**Impact of Solar Radiation Data and Its Absorption Schemes on Ocean Model Simulations**

Goro Yamanaka, Hiroshi Ishizaki, Hiroyuki Tsujino, Hideyuki Nakano and Mikitoshi Hirabara *Meteorological Research Institute, Japan Meteorological Agency Japan* 

#### **1. Introduction**

24 Solar radiation

76 Solar Radiation

[7] Cruz-González I., Avila R. & Tapia M., eds, (2003), Rev. Mex. AA (SC), 19. [8] Cruz-González I., Echevarría J. & Hiriart D., eds, (2007), Rev. Mex. AA (SC), 31

[9] Schöck M. et al., (2009), Publ. Astr. Soc. Pac., 121, 384

[10] Tapia M., (2003), Rev. Mex. AA (SC), 19, 75 [11] Hiriart D. et al., (1997), Rev. Mex. AA, 33, 59 [12] Hiriart D. et al., (2003), Rev. Mex. AA (SC), 19, 90 [13] Otárola A. et al., (2009), Rev. Mex. AA, 45, 161 [14] Otárola A. et al., (2010), Publ. Astr. Soc. Pac., 122, 470

> Since absorption of solar radiation plays a major role in heating the upper ocean layers, it is essential for modeling physical, chemical and biological processes (e.g., ocean general circulation or marine carbon cycle). In order to simulate the upper ocean thermal structures as realistically as possible, an ocean general circulation model (OGCM) requires accurate solar radiation data, used as the surface boundary condition. In this sense, it is important to recognize the quality of the solar radiation data being expected or suitable for OGCMs beforehand. The appropriate choice of absorption schemes of solar radiation is also important for ocean modeling in the upper ocean. The absorption of solar radiation is greatly affected by many factors, such as the wavelength of sunlight, the zenith angle and ocean optical properties in the ocean interior. Many absorption schemes have attempted to mimic these processes, but the impact of those schemes on the upper ocean thermal structures is not yet fully understood.

> The aim of this study is to determine the importance of solar radiation in ocean modeling. In particular, we examine the impact of both prescribed solar radiation data and its absorption schemes on OGCM simulations. The knowledge obtained here is expected to be useful for ocean modeling studies, as well as for understanding the upper ocean thermal structure.

> This article is organized as follows. Section 2 examines the impact of solar radiation flux on ocean model simulation, focusing on discrepancies between simulated and observed sea surface temperature (SST) variations. Yamanaka (2008) discussed such discrepancies over the tropical Indian Ocean, whereas this study deals extensively with discrepancies over the tropical Indo-Pacific Ocean. Section 3 introduces three types of absorption schemes in solar radiation into an ocean model and examines the impact of those schemes on ocean model simulation. Section 4 summarizes this study.

#### **2. Impact of incident solar radiation data on an ocean model simulation**

#### **2.1 Brief introduction**

Indian Ocean SSTs have notably increased since the late 20th century (Lau & Weng, 1999). Figure 1 clearly shows that the positive SST anomaly has dominated especially after the mid-1980s.

Fig. 1. Time series of the SST anomaly [◦C] averaged in the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E). The SST data set is based on COBE-SST (Ishii et al., 2005). The red (blue) shaded area denotes positive (negative) anomalies. The base period is from 1971 to 2000.

The warming of the tropical Indian Ocean is likely caused by climate variations, but may also, in turn, trigger some impacts on surrounding regions. Some studies using an atmospheric general circulation model (AGCM) with the prescribed SST suggest that the increasing trend in Indian Ocean SSTs can impact the climate. For example, Hoerling et al. (2004) indicated that local increases in precipitation associated with the warming of the Indian Ocean resulted in a remote response to the mid and high latitudes through the release of latent heat, and contributed to an increased trend of the North Atlantic Oscillation (NAO). Also, the warming of the Indian Ocean enhances the anti-cyclonic circulation anomaly at the lower level of the troposphere over the Philippines during the mature phase of El Nino (Watanabe & Jin, 2002), which has a major impact on the East Asian climate (Wang et al., 2000).

In order to understand the warming mechanism of the Indian Ocean, it is necessary to clarify the observation-based surface heat balance over the Indian Ocean. However, due to lack of long-term observation, many studies used OGCMs to diagnose the surface heat balance (e.g., Du et al., 2005; Murtugudde and Busalacchi, 1999).

The importance of the OGCM study is to know to what extent variations of the Indian Ocean are simulated by the model. Figures 2a and 2d show the anomaly correlation between observed and simulated SSTs, which is one of the means by which the model's performance may be determined. It is found that the anomaly correlation over the tropical Indian Ocean is below 0.6 and is less than that in other areas, such as the tropical Pacific and the mid and high latitudes. Poor simulation of the tropical Indian Ocean makes it difficult to analyze the surface heat balance over that area. However, the cause of this poor simulation is not yet fully understood.

This section aims to investigate the cause of the poor simulation, basically following Yamanaka (2008) and extensively looking at the tropical Indo-Pacific Ocean.

Fig. 2. (a) Annual mean anomaly correlation between the observed and the simulated SST anomalies for CTL. The statistical period is from 1971 to 2000. (b) Time series of the observed (red) and simulated (black) SST anomalies [◦C] averaged in the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) for CTL. The base period is from 1971 to 2000. (c) Time series of sea surface heat flux anomalies [W m−2] averaged in the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) for CTL. Lines denote net surface heat flux (red), solar radiation (green), long wave radiation (yellow), sensible heat flux (aqua), and latent heat flux (blue). The base period is from 1971 to 2000. (d)-(f) Same as (a)-(c) but for JRA. The base period is from 1979 to 2004. (g)-(i) Same as (a)-(c) but for CSR.

