Optimization over a climate ensemble

[LaurelineJ]

Given an uncertain climate described by an ensemble of predictions of precipitation, run-off and recharge, we would like to obtain the optimal management of the water resources for a given objective.

Namely, at each time step, we want to know the reservoirs releases, the water abstracted at each points of the water network and from each aquifers for each county, and decide them independently from what the climate is going to be.

This requires a bit of work:

• on the generation of the matrix for the optimization part
• defining the corresponding optimization function (expected value over the ensemble for instance)
• the configuration file should specify whether or not the optimization is going to be done for an ensemble or a single climate prediction

[jrising]

Can you move start putting any new issues like this on the awash repo?

• James

On Jul 22, 2016 11:47 AM, "LaurelineJ" [email protected] wrote:

Given an uncertain climate described by an ensemble of predictions of
precipitation, run-off and recharge, we would like to obtain the optimal
management of the water resources for a given objective.

Namely, at each time step, we want to know the reservoirs releases, the
water abstracted at each points of the water network and from each aquifers
for each county, and decide them independently from what the climate is
going to be.

This requires a bit of work:

• on the generation of the matrix for the optimization part
• defining the corresponding optimization function (expected value
  over the ensemble for instance)
• the configuration file should specify whether or not the
  optimization is going to be done for an ensemble or a single climate
  prediction

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[LaurelineJ]

Here is an update on this issue following today's discussion.

Our objective is to find the optimal decisions (e.g. water allocation and agricultural choices) under uncertain conditions (e.g. climatic and socio-economic) that are described by a set of n_s scenarios.
There are multiple ways one can define the set of optimal decisions, estimating the expected value using MC is one of them. However, the computational cost is quite important as this requires the optimization over all possible scenarios simultaneously (complexity of O(n_s^2)).

Prof. Lall suggested today that we instead focus on the median solution. The optimization is run for each individual scenario, and the median cost solution is identified as the optimal solution. The constraints matrix is thus much smaller, we simply need to repeat the exercise n_s times (overall complexity of O(n_s)), and the parallelization is straightforward.

The reduction in computational cost is not the only interest. By systematically solving the optimization problem for each considered scenario, we obtain the full distribution and can identify any quantile.

While we do not give up on obtaining the mean solution, we will privilege the second approach for now. As it is already the object of a branch in awash here, I suggest that we open a new issue there and close this one.

[ulall]

good

On Tue, Aug 23, 2016 at 5:34 PM, LaurelineJ [email protected]
wrote:

Here is an update on this issue following today's discussion.

Our objective is to find the optimal decisions (e.g. water allocation and
agricultural choices) under uncertain conditions (e.g. climatic and
socio-economic) that are described by a set of $n_s$ scenarios.
There are multiple ways one can define the set of optimal decisions,
estimating the expected value using MC is one of them. However, the
computational cost is quite important as this requires the optimization
over all possible scenarios simultaneously (complexity of O(n_s^2)).

Prof. Lall suggested today that we instead focus on the median solution.
The optimization is run for each individual scenario, and the median cost
solution is identified as the optimal solution. The constraints matrix is
thus much smaller, we simply need to repeat the exercise n_s times (overall
complexity of $O(n_s)$), and the parallelization is straightforward.

The reduction in computational cost is not the only interest. By
systematically solving the optimization problem for each considered
scenario, we obtain the full distribution and can identify any quantile.

While we do not give up on obtaining the mean solution, we will privilege
the second approach for now. As it is already the object of a branch in
awash here https://github.com/AmericasWater/awash/tree/conjunctiveoptim,
I suggest that we open a new issue there and close this one.

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Upmanu Lall
Alan & Carol Silberstein Professor of Engineering,
Dept. of Earth & Environmental Engineering
Dept. of Civil Eng. & Eng. Mechanics
Director, Columbia Water Center
Senior Research Scientist, International Research Institute for Climate &
Society
842F Mudd
Columbia University
500 W 120th Street
New York, NY 10027

http:https://www.columbia.edu/~ula2/
http:https://water.columbia.edu/
http:https://bigthink.com/users/upmanulall