There are several issues with nitrogen losses in this scenario: volatilization into the air of the ammonia form of N, runoff during spring thaw, and timing of applications relative to temperature and soil conditions.
Surface applications of manure are subject to ammonia loss via volatilization. Liquid hog manure can have a high proportion of total nitrogen in the ammonia form, so losses into the air can be significant.
For example, manure from a hog slurry operation can be 50% ammonia nitrogen. Ammonia nitrogen losses can range from 20 to 80% with average losses around 50% of ammonia nitrogen with surface application. In this example, if you applied 200 pounds per acre total nitrogen, on average 50 pounds per acre could be lost to the atmosphere as nitrogen volatilization.
The rate of ammonia loss is highly dependent on temperature and soil moisture conditions. Ammonia losses do occur in cold winter weather. The rate of nitrogen loss will be slowed by the cold weather, but with time, the amount lost can be similar to losses in warmer weather.
Injection of manure eliminates ammonia volatilization losses into the air. The ammonia is retained by the cover of soil. This is similar to the retention of injected anhydrous ammonia in soil.
Nitrogen loss by potential runoff is another consideration. A slope of less than 2% typically has only a slight risk of runoff from surface-applied manure. Other factors contribute to reducing the risk of runoff such as snowfall amounts, speed of snow melt, and surface residue. Manure that is surface applied onto a significant amount of snow could run off if there is little soil roughness or residue and if the snow melts very rapidly. Minimal snow that melts slowly probably will not have the opportunity to run off on a 2% slope.
Injected liquid manure is a much more reliable nitrogen fertilizer than surface-applied liquid manure because injection makes the ammonia nitrogen 100% available to the crop and reduces the risks of runoff.
For additional information see the web page Estimating Crop Nutrient Availability from Manure
Author: John Lory, University of Missouri
Natalie Rector, Michigan State University