Most geomorphic processes vary in terms of intensity and degree of variability over space and time. Such variability is often caused by different environmental conditions under which they operate. One of the fundamental enquiries about geomorphic processes is to understand the frequency with which events of different magnitudes occur in natural systems. Analysis of the size of various geomorphic processes over various time scales has clearly demonstrated that extreme, high magnitude events are rare while the low-to-medium magnitude events are much more frequent. This is termed as the magnitude-frequency relationship (Fig 1a) in geomorphology and plots showing this relationship have a positive-skewed form. Some of the common examples include flood frequency relationship (Fig 1b), earthquake recurrence and weather events. The underlying principle in these relationships is that most of the extreme events require a specific combination of factors and conditions, which while individually are not uncommon, are unlikely to occur simultaneously.
Extreme events incite and demand attention by researchers because of their rarity although they can induce tremendous changes in a geomorphic system and at times cause a major, lasting transformation of the landscape. Traditionally, scientists have been on guard against any tendency to explain a geomorphic feature due to the extreme and rare events as was done in the 17th and 18th centuries when a large Noah’s flood in the eastern Mediterranean region was sought as an explanation for features such as large isolated rocks in alpine meadows. Drawing upon new geophysical evidences, the current thinking, however, attributes the genesis of Noah’s biblical flood to the catastrophic flooding of the Black Sea at about 7150 BP (W B F Ryan et. al., 2003 ‘Catastrophic flooding of the Black Sea’, Annual Review of Earth and Planetary Sciences). Another example from a recent work by S Gupta et. al. 2007, ‘Catastrophic flooding origin of shelf valley systems in the English Channel’, in Nature, argues that the English Channel was carved out by scouring by fluvial channels sourced from a large lake formed due to damming by the Fennoscandian ice sheet to the north and east. Two large floods during a major glaciation phase between 450-400 kilo-annum (Ka) were the triggers for the carving of the canyon, which now forms the English Channel.
Number of such events are described in mythology or documented through archaeological investigations in several parts of the world, but are not recorded in the written human history. However, recent research has forced the scientific community to rethink about the role of such extreme and rare events. An added dimension is the scale of human interventions which have modified the rates of geomorphic processes; several events of dam-burst or levee-failure floods occur frequently now and most of these usually fall outside of the usual distribution of floods (Fig 1a).
Most geomorphic processes are naturally ‘thresholded’ which means that little events do nothing even if they are statistically significant. However, once above the threshold, the magnitude of the process increases non-linearly. As a result, large geomorphic events result in significant impact when they occur given the non-linearity of the process. Another common characteristic of the geomorphic systems is the feedbacks. While a negative feedback ‘regulates’ the process, a positive feedback may endanger the system as it reinforces the original output and eventually causes a system to shift to a new equilibrium state. Such snowballing effect is precipitated by the breaching of threshold in the system and can often result in an extreme event. A good example is a sediment-laden river that may not regularly flood, but a high sedimentation rate in channel belt may eventually limit the carrying capacity of the river and result in a catastrophic flood once the river crosses a threshold. The Kosi floods of 2008, reported earlier through G’nY and elsewhere falls into this category of extreme events which resulted partly due to human impact and partly due to bed aggradation.
The average length of time between the events of a certain magnitude is called recurrence interval or return period of that event. Historical data of such events help in analysing the recurrence (as well as the magnitude) of extreme events such as large floods. The technique involves using observed annual peak flow discharge data for a number of years to calculate recurrence intervals using a simple formula [(N+1)/M] where N is the number of years for which the data is available and M is the rank of the flood based on the magnitude (M =1 for the highest flood on record). The recurrence interval is then plotted against the magnitude of floods, which is called the flood frequency curve (Fig 1b). Based on the flood frequency curve, various floods corresponding to different return periods are calculated such as Q1.58, often taken as the bank-full discharge, Q2.33 (a measure of mean annual flood Qmaf), Q50 and Q100 (generally used as ‘design flood’ for most engineering projects and flood management).
It is important to note, however, that all such recurrence intervals of geomorphic processes are simply averages and do not indicate when an event of a particular magnitude will occur. Also, it is often very difficult to accurately estimate the recurrence interval of an extreme and rare event due to lack of temporal data.
There is a clear recognition of the fact that Earth’s climate has changed over time-scales of tens of thousands of years. Such shifts can involve marked changes in the probability distribution of weather parameters (temperature and precipitation) and are likely to modify the magnitude-frequency relationship of the geomorphic processes. Although most climate models are still at infancy stage but there is some agreement over the fact that the south Asian summer rainfall will increase by ~10 per cent by the year 2100. An influential paper by B N Goswami et. al., 2006, ‘Increasing trend of extreme rain events over India in a warming environment’, published in Science; has used a daily rainfall data set for the period 1871-2003, to show significant rising trends in the frequency and the magnitude of extreme rain events over central India. They have also demonstrated a significant decreasing trend in the frequency of moderate events in the region during the monsoon seasons from 1951 to 2000. Interestingly, the seasonal mean rainfall does not show a significant trend, and the authors attributed this to the fact that the contribution from increasing heavy events is offset by decreasing moderate events. This study has shown that central India and possibly other parts of India are likely to witness a substantial increase in hazards related to heavy rain in the future. If these projections are translated into hydrological models of river basins, the existing hydrograph with a peak discharge of M1 is likely to be modified significantly with a reduced magnitude (M2) or show a positive shift in flood magnitude (M3) (Fig 2, modified after De Marsily, 2008 ‘Population growth and climate change: Their impact on Planet earth and its human societies’, Planet Earth). Both these conditions are conducive for extreme events. An increased peak discharge (M3) will result in more severe floods and a modified distribution with a reduced peak discharge (M2) will result in more frequent droughts. A series of unprecedented floods in several parts of India namely Himachal Pradesh (July 2010), Leh (August 2010), several parts of Karnataka, Tamil Nadu, Andhra Pradesh and south Orissa during November-December 2010 should serve as an indicator to a modified hydrological regime. Globally, severe floods in east China (May 2010); Rio Lorogo, Brazil (June 2010); Pakistan (August 2010) and Queensland, Australia (December 2010); Rio de Janeiro, Brazil (January, 2011); and Queensland, Australia (February, 2011), should force us to think that extreme events can and do occur in our lifetime and they need to be given a serious thought in view of both natural as well as anthropogenic forcings which are often not easy to separate.