The SPI, first developed by Mckee et al. (1993), is a tool that was developed primarily to quantify the precipitation deficit for multiple timescales. These timescales reflect the impact of drought on the availability of water resources in different reservoirs—soil moisture, groundwater, and snowpack. The SPI allows an analyst to determine the rarity of a drought at a given time scale (e.g., 1 month, 3 months, 12 months) of a rainfall record at a particular location.

#### How SPI is Calculated

The SPI calculation involves fitting a long-term precipitation record for a desired period to a probability distribution, which is then transformed into a normal distribution so that the mean SPI for the location and desired period is zero. Here’s a step-by-step breakdown of the calculation:

**Data Collection**: Collect precipitation data for the location over a sufficiently long period (at least 30 years of data is recommended to get reliable results).**Determine the Probability Distribution**: The data are fitted to a probability distribution. Historically, the gamma distribution has been used because it can adequately model the skewed nature of precipitation data. However, other distributions like the Pearson Type III can also be used.**Fitting the Distribution**:- The gamma distribution is defined by its probability density function:

f(x) = \frac{1}{\beta^\alpha \Gamma(\alpha)} x^{\alpha - 1} e^{-x/\beta}

where: - ( \alpha ) is the shape parameter,
- ( \beta ) is the scale parameter,
- ( x ) is the precipitation amount,
- ( \Gamma(\alpha) ) is the gamma function.

- The gamma distribution is defined by its probability density function:
**Estimating Parameters**:- The parameters ( \alpha ) and ( \beta ) are estimated from the precipitation data, typically using methods like the Maximum Likelihood Estimation (MLE).

**Calculate Cumulative Probability**:- For each precipitation total, calculate the cumulative probability of observing a value equal to or less than that total under the fitted gamma distribution.

**Transform to the Standard Normal Variable**:- The cumulative probabilities are then transformed to the standard normal variable, Z, which is the SPI value. The transformation involves inverting the cumulative distribution function (CDF) of the normal distribution. Therefore, most the of SPI values you see in real life will be between -3.5 to 3.5.

#### Importance of SPI

The SPI is dimensionless, which makes it versatile and comparable across different regions with distinct climates. It can be computed for different timescales, which allows it to be used for monitoring short-term agricultural impacts as well as long-term hydrological impacts. A negative SPI indicates less than median precipitation (drought), while a positive SPI indicates more than median precipitation.

Understanding how the SPI is calculated provides us with a strong foundation to explore how we can implement this calculation in various programming tools. Interested Readers can also read more about SPI from this reseach article, which I, personally, find very detailed.

In the upcoming posts, we will delve into how to compute the SPI using MATLAB, Python, and R, providing code snippets and detailed explanations to guide even those new to these environments. Read our next article to get a hang of how the SPI can be evaluated using MATLAB, Python, and R.