1. of summer monsoon. Arabian Sea warm

1. Introduction:
The Monsoon is a significant contributor to both the economic and social growth of India. Ocean–atmosphere interactions play an important role in the monsoon phenomena thereby making it very much necessary to understand its behaviour. The key role of the Indian Ocean warm pool sea surface temperature (SST) > 28?C in triggering the Indian summer monsoon rainfall (ISMR) is well studied (Rao and Sivakumar, 1999; Deepa et al., 2007; Vinaychandran et al., 2007). This warm pool attained its maximum intensity during the pre-monsoon season and dissipated with the commencement of summer monsoon.  Arabian Sea warm pool (ASWP) and Bay of Bengal Warm pool (BoBWP), where the monsoon onset vortex is formed prior to the onset of summer monsoon , is a part of the Indian Ocean warm pool in the southeastern Arabian Sea and southern Bay of Bengal.  Over the ASWP region, the SST exceeds 30?C, 2–3 months before the onset of the Indian Summer Monsoon (Deepa et al., 2007; Vinaychandran et al., 2007; Vinaychandran and Kurian, 2008). A number of studies have explored the connection between the summer monsoon and the parameters such as the SST, ocean heat content, outgoing long wave radiation, heat fluxes and other such variables over the warm pool region. Out of these, majority of the studies had been done on the SST-rainfall relationship. But a couple of studies like Rao and Sivakumar (1999) explored the upper ocean heat content (OHC) from the surface to the depth of the 28?C isotherm during May–June and tried to exhibit the genesis location of the onset vortex. Rise in SST results the saturation of vapour pressure which causes water vapors and latent heat, causing the intensification of cyclones. . Observations indicate the existence of a temperature threshold necessary for the development of major hurricanes rather than a continuous positive relationship between maximum storm intensity and SST (Michaels et al., 2006). Mixed layer plays a crucial role in controlling the SST. So it is important to analyse the spatial and seasonal trend of mixed layer heat content (MLHC)  using satellite derived  data to step further to initiate a ground for regional climate and hazard monitoring.

It is well understood that the heat accumulated within a shallow and highly stratified layer prior to the onset of summer monsoon leads to the formation of the mini warm pool in Arabian sea (Rao and Sivakumar et al., 1999 ). The accumulation of heat under clear skies and weak winds (Rao and Sivakumar 1999) and  the presence of low salinity water in the surface layers in the eastern Arabian Sea are found to be some of the reasons behind the strong stratification. Besides, the low saline water from the Bay of Bengal brought into eastern Arabian Sea by the prevailing circulation pattern in the winter (Shenoi et al. 1999) was found further transported to the central as well as the western Arabian Sea by the Rossby waves radiated from the down welling coastal Kelvin waves (Bruce et al. 1994; Shankar and Shetye 1997; Shenoi et al. 1999). The circulation pattern changes to southerly along the west coast of India by April/May. With the dissipation of the Lakshadweep high and change in circulation pattern, this low saline water gets trapped in central and western Arabian Sea. So, during May, the low saline waters in the warm pool region cannot be brought by the prevailing circulation pattern. Therefore, one possibility is the re-circulation of the trapped low salinity waters from the interior Arabian Sea (Vinaychandran et al., 2007). 
Some studies showed that heat content up to 26?C isotherm increases significantly in the region of ASMWP during the period 1993-2010 relative to the north Indian Ocean, and propose that this increase could have caused the decrease in Indian Summer Monsoon Rainfall that occurred at the same time.Nagamani et al.,2015. Rao and Sivakumar (1999) also studied the the effect of upper ocean heat content up to 28?C isotherm on the genesis location of the onset vortex of summer monsoon in May-June.
 In this study, we continue the effort to explore the seasonal variance of Ocean Heat content up to mixed layer depth in Indian Ocean Warm pool  i.e. ASWP and BoBWP. Finally we are going to show the effect of Mixed Layer Heat Content(MLHC) in ASMWP on Indian summer monsoon rainfall, the details of which are given in the result and discussion section.
2.Data and Methodology:
In our study, Arabian Sea(AS) ,Bay of Bengal(BoBWP) regions were delineated separate to understand the long term behaviour of MLHC of each of the region and how the Arabian Sea warm pool  controlled the summer monsoon rainfall.

