Nitrogen-Based Land Application Rate: 22-Agric-B11 Principles of Waste Management, May 2015, Q5

Question 5: Nitrogen-Based Land Application Rate (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Quantity	Value
Total manure volume	10,000 m³
Solids content	4 wt% (not needed once fertilizer values are given per m³)
Organic N	1.0 kg/m³
NH₄⁺-N	0.3 kg/m³
NO₃^--N	0 kg/m³
Ammonia volatilization factor	30% (subsurface application still applies since it is stated as a fixed factor)
Organic-N mineralization	40% yr 1, 20% yr 2, 5% yr 3+
Starter nitrogen	15 kg/ha
Corn nitrogen uptake	120 kg/ha

Find. The steady-state annual application rate (m³/ha) and the land area required (ha).

Approach. Under continuous annual application, by year 2 the field carries nitrogen credit from two cohorts of manure: the current year's fresh application (mineralizing at the year-1 rate) plus the residual organic nitrogen from the prior year's application (now mineralizing at the year-2 rate) — build the per-m³ available-nitrogen figure from both cohorts plus the ammonium fraction that survives volatilization, then size the application rate against the crop's net nitrogen demand.

Available nitrogen per m³ of manure at year-2 steady state. Every m³ applied contributes ammonium nitrogen that survives volatilization, $NH_4(1-0.30)$, plus organic nitrogen mineralized in its own first year, $N_{org}(0.40)$; at steady state the identical application made the PRIOR year now contributes a second increment as its organic nitrogen continues mineralizing at the year-2 rate, $N_{org}(0.20)$: $$N_{avail} = NH_4(1-f_{volat}) + N_{org}(f_{yr1}) + N_{org}(f_{yr2})$$ $$N_{avail} = 0.3(1-0.30) + 1.0(0.40) + 1.0(0.20) = 0.21+0.40+0.20 = \boxed{0.81\ \text{kg N/m}^3}$$
Net nitrogen the manure must supply. The starter nitrogen already covers part of the corn's demand, so $$N_{needed} = N_{crop} - N_{starter} = 120-15 = \boxed{105\ \text{kg/ha}}$$
Annual application rate. $$\text{Rate} = \frac{N_{needed}}{N_{avail}} = \frac{105}{0.81} = \boxed{129.6\ \text{m}^3/\text{ha}}$$
Land area requirement. $$A = \frac{V_{total}}{\text{Rate}} = \frac{10{,}000}{129.6} = \boxed{77.1\ \text{ha}}$$

Quantity	Result
Available N per m³ (year-2 steady state)	0.81 kg N/m³
Net N required from manure	105 kg/ha
Annual application rate	129.6 m³/ha
Land area required	77.1 ha

2) Potential environmental impacts of land application: even at an agronomically nitrogen-balanced rate, subsurface-applied liquid manure carries real risk of nitrate leaching to groundwater if mineralization in a wet year outpaces crop uptake, of surface-water contamination from runoff or tile drainage if application precedes a heavy rainfall, of phosphorus over-application since manure is rarely balanced to match a P-based rather than N-based agronomic rate and P accumulates in soil over repeated seasons, of residual ammonia volatilization and odour even for subsurface injection at the injection slot, and of long-term soil-structure and pathogen concerns from repeated heavy liquid loading on the same field. A nutrient-management plan that tracks cumulative loading (not just the single-year N balance solved above) is the standard control for these risks.

Topic: Nitrogen-based manure land-application rate at continuous (steady-state) annual application.

Key relations: $N_{avail}=NH_4(1-f_{volat})+N_{org}(f_{yr1}+f_{yr2})$; $\text{Rate}=(N_{crop}-N_{starter})/N_{avail}$; $A=V_{total}/\text{Rate}$.

Why this works: Once a field has received manure for two or more consecutive years, every subsequent year's plant-available nitrogen pool is the sum of contributions from multiple past applications, each mineralizing at a rate that depends only on how long ago it was applied — not on the calendar year itself. "Year 2 as steady state" is the standard simplification for a mineralization schedule that only meaningfully separates years 1, 2, and 3+: by year 2 the pool already contains one full first-year and one full second-year cohort, and further years just repeat that same two-cohort pattern.

Common pitfall: crediting only the current year's application (omitting the prior year's residual mineralization) systematically understates available nitrogen once application becomes routine, which would lead to an over-application of manure and unnecessary nutrient loading to the field.

Source: Sommer & Christensen (eds.), Animal Manure Recycling: Treatment and Management (nitrogen availability and mineralization scheduling); MWPS-18 Livestock Waste Facilities Handbook (land-application rate design).

Question 5 of 5: Nitrogen-Based Land Application Rate

Question 5: Nitrogen-Based Land Application Rate (25 marks)