#### **2.2 Model and methodology**

2 Will-be-set-by-IN-TECH

Fig. 1. Time series of the SST anomaly [◦C] averaged in the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E). The SST data set is based on COBE-SST (Ishii et al., 2005). The red (blue) shaded

The warming of the tropical Indian Ocean is likely caused by climate variations, but may also, in turn, trigger some impacts on surrounding regions. Some studies using an atmospheric general circulation model (AGCM) with the prescribed SST suggest that the increasing trend in Indian Ocean SSTs can impact the climate. For example, Hoerling et al. (2004) indicated that local increases in precipitation associated with the warming of the Indian Ocean resulted in a remote response to the mid and high latitudes through the release of latent heat, and contributed to an increased trend of the North Atlantic Oscillation (NAO). Also, the warming of the Indian Ocean enhances the anti-cyclonic circulation anomaly at the lower level of the troposphere over the Philippines during the mature phase of El Nino (Watanabe & Jin, 2002),

In order to understand the warming mechanism of the Indian Ocean, it is necessary to clarify the observation-based surface heat balance over the Indian Ocean. However, due to lack of long-term observation, many studies used OGCMs to diagnose the surface heat balance (e.g.,

The importance of the OGCM study is to know to what extent variations of the Indian Ocean are simulated by the model. Figures 2a and 2d show the anomaly correlation between observed and simulated SSTs, which is one of the means by which the model's performance may be determined. It is found that the anomaly correlation over the tropical Indian Ocean is below 0.6 and is less than that in other areas, such as the tropical Pacific and the mid and high latitudes. Poor simulation of the tropical Indian Ocean makes it difficult to analyze the surface heat balance over that area. However, the cause of this poor simulation is not yet fully

This section aims to investigate the cause of the poor simulation, basically following

Yamanaka (2008) and extensively looking at the tropical Indo-Pacific Ocean.

area denotes positive (negative) anomalies. The base period is from 1971 to 2000.

which has a major impact on the East Asian climate (Wang et al., 2000).

Du et al., 2005; Murtugudde and Busalacchi, 1999).

understood.

We used a version of the Meteorological Research Institute community ocean model (MRI.COM) (Ishikawa et al., 2005), which is a z-coordinate primitive-equation model. The model domain is near global, from 75◦S to 75◦N. The horizontal resolution is 1◦ in longitude and 1◦ in latitude (0.3◦ near equator). The model has 50 vertical levels, with 24 levels in the top 200m.

Two sets of daily atmospheric reanalysis data are used as the surface boundary condition: ECMWF 40-year reanalysis data (hereafter ERA-40) (Uppala et al., 2005) from 1960 to 2001, and Japan Meteorological Agency 25-year reanalysis data (hereafter JRA-25) (Onogi et al., 2007) from 1979 to 2004. We used the bulk formula for the surface fluxes by Kara et al. (2000). After the model was integrated for 102 years as spin-up, three experiments were conducted with different interannual atmospheric forcing data. In CTL, the model was driven by atmospheric variables derived from ERA-40; in JRA, the model was driven by those derived from JRA-25. In CSR, the atmospheric forcing was the same as that in CTL, except that solar radiation data included only seasonal variations (no interannual or longer variations).

For comparison, we used the COBE-SST data set of in-situ measurements of SST (Ishii et al., 2005). The reanalyzed solar radiation data derived from ERA-40 and JRA-25 reanalysis were compared with satellite-based estimates of solar radiation: International Satellite Cloud Climatology Project (ISCCP) solar radiation data derived from the Common Ocean-ice Reference Experiment (hereafter CORE/ISCCP) (Large & Yeager, 2004). Also, the reanalyzed precipitation data derived from ERA-40 and JRA-25 were compared with two observation-based estimates of precipitation: Climate Prediction Center (CPC) Merged Analysis of Precipitation combined with NCEP/NCAR R1 reanalysis (hereafter CMAP) (Xie & Arkin, 1996), and Global Precipitation Climate Project Version 2 (hereafter GPCP) (Adler et al., 2003).

All data was converted to monthly means before further analysis. Monthly mean data for ERA-40 surface flux was produced using the daily mean data based on 36 hour forecast data at each 12UTC initials.

#### **2.3 Results**

#### **2.3.1 The simulated Indian Ocean with the prescribed solar radiation**

Figure 2b shows the time evolution of simulated SST anomalies over the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) for CTL. The model was successful in simulating the interannual SST variation of 4 to 5 years associated with ENSO, but failed to capture the long-term warming trend found in the observed SSTs. For example, the simulated SST anomaly was slightly higher than the observed one in the 1960s, whereas it was substantially lower than observed after the late 1990s, indicating a cooling bias. A similar tendency was also found in JRA (Fig. 2e), where the simulated SST anomaly in the Indian Ocean has been gradually cooler than the observed one since the late 1980s, and the difference has increased since 2000. This result implies that the poor simulation of the Indian Ocean SSTs in both experiments is due to the cooling bias, especially in the late 1990s.

Cooling of the model Indian Ocean after 1990 was observed not only at the surface, but also below the surface. Figure 3a shows the mixed layer change between 10 years in CTL. The deepening of the mixed layer depth (MLD) was found to be wide in the tropical Indian Ocean. Figures 3b and 3c show vertical profiles of temperature and potential density at the equatorial Indian Ocean (EQ, 90◦E) between January 1990 and January 2000 in CTL. Temperature decreased up to about 60 m depth, and the MLD increased to 100 m depth during that ten-year period. This simulated cooling trend in the upper ocean differs from the trend observed by Levitus et al. (2005), in which significant warming near the surface accompanied cooling in the upper thermocline (Han et al., 2006). The deepening of the mixed layer may have altered the surface heat balance of the Indian Ocean in the model.

