Crop Productivity Index
The Standardized Crop Production Index (SCPI) is a model that predicts the future production anomaly of alfalfa, barley and winter wheat for counties in Idaho, Montana, North Dakota, South Dakota, and Wyoming. The SCPI uses a linear model based on precipitation (in the form of the Standardized Precipitation Index) and crop prices to derive the production anomalies. The model is defined as:
SCPI_{i, j} = α_{i}_{, j, m, k}SPI_{m, j, k} + β_{i, j }SCVI_{s,i} +γ_{i, j, m, k}
where α and β are coefficients relating the precipitation anomaly to the production anomaly, and γ is a coefficient that captures the errors and factors that the model doesn’t explicitly account for. SCVI refers to the Standardized Crop Value Index, a state-level “index of lagged price anomalies”. The subscripts refer to the crop (i), state (s), county (j), month(m), and SPI time scale (k) of each parameter (Wurster et al., In Review).
This map shows the Standardized Crop Production Index for the crop and year specified in the selection panel. Blue colors are counties that have a projected positive crop production anomaly for the following year, while red counties have a projected negative crop production anomaly for the following year. Hovering over a county will pull up a chart with the exact SCPI value as well as the values of the variables used to calculate the SCPI. In this popup, SCPI, SCVI, SPI, Alpha Coefficient, Beta Coefficient, and Gamma Coefficient refer to each of the parameters given in the above equation. “Optimal Window” and “Optimal Month” in the popup refer to the month and time scale of SPI used to calculate the SCPI for a given county. For example, Missoula County's optimal window and month for alfalfa are 2 months and May, respectively. This means a that for each year, the alfalfa SCPI for Missoula county is calculated with using the May SPI with a window of 2 months. Clicking on a county pulls up a historical plot of crop production anomalies (blue line) and the modeled SCPI production anomalies (red line). To view a different year or crop, change the selections in the control panel and then click the “Change Inputs” button.
**NOTE: The map takes some time to load. It may take up to 30 seconds for the map to show up on the screen.
Legend of County Popups in SCPI Map
Legend Item |
Definition |
Units |
SCPI | Standardized Crop Production Index, defined above. | Standard deviations above/below normal county crop production. |
SCVI | Standardized Crop Value Index. A detrended and normalized index of crop price anomalies from 1980 - present. | Standard deviations above/below normal statewide crop price. |
SPI | Standardized Precipitation Index. A detrended and normalized index of county-wide precipitation anomalies from 1980 - present. | Standard deviations above/below normal county precipitation. |
RMSE | Root Mean Square Error of the Standardized Crop Production Index | Standard Deviations |
Optimal Window | The window that was used to calculate the SPI for the county. Window values are chosen to minimize the SCPI RMSE. | Number of Months |
Optimal Month | The month that was used to calculate the SPI for the county. The month is chosen to minimize the SCPI RMSE. | Month |
Alpha Coefficient | "Fraction of precipitation anomaly that translates to production anomaly."_{1} | Unitless |
Beta Coefficient | "Proportion of price anomaly that translates to production anomaly."_{1} | Unitless |
Gamma Coefficient | "Absorbs the effect of errors and the effect of other factors not explicitly included in the [SCPI] model."_{1} | Unitless |
1. Wurster et al., In Review