Sensitivity to cost - effects of extraction costs on optimize-allocation with irrigation model


Sensitivity analysis to cost models

Water demands can be met by numerous sources of water. AWASH performs the allocation of water by solving an optimization problem resulting in the least costly solution to meet water demands under the environmental constraints. In this notebook, we conduct a sensitivity analysis to the choice of cost model for water.

Impact on optimize-allocation

Water use estimates are generally known at facility-, municipality- or county-level (e.g. USGS). To relate these numbers to the natural system, an optimization problem is solved to determine the withdrawals at each canals linking nodes of the network (gauges) to the counties, and groundwater extractions. In this particular test case, before the optimization is performed, a simulation is first run to evaluate irrigation needs.

Two situations are considered here: 1. cost is uniform, 2. cost is proportional to the relative elevation of the point of source and point of use. We explore four scenarios:

A. SW: 1 | GW: 1

B. SW: 2 | GW: 1

C. SW: 1 | GW: 2

D. SW: 2 | GW: 2


In [1]:
cd("../../src/");
include("nui.jl");
include("lib/readconfig.jl");
config = readconfig("../configs/standard-1year.yml")
# setting extraction cost to 0 (option 1: cost is uniform)
config["watercost-extraction"] = false;
config["watercost-treatment"] = false;
include("optimize-waterallocation.jl");
include("simulate.jl");
# getting volumes and costs at the county level from the simulation
sw11 = getdata(:Allocation, :swsupply);
swc11 = getdata(:WaterCost, :swcost);
gw11 = getdata(:Allocation, :gwsupply);
gwc11 = getdata(:WaterCost, :gwcost);


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Welcome to AWASH, the America's Water Model, version 0.7.

WARNING: using RCall.isna in module Main conflicts with an existing identifier.
Loading from saved region network...
WARNING: Base.String is deprecated, use AbstractString instead.
  likely near /home/laureline/.julia/v0.4/Graphs/src/common.jl:3
WARNING: Base.String is deprecated, use AbstractString instead.
  likely near /home/laureline/.julia/v0.4/Graphs/src/dot.jl:80
WARNING: imported binding for edges overwritten in module Main
Loading from saved water network...
Loading from saved region network...
Creating model...
Running model...
  0.198348 seconds (631.57 k allocations: 13.219 MB, 3.81% gc time)
Loading from saved region network...
Loading from saved water network...
WARNING: replacing module _mimi_implementation_WaterDemand
Optimize a model with 68238 rows, 112306 columns and 3739174 nonzeros
Coefficient statistics:
  Matrix range    [1e+00, 1e+00]
  Objective range [6e+00, 1e+06]
  Bounds range    [0e+00, 0e+00]
  RHS range       [7e-02, 2e+06]

Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...

Presolve removed 17399 rows and 18766 columns
Presolve time: 1.41s
Presolved: 50839 rows, 93540 columns, 2319344 nonzeros

Ordering time: 0.10s

Barrier statistics:
 AA' NZ     : 1.422e+06
 Factor NZ  : 1.844e+06 (roughly 70 MBytes of memory)
 Factor Ops : 1.044e+08 (less than 1 second per iteration)
 Threads    : 1

Barrier performed 0 iterations in 2.29 seconds
Barrier solve interrupted - model solved by another algorithm