Next, we examine surface fluxes used as the surface forcing for the model. Figure 2c shows the time duration of each component (net flux, solar radiation, long wave radiation, sensible heat flux, and latent heat flux) of the model surface flux anomalies. It is noted that the solar radiation anomaly (green line) in CTL exhibits a significant decreasing trend. From the 1960s to early 1970s, the solar radiation anomaly was positive, corresponding to the simulated warmer SST anomaly. After the mid-1990s, the negative solar radiation anomaly became

derived from JRA-25. In CSR, the atmospheric forcing was the same as that in CTL, except that solar radiation data included only seasonal variations (no interannual or longer variations). For comparison, we used the COBE-SST data set of in-situ measurements of SST (Ishii et al., 2005). The reanalyzed solar radiation data derived from ERA-40 and JRA-25 reanalysis were compared with satellite-based estimates of solar radiation: International Satellite Cloud Climatology Project (ISCCP) solar radiation data derived from the Common Ocean-ice Reference Experiment (hereafter CORE/ISCCP) (Large & Yeager, 2004). Also, the reanalyzed precipitation data derived from ERA-40 and JRA-25 were compared with two observation-based estimates of precipitation: Climate Prediction Center (CPC) Merged Analysis of Precipitation combined with NCEP/NCAR R1 reanalysis (hereafter CMAP) (Xie & Arkin, 1996), and Global Precipitation Climate Project Version 2 (hereafter GPCP) (Adler et

All data was converted to monthly means before further analysis. Monthly mean data for ERA-40 surface flux was produced using the daily mean data based on 36 hour forecast data

Figure 2b shows the time evolution of simulated SST anomalies over the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) for CTL. The model was successful in simulating the interannual SST variation of 4 to 5 years associated with ENSO, but failed to capture the long-term warming trend found in the observed SSTs. For example, the simulated SST anomaly was slightly higher than the observed one in the 1960s, whereas it was substantially lower than observed after the late 1990s, indicating a cooling bias. A similar tendency was also found in JRA (Fig. 2e), where the simulated SST anomaly in the Indian Ocean has been gradually cooler than the observed one since the late 1980s, and the difference has increased since 2000. This result implies that the poor simulation of the Indian Ocean SSTs in both experiments is due to the

Cooling of the model Indian Ocean after 1990 was observed not only at the surface, but also below the surface. Figure 3a shows the mixed layer change between 10 years in CTL. The deepening of the mixed layer depth (MLD) was found to be wide in the tropical Indian Ocean. Figures 3b and 3c show vertical profiles of temperature and potential density at the equatorial Indian Ocean (EQ, 90◦E) between January 1990 and January 2000 in CTL. Temperature decreased up to about 60 m depth, and the MLD increased to 100 m depth during that ten-year period. This simulated cooling trend in the upper ocean differs from the trend observed by Levitus et al. (2005), in which significant warming near the surface accompanied cooling in the upper thermocline (Han et al., 2006). The deepening of the mixed layer may

Next, we examine surface fluxes used as the surface forcing for the model. Figure 2c shows the time duration of each component (net flux, solar radiation, long wave radiation, sensible heat flux, and latent heat flux) of the model surface flux anomalies. It is noted that the solar radiation anomaly (green line) in CTL exhibits a significant decreasing trend. From the 1960s to early 1970s, the solar radiation anomaly was positive, corresponding to the simulated warmer SST anomaly. After the mid-1990s, the negative solar radiation anomaly became

**2.3.1 The simulated Indian Ocean with the prescribed solar radiation**

have altered the surface heat balance of the Indian Ocean in the model.

al., 2003).

**2.3 Results**

at each 12UTC initials.

cooling bias, especially in the late 1990s.

Fig. 3. (a) Mixed layer depth difference [m] between the 1996-2000 mean and the 1986-1990 mean. The shaded area denotes where the difference is positive. (b) Vertical profile of temperature [◦C] in the equatorial Indian Ocean in CTL on January 1990 (black) and on January 2000 (green). (c) Same as (b) but for potential density [*σθ* ].

dominant, corresponding to the cold bias of the model in this period. Sensible and latent heat fluxes partly weakened the decreasing trend caused by solar radiation because they were restored to the observed atmospheric variables based on the bulk formula. However, a decreasing trend remained in the simulated SSTs. A similar decreasing trend in the solar radiation anomaly was also found in JRA (Fig. 2f).

In order to clarify the role of the reanalyzed solar radiation data on the cooling bias in the simulated SSTs, an additional experiment (CSR) was carried out, where the atmospheric forcing was the same as at CTL except that the daily-mean climatological solar radiation data was used. Figure 2h shows that the simulated SSTs in CSR agree better with the observed SSTs (e.g., improvement in both the warming bias in the 1960s and the cooling bias in the late 1990s, compared to those in CTL). Also, the warming of the Indian Ocean in the 1990s was roughly captured in CSR even under climatological solar radiation forcing. According to the sea surface flux anomalies (Fig. 2i), the variability of the net heat flux was controlled by long wave radiation on a longer time scale, as well as by latent heat flux on an interannual time

scale. These results suggested that increases in downward long wave radiation contributed to the simulated warming of the Indian Ocean in the 1990s in CSR.

Improvement of the bias in the simulated SSTs of the Indian Ocean was expected to result in better performance of the simulated SSTs. Figure 2g shows the annual mean anomaly correlation between the observed and the simulated SST anomalies in CSR. It was found that removal of the variations of the reanalyzed solar radiation on an interannual or longer timescale improved the simulated SST variability, especially in the tropical Indian Ocean. The SST skill increased by 0.1 to 0.3 in this region, compared to that of CTL. In the central to eastern equatorial Pacific, however, no significant change in SST variability was observed between CTL and CSR. It is suggested that the SST variability in the central to eastern equatorial Pacific is determined mainly by wind stress, rather than solar radiation. However, in the mid and high latitudes, the SST skill is significantly reduced in CSR, implying that SST variability in these regions is determined by variation in solar radiation.

These results strongly suggest that the cooling of simulated Indian Ocean SSTs is primarily caused by the atmospheric reanalysis data used as the surface boundary condition. Next, we examine why the atmospheric reanalysis products display decreasing trends in solar radiation.

