Energy Technology Expert

How to predict early dam water release – the key to minimizing flooding during typhoons

The Philippines is in the news around the world today.  CNN, local media ABS-CBN and other international and local news media reported that five (5) major hydro dams have released water at the onset of Typhoon “Ondoy”, and after a lull, did some pre-emptive release again in anticipation of a new Typhoon “Pepeng”, only to be overwhelmed again with the return of Typhoon “Ondoy” as a result of the “Fujiwara” effect when two adjacent weather disturbances are close to one another.

Unless the dam itself is in danger of collapsing under the weight of its stored water, one could not release dam water at the height of a storm as this will either aggravate existing flooding or initiate wide spread flooding as the rampaging waters will cause land slides and casualties, and destroy earthen dikes, bridges, roads, homes and agricultural lands.

The value of damage and loss of lives could simply not justify the storage of water for future use during summer months for irrigation and power generation.  This necessitates a closer review of the operating “rule curve” of the dam being followed by dam operators in the light of the very recent severe storms bringing large volumes of water over a very short period of time, perhaps as a result of global warming and climate change (warm waters and low pressure areas create extreme weather disturbances characterized with strong winds, heavy rainfall and storm surges that flood coastal areas).

Well, as the news unfold today, the entire flood plain of Central Luzon were inundated as the San Roque Dam in Pangasinan, Pantabangan Dam in Nueva Ecija, Magat Dam in the Cagayan region, the Ambuklao and Binga tandem dams in the Benguet, and Angat Dam in Bulacan had no choice but to release water at the volumetric rate equal to the rainfall as if there were no dam at all since the water levels have almost reached their maximum safe height and have to open their spillways to discharge whatever nature gave to its catchment area.

Coupled with the lack of advanced “Doppler radar” that should have been purchased by the Philippine Government to predict precisely the typhoon path and quantity of rainfall laden in its whirling clouds, the operators of the five major dams were unable to do pre-emptive discharge well in advance of the approaching storms in order to have storage capacity sufficient to contain the water unleashed by these two storms.  I guess the government has failed its people again as it could not do the simple task of providing state-of-the-art equipment for the country’s weather forecasting bureau, the PAGASA.

It is the responsibility of PAGASA to provide flood forecasting services to the dam operators in order to safeguard lives and properties to be affected and inundated by the release of water along the downstream rivers and into the flood plains of Luzon.  So the provinces of Pangasinan, Tarlac, Isabela, Nueva Viscaya, Nueva Ecija, Pampanga and Bulacan – all under the path of the major Agno River and Pampanga River – are now under water up to their rooftops, necessitating rescue from the Philippine and US military assets (helicopters, amphibian vehicles, heavy duty military trucks, rubber boats) that would have participated in a joint military exercise.

I presume that our country’s leading scientists at the Department of Science and Technology (DOST) under which PAGASA is attached, and the dam operators themselves, have done a simulation of the impact on rainfall on the levels of the dams given previous experience on rainfall dumped by typhoons in a short period of time.

Somehow, somebody forgot their mathematics and differential calculus:

dQ/dt = d(AH)dt = (catchment area, m2) x (rainfall, mm/hr) x (cm/10 mm) x (m/100 cm) x (hr/60 min) x (min/60 sec) = C x R x k

where Q = volume of water in dam, m3 (cubic meters)

dQ/dt = volumetric flow rate, m3/sec (cubic meters per second)

A = cross sectional area of dam at given elevation H, m2 (square meters)

= a + b H + c H2 + d H3 + …. +  = polynomial function

H = dam height, m (meters) above mean sea level

t = time, sec (seconds)

C = catchment area = rainfall catchment area of the given river system bounded by the high ridges of the mountains until it exits to the sea, m2 (square meters)

R = rainfall = rainfall intensity per unit area, could be measured by the “Doppler radar”, mm of rainfall per hour

k = constant to convert mm (milli meters) to m (meters) and hours (hr) to sec (seconds)

= 1 / (10 x 100 x 60 x 60)

The next step is to integrate the equation over time to come up with the height of the water elevation (H):

integral (dQ) = integral d(AH) = integral (C x R x k) dt

The above equation could then be integrated either numerically in a digital computer or spreadsheet or analytically into formulas.

If we assume that near the crest (highest point the dam) the cross sectional area is approximately constant as Am, then integrating between the limits (t = to to t; H = Ho to H) we get:

Am x (H – Ho) = (C x R x k) x (t – to)

And the height of the dam water at time t is:

H = Ho + (C x R x k / Am) x (t – to)

The volume of water dumped by the typhoon is also given by:

V = (C x R x k) x (t – to) = Am x (H – Ho)

In the absence of Doppler radar measurement of rainfall, we could use the local rain gages in the catch basin of the dam, or alternatively, calibrate the model using hourly readings of dam height H.  This leads to the hourly value of rainfall R as follows:

R = Am x (H – Ho) / ( ( C x k ) x (t – to) )

Hourly values of R may then be averaged over the time period to arrive at a mean rainfall intensity measured in mm per hour.

The time needed for the dam to overtop itself or reach the critical spillway height is calculated as follows:

(t – to) = Am x (H – Ho) / (C x R x k)

Once the computer model or the analytical model has been derived, the next step is to do simulation on its behavior over time using the above equation for height H and volume V.

The key here is in running this simulation before the approach of a known weather disturbance while it is still “outside of the area of responsibility” of PAGASA.

A key assumption here is a prediction on the severity of the storm, a correlation of the severity with known rainfall data based on previous storm events, in order to have an idea on the value of rainfall R.  This simulation will provide the time and volume of water that will be contained by the dam between the start of the storm up to the spilling safe level of the dam.

Once known, we could do pre-emptive discharge at a given lower rate that is safe enough for the downstream communities without causing serious floodings and damage to local communities:

V = safe volume to be stored for the typhoon = (safe discharge, m3/sec) x (time for safe discharge, day) x (24 hr/day) x (60 min/hr) x (60 sec/min)

= S x D x (24 x 60 x 60)

Where    S = rate of safe discharge, m3/sec

Hence the number of days needed to drain the dam to provide safe storage for the incoming typhoon would be:

D = V / (S x 24 x 60 x 60)

The above equation gives us the lead time needed to discharge safely before the arrival of the typhoon.

Hope this article would be of help to our weather forecasting scientists and dam operators as well as provide information to the top government officials to do some advance planning simulations to prevent further loss of lives and property.

Please leave your comments and suggestions.

Marcial T. Ocampo

Energy Technology & Pricing Expert

Business Development Consultant

B. S. Ch. E., M. S. Ch. E., M. S. Combustion & Energy (University of Leeds, UK)

(Friendly note: All content written by Engr. Marcial T. Ocampo are copyrighted and may not be redistributed in any way or form.)