The Northwestern Mediterranean (NWMed) Sea includes one of the best observed ocean deep convection sites in the World. An observing system simulation experiment (OSSE) is developed to provide a methodology for estimating observing network errors. It is applied to quantify dense water volumes in the NWMed during 2012-2013 with their observation error from MOOSE network. Results from the OSSE show low spatiotemporal sampling errors, which confirms MOOSE network ability to measure dense waters. However, results are highly sensitive to instrumental stability. The dense water volume is then estimated in observations from four ship cruises between summers 2012 and 2013. A large seasonal cycle is found, maximal in spring 2013 and dominated by the area west of 6.58E. The dense water volume ( \sigma₀ 29.11 kg/m³) is stable between summer 2012 (13.3 +/- 0.6 x 10¹³ m³) and winter 2013 (13.7 +/- 1.3 x 10¹³ m³). It increases dramatically in spring 2013 (17.7 +/- 0.9 x 10¹³ m³) due to an intense convective event, and it finally decreases rapidly in summer 2013 (15.1 +/- 0.6 x 10¹³ m³) due to restratification and spreading. We estimate an open-sea dense water formation (DWF) rate of 1.4 +/- 0.3 Sv between summer 2012 and spring 2013 over the studied area, extrapolated to 2.3 +/- 0.5 Sv over the whole NWMed Sea and for the optimal timing. This is to our knowledge the highest measured DWF rate, suggesting winter 2013 was exceptionally convective. The observed restratification rate between spring and summer 2013 is -0.8 +/-0.4 Sv. This study provides robust quantifications of deep convection during an exceptional event that will allow to evaluate numerical simulations.