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The importance of fractal capacitance

Nandkumar M Kamat

Nichersu and others in 2016 while applying the knowledge to the Danube River Delta explained that the fractal can be simply understood as a model where there are smaller models but similar. For example, the geographical characteristics of morphohydrographic networks, and maps at scales much larger than models of maps at small scales for the same geographic region.

Depending on the scale at which the object is examined there will be different levels of detail. In addition to the levels of detail, most objects in nature have the property of self-similarity, fundamental characteristic of fractals. For this reason, fractals maintain their size, about the used scale. This is evident for natural elements such as: mountains, coastlines, clouds, hurricanes, and lightning. The problem of flooding in Goa is mostly due to human interference destroying the fractal hydrography. It has caused simplification of millions of years old complex lotic hydrological systems.

Planning against flooding which causes losses of lives and property needs a fractal approach because the river basins display fractal dimensions – comprising very small and narrow primary streams, wider and longer secondary streams and larger tertiary streams culminating into rivulets and tributaries. Several tributaries empty into a river. Goa has nine major and two minor river basins and 41 tributaries. A mind boggling network of streams feed these tributaries. Their hydrography is distinctly fractal on maps.

The simplest scientific principle of controlling flooding and floods is river basin contour integrated drainage planning with full respect for local fractal hydrography and topography. Once primary, secondary and tertiary streams are taken care of the flood plain comes next. Town planners, architects and engineers have no idea of flood plains. Take for example the real flood plain of River Mandovi. It is up to the steps of the Immaculate Conception Church and the main post office in Panaji. Because of the reclamation of this flood plain in 19th century people have forgotten where the original line of flood waters of Mandovi touched.

Since 2010 Goa has been witnessing sporadic flooding. This year flooding reached a critical point. Almost all the low lying areas in the state are flooded. Rivers have crossed their banks. Some areas like Camurlim in Bardez appear like Sunderbans. In the entire history of Goa flooding has been sporadically recorded. A closer scrutiny and interactions with knowledgeable elders shows that local stakeholders had understood the fractal dimension of the hydrography. Their hydrotechnical interventions were simple, logical and sustainable. Amazingly maintenance parameters and protocols were built in the design itself. Therefore even before the term ‘geofabric’ became popular, local communities were using ‘thor’ or a technique which uses alternate layers of mud and dry mangrove leaves to strengthen the Khazan embankments. The anti-flooding approach of these communities was from ridge to the river- or plan from higher ground till one reaches the mouth of the river discharging as an estuary in the Arabian Sea.

There are 23 coastal creeks in Goa with stunning fractal dimension. These appear to have been partially engineered by the local communities. These creeks drain the hinterland. Village communities, communidades saved themselves from flooding for 2000 years. They had absolutely no maps or technical drawings but by walking, their teams surveyed the contours in each micro watershed. They used to begin planning drainage backwards from sea, where estuaries have wide, open mouths. Then they made hydrogeotechnical interventions backwards from estuaries to rivers and then planned drainage backwards to conjunction of tributaries. The process finally got terminated till the source of the primary stream.

Here the story becomes very interesting because suddenly you find that all these sources have a sacred grove. That’s how protection was provided. Since ‘gaunkaris’ coexist as neighbourhood administrative entities all the stakeholders in a particular river basin used to gather to finalise the anti flooding measures. This system used the river basin as the fundamental ecotopohydrograhic drainage planning unit. Micro watershed topography was used for designing local monsoon drainage. Water was allowed to flow by gravity. There were no pumps. Drains were constructed using clayish soil to permit smooth streamline flow. At regular intervals taking the benefit of level ground, anti flooding capacitance was created. For areas subjected to tidal drainage, sluice gates (manos) were installed strategically. All embankments along the rivers and Cumbarjua canal had a uniform height of six metres. When rains fell it was ensured that the monsoon stormwater would flow from all micro watersheds and pass over soft soil for percolation and aquifer recharge. No artificial impervious areas were created. All along the drains and channels local natural hydrophytes were maintained to remove the sediment. During summer they cleaned the drains and used the bottom sediment to strengthen the embankments. All the ‘poim’ or saline backwaters were lined with millions of rough undressed laterite rubble stones. This introduced another fractal complexity in the landscape. Hydrological inspectors were appointed to keep vigil and repair any damages.

Now we don’t have anything to replace this system. The original built-in fractal capacitance of age-old anti flooding systems has been destroyed. The situation will worsen further as more steel and concrete will be used to build impervious drainage systems. But there is no attention to understand the fractal dimension of the basin wise hydrography and pre-existing drainage systems. Goa can be saved from monsoon flooding only if the fractal dimension of the anti flooding capacitance is understood by the government.

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