Probability Distributions and Return Periods of Extreme Rainfall Events in the Zagros Mountains: Karkheh Basin Floods

Rain is a fundamental part of life, but when it falls too hard or too fast, it transforms from a life-giving resource into a destructive force. In the world of hydrology, the science of water movement, researchers do not just count how much rain falls; they try to understand how often the most extreme storms happen. This is the study of "return periods," a concept that estimates how many years might pass before a rainfall event of a specific size occurs again. It is a crucial calculation for engineers designing bridges and dams, and for communities planning where to build homes. When the climate shifts, these patterns can change, making old maps of risk unreliable. Understanding whether a flood is a rare anomaly or a sign of a new normal is essential for protecting lives and infrastructure in a warming world.

In the rugged Zagros Mountains of western Iran, a team of scientists recently turned their attention to the Karkheh River Basin, a region that faced devastating floods in the spring of 2019. The researchers set out to analyze the rainfall data from this area to determine just how extreme those storms were and to figure out the best way to predict future disasters. They focused on the heaviest rainfall recorded in a single day at several weather stations scattered across the basin. By looking at decades of historical data, they sought to find the mathematical pattern that best describes these rare, high-intensity events. Their goal was to move beyond simple averages and understand the true nature of the most dangerous storms, which often do not follow the same rules as typical weather.

The study revealed that while the total amount of rain falling in the region over a whole year has not changed significantly, the intensity of the heaviest daily downpours is increasing. This suggests that the region is seeing more frequent extreme events, even if the overall wetness of the year remains steady. The researchers examined data from seven monitoring stations, but they concentrated their detailed analysis on four locations that had long enough records to be statistically reliable. At these sites, they found that the rainfall data did not follow a standard, bell-shaped curve. Instead, the data was skewed, meaning that extreme values were more common than a simple average would predict. This skewness indicates that the region is prone to sudden, violent bursts of rain that can overwhelm the landscape.

One of the most significant findings concerned the specific storms that struck in March and April 2019. At the Poldokhtar station, located upstream near the river's source, a single day in March saw 139.4 millimeters of rain. At the Nurabad station, another location in the basin, 101 millimeters fell in April. These were not just heavy days; they were statistical outliers. When the researchers calculated how often such events should happen, they found that these storms were likely to occur only once every 70 to 200 years. This places the 2019 floods firmly in the category of extreme, rare disasters. The analysis showed that the river discharge, or the volume of water flowing through the river, surged to nearly 4,700 cubic meters per second during the peak of the event, a level that caused widespread flooding and damage across several provinces.

To make these predictions, the team tested several different mathematical models, which are essentially different ways of fitting a curve to the rainfall data. They found that no single model worked perfectly for every location. For the station with the longest history of records, spanning 72 years, a model known as the Gumbel distribution provided the best fit. However, for the stations with shorter records, a different model called the Inverse Gamma distribution proved to be more accurate. This distinction is vital because using the wrong model can lead to underestimating the risk of a flood. The researchers also calculated the "Probable Maximum Precipitation," which is an estimate of the absolute heaviest rain that could physically fall in the region under the most extreme conditions. Using a refined method, they estimated that Poldokhtar could potentially see up to 161 millimeters of rain in a day, a figure slightly higher than what was actually recorded in 2019.

The study also addressed the causes of the 2019 devastation. While changes in land use and construction along riverbanks certainly made the damage worse, the primary trigger was the sheer volume of rain. The researchers noted that the storms were part of a larger atmospheric phenomenon that brought record-breaking moisture to the mountains. The timing was particularly cruel; the heavy rains fell in the spring when the ground was already saturated from winter snowmelt, leaving the soil unable to absorb any more water. This combination of intense rainfall and a saturated landscape turned the Karkheh Basin into a flash flood zone. The data suggests that while the total annual rainfall has not shifted dramatically, the frequency of these high-intensity, short-duration storms is rising, a pattern that aligns with broader concerns about climate change intensifying extreme weather.

Ultimately, this research provides a clearer picture of the flood risks facing the Zagros Mountains. By identifying that the Inverse Gamma distribution is the most reliable tool for analyzing shorter data sets in this region, the study offers a better method for future risk assessments. The findings confirm that the 2019 floods were indeed rare, 70-to-200-year events, but they also highlight a worrying trend: the daily maximum rainfall is on the rise. This means that what was once considered a once-in-a-century storm may become more common. For the communities living in the basin, this knowledge is not just academic; it is a critical tool for planning and survival, reminding them that the landscape is changing and that the rules of the past may no longer apply to the storms of the future.