An Analytical, Holistic Approach to Drainage and Infiltration on Flatland Agricultural Areas.

The effect of global climate change  and the need for increasing the food production on agricultural land  require improvements in water management of existing agricultural land. This is also  true for the already intensively productive agricultural low lying land areas where traditionally production has been favorable.  Most advanced water management research has been process oriented  and has focused  either on drainage or on infiltration/irrigation  problems. Much more needs to be done in areas where both of these water management problems exist. In low lying flat land areas the water supply is usually adequate or excessive part of the year and deficient for the remainder of the year. Only limited research has been conducted  with a holistic approach to these conditions. In this regard, the work by J.J. van Deemter is noteworthy which was conducted under the leadership of S. Hooghoudt, a well-known Dutch drainage engineer  who played a key role in the drainage of newly reclaimed land from the sea in the 1930s and 1940s in the Netherlands.  While this work was primarily motivated with drainage in mind through ditches and tiles, the solution approach that van Deemter came up with and was published as his doctoral dissertation  covers in fact a wide range of water management problems from infiltration by rainfall, overland flow and subsurface irrigation, drainage through tiles and ditches, seepage from and deep drainage losses to groundwater, as well as evaporative water losses. His work considers steady flow regimes in homogeneous, isotropic aquafers, where Laplaces equation can be solved for potential flow if suitable boundary conditions exist. His analytical technique uses conformal transformations in which the geometry of the spatial potential plane and the flow potential of this flow field are projected on the upper half a common potential plane  of which the real axis is represented by the vertices of the flow field. Then, a 1:1 correspondence can be established  through a broken linear transformation that yields the solution to the flow regime. This presentation will discuss the main features of van Deemter's work with emphasis on drainage and sub-irrigation using tiles. The mathematical analysis will be complemented with results of calculations  for specific  flow regime situations.