Fig. 4. Time series of 13-month running mean precipitation anomalies [mm/day] averaged over (a) the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) and (b) the western tropical Pacific (10◦S-10◦N, 130◦E-180◦) for CMAP (red), GPCP (acua), ERA-40 (green), and JRA-25 (blue).

#### **2.3.2 Spurious trends included in atmospheric reanalysis data**

6 Will-be-set-by-IN-TECH

scale. These results suggested that increases in downward long wave radiation contributed to

Improvement of the bias in the simulated SSTs of the Indian Ocean was expected to result in better performance of the simulated SSTs. Figure 2g shows the annual mean anomaly correlation between the observed and the simulated SST anomalies in CSR. It was found that removal of the variations of the reanalyzed solar radiation on an interannual or longer timescale improved the simulated SST variability, especially in the tropical Indian Ocean. The SST skill increased by 0.1 to 0.3 in this region, compared to that of CTL. In the central to eastern equatorial Pacific, however, no significant change in SST variability was observed between CTL and CSR. It is suggested that the SST variability in the central to eastern equatorial Pacific is determined mainly by wind stress, rather than solar radiation. However, in the mid and high latitudes, the SST skill is significantly reduced in CSR, implying that SST variability in

These results strongly suggest that the cooling of simulated Indian Ocean SSTs is primarily caused by the atmospheric reanalysis data used as the surface boundary condition. Next, we examine why the atmospheric reanalysis products display decreasing trends in solar

Fig. 4. Time series of 13-month running mean precipitation anomalies [mm/day] averaged over (a) the tropical Indian Ocean (10◦S-10◦N, 40◦E-100◦E) and (b) the western tropical Pacific (10◦S-10◦N, 130◦E-180◦) for CMAP (red), GPCP (acua), ERA-40 (green), and JRA-25

the simulated warming of the Indian Ocean in the 1990s in CSR.

these regions is determined by variation in solar radiation.

radiation.

(blue).

Figure 4 shows a time series of precipitation anomalies averaged over the tropical Indian Ocean and the western tropical Pacific, based on the reanalysis data with the CMAP and GPCP data sets as reference. Over the tropical Indian Ocean, ERA-40 precipitation (green line) is generally greater than the observed precipitation, and an increasing trend is clearly seen since 1979. JRA-25 precipitation (blue line) also exhibits a similar increasing trend, though not as great as that of the ERA-40 precipitation. On the other hand, the observed precipitations in CMAP and GPCP exhibit no significant increasing trend, and also may be the observed cloud amount. In contrast, over the western tropical Pacific, the observed precipitation and the JRA-25 precipitations show a slight decreasing trend, though the ERA-40 precipitation indicates no significant trend.

Fig. 5. Average trends from 1979 to 2001 in the reanalysis products (ERA-40 and JRA-25) and observed data (CORE/ISCCP, CMAP and GPCP) for solar radiation (upper), precipitation (middle), and the prescribed SST for the reanalyses (lower) over the Indian Ocean. The contour interval is 0.5 Wm−2/year for solar radiation, 0.1 mm day−1/year for precipitation, and 0.01 ◦C/year for SST. The red (blue) shaded areas denote where the rate of change is positive (negative) with statistical significance.

Figure 5 shows average trends during the period 1979 to 2001 in the atmospheric reanalysis products (ERA-40 and JRA-25) with the prescribed SSTs for the reanalyses, in addition to CORE/ISCCP solar radiation and CMAP precipitation. Over the tropical Indian Ocean, the

reanalysis products exhibit decreasing trends in solar radiation, and their spatial patterns are almost the reverse of the precipitation patterns. This feature is generally found in all the reanalysis products, though it seems more pronounced in JRA-25 and ERA-40 than in NCEP/NCAR 40-year reanalysis (Kalnay et al., 1996) and NCEP-DOE AMIP-II reanalysis (Kanamitsu et al., 2002) as described in Yamanaka (2008). The increasing trend in precipitation roughly corresponds to the increasing trend in SSTs prescribed as the lower boundary condition for the reanalyses. Hence, the decrease in solar radiation may be associated with increase in precipitation directly over the region of the most rapidly warming SST. In contrast, no increasing trend in solar radiation over the Indian Ocean was observed in the CORE/ISCCP data. Also, the CMAP data showed no increasing trend in precipitation nor a decreasing trend over the southern Indian Ocean. Over the western tropical Pacific, the situation was almost the same; the area with a slightly decreasing trend in precipitation or a slightly increasing trend in solar radiation corresponds to the cooling SST region, suggesting a linkage between the trends in atmospheric reanalysis and the SST.

Several problems in the atmospheric reanalyses may have caused this spurious increasing trend in precipitation over the tropical Indian Ocean. One problem may arise from bias in the assimilation, for example, ERA-40 has rainfall problems over tropical oceans from the early 1990s, associated with the bias of satellite radiance corrupted by the Pinatubo eruption (Dee et al., 2008), and JRA-25 has major discontinuous changes associated with transition from TOVS to ATOVS in November 1998 (Tsutsui & Kadokura, 2008). Another problem may come from the bias in the model. Over the tropical oceans, where in-situ observations are infrequent and sparse, a reanalysis dataset would be equivalent to AGCM outputs where SST is given as the lower boundary condition (Arakawa & Kitoh, 2004). Hence, responding to the warming of the Indian Ocean, AGCM tends to enhance convective activities and thus to increase precipitation and cloud amounts.

As a result, the decrease in the solar radiation caused a cooling trend of the simulated SSTs in the Indian Ocean, which is inconsistent with the observed SSTs (Fig. 1). This is supported by the fact that the area with a relatively low skill of simulated SSTs in the tropical Indian Ocean approximately corresponds to that with a decreasing trend in solar radiation (Fig. 2a).