Solved with dual simplex
Solved in 16058 iterations and 2.53 seconds
Optimal objective  1.689858355e+10
  4.540868 seconds (3.84 M allocations: 292.589 MB, 3.82% gc time)
Loading from saved region network...
Loading from saved water network...
Loading from saved region network...
WARNING: replacing module _mimi_implementation_Thermoelectric
WARNING: replacing module _mimi_implementation_Livestock
WARNING: replacing module _mimi_implementation_Agriculture
WARNING: replacing module _mimi_implementation_IndustrialDemand
WARNING: replacing module _mimi_implementation_UrbanDemand
WARNING: replacing module _mimi_implementation_WaterDemand
Creating model...
WARNING: replacing module _mimi_implementation_PopulationDemand
WARNING: replacing module _mimi_implementation_ReturnFlows
WARNING: replacing module _mimi_implementation_WaterNetwork
WARNING: replacing module _mimi_implementation_Aquifer
WARNING: replacing module _mimi_implementation_Allocation
WARNING: replacing module _mimi_implementation_Reservoir
Running model...
WARNING: replacing module _mimi_implementation_WaterCost
Missing canal.09475501
Missing usgs.11230500
Missing usgs.11075720
Missing usgs.11075720
Missing usgs.11063000
Missing usgs.11063000
Missing usgs.11413320
Missing reservoir.1894
Missing reservoir.2696
Missing canal.02248600
Missing canal.02280500
Missing reservoir.737
Missing usgs.03337000
Missing usgs.01396580
Missing usgs.01403535
Missing usgs.01356190
Missing usgs.01446775
Missing usgs.01432000
Missing usgs.03433640
Missing canal.08437600
Missing usgs.09277800
Missing reservoir.1286
Missing usgs.01659000
Missing usgs.12396900
Missing usgs.12181100
Missing canal.0208463140
Missing canal.02248600
Missing canal.02280500
Missing canal.02280500
Missing canal.09475501
Missing canal.09522701
Missing canal.10170700
Missing canal.09475501
Missing canal.09522701
Missing usgs.11230500
Missing usgs.11075720
Missing usgs.11075720
Missing usgs.11063000
Missing usgs.11063000
Missing usgs.11413320
Missing reservoir.1894
Missing canal.02248600
Missing canal.02248600
Missing reservoir.737
Missing usgs.03337000
Missing usgs.01403535
Missing usgs.01403535
Missing usgs.01356190
Missing usgs.01446775
Missing usgs.01432000
Missing usgs.03433640
Missing canal.08437600
Missing usgs.09277800
Missing reservoir.1286
Missing usgs.01659000
Missing usgs.12396900
Missing usgs.12181100
Missing canal.0208463140
Missing canal.02280500
Missing canal.02280500
Missing canal.02280500
Missing canal.02280500
Missing canal.09475501
Missing canal.10170700
  8.976563 seconds (7.28 M allocations: 939.320 MB, 1.95% gc time)

In [2]:
# setting extraction cost proportional to relative elevation (option 2)
config["watercost-extraction"] = true;
config["watercost-treatment"] = false;

include("optimize-waterallocation.jl");
include("simulate.jl");
# getting volumes and costs at the county level from the simulation
sw22 = getdata(:Allocation, :swsupply);
swc22 = getdata(:WaterCost, :swcost);
gw22 = getdata(:Allocation, :gwsupply);
gwc22 = getdata(:WaterCost, :gwcost);


Loading from saved region network...
Loading from saved water network...
Loading from saved region network...
WARNING: replacing module _mimi_implementation_Thermoelectric
WARNING: replacing module _mimi_implementation_Livestock
WARNING: replacing module _mimi_implementation_Agriculture
WARNING: replacing module _mimi_implementation_IndustrialDemand
WARNING: replacing module _mimi_implementation_UrbanDemand
WARNING: replacing module _mimi_implementation_WaterDemand
Creating model...
WARNING: replacing module _mimi_implementation_PopulationDemand
Running model...
  0.139843 seconds (555.63 k allocations: 9.869 MB, 7.02% gc time)
Loading from saved region network...
Loading from saved water network...
WARNING: replacing module _mimi_implementation_WaterDemand
WARNING: replacing module _mimi_implementation_WaterNetwork
Loading extraction cost from saved data...
WARNING: replacing module _mimi_implementation_Allocation
WARNING: replacing module _mimi_implementation_ReturnFlows
WARNING: replacing module _mimi_implementation_Reservoir
WARNING: replacing module _mimi_implementation_Aquifer
Optimize a model with 68238 rows, 112306 columns and 3739174 nonzeros
Coefficient statistics:
  Matrix range    [1e+00, 1e+00]
  Objective range [5e+00, 1e+06]
  Bounds range    [0e+00, 0e+00]
  RHS range       [7e-02, 2e+06]

Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...

