Its far more complex:

" This results in annual CO2 emissions from fuel of 1469 g CO2 m−2 yr−1, 3 times more than OC storage per m−2 in ornamental lawn soils (Figure 3b). Pumping irrigation water consumes energy at 53 g C m−2 yr−1 [Schlesinger, 1999], or 193 g CO2 m−2 yr−1 (Figure 3b). CO2 is also formed during fertilizer production by the Haber-Bosch process + during transport + application, producing @ 1.436 moles of C per mole of N produced [Schlesinger, 1999]. In the current study, this corresponds to emissions of 45-339 g CO2 m−2 yr−1 for low + high fertilizer regimes (Figure 3b).
[18] Our work clearly shows that high OC sequestration rates in some turfs are dwarfed by soil N2O emissions and CO2 released during management, with a total GWP of ornamental lawns of +1238-+1632 g CO2 m−2 yr−1, depending on fertilization rate (Figure 3b). Because athletic fields do not store OC, they have a total GWP of +1752-+2145 g CO2 m−2 yr−1 (Figure 3b)."

wiley.com/doi/10.1029/2009GL041675/full