One key aspect of market liquidity is the resilience of liquidity. This is not a word that has been sharply defined in the literature; it has a few dimensions. One aspect is the time in which a limit order book restores to having the low impact cost prior to the placement of a large trade. If one could measure this in an experimental setting for a given security, suppose a large order is placed at t=0. Measuring resilience is about obtaining a graph with transaction size on the x axis and the time taken for impact cost to "substantially" revert to conditions that were prevalent at t=0.
Another dimension of liquidity is the ability of market liquidity to handle bad news or negative returns. I don't really understand why, but it often seems that market liquidity is diminished after negative news. One part of this is just a measurement issue : dollar turnover is higher after prices have gone up and lower after prices have gone down. But even if one is using measures of liquidity which are not affected by this problem, the hallmark of a successful financial market is resilience in the sense of being able to handle sharp movements, particularly sharp negative movements, and continue to deliver a continual supply of liquidity. Participants face greater liquidity when this is not the case.
Susan Thomas has an EPW article on the resilience of liquidity on the Indian equity and debt markets. The main finding is that the equity market has considerable resilience while the debt market does not. I think this is related to RBI's belief that the bond market should have no speculators compared with SEBI's belief that speculators are a legitimate part of the equity market.