#### **2.3.3 Discussion**

We found that the poor simulation of the Indian Ocean SST was due to the atmospheric reanalysis data (ERA-40 and JRA-25) used as the surface boundary condition for OGCM, which included decreasing trends in solar radiation there. This decreasing trend in solar radiation was related to the increasing trend in precipitation over the Indian Ocean, which was partially as a response to the local warming of the SSTs.

The spurious trends in the atmospheric reanalysis products constitute a crucial problem for long-term ocean modeling studies, because surface flux data based on the atmospheric reanalysis products are widely used as the surface boundary conditions for OGCMs. Thus, caution is necessary when using atmospheric reanalysis data as the surface boundary conditions for OGCMs. One approach to avoid the unrealistic cooling of the model Indian Ocean is to use the CORE/ISCCP solar radiation. The CORE/ISCCP solar radiation data do not exhibit significant decreasing trend over the tropical Indian Ocean (Fig. 5), although it should be noted that the CORE/ISCCP solar radiation data included no interannual variations before mid-1983, because of the limited availability of satellite data. In fact, a recent study demonstrated that the ocean model driven by the CORE forcing (Large & Yeager, 2009) reasonably simulated long-term variations in the tropical Indian Ocean (Tsujino et al., 2011).

Several studies suggest that there may be no increase or even decrease in precipitation over the Indian Ocean. Copsey et al. (2006) reported a rise in sea surface pressure, as a proxy for precipitation, over the Indian Ocean between 1950 and 1996. Deser & Phillips (2006) concluded that there was no significant increase in precipitation over the Indian Ocean, based on analysis of the cloud amount and wind convergence over the ocean. Norris (2005) suggested a negative trend in upper level cloud cover in the equatorial Indian Ocean between 1952 and 1997. Further study based on observation is needed to clarify the long-term trend of precipitation in the Indian Ocean.

#### **3. Impact of absorption schemes in solar radiation on an ocean model simulation**

#### **3.1 Brief introduction**

8 Will-be-set-by-IN-TECH

reanalysis products exhibit decreasing trends in solar radiation, and their spatial patterns are almost the reverse of the precipitation patterns. This feature is generally found in all the reanalysis products, though it seems more pronounced in JRA-25 and ERA-40 than in NCEP/NCAR 40-year reanalysis (Kalnay et al., 1996) and NCEP-DOE AMIP-II reanalysis (Kanamitsu et al., 2002) as described in Yamanaka (2008). The increasing trend in precipitation roughly corresponds to the increasing trend in SSTs prescribed as the lower boundary condition for the reanalyses. Hence, the decrease in solar radiation may be associated with increase in precipitation directly over the region of the most rapidly warming SST. In contrast, no increasing trend in solar radiation over the Indian Ocean was observed in the CORE/ISCCP data. Also, the CMAP data showed no increasing trend in precipitation nor a decreasing trend over the southern Indian Ocean. Over the western tropical Pacific, the situation was almost the same; the area with a slightly decreasing trend in precipitation or a slightly increasing trend in solar radiation corresponds to the cooling SST region, suggesting

Several problems in the atmospheric reanalyses may have caused this spurious increasing trend in precipitation over the tropical Indian Ocean. One problem may arise from bias in the assimilation, for example, ERA-40 has rainfall problems over tropical oceans from the early 1990s, associated with the bias of satellite radiance corrupted by the Pinatubo eruption (Dee et al., 2008), and JRA-25 has major discontinuous changes associated with transition from TOVS to ATOVS in November 1998 (Tsutsui & Kadokura, 2008). Another problem may come from the bias in the model. Over the tropical oceans, where in-situ observations are infrequent and sparse, a reanalysis dataset would be equivalent to AGCM outputs where SST is given as the lower boundary condition (Arakawa & Kitoh, 2004). Hence, responding to the warming of the Indian Ocean, AGCM tends to enhance convective activities and thus to increase precipitation

As a result, the decrease in the solar radiation caused a cooling trend of the simulated SSTs in the Indian Ocean, which is inconsistent with the observed SSTs (Fig. 1). This is supported by the fact that the area with a relatively low skill of simulated SSTs in the tropical Indian Ocean approximately corresponds to that with a decreasing trend in solar radiation (Fig. 2a).

We found that the poor simulation of the Indian Ocean SST was due to the atmospheric reanalysis data (ERA-40 and JRA-25) used as the surface boundary condition for OGCM, which included decreasing trends in solar radiation there. This decreasing trend in solar radiation was related to the increasing trend in precipitation over the Indian Ocean, which

The spurious trends in the atmospheric reanalysis products constitute a crucial problem for long-term ocean modeling studies, because surface flux data based on the atmospheric reanalysis products are widely used as the surface boundary conditions for OGCMs. Thus, caution is necessary when using atmospheric reanalysis data as the surface boundary conditions for OGCMs. One approach to avoid the unrealistic cooling of the model Indian Ocean is to use the CORE/ISCCP solar radiation. The CORE/ISCCP solar radiation data do not exhibit significant decreasing trend over the tropical Indian Ocean (Fig. 5), although it should be noted that the CORE/ISCCP solar radiation data included no interannual variations before mid-1983, because of the limited availability of satellite data. In fact, a recent study

a linkage between the trends in atmospheric reanalysis and the SST.

was partially as a response to the local warming of the SSTs.

and cloud amounts.

**2.3.3 Discussion**

The optical properties of seawater, which dominate the distribution of the penetration and absorption of the given outer radiation, are primarily determined by the phytoplankton biomass, measured by chlorophyll-a concentration in seawater, with their accompanying retinue of dissolved and particulate materials of biological origin (Case 1 Waters) (e.g., Morel, 1988; Morel & Prieur, 1977). Many studies have focused on the development of shortwave penetration schemes including the effects of chlorophyll-a concentration either in bulk or spectral formulae (e.g., Manizza et al., 2005; Morel, 1988; Morel & Antoine, 1994; Ohlmann, 2003; Ohlmann et al., 2000; Ohlmann & Siegel, 2000) and on the effects of these parameterizations on the ocean dynamics and thermodynamics through forced ocean model experiments (e.g., Anderson et al., 2007; Manizza et al., 2005; Murtugudde et al., 2002; Nakamoto et al., 2001). While the direct effect of including the chlorophyll-a concentration increased absorption in shallower layers, one of the most pronounced changes was the indirect effect: an increased cooling in SST in the eastern equatorial Pacific. This increased cooling resulted from increased upwelling through changes in the equatorial current system (Gnanadesikan & Anderson, 2009; Manizza et al., 2005; Murtugudde et al., 2002; Nakamoto et al., 2001; Sweeney et al., 2005).

