26 June 2010

## Attabad – situation as of 25th June,

*Posted by Dave Petley*

**NB I have updated this post, and changed the title.**

Apologies for the lack of posts over the last few days – I have been in a meeting in Bermuda that has left little time to tend to this blog. Meanwhile, although small scale blasting of the spillway has reportedly continued, as of yesterday the lake level at Attabad is continued to rise by 10 to 20 cm per day, with the effect of both further drowning houses, hotels and roads upstream, and increasing the volume of water in the lake. Unfortunately I do not have any information about the blasting, or any pictures, but my analysis of the flow of the data is that the short term lake level graph now looks like this (correct to yesterday morning)

The lake level is now about 5.5 metres above the overtopping level, and at the moment there is little sign that this is reducing. Thus, the long term lake level graph now looks like this:

Meanwhile, spillway discharge has increased, driven primarily by a substantial rise in inflow:

I am intrigued to know whether this increased discharge has started to drive a new wave of erosion downstream. Finally, this graph compares inflow and spillway flow over the last ten days or so:

It is clear that at the moment inflow and outflow are directly linked – i.e. that the increase in spillway flow is due at least in part to increasing inflow. The grey line represents the point at which spillway flow equals inflow – i.e. the point at which the lake volume should stop increasing. This does not account for seepage, but as this is now a tiny fraction of spillway flow this is not a major problem. It is clear that recent increases in inflow were not being balanced by increasing outflow.

It should be expected that the inflow will continue to rise over the next few weeks, so this graph will be interesting to observe. Hopefully the spillway operations will start to increase the outflow in a controlled manner in the next few days, such that the lake level starts to fall.

In regards to the last graph: If the lake is rising, then the outflow is less than the inflow.

Has anyone seen new pics of the dam?

Where are the glaciers in relation to the lake and spillway? Whatever the increased inflows are, they will take time — hours to days — to appear at the spillway. So, it seems likely that whatever is done at the spillway end, the upper part of the lake will continue to rise as the glacier melting increases.

I very much miss the excellent photos provided by FOCUS and Pamir Times photographer Zulfiqar Ali Khan. Without them, the world is blind to the state of the spillway. Hopefully the Chinese engineers reported to have visited the site can get something efective happening — which counts more than feeding our curiosity.

"Whatever the increased inflows are, they will take time — hours to days — to appear at the spillway."Once the water arrives at the lake, the lake level at all points is raised. The lake level is the same at all points in the lake, even if there are a few waves…The rate of inflow being greater than rate of outflow is what causes the lake to rise. The outflow is restricted by the bottleneck of the dam. If the spillway were wide enough, then the lake level would not rise.This, however, is not true:"So, it seems likely that whatever is done at the spillway end, the upper part of the lake will continue to rise as the glacier melting increases."If the spillway were lowered, then the lake level would go down.(There is a bit of fluid flow dynamics in play here–a river flows down a gradient; it's not instant. But at the same time, the water in the lake seeks a single elevation.)

Tropical, this is not correct by any means. Even a moderate wind will cause the water to move, such that for example the water level at the spillway end might reduce whilst the upstream end might increase. This effect can be substantial. Thus, a reported rise in the water level at the spillway may well not mean that the overall lake level is rising.

Dr. Dave-The basic claim is that glacier melt will cause an inflow, and that inflow will cause one end of the lake to rise without regard to the other end.Waves, including wind driven waves, are a problem. Flow is a problem too, as flow requires some force, such as gravity on a gradient, or the wind can put a force on the water. Changes in atmospheric pressure, which causes wind flow, is another consideration.I suppose to some small level the lake has tides too. I've visited the Great Lakes, and the tides are essentially nothing (less than 12 inches). Wind can drive waves on the Great Lakes, and I am sure that there are elevation differences, but it's really not that significant, at least by my personal observations. The Great Lakes do change elevation, but that's mainly a result of inflow versus outflow and evaporation.As you might guess, I am particularly sensitive to storm surge. When the maximum surge occurs at high tide and under the right conditions, the storm surge can be quite significant (15-25 feet). I am very confident, however, that the storms over this area do not produce surges of 20 feet.Ultimately the main factor driving the Attabad lake level is not wind, or tides, but rather, inflow versus outflow. Also the elevation where the Hunza flows into the lake is approximately the same as the dam area, excluding the little bit of wave action.Alternatively, we will need to define what is "substantial" in terms of elevation differences. Someone might toss a stone into the water or if a landslide dumps into the lake, there will be some waves, and thus, there will be different elevations at different points on the lake, but is that "substantial?" Similarly, how much will a perfect wind raise the level of one end of the lake?The tropical storm season is here, and with Alex now formed, I am spending more energy on the Atlantic.

From first principles we know that the water level at the inflow end will be higher than the outflow end. (F = P/R). But absent any other factor (such as wind setup due to a storm blowing down the long axis of the lake) the actual difference is going to be quite small because of the extremely low R of the lake. Like, (off the top of my head) less than an inch.Once you get to the point where the flow rate results in a substantial difference in water level, you no longer have a lake: you have a pool embedded within a river.Sure would be interesting to see some recent photographs or videos. I think all measures of flow rate are at least double what was occuring when we last got a view of the site.

Quick web search on fluid flow:http://www.weizmann.ac.il/home/fnfal/FluidMech09.pdf"Fluid MechanicsA short course for physicistsGregory Falkovich"Take a look at page 33:"Navier-Stokes equation is a nonlinear partial differential equation of thesecond order. Not many steady solutions are known. Particularly easy isto find solutions in the geometry where (v · ∇)v = 0 and the equation iseffectively linear. In particular, symmetry may prescribe v ⊥ ∇v. Oneexample is the flow along an inclined plane as a model for a river."After some boundary value conditions, the author continues,"For slow plain rivers (like Nile or Volga)with h ≃ 10m and α ≃ 0.3 km/3000 km ≃ 10−4 one gets v(h) ≃ 100 km/secwhich is evidently impossible (the resolution of that dramatic discrepancyis that real rivers are turbulent as discussed in Sect. 2.2.2 below). Whatdistinguishes puddle and river, why they are not similar? To answer thisquestion, we need to characterize flows by a dimensionless number."2.2.2 is on page 60, which includes,"River. Now that we know that turbulence makes the drag at large Re muchlarger than the viscous drag, we can understand why the behavior of realrivers is so distinct from a laminar solution from Sect. 1.4.3. At small Re,the gravity force (per unit mass) gα was balanced by the viscous drag νv/h2.At large Re, the drag is v2/h which balances gα so that v ≃√αgh. Indeed,as long as viscosity does not enter, this is the only combination with thevelocity dimensionality that one can get from h and the effective gravityαg. For slow plain rivers (the inclination angle α ≃ 10−4 and the depthh ≃ 10 m) we thus get reasonable v ≃ 10 cm/s. Another way to describe thedrag is to say that molecular viscosity ν is replaced by turbulent viscosityνT ≃ vh ≃ νRe and the drag is still given by viscous formula νv/h2 but withν → νT . Intuitively, one imagines turbulent eddies transferring momentumbetween fluid layers."It looks like a good read.

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