Why is the daily change in sea ice extent in the northern hemisphere larger at the beginning of each month?
If you plot the average daily change in sea ice extent in the northern hemisphere, based on the data from 'Sea_Ice_Index_Daily_Extent_G02135_v3.0.xlsx', you may notice that at the beginning of each month, particularly in the summer, the daily change is larger.
This is related to the valid ice masks that are used in the processing of the Sea Ice Index. It is really a land spillover effect: that is, even when there is not ice in a coastal sea, ice can appear to fringe the coast, and fill fjords. This happens because there are mixed land-ocean areas within the sensor's field of view. That mixture of land and ice "looks" like sea ice to the algorithms interpreting the sensor data.
A correction for land spillover is applied, but it is not perfect. Monthly valid ice masks are also used and these mask out areas where sea ice is not realistic in a given month, including along the coast due to land spillover. When you switch to the next month there is a change in the ice mask. Going from May to June to July, the valid ice mask moves north in the Arctic and crops out more potential ice areas south of the valid ice line. Ice may have receded in a coastal sea by the end of May, for instance, but may still appear to be along the coastline. On the first day of June the new mask removes more of the invalid ice, which is why you see a sudden change in sea ice.