The solar zenith angle or the solar altitude affects penetrating radiation and the vertical distribution of heating by absorbing the radiation in a water column under clear sky condition. Some shortwave penetration schemes explicitly examined the effects of solar altitude on this (e.g., Morel & Antoine, 1994; Ohlmann, 2003). Ishizaki & Yamanaka (2010) (hereafter referred to as IY10) examined the impact of sun altitude on ocean radiant heating, assuming that all sunlight is direct solar rays. They introduced sun altitude into the simple radiation formulation of Paulson & Simpson (1977) (hereafter referred to as PS77) with diurnal changing incident angle, and studied the sensitivity of an ocean model to the formulation. Introduction of the solar angle caused the effective attenuation depth for the diurnal-mean penetrating radiation shallower than that of the downward vertical radiation, and caused the locus of radiation absorption to shift upward. This was qualitatively the same as including chlorophyll-a concentration, resulting in the same indirect effect of cooling in SST in the eastern equatorial Pacific.

Here we examined the impact of solar radiation absorption schemes on ocean model simulation. We considered three absorption schemes. The first is a conventional scheme based on PS77, in which sunlight has diurnal constant intensity and is vertically downward. The second is the above-mentioned IY10 scheme, in which sunlight has a diurnal changing incident angle, leading to vertical change in the diurnal-mean attenuation rate of the sun light. The third scheme introduces the effect of chlorophyll-a concentration by Morel & Antoine (1994)'s (hereafter referred to as MA94) formulation, in addition to the second scheme. We confirmed the impact of these three schemes on the mean ocean state, especially focusing on the effective euphotic layer depth, temperature and current fields.

#### **3.2 Formulations of three absorption schemes**

#### **3.2.1 Basic assumption**

We made the following assumptions for formulating the changing solar altitude angle of the sun: (a) All sunlight consists solely the direct rays without any scattered light. (b) The sun is a point source of light, i.e., the visual angle of the sun is zero. (c) The ratio of the actual to the mean earth-sun separation is assumed to be unity, that is, the earth's revolution orbit is perfectly circular. (d) The declination angle, *δ*, of the sun (i.e., its latitude on the celestial sphere) is constant on a diurnal time scale. (e) The effective radiation intensity *Iorg* of sunlight on a plane perpendicular to the ray is diurnal constant, regardless of the sun altitude, and is calculated from the diurnal-mean irradiance *IDM* given as a boundary condition (IY10). (f) The refractive index of seawater *γ* is a constant, i.e., *γ* = 1.34. (g) The optical characteristics of seawater are homogeneous with depth, in horizontal direction, and over time, and are assumed to be of Jerlov (1968) Water Type I (PS77) for the first (PS77) and the second (IY10) absorption scheme. This water has an e-folding depth (attenuation depth) of 23 m for the shorter wavelength part (PS77). (h) Sea surface albedo *α* is set to be a constant, 0.066, independent of sun altitude.

#### **3.2.2 Formulation**

According to PS77, incoming solar radiation is divided into two parts: the longer-wavelength (infrared (IR)), which is absorbed immediately at the sea surface and the shorter-wavelength (visible plus ultra-violet (visible-UV)), which penetrates a relatively long distance, which is expressed as

$$\mathbf{I}/\mathbf{I}\_0 = \operatorname{Re} p(-z/\mathbb{Q}\_1) + (1 - \mathbb{R}) \exp(-z/\mathbb{Q}\_2) \tag{1}$$

where *Io* and *I* are the irradiances just under the sea surface and at depth z, respectively; *R* is the ratio of the IR part to the total at the surface; and *ζ*<sup>1</sup> and *ζ*<sup>2</sup> are the e-folding depths (attenuation depths) of the IR and visible-UV parts, respectively. We take this formulation as our first absorption scheme with *R* = 0.58, *ζ*<sup>1</sup> = 0.35 m, and *ζ*<sup>2</sup> = 23 m (for Water Type I) (PS77) and call it the "PS77-scheme".

For the second absorption scheme, the incoming radiation with incident angle *A* at the sea surface penetrates the sea with refracted angle *A*� . The sun altitude *A* is given by the observer's latitude *θ*, declination of the sun *δ* (−23.5◦ < *δ* < 23.5◦), and the local time *t* as

$$
\sin A = \sin \delta \sin \theta - \cos \delta \cos \theta \cos \omega t \tag{2}
$$

where *ω* is the diurnal angular velocity of the sun for the observer, i.e., *ω* = 2*π*/24 hours. The relationship between *A* and *A*� is given by Snell's law:

$$
\cos A / \cos A' = \gamma (=1.34) \tag{3}
$$

so that

10 Will-be-set-by-IN-TECH

The second is the above-mentioned IY10 scheme, in which sunlight has a diurnal changing incident angle, leading to vertical change in the diurnal-mean attenuation rate of the sun light. The third scheme introduces the effect of chlorophyll-a concentration by Morel & Antoine (1994)'s (hereafter referred to as MA94) formulation, in addition to the second scheme. We confirmed the impact of these three schemes on the mean ocean state, especially focusing on