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The region from 68?E to 78?E longitude and 4?N to 14?N latitude had been considered as ASWP following Nagamani et al., 2015.The region from 50?E to 72?E longitude and 5?N to 24?N latitude had been considered as Arabian Sea.The region from 78?E to 95?E longitude and 5?N to 15?N latitude had been considered as Arabian Sea
                     Time Series, Hovmoller and scatter (regression) plots were generated in order to understand the long term trends in the warm pool and ISMR. The regression analysis has been done to examine the correlation between the parameters with detailed interpretations and discussions. 
                            For the calculation of MLHC the given formula is used.
            MLHC=    ———————-(2)
Where MLD is calculated using the temperature criteria that the depth at which the temperature change from the surface temperature is 0.5 °C.The ocean potential temperature  is obtained  from ORAS4 which is a is ECMWF current ocean reanalysis product.Here ? is the sea water density, Cp is the specific heat capacity at constant pressure, T(z) is ocean temperature (°C), In our  calculation, the product of ?Cp is taken as 4?×?106?J?K?1?m?3. CRU Rainfall 1956-2015 is used to calculate the long term trend  of the precipitation. ECMWF wind speed and NOAA OLR data are used to generate a long term relationship within  OLR,Wind Speed and MLHC.
3.Results and Discussion:

Ocean profile plays an important role in the upper part of the ocean in which the temperature, density as well as salinity are approximately homogenous. In this layer active vertical mixing near the surface is observed which is due to wind-stirring, waves, turbulence and night time conctive mixing. The mixed layer is important in establishing the world ocean’s mean state and variability as it acts as an interface between the atmosphere and interior ocean. So, here heat content up to the mixed layer depth is taken for analysis and finally its statistical relationship with the Indian summer monsoon has been shown.

3.1:Analysis of the MLHC:

Spatial and temporal analysis of monthly average heat content between 1958 and 2015 has been carried out. Seasonally, the highest value of the MLHC  is recorded in both monsoonal seasons(Summer monsoon and winter monsoon) and the lowest value is observed in the inter monsoonal seasons(pre monsoon (MAM) and post monsoon(ON)).During summer monsoon ,the MLHC increases markedly in the interior Arabian Sea due to the Increase in MLD which results the Ekman convergence associated with the Findlater jet (Findlater 1969) and shallows west to the jet axis. In summer monsoon, high wind stress and low sunlight plays a crucial role in deepening the MLD. In the winter monsoon, the MLHC increases due to the negative buoyancy fluxes which plays a major role in the convective deepening  of the MLD. In contrast inter monsoonal seasons the MLHC is decreased due to weaker winds along with strong incoming solar radiation that results in a thin Mixed layer. For simplification, all MLHC data are divided by 109. The low standard deviations of monthly values over more than a decade of observation (Table 1,Table 2) reveal the persistence of the seasonal cycle of MLHC.

Statistical Analysis:
 A regular and repeated trend of MLHC in both Arabian Sea and Bay of Bengal since 2000–2015 leads us to develop a statistical model that could predict a value of monthly MLHC with significant accuracy. In this regard, the authors have applied Fourier fit of order 4 on the time series. Eq. (1)shows the model equation;

MLHC=a0+a1*cos(x*w)+b1*sin(x*w)+a2*cos(2*x*w)+b2*sin(2*x*w) +a3*cos(3*x*w)+b3*sin(3*x*w)+a4*cos(4*x*w)+b4*sin(4*x*w)


In case of Arabian Sea after the analysis The constant values which are found are; a0=    4.178, a1=-0.1322, b1= -0.225, a2=0.05874, b2=1.463, a3= -0.1809, b3=-0.02524, a4= -0.07995, b4= -0.1264   and w=0.5236. X shows the months starting from January 2000 to December 2015. Here, w term is also a measure of period. 2*?/w which converts to the period in months and it is found to be 11.99 presenting the pattern repeats itself yearly. Fig. 6 shows the graph between observed values and predicted values of MLHC. The Correlation coefficient is found to be of 0.8478 (i.e. R2 = 0.8478) with root mean squared error of 0.4623. All the results have been obtained with 95% confidence level

