A Process-Based Transfer Function Approach to Model Tile Drain Hydrographs

1. A Process-Based Transfer Function Approach to Model Tile Drain Hydrographs Mazdak Arabi, Jennifer Schmidt and Rao S. Govindaraju World Water & Environmental Resources Congress 2005 May 17, 2005

2. Overview • Rationale and Background • Methodology • Available Data • Results and Discussion • Conclusions Rao S. Govindaraju School of Civil engineering Purdue University

3. Rationale and Background • Tile Drains • Controlling the height of the water table • Earlier planting • More developed root system • Expedite the transport of nutrients and pesticides to surface waters • Water quality problems Rao S. Govindaraju School of Civil engineering Purdue University

4. Rationale and Background • Previous Work (Reviewed by Youngs, 1999 ) • Numerical solutions of Richards’ equation • Solutions using the concept of specific yield in Boussinesq’s equation • Method of continuous succession of steady states Rao S. Govindaraju School of Civil engineering Purdue University

5. Rationale and Background • Objectives • To develop a mathematical model for tile drain response to rainfall events • Transfer function from physical principles • Unsaturated vertical flow • Saturated horizontal flow • Parameter estimation in the context of method of moments • To evaluate model performance utilizing data from a field study Rao S. Govindaraju School of Civil engineering Purdue University

6. x z Soil Surface Recharge Water table at time t no-flow boundary (x=0) h(x,t) Tile Drain Initial Water table a Impervious barrier L Schematic of the Tile Drain Problem Methodology • Tile Drain Problem and Parameter Definition Rao S. Govindaraju School of Civil engineering Purdue University

7. x z h(x,t) Q(x,t) a L K: hydraulic conductivity S: drainable porosity Methodology • Mathematical Development • Saturated horizontal flow • Water flux in x-direction throughout the saturated thickness • Continuity equation • Boussinesq equation Rao S. Govindaraju School of Civil engineering Purdue University

8. x z Soil Surface Water table at time t no-flow boundary (x=0) h(x,t) Tile Drain Initial water table a L Methodology • Initial Conditions • Boundary Conditions Rao S. Govindaraju School of Civil engineering Purdue University

9. Methodology • Unsaturated vertical flow • Time dependant recharge (from sharp-front analogy) Rao S. Govindaraju School of Civil engineering Purdue University

10. Methodology • After simplification, tile drain response is expressed as: Rao S. Govindaraju School of Civil engineering Purdue University

11. Methodology • Parameter estimation based on method of moments. Rao S. Govindaraju School of Civil engineering Purdue University

12. Available Data • Description of Experimental Site • Purdue Water Quality Field Station (WQFS) • Silty clay loam • Glacial till at approximately 2 m below the surface • The field contains cracks and other features • A group of 48 plots each with a 10m by 24m clay lysimeter • Slurry walls to create a hydrologically isolated “box” • Dimensions L = 5m, a = 0.53m, and z = 1m. Rao S. Govindaraju School of Civil engineering Purdue University

13. Available Data • Events used in this study • Calibration Event: Event 2, single burst • Using first moment Rao S. Govindaraju School of Civil engineering Purdue University

14. Results and Discussion Comparison of observed hydrographs and the transfer function model for Event 2, calibration event. Rao S. Govindaraju School of Civil engineering Purdue University

15. Results and Discussion • maintained at 0.265 hr-1 for all events • C from zeroth moment, and t0from rainfall hyetograph Rao S. Govindaraju School of Civil engineering Purdue University

16. Results and Discussion Comparison of observed hydrographs and model results for Event 1. Rao S. Govindaraju School of Civil engineering Purdue University

17. Results and Discussion Comparison of observed hydrographs and model results for Event 3. Rao S. Govindaraju School of Civil engineering Purdue University

18. Results and Discussion Comparison of observed hydrographs and model results for Event 4. Rao S. Govindaraju School of Civil engineering Purdue University

19. Results and Discussion Comparison of observed hydrographs and model results for Event 5. Rao S. Govindaraju School of Civil engineering Purdue University

20. Results and Discussion • Evaluation of Model Performance based on Error-Statistics Rao S. Govindaraju School of Civil engineering Purdue University

21. Conclusions • A solution for the response of a single tile drain • Semi-analytical • Three-parameter transfer function (note: all parameters have physical interpretation) • : time lag for infiltrated water to reach the groundwater table • C : scaling parameter that ensures mass balance • : a function of soil properties and geometry of the plot Rao S. Govindaraju School of Civil engineering Purdue University

22. Conclusions • Tile-drain response scales linearly with the infiltrated depth raised to a power; i.e. as . • Satisfactory model performance, especially for events with data from multiple experimental plots • The solution is amenable to moment analysis thereby allowing for parameter estimation Rao S. Govindaraju School of Civil engineering Purdue University