That's really hard to understand because methane emission is moslty Anthropogenic :
Anthropogenic sources (340 Tg/yr) predominate over natural sources (160 Tg/yr), and 80% of the total methane emission is of modern biogenic origin. Only 20% is due to fossil carbon sources (Wahlen et al. 1989)."

There are also natural methane sinks:

Woodland soils can act as effective sinks for both atmospheric methane, and for methane produced in deeper soil layers. The Intergovernmental Panel on Climate Change (IPCC) estimate that soils represent a methane sink of around 30 million tonnes per year. The methane is predominantly used by bacteria in the soil (methanotrophs) which use the methane as a source of carbon in a process called methane oxidation
src: www.ghgonline.org
There has been a big change in the way landfills are used in the US.  More stuff is filtered out before it gets there (a higher portion of yard wastes are now composted), and care is made to keep moisture content (and therefore decomposition) down ... I don't know if this is the key, but it might be over the same timeframe.
Landfills in the US now have to include landfill gas collection equipment per EPA requirement.  This is a network of wellpoints to collect the methane and CO2 generated and deliver it to central treatment equipment.  Older and abandoned landfills have to retrofitted.

That equipment is either a flare, to burn the methane, or a small, low BTU-capable engine/generator set.  Of course, some landfills like in LA can generate MWs of electricity.

Not a huge source of anthrogenic methane but not trivial either.

I suggest one possible explanantion:

The thinning ozone layer has increased the UV radiation reaching the lower layers of atmosphere. The UV rays cause the formation of more OH radicals in the atmosphere, which react with CH4 and oxidize it (via a chain of recations) to CO2 and H2O:

Photolysis of O3 to O(1D) in the troposphere is determined by a narrow band of radiation in the 290-330 nm range, reflecting the combined wavelength dependences of the actinic flux, O3 absorption cross-section, and O(1D) quantum yield ( Figure 1 ). Radiation in this wavelength range is strongly absorbed by overhead O3 and hence the production of O(1D) is strongly dependent on the thickness of the stratospheric O3 layer [Madronich and Granier, 1992].

http://www-as.harvard.edu/chemistry/trop/publications/jacob2000/text.html#77032

The atomic oxygen O(1D) is the cause of formation of OH radicals in the atmosphere via the reaction:

H2O + O(1D) -> 2OH

Thus the more UV light reaches troposphere, the shorter the CH4 lifetime.

More seriously, here's a slide presentation on atmos. methane:

http://www.cmdl.noaa.gov/gallery/annual_meeting_2004_dlugokencky/Slide1?full=1