                    In case of Bay of Bengal after the analysis The constant values which are obtained  are; a0= 4.863, a1= 0.7442, b1= -0.2406, a2=0.5951, b2=1.219, a3= -0.3082, b3=0.25, a4= 0.03349,b4= -0.1597 and w=0.5231. X shows the months starting from January 2000 to December 2015. Here, w term is also a measure of period. 2*?/w which converts to the period in months and it is found to be 12.011 presenting the pattern repeats itself yearly. Fig. 7 shows the graph between observed values and predicted values of MLHC. The Correlation coefficient is found to be of 0.8787 (i.e. R2 = 0.8787) with root mean squared error of 0.4379Jm-2. All the results have been obtained with 95% confidence level.
             Here the long term trend of MLHC has a decreasing trend(Figure) during monsoon months from 1958-2015.The main factors which controls the mixed layer depth are wind speed and temperature.In that same timespan, both zones and meridional wind show a decreasing trend(Figure) whereas the temperature exhibits a increasing trend().The increasing trend is associated with a decreasing OLR trend(Figure).The OLR trend signifies the absorbance of radiation in that period which may be a combine effect of both green house gases and aerosols.                         

4.2: Relation with ISMR and ASMWP MLHC:

Here both the factors that is mixed layer heat content and rainfall were decreased in past 58 years. The MLHC was decreased with a slope -0.0083 and Pearson’s correlation constant -0.35927 as well as the rainfall was decreased with slope                 -0.2952 and Pearson’s correlation constant -0.098. Again, linear trend between MLHC in ASMWP and ISMR was calculated with correlation value 0.49 which signifies an existence of moderate positive relationship between these two factors.
                   For other three seasons, the Pearson’s correlation coefficient which has been derived   are near to zero. The values are as follows; Winter monsoon (0.01586), Pre-monsoon (0.09159) and post-monsoon (-0.0801). Here in those three seasons approximately no correlation has been observed.
Again, analysis between two datasets that is ORAS4 and Soda were observed which also showed the same pattern.
Figure9: Seasonal comparison of 2 data sets in ASMWP MLHC i.e. ORAS4(Green) and SODA (Blue)
Here SODA data set is available from 1980. Here these two data sets behave like same way. Here also for the summer monsoon using SODA data from 1980 to 2015 calculation of Pearson’s correlation coefficient has been done which results the value 0.317. The difference may be due to the time span which is more in case of ORAS4 as compared to SODA. 


The ASWP plays a crucial role on the onset of vortex. Using satellite estimations and model stimulations, decrease in MLHC in ASWP along with decrease in ISMR has been found.
We recognize that other factors also affect the summer monsoon rainfall. These factors include; increased aerosols, regional SST and OHC changes elsewhere in the Indian Ocean, and ‘noise’ due to climate variability such as ElNino southern oscillation(ENSO) and the Indian ocean dipole(IOD). In the field of aerosols, some studies show that black carbons or sulphate aerosols mask surface warming resulting cooling in SST which eventually plays a role in decrease in ISMR.(Ramanathan et al.,(2005),Bollasina et al.,(2011)).One more study showed that weakening in summer monsoon results warming of the equatorial Indian Ocean and this warming in turn contributed to the further weakening of the monsoon(Swapna et al.,2013).Here in this model, we suggest that MLHC of the ASWP could also be one of the factors that impact ISMR. Here the isolation of the seasonal impacts has done above and moderate uphill(Positive) linear relationship has been found between the MLHC and rainfall. The decrease of the MLHC is mainly due to the decrease long term trend of both zonal and meridional wind stress. 


Our study suggests the importance of further investigation the influence of ASWP heat content in the monsoon dynamics. It emphasizes the need for detailed observational efforts that allows the statistical relationship between MLHC and ISMR to be accurately determined.  Hence, the critical role of the decrease in MLHC in monsoon of Indian Ocean deserves special attention for its decisive effect on the food security of a large fraction of the world’s population along with the economic growth of India.

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