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Utilizing Drought-Days in Evaluating Irrigation and Fertility Response Studies¹

ABSTRACT

It is expected that a crop grown during a year of insufficient moisture will economically require less fertilizer than a similar crop grown with an ample supply of moisture. Likewise, crop response to supplemental irrigation would be greater during a year of low rainfall than during a year of adequate rainfall.

The moisture deficiencies may be expressed as "drought-days" for any specific soil-crop-fertility situation. Incorporating "drought-days" as a production function to characterize the factor-product relationship as shown in the general equation below permits an evaluation of the effects of drought on yield and on the interactions with other variables such as fertility.

Y = b₀ + b₁N + b₂N² + b₃D + b₄D² + b₅ND. Where Y = yield, N = pounds of nitrogen per acre and D = drought-days or drought index.

A history of drought conditions for an area may then be used to obtain probabilities of the frequency of occurrence of varying degrees of drought and consequently the effect on yield outcome. This permits the presentation of yield outcome in terms of risks for various inputs rather than as single valued outcomes.

Irrigation may be expected to reduce the number of drought-days encountered in any cropping situation. Expressing crop yields as a function of drought-days and fertility level permits the evaluation of irrigation on yield and subsequent crop income. Combining this with the probabilities for drought occurrence provides a means for determining the expected irrigation response in an area and attaching probability statements relative to such a response.

¹ Contribution from the Department of Agronomy, University of Tennessee Agr. Exp. Sta. and the Tennessee Valley Authority. The authors acknowledge the assistance of J. R. Overton and E. J. Chapman in collecting field data and of Betty Prater for statistical computations. Presented before Div. IV, Soil Science Society of America, Nov. 19, 1959, at Cincinnati, Ohio.

² Agronomist, University of Tennessee, and Agricultural Economist, Tennessee Valley Authority, respectively.

Received for publication December 7, 1959. Accepted for publication January 5, 1960.