Trends and Attributions

Look at this chart.

On the x-axis, I am showing 80 years starting with some reference. On the y-axis, I am plotting the counts or the number of extreme rainfall days each year.

Do you think there is an increasing trend is this data? Is there an overall increase in the number of extreme rainfall days?

Perhaps. Let’s add a trend line and see.  

Once we superimpose a linear trend line on the plot, it becomes apparent. We still see variability from year to year, but in the long run, we see that the number of extreme rainfall days each year is increasing.

Can you guess why there is a trend in the data? In other words, can you think of some reasons for this trend?


Wait. Hold on to your reasons till I unveil how I created this data.

Look at this chart. It is time vs. a constant number of extreme rainfall events, 10, in each year.

Now, look at this chart which is a pure sine wave with a periodicity of 5 years and amplitude of 1.

Another sine wave with a periodicity of 10 years and amplitude of 1.

This one is with a periodicity of 20 years and amplitude of 1.

And, finally, take a look at this sine wave with a periodicity of 100 yearsand amplitude of 1.

If we add these sine waves and the constant plus some noise to the resultant number we get the original data. 

Did you see the pattern? The trend we initially observed is due to a combination of four different periodic sine waves. Were these periodic oscillations in your reasons?

If not, why not?

Saman Armal, a Ph.D. student in the Department of Civil Engineering and NOAA CREST at the City College of New York, CUNY, working on extreme rainfall events, was also asking this question.

“We find trends in the data. What can we attribute these trends to?”

We started with anthropogenic influence, but, anthropogenic forcings cannot solely explain the trend. Climate has a cyclical nature. In a particular region, its manifestation can be entirely different for a given decade or century.

For instance, if we suppose that rainfall in a given area is influenced by interannual to decadal to multidecadal climate oscillations (like the periodic sine waves we saw before), any given decade or a block of time can manifest as runs of wet or dry years.

If the region has observed records long enough to capture these cyclicities, periods of wet years will be transposed by periods of dry years and the resulting long-term time trend as a result of climate cycles in rainfall will be nonexistent. On the contrary, if the region has limited observed records, one can detect a long-term increasing or decreasing trend in the data depending on whether the climate is manifested as wet or dry years.

The effect of natural climate variability in rainfall patterns including the impact of El Niño–Southern Oscillation (ENSO), the interdecadal Pacific oscillation (IPO), the Pacific decadal oscillation (PDO), the North Atlantic Oscillation (NAO), and the Atlantic multidecadal oscillation (AMO) is well documented. Hence, we wanted to understand the influence of anthropogenic forcing and natural climate variability on the occurrence of extreme events in an integrated framework.

This objective motivated Armal’s recent work which got published in the Journal of Climate. The paper provides a hypothesis-driven methodology to understand the association of trends in extreme rainfall event frequency to anthropogenic forcing and natural climate variability over the contiguous United States.

In our analysis, we consider two hypotheses:

  1. The monotonic trend in the annual frequency of extreme rainfall events is solely attributed to anthropogenic forcing, and
  2. The monotonic trend in the annual frequency of extreme rainfall events is attributed to anthropogenic forcing and cyclical climate variability.

The models get information from global near-surface temperature and climate indices, and the residual trends for each hypothesis are examined. The choice of the best alternative hypothesis is made based on the Watanabe–Akaike information criterion, a Bayesian pointwise predictive accuracy measure.

Statistically significant time trends are observed in 742 of the 1244 stations in the continental United States. Trends in 409 of these stations, predominantly found in the U.S. Southeast and Northeast climate regions can be attributed to changes in global surface temperature anomalies. The trends in 274 of these stations, mainly found in the U.S. Northwest, West and Southwest climate regions can be attributed to El Niño–Southern Oscillation, the North Atlantic Oscillation, the Pacific decadal oscillation, and the Atlantic multidecadal oscillation along with changes in global surface temperature anomalies.

Please read the paper and let us know what you think. You can get the paper from AMS website here. If you need a copy of it, please write to me. I will be happy to share. We welcome any comments and critics.

‘Dam’n Floods

December 2016: San Francisco – Kary, who I shared an Uber ride with, thinks that Pineapple Express is a funny name for a storm.

November 2016: Vietnam – Ha Ting, Quang Tri and Quang Binh provinces that experienced rainfall in October, are hit by another wave of heavy rainfall events. Tens of thousands of people displaced.

October 2016: Argentina – Long-term flooding in Buenos Aires affects rural and farming areas. Persistent rainfall leads to an overflowing Quinto River. Agricultural emergency declared.

July 2016: China – Yangtze River overflows. Around 40,000 houses destroyed. More than 1.5 million hectares of cropland damaged.

June 2016: Texas – Heavy rain has increased river levels. President Declares Disaster for 12 counties.

A common thread in all these events is that the floods lasted for more than 30 days and are associated with repeated rainfall into the region. These are colloquially called long duration floods. Understanding the causes of these types of floods and using that information for managing water infrastructure is a recent area of research.

Nasser Najibi is working in this field and has recently published an article in Advances in Water Resources Journal on the atmospheric teleconnections of long duration floods. Large dams along the main stem of the Missouri River Basin are selected for this investigation. For each dam, we differentiate long duration floods from short duration floods and identify what hydrological, climatological and atmospheric conditions cause the long duration floods. Nasser derived a precursor index that shows an incipient condition for long duration floods. There is an organized atmospheric structure (spatial arrangement of high-pressure nad low-pressure areas) that draws the storm tracks repeatedly into the region causing recurrent rainfall events. These repeated waves of rainfall events fill up the dams and cause river overflows. We are now developing reservoir operation models using this prognostic information for managing flood hazards better . More information can be found in the journal article. We welcome any comments.

Oh, and Pineapple Express is not just a 2008 comedy film or a funny name for a storm. It is also a common term for a strong and persistent flow of atmospheric moisture that causes heavy precipitation in mid-latitudes. Its discovery initiated this new field of climate-informed flood risk research.