 2007, 2008; Anderson et al., 2009; Gnanadesikan and Anderson, 2009; Löptien et al., 2009; Jochum et al., 2010; Park et al., 2014). To better understand the CHL effects on the upper ocean, Ballabrera-Poy et al. (2007) performed a Taylor expansion of the equation for the absorbed radiation heat budget in the mixed layer; when considering only the first term, they pointed out that the sign of Q_abs is determined by the relative amplitude of the direct term (variation in the transparency) and indirect term (variation in the MLD), respectively. By analyzing the heating terms associated with the MLD, it is feasible to isolate and quantitatively diagnose the direct OBH effects on marine physical fields.

Moreover, the ED is analyzed in this study to represent the bio-effects compared with the penetration depth (H_p; Zhang et al., 2011). The physical meaning of the ED is more apparent than the penetration depth (also called e-fold depth, a mathematically derived concept). Below the euphotic layer, there is little shortwave radiation, and phytoplankton is difficult to flourish. The relative positions of the euphotic layer and the mixed layer in the vertical direction are important factor affecting the variations in the related bio-heating terms and their effects on ocean thermodynamics and dynamics.

In this study, a two-way coupling between ocean physical-ecological models is constructed within the ROMS, providing a useful numerical modeling tool to represent chlorophyll-induced heating effects and the interactions between ocean physical and biogeochemistry processes in the tropical Indo-Pacific region at the basin scale. The comparison between the model output and observation shows that the model is capable of reproducing the spatial structure and temporal variations in ocean physical and ecological fields. For example, the simulated variations of SST and the MLD are consistent with observations. In addition, sea surface chlorophyll anomalies are out-of-phase with SST anomalies during the ENSO events, which reflects a coherent relationship between ecological and physical fields. These outcomes indicate that the model can well reproduce the spatial pattern of chlorophyll in the eastern Pacific.

Processes underlying the effects are analyzed. Three heating terms are calculated to quantitatively diagnose the direct heating effects induced by ocean biology. The results show that the mixed layer depth plays a dominant role in the allocation of solar radiation between the mixed layer and subsurface. In addition, the ED also has a modulation effect on penetrative solar radiation, especially in the central-western equatorial Pacific, where the interannual variability of the ED exhibits a comparable amplitude to that of the MLD. This modulation is asymmetric and more pronounced during El Niño events relative to La Niña events. As the chlorophyll decreases, the euphotic layer deepens and its maximum depth lies below the mixed layer. The shortwave radiation penetrating below the mixed layer increases significantly. In contrast, the structure and variation of R s r are less affected by the ED, and are dominated by the MLD. These findings are consistent with those based on observational analyses (Zhang et al., 2019b).

There are obvious discrepancies between the simulated and observed chlorophyll fields in the tropical Pacific. For example, the simulated annual-mean chlorophyll is relatively higher than the observed in the eastern equatorial Pacific, which is due to the overestimation of upwelling and nutrients. This can also result from the simplicity of the components and marine food web in the ecological model used in this study. Since the ROMS also provides a variety of ecological modules, other more complex ecological submodels can be selected and tested to better represent CHL fields and explore its effects on the climate system in the tropical Pacific.

More numerical experiments based on this model are under way to better represent and understand how chlorophyll influences the physical environment, including the climate system over the tropical Pacific. For example, it has been planned to integrate this ROMS-based ocean model with a statistical atmospheric model to form a hybrid coupled model (HCM), which can achieve a multi-way coupling not only between its physical and ecological model components, but also between the atmosphere and ocean, representing interactive impacts of the marine ecological field on the physical field; such a constructed HCM can have a variety of applications. For instance, previous research suggested that the ocean-atmosphere interactions tend to increase the uncertainty in representing these bio-effects. So, the model can be used to examine the modulating impacts of chlorophyll interannual variability on ENSO in the tropical Pacific; it can be used to quantify how the ocean-atmosphere coupling intensity influences the chlorophyll-induced SST variation in the tropical Pacific, and so on. Additionally, the model covers both the Indian Ocean and the Pacific Ocean, and further research should be undertaken to find out the remote inter-basin effects from the Indian Ocean on conditions in the Pacific basin. Also, comparisons with other modeling results can be made with different model configurations (Zeng et al., 1991; Zhang and Endoh,1992; Timmerman and Jin, 2002; Lin et al., 2011).