Presolve removed 18498 rows and 22951 columns
Presolve time: 1.59s
Presolved: 49740 rows, 89355 columns, 2271614 nonzeros

Ordering time: 0.11s

Barrier statistics:
 AA' NZ     : 1.411e+06
 Factor NZ  : 1.826e+06 (roughly 70 MBytes of memory)
 Factor Ops : 1.037e+08 (less than 1 second per iteration)
 Threads    : 1

                  Objective                Residual
Iter       Primal          Dual         Primal    Dual     Compl     Time
   0   2.39758246e+12  1.68364411e+10  3.30e+08 2.10e+02  6.78e+08     3s
   1   1.34264064e+12 -1.88978867e+11  9.60e+07 1.37e+02  2.08e+08     3s
   2   6.34896925e+11 -2.50822264e+11  1.87e+07 2.82e+01  4.65e+07     3s
   3   1.81544667e+11 -1.88986984e+11  1.88e+06 4.21e+00  7.35e+06     3s
   4   8.66594161e+10 -7.32356751e+10  2.92e+05 6.07e-01  1.77e+06     3s

Barrier performed 4 iterations in 3.31 seconds
Barrier solve interrupted - model solved by another algorithm


Solved with dual simplex
Solved in 31165 iterations and 3.50 seconds
Optimal objective  5.025193460e+10
  3.965217 seconds (475.88 k allocations: 158.841 MB, 4.19% gc time)
WARNING: replacing module _mimi_implementation_WaterCost
Loading from saved region network...
Loading from saved water network...
Loading from saved region network...
WARNING: replacing module _mimi_implementation_Thermoelectric
WARNING: replacing module _mimi_implementation_Livestock
WARNING: replacing module _mimi_implementation_Agriculture
WARNING: replacing module _mimi_implementation_IndustrialDemand
WARNING: replacing module _mimi_implementation_UrbanDemand
WARNING: replacing module _mimi_implementation_WaterDemand
Creating model...
WARNING: replacing module _mimi_implementation_PopulationDemand
WARNING: replacing module _mimi_implementation_ReturnFlows
WARNING: replacing module _mimi_implementation_Market
WARNING: replacing module _mimi_implementation_Transportation
WARNING: replacing module _mimi_implementation_WaterNetwork
WARNING: replacing module _mimi_implementation_Aquifer
Loading extraction cost from saved data...
WARNING: replacing module _mimi_implementation_Allocation
WARNING: replacing module _mimi_implementation_Reservoir
Running model...
WARNING: replacing module _mimi_implementation_WaterCost
Missing canal.09475501
Missing usgs.11230500
Missing usgs.11075720
Missing usgs.11075720
Missing usgs.11063000
Missing usgs.11063000
Missing usgs.11413320
Missing reservoir.1894
Missing canal.02248600
Missing reservoir.2684
Missing reservoir.737
Missing usgs.03337000
Missing usgs.01396580
Missing usgs.01396580
Missing usgs.01356190
Missing usgs.01432000
Missing usgs.03433640
Missing canal.08437600
Missing usgs.09277800
Missing canal.10170700
Missing reservoir.1286
Missing usgs.01659000
Missing usgs.12396900
Missing usgs.12181100
Missing canal.0208463140
Missing canal.02280500
Missing canal.02280500
Missing canal.02280500
Missing canal.09475501
Missing canal.09475501
Missing canal.09475501
Missing usgs.11230500
Missing usgs.11075720
Missing usgs.11075720
Missing usgs.11063000
Missing usgs.11063000
Missing usgs.11413320
Missing reservoir.1894
Missing reservoir.2684
Missing reservoir.737
Missing usgs.03337000
Missing usgs.01396580
Missing usgs.01403535
Missing usgs.01356190
Missing usgs.01432000
Missing usgs.03433640
Missing usgs.09277800
Missing canal.10170700
Missing reservoir.1286
Missing usgs.01659000
Missing usgs.12396900
Missing usgs.12181100
Missing canal.0208463140
Missing canal.02248600
Missing canal.02280500
Missing canal.02280500
Missing canal.02280500
Missing canal.08437600
  9.036487 seconds (7.10 M allocations: 930.280 MB, 2.10% gc time)

In [3]:
# comparison with usgs estimates - loading the data
recorded = readtable(datapath("extraction/USGS-2010.csv"));
swusgs = recorded[:, :TO_SW] * 1383. / 12 *config["timestep"] * numsteps;
gwusgs = recorded[:, :TO_GW] * 1383. / 12 *config["timestep"] * numsteps;

In [4]:
# verifying that demands are met
include("mapping.jl")
println("Total differences between USGS and model case 1: ", sum(abs(swusgs.data+gwusgs.data-sum(sw11+gw11,2))), " 1000m3")
println("Total differences between USGS and model case 2: ", sum(abs(swusgs.data+gwusgs.data-sum(sw22+gw22,2))), " 1000m3")
#mapdatacty(swusgs.data -sum(sw2+supw2,2), true)


