Yield = f(solar energy, soil, water, seed, farmer, pest/disease, ...)
Conceptually, in its simplest form, one may liken the cultivation of a crop in the field to a mathematical function. For a given set of inputs (e.g., water, nutrient, seed), a crop produces a set of outputs (e.g., biomass, yield, residue). If the input-output relationships were all linear, it might even be (relatively) simple and easy to estimate the outcome. For example, one might say more yield with more fertilizer. Or, more yield with more water. In reality, however, this is often not the case; the interactions between each cropping system factor is very complex. A classic example is the interaction between nitrogen and water. When soil is very dry, additional nitrogen input can not reach plant roots. When soil is sandy, water leaches out nitrogen.
Complex crop models operate mechanistically, so that these complex interactions of multiple factors are being modeled in a systematic way. The following example case illustrates the complexity of crop yield estimation with a range of water and nitrogen management in rainfed maize cultivation in South Wollo Zone of Amhara region in Ethiopia. In an earlier simulation analysis, the South Wollo was one of the areas with largest rainfed yield gap.
- Crop: Maize
- Traditional with long maturity
- Improved with medium maturity
- Improved with short maturity
- Site: South Wollo, Amhara, Ethiopia
- Soil: HC_GEN0018 (low fertility, shallow depth, loamy texture)
- Weather: CRU-Mashup v1.0
- Years: 1955-2003
- Nitrogen managements:
- No fertilizer
- Urea application at 20 kg[N]/ha rate
- Urea application at 40 kg[N]/ha rate
- Urea application at 60 kg[N]/ha rate
- Urea application at 80 kg[N]/ha rate
- Urea application at 100 kg[N]/ha rate
- Water management:
- Irrigated low-level
- Irrigated medium-level
- Irrigated high-level
- Output: Average yield (kg/ha)
As the site's soil fertility is low in general, the additional application of inorganic nitrogen fertilizer increases the average yield, especially in lower dosages (less than 60 kg[N]/ha rates in this case) (Figure 1). However, for higher rates, the yield increasing trend is not as high as the lower rates. The amount of leached-out nitrogen increases (Figure 2), thus the overall use of nitrogen gets lower. Using this non-linear relationship, one can estimate the economically-optimum fertilizer application rate, at which the marginal gain of yield is maximum from the additional amount of fertilizer application (i.e., the value:cost ratio). It may be possible to increase the nitrogen use efficiency by optimizing the application scheme on when, how often, and how much to apply throughout the season, but it is not a trivial task.
Nitrogen and Water Responses
Nitrogen and water interact in the soil. Nitrogen needs water to be mobile and get absorbed by plant roots, and soil characteristics play an important role. The same rate of nitrogen application, in general, the more water irrigated, the higher yield it gets. However, the efficiency and effectiveness of irrigation on the crop growth and yield is quite complex, thanks to the complex interaction between soil, water (irrigation and/or rainfall patterns), and nitrogen, and crop's growth stage-dependent sensitivity to water stress. This could result in seemingly inconsistent and unintuitive results. For example, Figure 3 shows the overall increasing trend of increasing yield with more amounts of irrigated water, yet there are variability within the same amount of nitrogen fertilizer application rate (e.g., urea 40 kg[N]/ha). This does not mean that there is not much incentive to irrigate with 40 kg[N]/ha of urea, but more careful management of water and nitrogen is needed at the level. For higher rate of fertilizer application rates (e.g., 80 and 100 kg[N]/ha of urea), an overall yield-increasing trend was clearer.