The Agricultural model determines the yield and production, as well as the costs of cultivation, for agricultural products.
Yields are estimated using a linear expression: $$log y_t = \alpha + \gamma g_t + \kappa k_t + \omega w_t + \tau t$$
where $y_t$ are the yields, in crop-specific units, per acre; $g_t$ and $k_t$ are growing-degree days and extreme degree-days, with crop-specific limtis; $w_t$ is the season-cumulative water deficit; and $t$ is the year. Greek letters denote calibrated coefficients.
Currently, nation-wide coefficients for each crop are determined by a pooled regression of available data. These are then combined with county-specific for counties with observed data, according to: $$\beta \sim \mathcal{N}\left(\frac{\frac{\hat\beta}{\hat\sigma^2} + \frac{\bar\beta}{\bar\sigma^2}}{\frac{1}{\hat\sigma^2} + \frac{1}{\bar\sigma^2}}, \frac{1}{\frac{1}{\hat\sigma^2} + \frac{1}{\bar\sigma^2}}\right)$$
where $\hat\beta$ is a given county unpooled coefficient (one of $\alpha$, $\gamma$, $\kappa$, $\omega$, and $\tau$), $\hat\sigma$ is its standard error, and $\bar\beta$ and $\bar\sigma$ are the corresponding national pooled coefficients.
This will be replaced with county-specific parameters from the hierarchical method, when these are available.
The list (and order!) of crops is defined in world.jl:
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crops = ["alfalfa", "otherhay", "Barley", "Barley.Winter", "Maize", "Sorghum", "Soybeans", "Wheat", "Wheat.Winter"]
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The key crop-specific definitions are listed in the table below.
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using DataFrames
readtable("../prepare/agriculture/cropmapping.csv")[:, [:crop, :unit, :yieldfile, :deficitfile, :eddprefix1, :eddprefix2, :gdd0, :kdd0, :notes]]
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The yield file and deficit files are available from Naresh. The EDD suffixes describe the source of season spans, from Sacks et al. 2010 and USDA 1997. The information for agricultural production comes from quickstats.
In the model, the coefficients on temperature, $\gamma$ and $\kappa$ are not used, and $\tau$ is not used (but all regressions have time centered on 2000). Instead, irrigated regions are assumed to have $\bar{y}_t = e^\alpha$. Rainfed areas have yields $\ddot{y}_t = e^{\alpha + \omega (m - p_t)}$, where $m$ is the water requirement of each crop, determined as the maximum water deficit observed for that crop from Naresh's data. $p_t$ is the season-total precipitation, with seasons currently corresponding to timesteps (typically 6 months).
The water requirements by crop are below, in m.
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todata = "../data"
include("../src/Agriculture.jl")
water_requirements
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The total production for a county is $$q_t = \bar{y}_i \bar{a}_i + \ddot{y}_i \ddot{a}_i$$
where $\bar{a}_i$ is the area used for irrigated production, and $\ddot{a}_i$ is the area used for rainfed irrigation.
According to the definitions above, irrigated regions are fully and exactly irrigated. Irrigation water demand for each crop is $\bar{a}_i (m - p_t)$
The Agriculture component also defines cultivation costs, below, as USD per acre, from some source.
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cultivation_costs
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