Total differences between USGS and model case 1: 1.775398544493447e8 1000m3
Total differences between USGS and model case 2: 1.775398544493447e8 1000m3

In [5]:
# comparing case 11 and case 22
println("Total volume model case 11: ", sum(gw11)+sum(sw11), " 1000m3")
println("Total volume model case 22: ", sum(gw22)+sum(sw22), " 1000m3")

println("Total sw volume model case 11: ", sum(sw11), " 1000m3")
println("Total sw volume model case 22: ", sum(sw22), " 1000m3")
println("Total gw volume model case 11: ", sum(gw11), " 1000m3")
println("Total gw volume model case 22: ", sum(gw22), " 1000m3")

println("Total sw volume differences between model case 11 and 22: ", sum(abs(sw11-sw22)), " 1000m3")
println("Total gw volume differences between model case 11 and 22: ", sum(abs(gw11-gw22)), " 1000m3")


Total volume model case 11: 5.453667662238202e8 1000m3
Total volume model case 22: 5.453667662238202e8 1000m3
Total sw volume model case 11: 4.0772653440648174e8 1000m3
Total sw volume model case 22: 3.826736695710698e8 1000m3
Total gw volume model case 11: 1.376402318173385e8 1000m3
Total gw volume model case 22: 1.626930966527505e8 1000m3
Total sw volume differences between model case 11 and 22: 1.1221349462452081e8 1000m3
Total gw volume differences between model case 11 and 22: 1.122134946245208e8 1000m3

Comparison of the results


In [6]:
# Reliance sw option 11
mapdatacty(sum(sw11,2))


WARNING: RCall.jl: 
-----------------------------------------------------------
PBS Mapping 2.69.76 -- Copyright (C) 2003-2016 Fisheries and Oceans Canada

PBS Mapping comes with ABSOLUTELY NO WARRANTY;
for details see the file COPYING.
This is free software, and you are welcome to redistribute
it under certain conditions, as outlined in the above file.

A complete user guide 'PBSmapping-UG.pdf' is located at 
/home/laureline/anaconda2/lib/R/library/PBSmapping/doc/PBSmapping-UG.pdf

Packaged on 2015-04-23
Pacific Biological Station, Nanaimo

All available PBS packages can be found at
http://code.google.com/p/pbs-software/

To see demos, type '.PBSfigs()'.
-----------------------------------------------------------


WARNING: RCall.jl: Loading required package: maptools
Loading required package: sp
Checking rgeos availability: TRUE
Loading required package: foreign
Out[6]:
RCall.RObject{RCall.VecSxp}

In [7]:
# Reliance sw option 22
mapdatacty(sum(sw22,2))


Out[7]:
RCall.RObject{RCall.VecSxp}

In [8]:
# Comparison of reliance on surface water between option 11 and 22
mapdatacty(sum(sw11-sw22,2),true)


Out[8]:
RCall.RObject{RCall.VecSxp}

Counties in red use more surface water when extraction costs are taken in consideration.


In [9]:
# Reliance gw option 11
mapdatacty(sum(gw11,2))


Out[9]:
RCall.RObject{RCall.VecSxp}

In [10]:
# Reliance gw option 22
mapdatacty(sum(gw22,2))


Out[10]:
RCall.RObject{RCall.VecSxp}

In [11]:
# Comparison of reliance on groundwater between option 11 and 22
mapdatacty(sum(gw11-gw22,2),true)


Out[11]:
RCall.RObject{RCall.VecSxp}

In [12]:
# Percentage of sw option 11
mapdatacty(sum(sw11,2)./sum(sw11+gw11,2)*100)


Out[12]:
RCall.RObject{RCall.VecSxp}

In [13]:
# Percentage of sw option 22
mapdatacty(sum(sw22,2)./sum(sw22+gw22,2)*100)


Out[13]:
RCall.RObject{RCall.VecSxp}

In [14]:
# Percentage of sw option 22
mapdatacty(sum(gw22,2)./sum(sw22+gw22,2)*100)


Out[14]:
RCall.RObject{RCall.VecSxp}

In [15]:
# Comparison percentage of reliance on surface water
mapdatacty(sum(sw11,2)./sum(sw11+gw11,2)*100-sum(sw22,2)./sum(sw22+gw22,2)*100, true)