Spatial dynamics of water and nitrogen management in irrigated agriculture.

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(1) Worldwide freshwater consumption rose more than sixfold in the 1990s, twice the rate of population growth, resulting in one-third of the world's population living in countries with moderate to high water stress (UNEP 1999). While household demand is rising rapidly, industrial use is expected to double by 2025, driven largely by a near fivefold increase in use by China.

(2) Nitrate contamination can have immediate health effects in the form of acute toxicity (California State Water Resources Control Board 2002). Contaminate levels are often established to prevent methemoglobinemia that can be potentially fatal, especially to children under six months (Criss and Davidson 2004). Methemoglobinemia has occurred in infants exposed to nitrate concentrations only slightly above 10 mg/L. Nitrate-contamination in drinking water in Taiwan, Spain, China, has been linked to increased risk of gastric cancer (Knobeloch et al. 2000; Morales-Suarez-Varela, Llopis-Gonzalez, and Tejerizo-Perez 1995; Xu, Song, Reed 1992; Yang et al. 1998). Nitrate contamination can also inhibit thyroid iodine uptake.

(3) Nitrogen dynamics in Vickner et al. (1998) also differs from the dynamics modeled in this article. They specify nitrogen carryovers for both the under- and over-irrigated portions of the field; however, these fractions are endogenous and can vary over time. The carryover equations are, therefore, inaccurate if portions of the field in a given year are a mix of previous fractions. While not likely quantitatively significant in their application, this could be a difficulty elsewhere. The equations of motion in the model developed here are for exogenous fractions of the field and avoid this difficulty.

(4) A sophisticated literature on precision agriculture exists for rain-fed agriculture. While irrigated producers can do little to mitigate infiltration variability for a given irrigation system, they could in principle modify fertilizer applications as a reviewer pointed out. The scientific and engineering information to analyze this does not exist for irrigated agriculture to our knowledge. Regardless, not all spatial variability can be met, and analyses as here are necessary for benefit/cost calculations of precision farming activities.

(5) All irrigation systems exhibit nonuniform water distribution. This includes travel and residence time disparities (furrow), friction losses (sprinkler and drip), and emitter variability (drip and LEPA). Well-maintained modern systems can achieve significant infiltration uniformity with higher yield and/or reduced water inputs. This article focuses on furrow systems but the model applies to investment in any system.

(6) We consider the downward movement of water and nutrients in the rootzone only and no horizontal interaction within the rootzone, implying that only the distribution of infiltration coefficients is necessary. The particular spatial configuration of the field is not needed and, in general, there are infinite spatial configurations consistent with an assumed distribution. The assumed sub-areas of the field with a given [beta] value need not be contiguous. Also note that this formulation still implies externalities. Nitrates percolate below the rootzone to the water table and then move laterally through various mechanisms, eventually influencing water quality throughout the aquifer.

(7) The shapes of the estimated spatial density functions are some what dependent on the selected grid interval for soil nitrogen values, an issue that generally arises with any nonparametric density estimation. A grid with 11 intervals was selected here as being most informative. The grid interval for the estimated density function is independent and conceptually distinct from the number of state variables. At any point in time, 0, 1, or multiple state variables could take values lying within a specified nitrogen interval in figure 3. The discretization determining the number of plots in the field and state variables is for [beta] values; the fact that there are the same number of intervals in figure 3 as there are state variables is purely coincidental.

(8) Additional spatial results are presented in Knapp and Schwabe (2007). Referring to figure l(c), results show that infiltrated water occurs in the convex, concave, and plateau maximum of the emissions function, supporting the earlier conceptual discussion that global plant-level functions are needed with spatial variability. Another figure demonstrates that the bulk of N-emissions in the steady-state come from plots with intermediate [beta] values; low [beta] values imply low deep percolation depths hence reduced N leaching; high [beta] values imply low soil N levels entering the year and hence reduced N available to be leached.