I often come across this statistic: the ammonia industry is responsible for 1% of global greenhouse gas emissions. Where did this “1%” number come from?

The statistic holds true today – the number is closer to 1.024%, as I’ll demonstrate.
We only need three pieces of data (beyond unit conversions):

• Total global ammonia production, which I get from the US Geological Survey (USGS).
• Total global CO2 emissions, which I get from the World Resources Institute (WRI).
• Global average CO2 emissions per ton ammonia produced, which I get from the Institute for Industrial Productivity.

Total global ammonia production

In 2012, global production of ammonia was 140 million metric tons of contained nitrogen. But this is the weight of the nutrient, not the product: nitrogen is 82.2% of ammonia by weight, so global production was 170 million metric tons of ammonia. This is from the USGS Mineral Commodity Summary, Nitrogen, 2014.

Total global CO2 emissions

In 2012, global emissions totaled 33,843.05 million metric tons of CO2. This number excludes emissions of other greenhouse gases (GHGs) and carbon impacts of land use changes and forestry – it’s a count of pure CO2 emissions. I’ll address GHG emissions later. The WRI data is available online.

Global average CO2 emissions per ton ammonia

This data is harder to determine because the amount of CO2 emitted will change depending on whether the ammonia is produced using coal, natural gas, naphtha, or oil as a feedstock; also some ammonia plants are more efficient and/or less polluting than others. The Institute for Industrial Productivity publishes an extremely useful Industrial Efficiency Technology Database (IETD) which benchmarks CO2 emissions per ton ammonia for producers in every region, based on the local feedstock usage. The IETD gives total global ammonia production in 2010 as 157.3 million tons (implying a ~4% annual growth rate, to match USGS’s 170 million tons in 2012), with total global CO2 emissions from ammonia production of 451 million metric tons. Therefore, the global average is 2.867 tons CO2 emitted per ton NH3 produced (451/157.3).
You may be interested to know that North American producers emit, on average, 2.129 tons CO2 per ton NH3 produced. North American producers emit more CO2 per ton ammonia than most but, on the other hand, Chinese producers emit, on average, 4.429 tons CO2 per ton NH3 produced. Again, this data relates to 2010.
There are issues with this dataset: it is patched together from data and methodologies published by the IEA in 2007, the US EPA in 2005, the IPCC in 2006, and others. It is obviously imprecise: for example, it calculates North American emissions by assuming 100% of production uses natural gas feedstock. In reality, US producers also use coal, pet coke, byproduct hydrogen, and landfill gas – each with a different carbon content. But this data is close enough for me, and it’s the best I know. The site holds a wealth of other information about international ammonia industry energy use.
The next calculations assume that the global average CO2-per-NH3 rate is constant. This is unlikely to be true: modern, efficient plants tend to replace older, dirtier plants. I don’t believe, however, that this global average CO2-emission rate will yet have changed significantly – but I’d welcome any data demonstrating this assumption to be true or false.

Over 1% of global CO2 emissions

The product of 170 million tons of ammonia each emitting 2.867 tons of CO2, will total 487.39 million metric tons of CO2 emitted by the ammonia industry in 2012. Which is 1.44% of global CO2 emissions.

Over 1% of global GHG emissions

In addition to pure CO2 emission data, the WRI also provides total GHG emission data, including other GHGs (CH4, N2O, F-gases) and the impact of land use changes and forestry. Running the same calculation against 2012’s total GHG emissions of 47,598.55 million tons CO2-equivalent (CO2e), the ammonia industry is responsible for 1.024% of global GHG emissions.