## 2 Materials and Methods
### Data Analysis  
All the datasets were resampled to a 0.05\({}^{\circ}\)\(\times\) 0.05\({}^{\circ}\) grid using the nearest neighbour method after being processed to a monthly scale for June, July, August and September. The SST indices were derived for the WIO, NIO, CIO and the difference between the Western and Central India Ocean (W-CIO) by taking area averages over those domains. The wind speed was calculated using the formula. Wind speed = \(\sqrt{\mathrm{u}^{2}+\mathrm{v}^{2}}\), where u and v are the zonal and meridional components of the wind, respectively [63]. An outline of the methodology adopted in this study is provided in Figure 2. The 18-year climatology was generated for SIF, SST, specific humidity, rainfall, soil moisture, air temperature and wind speed for June, July, August and September. Anomalies are calculated as departures from the long-term average. Here, an anomaly time series was created for each variable at a monthly scale as \(\mathrm{A_{i}}\ =\ \mathrm{X_{i}}\ -\ \overline{\mathrm{X}}\), where \(\mathrm{X_{i}}\) is the actual mean monthly value of the data point at ith time series and \(\overline{\mathrm{X}}\) is the monthly climatology of the variable during the period of study (2001-2018). Detrended data means the data after removing the linear trend present in the data. Time series datasets may contain trends that result in a varying mean over time. The trend is the overall change over time, but the present study deals with variability. The variability is the remaining data in  
Figure 2: Methodology Flow Diagram with various steps followed for establishing the relationship between oceanic climate and terrestrial photosynthesis in the study area. a given data span after the trend has been eliminated. Hence, excluding the trend from the time series is essential in order to capture the variability. Each monthly anomaly time series is de-trended using the first difference method, where the value at the current time step is estimated as the difference between the actual value and the value at the previous time step (\(\text{y}_{t}\) = \(\text{y}_{t}-\text{y}_{t-1}\)). A de-trended time series was generated for the SST anomalies in each of the three demarcated regions in the Indian Ocean and the SIF anomalies of the 14 ACZs separately. To capture the interactions related to the climate events (ENSO and IOD), the de-trended time series of the NINO3 index and DMI were incorporated into the analysis. In addition, we calculated the difference between SST averaged for the regions of WIO and CIO (W-CIO) used in this study at a monthly scale as W-CIO = SST\({}_{\text{WIO}}\) \(-\) SST\({}_{\text{CIO}}\). The Pearson correlation coefficient was determined for all the region's average SST and SIF anomaly combinations to understand SST-SIF relationships' spatial and temporal variability during the summer monsoon months. To exclude the influence of concurrent ENSO and IOD events that may intrude into the direct relationship between the Indian Ocean and Indian vegetation, a partial correlation between the SST anomalies in the tropical Indian Ocean and the SIF anomalies in the ACZs was calculated by taking DMI and NINO3 index as independent variables. Moreover, a lagged correlation between the NINO3 index and SIF anomalies was estimated to understand the delayed influence of ENSO on Indian vegetation. All the combinations of SST-SIF correlations were tested for statistical significance at 95% confidence level. Composite anomalies of SIF, specific humidity, rainfall, soil moisture, air temperature and wind speed were made for the years in which the SST variability of the tropical Indian Ocean regions fell above (below) the standard deviation of the SST anomalies observed during the period of study (2001-2018). All the composite anomalies were tested for statistical significance at a confidence level of 95% using the two-tailed Student's \(t\)-test, which is the most commonly accepted level of significance (\(\alpha\) = 0.05) considered in climate studies [64].