A rough picture about the ground-level ammonia (NH3) Ammonia is the only alkaline gas in the atmosphere. It is one of the key features to control the acidity of aerosols and the formation of ammonium salts. 

In the environment of $NH_3$-rich and $NH_3$-poor, the formation pathway of the secondary aerosol would be distinct.     


  For example, if $NH_3$ is redundant after the combination with $_2SO_4$, they would continue to react with $HNO_3$ to form $NH_4NO_3$. However, if in the $NH_3$-poor environment, $HNO_3$ would react with the crustal material and thus form nitrate in the coarse mode.   
  
  In this way, the concentration levels of $NH_3$ affect the chemical composition, size distribution of atmospheric aerosols.   


However, the ground-level monitoring of $NH_3$ is still limited in China with several published ones in limited spots. 

Therefore, I want to learn that:   


Is there any method to estimate NH3 concentration by other species?     
Is there any dataset (e.g. remote sensing, measurements) offering the distribution of $NH_3$ concentration?
It seems difficult to find a reasonable proxy species for $\mathrm{NH}_3$, since its sources (primarily agriculture) are quite distinct from the sources of more commonly observed pollutants. Some observations of aerosol-bound $\mathrm{NH}_4^+$ might (or might not) be available, but due to the reasons you explain, it is non-trivial to infer the gas-phase $\mathrm{NH}_3$ concentration from the $\mathrm{NH}_4^+$ in aerosols.
There are papers about estimating atmospheric $\mathrm{NH}_3$ from satellite data, see for example here or here. These are for column-integrated and not surface $\mathrm{NH}_3$, however.