We made the following assumptions for formulating the changing solar altitude angle of the sun: (a) All sunlight consists solely the direct rays without any scattered light. (b) The sun is a point source of light, i.e., the visual angle of the sun is zero. (c) The ratio of the actual to the mean earth-sun separation is assumed to be unity, that is, the earth's revolution orbit is perfectly circular. (d) The declination angle, *δ*, of the sun (i.e., its latitude on the celestial sphere) is constant on a diurnal time scale. (e) The effective radiation intensity *Iorg* of sunlight on a plane perpendicular to the ray is diurnal constant, regardless of the sun altitude, and is calculated from the diurnal-mean irradiance *IDM* given as a boundary condition (IY10). (f) The refractive index of seawater *γ* is a constant, i.e., *γ* = 1.34. (g) The optical characteristics of seawater are homogeneous with depth, in horizontal direction, and over time, and are assumed to be of Jerlov (1968) Water Type I (PS77) for the first (PS77) and the second (IY10) absorption scheme. This water has an e-folding depth (attenuation depth) of 23 m for the shorter wavelength part (PS77). (h) Sea surface albedo *α* is set to be a constant,

According to PS77, incoming solar radiation is divided into two parts: the longer-wavelength (infrared (IR)), which is absorbed immediately at the sea surface and the shorter-wavelength (visible plus ultra-violet (visible-UV)), which penetrates a relatively long distance, which is

where *Io* and *I* are the irradiances just under the sea surface and at depth z, respectively; *R* is the ratio of the IR part to the total at the surface; and *ζ*<sup>1</sup> and *ζ*<sup>2</sup> are the e-folding depths (attenuation depths) of the IR and visible-UV parts, respectively. We take this formulation as our first absorption scheme with *R* = 0.58, *ζ*<sup>1</sup> = 0.35 m, and *ζ*<sup>2</sup> = 23 m (for Water Type I)

For the second absorption scheme, the incoming radiation with incident angle *A* at the

where *ω* is the diurnal angular velocity of the sun for the observer, i.e., *ω* = 2*π*/24 hours. The

observer's latitude *θ*, declination of the sun *δ* (−23.5◦ < *δ* < 23.5◦), and the local time *t* as

*I*/*Io* = *Rexp*(−*z*/*ζ*1)+(1 − *R*)*exp*(−*z*/*ζ*2) (1)

*sinA* = *sinδsinθ* − *cosδcosθcosωt* (2)

*cosA*/*cosA*� = *γ*(= 1.34) (3)

. The sun altitude *A* is given by the

the effective euphotic layer depth, temperature and current fields.

**3.2 Formulations of three absorption schemes**

**3.2.1 Basic assumption**

0.066, independent of sun altitude.

(PS77) and call it the "PS77-scheme".

sea surface penetrates the sea with refracted angle *A*�

relationship between *A* and *A*� is given by Snell's law:

**3.2.2 Formulation**

expressed as

$$
\sin A' = ((\gamma^2 - 1) + \sin^2 A)^{1/2} / \gamma \tag{4}
$$

The minimum of *A*� is 41.7◦ for *A* = 0◦. The path length is expressed as *z*/*sinA*� where *z* is the depth, so that

$$\mathbf{I}\prime\prime\mathbf{I}\_0 = \text{Rexp}(-z\prime(\zeta\_1 \sin A')) + (1 - \mathbb{R})\exp(-z\prime(\zeta\_2 \sin A'))\tag{5}$$

where the values of *R*, *ζ*1, and *ζ*<sup>2</sup> are the same as those of the first scheme. We call this the "IY10-scheme". The practical calculation procedure of solar radiation from a given diurnal-mean irradiance *IDM* is given in IY10.

For the third absorption scheme, MA94's formulation is used with a climatological chlorophyll-a data at 1 m depth. Chlorophyll-a data is derived from a Sea-viewing Wide Field-of-view Sensor (SeaWiFS; http://oceancolor.gsfc.nasa.gov/SeaWiFS). Their formulation is expressed as

$$\mathbf{I}/\mathbf{I}\_0 = \mathbf{F}\_{\text{IR}} \exp(-z/(\mathbf{Z}\_{\text{IR}} \sin A')) + \mathbf{F}\_{\text{VIS}} (\mathbf{V}\_1 \exp(-z/\mathbf{Z}\_1) + \mathbf{V}\_2 \exp(-z/\mathbf{Z}\_2)) \tag{6}$$

where *FIR* is the fraction of the infrared (IR) radiation (wavelengths > 0.75*μm*) to the total, *FVIS* is that for the visible- UV radiation (*FIR* + *FVIS* = 1), and *ZIR* = 0.267 m, is the attenuation length of the IR radiation. The visible-UV part consists of two exponentials with the partitioning factors and attenuation depths, *V*1, *V*<sup>2</sup> (*V*<sup>1</sup> + *V*<sup>2</sup> = 1), *Z*1, and *Z*2, depending on the chlorophyll-a concentration *C*. Here, the term including *Z*<sup>1</sup> in (6) represents the longer wavelength range of the visible-UV part, with *Z*<sup>1</sup> being of a few meters over the whole range of the chlorophyll-a concentration. They are expressed by polynomials of *log*10*C*, and values of their coefficients and the functional forms of the four parameters are given for the range of *C* between 0.02 and 20 mg m−<sup>3</sup> in MA94. Two sets of coefficients of the polynomials are given, one for uniform pigment profiles and the other for nonuniform ones. Here we use (6) with the variable solar incident angle even for the visible-UV part:

$$1/\text{I}\_0 = \text{F}\_{\text{IR}} \exp(-z/(\text{Z}\_{\text{IR}} \sin A')) + \text{F}\_{\text{VIS}}(V\_1 \exp(-z/(\text{Z}\_1 \sin A')) + V\_2 \exp(-z/(\text{Z}\_2 \sin A'))) \tag{7}$$

The value of *FVIS* depends on the atmospheric condition and the solar zenith angle; MA94 gives the values 0.54 - 0.57 for clear skies and 0.60 for overcast skies. Here, however, we use *FVIS* = 1 − *R* (*FIR* = *R* = 0.58) for the sake of consistency with the first and second absorption scheme. The polynomials for non-uniform pigment profiles are used because we used the chlorophyll-a data obtained by satellites (Morel & Berthon, 1989). We call this a modified MA94-scheme, that is, the "mMA94-scheme".

