Stochastic dynamic programming model for joint optimization of crop production and reduction of nutrient run-off

1. Stochastic dynamic programming model for joint optimization of crop production and reduction of nutrient run-off Kari Hyytiäinen, Jarkko K. Niemi, Kauko Koikkalainen, Taru Palosuo and Tapio Salo MTT, Finland Risk and Crisis management in Nordic Agriculture, 16-17 September 2010, Uppsala Sweden

2. Introduction Producer faces uncertainty about yield and revenue Variability and unpredictability of weather Inability to control for weather Risk affects input use and return on production The effects of fertilizer application are irreversible Current practice: Decide input use when growing season begins Alternative: Adapt input use according to production potential Economic and environmental benefits? Increased yield potential when there is lack of nitrogen in the soil? Requires taking into account that yield uncertainty is resolved gradually

3. Objective Can farmer benefit from applying the fertilizer several times during the growing season as opposed to fertilizer applied upon sowing only? How yield uncertainty and information about the amount of nitrogen available to plant roots in soil at each period impacts the optimal input allocation? Environmental benefits (reduced N leaching)? How do farmers respond to environmental policy instruments (pollution tax) in this context?

4. Data and models

5. Land parcel characteristics and crop choice Meteorological data Simulated cropt growth (WOFOST) Simulated soil processes (COUP) Economic parameters Stochastic simulation: probability distributions for state variables and cash flow, transition equations Dynamic programming: optimal solutions Simulate crop growth using on optimal solutions

6. Case: two-row barley • For malting or animal feed depending on protein content • A clay soil site in Jokioinen (●,60° 48' , 23° 30') • The site is highly productive in Finnish standards • Meteorological data for 1981-2006 • Crop growth simulation model WOFOST 7.1: lengths of periods, the potential development of barley during growing season, response to meteorological data • Soil process model COUP: denitrification, leaching, the net effect of denitrification and immobilization of nitrogen • Information about the unit costs of activities and prices • Recursive stochastic dynamic programming model

7. State and control variables • State variables • Characterize the state of affars • t = time period (year, 7 stages within a year) • Nt = the amount (kg per ha) of plant available nitrogen in the soil • Bt = the amount (kg per ha) of nitrogen in the plant ( biomass) • Control variables • Endogenous in the model, adjusted according to the state variables • ut = the amount (kg per ha) of nitrogen applied in period t • 2nd stage along with sowing • 3rd stage and 4th stage by spreading the fertilizer on surface • 5th stage by using leaf fertilizer

8. State variables – t(i,j) • Duration of each period is determined by the temperature sum, which is based on actual weather data • The timing of harvesting is affected also by rainfall Source: Meteorological data and Wofost-simulations (years 1981-2005)

9. Bellman equation Value of plot at time t State variables Expectations operator Control variables Discount factor One-period net returns St. (transition equation for nitrogen stock) (transition equation for the biomass) BTand NTaregiven (initial state given) given (the terminal value of plot)

10. Transition equations I Soil nitrogen stock in the next period = Current nitrogen stock in the soil +Fertilizer deposited into the soil in the current period +Demineralization and immobilization from humus and litter +Athmospheric deposition of nitrogen - Nitrogen uptake of plant - Nitrogen removed from the soil through denitrification - Nitrogen removed from the soil through leaching • The items above are affected by the weather

11. Transition equations II Nitrogen in the plant in the next period = Current amount of nitrogen in the plant + Nitrogen uptake by the plant • Plant growth can be limited • From above by its growth potential • From below by drought stress or by the lack of nitrogen in the soil • Stochastic due to weather

12. Transition equations • Other items of interest • The price of barley depends on its’ protein content • Rainfall affects harvesting and drying costs

13. Results

14. Optimal fertilizer applicationNo pollution tax

15. Optimal fertilizer applicationNo pollution tax

16. Pollution tax introduced:effects on fertilizer application

17. Fertilization technology and environmental fee —●— One-time application —o— Split application

18. Fertilization technology andenvironmental fee —●— One-time application —o— Split application

19. Conclusions • The option to split fertilizer application increases return on land parcel and rationalizes input use according to production possibilities by taking into account that uncertainty about yield is resolved gradually • Excessive use of fertilizer can be reduced when the soil is rich in N or yield be improved when the soil is poor in N • However, internalizing the negative externalities (N leaching to water bodies) in the land-owner’s decision problem makes split fertilization application rational

20. Thank you for your attention! We gratefully acknowledge funding from the Finnish Ministry of Agriculture and Forestry