Evaluating Drought Characteristics Using MATLAB

Droughts are among the most impactful natural disasters, affecting vast areas and populations. Understanding the characteristics of droughts—such as their duration, severity, and intensity—is crucial for effective water resource management and planning. In this blog post, we’ll explore how to evaluate these characteristics using the self-calibrated Palmer Drought Severity Index (sc-PDSI) in MATLAB.

Definitions of Drought Characteristics

Before we dive into the analysis, let’s define the terms we’ll use to describe drought events:

• Drought Event: Occurs when the drought index (e.g., SPI, sc-PDSI) falls below a threshold of -1 and continues for at least two months. Two drought events are considered part of the same event if they are not separated by more than one month. This rule helps in understanding prolonged drought conditions by combining closely spaced dry spells into a single event. This is how many journal articles define drought.
• Duration: The length of time (in months) a drought event persists.
• Severity: The sum of the negative values of the sc-PDSI during the drought event.
• Intensity: The severity of the drought divided by its duration, representing the average severity per month.

Incorporating Run Theory

To enhance our understanding of these drought characteristics, we apply run theory. Run theory, first proposed by Yevjevich (1967), is a statistical method used to analyze sequences in data where a “run” is defined as a consecutive series of data points that meet certain criteria. In the context of drought analysis, theory of runs has been employed to recognize the drought characteristics such as duration, severity, intensity, and interarrival time. Readers can follow the paper by Shiau and Shen (2001) for detailed explaination about drought run theory.

• A run (or drought event) is initiated when the sc-PDSI falls below -1, signifying the start of a drought period.
• The run continues as long as the index remains below -1.
• The run ends when the index rises above -1, indicating the end of the drought.

This method is particularly useful for identifying and quantifying periods of drought by examining the duration, severity, and intensity of these runs. This aligns with our definitions and enhances the robustness of our analysis.

sc-PDSI Data

We’ll illustrate this procedure using sc-PDSI data obtained for Climate Division 9 in Texas, from January 1901 to December 2017. The time series of the data is plotted below using MATLAB:

Figure 1: PDSI time series from 1900 to 2017 at Climate Division 9, Texas

Here’s a MATLAB function that fulfills your requirements to evaluate the onset, departure, duration, severity, and intensity of drought events in a PDSI time series. The function accepts a time series of PDSI values and thresholds to define and merge droughts, and outputs a table with the specified characteristics. You can download the necessary files and codes from this Github repository: HydroThink. Feel free to leave any comments if you face any difficulty. 

Function Parameters

1. pdsi: The time series of Palmer Drought Severity Index (PDSI) values.
2. threshold: The value below which the index indicates drought conditions (e.g., -1).
3. minDuration: The minimum duration for a drought event (in months).
4. mergeDuration: The maximum separation between consecutive drought events to merge them into a single event (in months).

Function Output

1. droughtTable: A table containing the following columns:
   • DroughtNumber: The identifier for each drought event.
   • Onset: The starting index of the drought.
   • Departure: The ending index of the drought.
   • Duration: The length of the drought (in months).
   • Severity: The sum of the PDSI values during the drought.
   • Intensity: The average severity per month of the drought.

Finally, we call the above function that calculates the drought characteristics and save them in a csv file. You can also download the csv file from my github page.

I hope you like the blog post. In this post, I tried to help you understand about the drought characteristics and their evaluation using MATLAB. Please let me know about your thoughts below.