#### **3.3 General features of optical property of sea surface layer**

Before describing the implementation of the above schemes in an ocean model, we theoretically discuss the annual-mean of the diurnal-mean euphotic layer depth, attenuation depth (e-folding depth), and absorption of the penetrating radiation (only for the visible-UV part). To calculate the diurnal-mean radiation, the time step was taken as 1 min with the incident angle (*sinA*) calculated by (2) at every time step. Here, the radiation intensity of sunlight is assumed to be the solar constant 1.37 kW m−<sup>2</sup> only in this subsection and the sea surface irradiance *Io* is the intensity multiplied by *sinA*.

Fig. 6. (a) Diurnal-mean euphotic layer depth *de* [m] for IY10, for the sun declination *δ* and the northern latitude *θ*. (b) Meridional section of the effective attenuation depth *ζ* [m] defined in each 1 m-layer for annually averaged diurnal-mean penetrating irradiance of IY10. (c) Absorption of annually averaged irradiance of PS77 [W m−3]. (d) Difference in absorption between IY10 and PS77 [W m−3] (IY10 - PS77). The thick lines in (b) indicate the annual mean euphotic layer depth for IY10 and PS77 (constantly 105.9 m).

#### **3.3.1 Difference between IY10 and PS77 schemes**

The diurnal-mean euphotic layer depth *de* for the IY10-scheme is a function of *θ* and *δ* (Fig. 6a), which was numerically obtained as the depth where diurnal-mean irradiance of the visible-UV part of the incident radiation became 1 % of its surface value. Depth *de* ranged from less than 71 m in winter at high latitudes to more than 96 m at equatorial equinox through the Tropic of Cancer at summer solstice. For the PS77-scheme, *de* theoretically had a constant value of 105.9 m; thus, the difference ranged from 10 m to 35 m (9 - 33 % of 105.9 m).

Figure 6b shows the vertical structure of the effective vertical attenuation for the annual-mean radiation, defined in each 1m-layer and expressed by the e-folding depth *ζ*(*ζ*(*z*) = 1/*ln*(*I*(*z* − 0.5)/*I*(*z* + 0.5))). The maximum vertical difference in *ζ* of about 1 m is seen in the upper 100 m layer at the equator, while *ζ* is almost vertically homogeneous at the high latitudes. The vertical structure originates from the diurnal and seasonal variations of the solar altitude. For PS77, *ζ* is a constant 23 m. Also shown in Fig. 6b are the annual-mean euphotic layer depths

Fig. 6. (a) Diurnal-mean euphotic layer depth *de* [m] for IY10, for the sun declination *δ* and the northern latitude *θ*. (b) Meridional section of the effective attenuation depth *ζ* [m] defined in each 1 m-layer for annually averaged diurnal-mean penetrating irradiance of IY10. (c) Absorption of annually averaged irradiance of PS77 [W m−3]. (d) Difference in absorption between IY10 and PS77 [W m−3] (IY10 - PS77). The thick lines in (b) indicate the

The diurnal-mean euphotic layer depth *de* for the IY10-scheme is a function of *θ* and *δ* (Fig. 6a), which was numerically obtained as the depth where diurnal-mean irradiance of the visible-UV part of the incident radiation became 1 % of its surface value. Depth *de* ranged from less than 71 m in winter at high latitudes to more than 96 m at equatorial equinox through the Tropic of Cancer at summer solstice. For the PS77-scheme, *de* theoretically had a constant

Figure 6b shows the vertical structure of the effective vertical attenuation for the annual-mean radiation, defined in each 1m-layer and expressed by the e-folding depth *ζ*(*ζ*(*z*) = 1/*ln*(*I*(*z* − 0.5)/*I*(*z* + 0.5))). The maximum vertical difference in *ζ* of about 1 m is seen in the upper 100 m layer at the equator, while *ζ* is almost vertically homogeneous at the high latitudes. The vertical structure originates from the diurnal and seasonal variations of the solar altitude. For PS77, *ζ* is a constant 23 m. Also shown in Fig. 6b are the annual-mean euphotic layer depths

value of 105.9 m; thus, the difference ranged from 10 m to 35 m (9 - 33 % of 105.9 m).

annual mean euphotic layer depth for IY10 and PS77 (constantly 105.9 m).

**3.3.1 Difference between IY10 and PS77 schemes**

for the PS77 (constant, 105.9 m) and IY10 (sinusoidal) schemes. The range of the latter (75 - 94 m) is somewhat narrower than that in Fig. 6a because of the annual averaging process.

Panels c and d of Fig. 6 show absorption of the annually averaged irradiance of the PS77 scheme expressed by its vertical convergence, and the difference in absorption between IY10 and PS77 (IY10-PS77), respectively. The absorption pattern naturally indicates latitudinal variation for both PS77 and IY10 (not shown for IY10), but the difference between the two hardly has any latitudinal variation (Fig. 6d), with the zero line staying at about 20 m at all latitudes. Introducing the solar altitude variation results in more warming at levels shallower than 20 m and more cooling below that level.

Fig. 7. (a) Annual-mean chlorophyll concentration (SeaWifs) [mg m−3]. (b) Annual-mean euphotic layer depth [m] base on MA94 with diurnal variation of sun altitude (mMA94). (c) Effective attenuation depth *ζ* (m) for zonally averaged annual-mean penetrative irradiance of mMA94. (d) Difference in absorption between mMA94 and PS77 [W m−3] (mMA94 - PS77). The thick lines in (c) indicate the zonally averaged annual-mean euphotic layer depth for mMA94 (uppermost), IY10 (middle) and PS77 (lowest, constantly 105.9 m).
